<?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_27.out</source>

<heading><![CDATA[
Prover9 (64) version 2022-12A (+ restricted para), January 2023.
Process 2482657 was started by veroff on b146-19,
Thu Jan 15 11:43:23 2026
The command was "prover9 -f nil3_23_32_to_27.in".
]]></heading>

<proof number="1" length="18090" max_count="65">

<comments><![CDATA[
% Proof 1 at 4541.32 (+ 258.96) seconds: "nil3 27, aa1-Nm".
% Length of proof: 18090 (0 new hints)
% Level of proof: 930
% Maximum clause weight: 65.000
% Given clauses in run: 18078
% Given clauses in proof: 18078 (0 new hints)
]]></comments>

  <clause id="1" type="goal">
    <literal><![CDATA[
      a(x,a(a(y,z,u),w,v5),v6) = 1
    ]]></literal>
    <attribute><![CDATA[
      label("nil3 27, aa1-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(a(c2,c3,c4),c5,c6),c7) != 1
    ]]></literal>
    <attribute><![CDATA[
      label("nil3 27, aa1-Nm")
    ]]></attribute>
    <attribute><![CDATA[
      answer("nil3 27, aa1-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(53,a,217,a)].">
      <j1 rule="hyper" parents="53 217"/>
    </justification>
  </clause>

  <clause id="395">
    <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="396">
    <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="397">
    <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="398">
    <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="399">
    <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="400">
    <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="401">
    <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="402">
    <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="403">
    <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="404">
    <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="405">
    <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="406">
    <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="407">
    <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="408">
    <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="409">
    <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="410">
    <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="411">
    <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="412">
    <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="413">
    <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="414">
    <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="415">
    <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="416">
    <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="417">
    <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="418">
    <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="419">
    <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="420">
    <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="421">
    <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="422">
    <literal><![CDATA[
      x / L(y,1 / y,x) = x * (1 / y)
    ]]></literal>
    <justification jstring="[para(75(a,1),396(a,1,2,1))].">
      <j1 rule="para" parents="75 396"/>
    </justification>
  </clause>

  <clause id="423">
    <literal><![CDATA[
      (x * y) \ x != z
    ]]></literal>
    <literal><![CDATA[
      L(y \ 1,y,x) = z
    ]]></literal>
    <justification jstring="[para(396(a,1),267(a,1,1)),flip(b)].">
      <j1 rule="para" parents="396 267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="424">
    <literal><![CDATA[
      L(L(x \ 1,x,y),y * x,z) = (z * (y * x)) \ (z * y)
    ]]></literal>
    <justification jstring="[para(397(a,1),13(a,2,2,2))].">
      <j1 rule="para" parents="397 13"/>
    </justification>
  </clause>

  <clause id="425">
    <literal><![CDATA[
      R(x,x \ 1,y) \ y = (x \ 1) * y
    ]]></literal>
    <justification jstring="[para(72(a,1),406(a,1,1,1))].">
      <j1 rule="para" parents="72 406"/>
    </justification>
  </clause>

  <clause id="426">
    <literal><![CDATA[
      x / (y * x) != z
    ]]></literal>
    <literal><![CDATA[
      R(1 / y,y,x) = z
    ]]></literal>
    <justification jstring="[para(406(a,1),330(a,1,2)),flip(b)].">
      <j1 rule="para" parents="406 330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="427">
    <literal><![CDATA[
      T(x,x \ y) != z
    ]]></literal>
    <literal><![CDATA[
      (x \ y) \ y = z
    ]]></literal>
    <justification jstring="[para(72(a,1),420(a,1,1))].">
      <j1 rule="para" parents="72 420"/>
    </justification>
  </clause>

  <clause id="428">
    <literal><![CDATA[
      T(x,T(y,x)) != z
    ]]></literal>
    <literal><![CDATA[
      T(y,x) \ (y * x) = z
    ]]></literal>
    <justification jstring="[para(187(a,1),420(a,1,1))].">
      <j1 rule="para" parents="187 420"/>
    </justification>
  </clause>

  <clause id="429">
    <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(396(a,1),420(a,1,1))].">
      <j1 rule="para" parents="396 420"/>
    </justification>
  </clause>

  <clause id="430">
    <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="431">
    <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="432">
    <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="433">
    <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="434">
    <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="435">
    <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="436">
    <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="437">
    <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="438">
    <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="439">
    <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="440">
    <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="441">
    <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="442">
    <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="443">
    <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="444">
    <literal><![CDATA[
      (x / ((y * z) \ y)) * L(z \ 1,z,y) = x
    ]]></literal>
    <justification jstring="[hyper(119,a,217,a,b,75,a)].">
      <j1 rule="hyper" parents="119 217 75"/>
    </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) * u = ((z * x) \ (z * y)) * u
    ]]></literal>
    <justification jstring="[hyper(52,a,92,a)].">
      <j1 rule="hyper" parents="52 92"/>
    </justification>
  </clause>

  <clause id="493">
    <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="494">
    <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="495">
    <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="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),420(a,1,1))].">
      <j1 rule="para" parents="186 420"/>
    </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 * (x \ 1)) * y != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ y = u
    ]]></literal>
    <justification jstring="[para(163(a,1),339(a,1))].">
      <j1 rule="para" parents="163 339"/>
    </justification>
  </clause>

  <clause id="578">
    <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="579">
    <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="580">
    <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="581">
    <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="582">
    <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="583">
    <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="584">
    <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="585">
    <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="586">
    <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="587">
    <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="588">
    <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="589">
    <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="590">
    <literal><![CDATA[
      T(x \ (x / y),z) = L(T(y \ 1,z),y,x / y)
    ]]></literal>
    <justification jstring="[para(398(a,1),20(a,2,1)),flip(a)].">
      <j1 rule="para" parents="398 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="591">
    <literal><![CDATA[
      x * R(1 / y,y,y \ z) = x * ((y \ z) / z)
    ]]></literal>
    <justification jstring="[hyper(119,a,407,a,b,4,a)].">
      <j1 rule="hyper" parents="119 407 4"/>
    </justification>
  </clause>

  <clause id="592">
    <literal><![CDATA[
      ((x \ y) / y) * (R(1 / x,x,x \ y) \ z) = z
    ]]></literal>
    <justification jstring="[hyper(281,a,407,a(flip))].">
      <j1 rule="hyper" parents="281 407"/>
    </justification>
  </clause>

  <clause id="593">
    <literal><![CDATA[
      T((x \ y) / y,z) = R(T(1 / x,z),x,x \ y)
    ]]></literal>
    <justification jstring="[para(407(a,1),22(a,2,1)),flip(a)].">
      <j1 rule="para" parents="407 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="594">
    <literal><![CDATA[
      T(1 / (x / y),y / x) = 1 / (x / y)
    ]]></literal>
    <justification jstring="[para(408(a,1),172(a,1,2))].">
      <j1 rule="para" parents="408 172"/>
    </justification>
  </clause>

  <clause id="595">
    <literal><![CDATA[
      (((x / y) / z) * z) * y != u * w
    ]]></literal>
    <literal><![CDATA[
      x / w = u
    ]]></literal>
    <justification jstring="[para(7(a,2),413(a,1,1))].">
      <j1 rule="para" parents="7 413"/>
    </justification>
  </clause>

  <clause id="596">
    <literal><![CDATA[
      ((x / y) * y) * z != u * w
    ]]></literal>
    <literal><![CDATA[
      (x * z) / w = u
    ]]></literal>
    <justification jstring="[para(156(a,1),413(a,1,1))].">
      <j1 rule="para" parents="156 413"/>
    </justification>
  </clause>

  <clause id="597">
    <literal><![CDATA[
      x * (y \ (y * (x \ z))) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ z = w
    ]]></literal>
    <justification jstring="[para(4(a,2),416(a,1,2))].">
      <j1 rule="para" parents="4 416"/>
    </justification>
  </clause>

  <clause id="598">
    <literal><![CDATA[
      x * (y * (y \ (x \ z))) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ z = w
    ]]></literal>
    <justification jstring="[para(5(a,2),416(a,1,2))].">
      <j1 rule="para" parents="5 416"/>
    </justification>
  </clause>

  <clause id="599">
    <literal><![CDATA[
      x * (y * (y \ z)) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (x * z) = w
    ]]></literal>
    <justification jstring="[para(160(a,1),416(a,1,2))].">
      <j1 rule="para" parents="160 416"/>
    </justification>
  </clause>

  <clause id="600">
    <literal><![CDATA[
      x \ y != (z \ 1) * y
    ]]></literal>
    <literal><![CDATA[
      R(z,z \ 1,y) = x
    ]]></literal>
    <justification jstring="[para(425(a,1),43(a,1)),flip(a)].">
      <j1 rule="para" parents="425 43"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="601">
    <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),427(a,1))].">
      <j1 rule="para" parents="22 427"/>
    </justification>
  </clause>

  <clause id="602">
    <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),427(a,1,2))].">
      <j1 rule="para" parents="106 427"/>
    </justification>
  </clause>

  <clause id="603">
    <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),434(a,1,1))].">
      <j1 rule="para" parents="106 434"/>
    </justification>
  </clause>

  <clause id="604">
    <literal><![CDATA[
      x \ L(y,x \ 1,x) != (x \ 1) * z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(437(a,2),38(a,1))].">
      <j1 rule="para" parents="437 38"/>
    </justification>
  </clause>

  <clause id="605">
    <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="606">
    <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),420(a,1,1))].">
      <j1 rule="para" parents="471 420"/>
    </justification>
  </clause>

  <clause id="607">
    <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="608">
    <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="609">
    <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="610">
    <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="611">
    <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="612">
    <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="613">
    <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="614">
    <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="615">
    <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="616">
    <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="617">
    <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="618">
    <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="619">
    <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="620">
    <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="621">
    <literal><![CDATA[
      (x * y) \ x != z * u
    ]]></literal>
    <literal><![CDATA[
      L(y \ 1,y,x) / u = z
    ]]></literal>
    <justification jstring="[para(397(a,1),575(a,1,2))].">
      <j1 rule="para" parents="397 575"/>
    </justification>
  </clause>

  <clause id="622">
    <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="623">
    <literal><![CDATA[
      x \ y != (z * u) / u
    ]]></literal>
    <literal><![CDATA[
      x * z = y
    ]]></literal>
    <justification jstring="[para(156(a,2),581(a,2))].">
      <j1 rule="para" parents="156 581"/>
    </justification>
  </clause>

  <clause id="624">
    <literal><![CDATA[
      x \ y != (z / (u \ z)) * w
    ]]></literal>
    <literal><![CDATA[
      x * (u * w) = y
    ]]></literal>
    <justification jstring="[para(181(a,1),581(a,2,1))].">
      <j1 rule="para" parents="181 581"/>
    </justification>
  </clause>

  <clause id="625">
    <literal><![CDATA[
      x \ (y * (y \ (x * z))) != u \ w
    ]]></literal>
    <literal><![CDATA[
      u * z = w
    ]]></literal>
    <justification jstring="[para(5(a,2),582(a,1,2))].">
      <j1 rule="para" parents="5 582"/>
    </justification>
  </clause>

  <clause id="626">
    <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),582(a,1,2))].">
      <j1 rule="para" parents="90 582"/>
    </justification>
  </clause>

  <clause id="627">
    <literal><![CDATA[
      x * ((y * z) \ y) != u
    ]]></literal>
    <literal><![CDATA[
      x * L(z \ 1,z,y) = u
    ]]></literal>
    <justification jstring="[para(397(a,1),585(a,1,2,2))].">
      <j1 rule="para" parents="397 585"/>
    </justification>
  </clause>

  <clause id="628">
    <literal><![CDATA[
      K(x,1 / x) * y != x
    ]]></literal>
    <literal><![CDATA[
      L(x,1 / x,x) = y
    ]]></literal>
    <justification jstring="[para(619(a,1),38(a,1)),flip(a)].">
      <j1 rule="para" parents="619 38"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="629">
    <literal><![CDATA[
      x \ y != (z * T(u,z)) / z
    ]]></literal>
    <literal><![CDATA[
      x * u = y
    ]]></literal>
    <justification jstring="[para(105(a,2),623(a,2,1))].">
      <j1 rule="para" parents="105 623"/>
    </justification>
  </clause>

  <clause id="630">
    <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="631">
    <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="632">
    <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="633">
    <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="634">
    <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="635">
    <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="636">
    <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="637">
    <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="638">
    <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="639">
    <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="640">
    <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="641">
    <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="642">
    <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="643">
    <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="644">
    <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="645">
    <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="646">
    <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="647">
    <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="648">
    <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="649">
    <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="650">
    <literal><![CDATA[
      R((x / y) \ 1,x / y,y) = T(y / x,x / y)
    ]]></literal>
    <justification jstring="[para(408(a,1),248(a,1,1)),flip(a)].">
      <j1 rule="para" parents="408 248"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="651">
    <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="652">
    <literal><![CDATA[
      (x / (y * x)) * y = y * R(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,646,a(flip),b,17,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 646 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="653">
    <literal><![CDATA[
      x * R(x \ 1,x,y) != z
    ]]></literal>
    <literal><![CDATA[
      (y / (x * y)) * x = z
    ]]></literal>
    <justification jstring="[para(646(a,1),284(a,1,2))].">
      <j1 rule="para" parents="646 284"/>
    </justification>
  </clause>

  <clause id="654">
    <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="655">
    <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="656">
    <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="657">
    <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="658">
    <literal><![CDATA[
      T(x \ T(y,y \ z),x \ ((y \ z) \ z)) = x \ ((y \ z) \ z)
    ]]></literal>
    <justification jstring="[hyper(443,a,310,a,b,xx)].">
      <j1 rule="hyper" parents="443 310"/>
    </justification>
  </clause>

  <clause id="659">
    <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="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),585(a,1))].">
      <j1 rule="para" parents="315 585"/>
    </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),423(a,1,1))].">
      <j1 rule="para" parents="7 423"/>
    </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),426(a,1,2))].">
      <j1 rule="para" parents="105 426"/>
    </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),426(a,1,2))].">
      <j1 rule="para" parents="260 426"/>
    </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,430,a)].">
      <j1 rule="hyper" parents="320 85 430"/>
    </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),589(a,1,2))].">
      <j1 rule="para" parents="4 589"/>
    </justification>
  </clause>

  <clause id="683">
    <literal><![CDATA[
      T(x * y,(x \ 1) \ y) = x * y
    ]]></literal>
    <justification jstring="[hyper(49,a,610,a)].">
      <j1 rule="hyper" parents="49 610"/>
    </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(439,a,xx,b,80,a)].">
      <j1 rule="hyper" parents="439 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[
      L(a(x,y,z) \ u,a(x,y,z),x * (y * z)) = ((x * y) * z) \ ((x * (y * z)) * u)
    ]]></literal>
    <justification jstring="[para(80(a,1),92(a,2,1))].">
      <j1 rule="para" parents="80 92"/>
    </justification>
  </clause>

  <clause id="693">
    <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="694">
    <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),582(a,1,2))].">
      <j1 rule="para" parents="80 582"/>
    </justification>
  </clause>

  <clause id="695">
    <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="696">
    <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="697">
    <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="698">
    <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="699">
    <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="700">
    <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="701">
    <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="702">
    <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="703">
    <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="704">
    <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="705">
    <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="706">
    <literal><![CDATA[
      x * a(x,y,y \ 1) = R(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(134,a,705,a)].">
      <j1 rule="hyper" parents="134 705"/>
    </justification>
  </clause>

  <clause id="707">
    <literal><![CDATA[
      L(x \ a(y,z,z \ 1),x,y) = (y * x) \ R(y,z,z \ 1)
    ]]></literal>
    <justification jstring="[para(705(a,1),298(a,1,1,2))].">
      <j1 rule="para" parents="705 298"/>
    </justification>
  </clause>

  <clause id="708">
    <literal><![CDATA[
      x \ R(x,y,y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      a(x,y,y \ 1) = z
    ]]></literal>
    <justification jstring="[para(706(a,1),287(a,1,2)),flip(b)].">
      <j1 rule="para" parents="706 287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="709">
    <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="710">
    <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="711">
    <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="712">
    <literal><![CDATA[
      T(L(x,y,x),y) = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,20,a(flip),b,711,a)].">
      <j1 rule="hyper" parents="58 20 711"/>
    </justification>
  </clause>

  <clause id="713">
    <literal><![CDATA[
      L(T(T(x,y),z),y,x) = T(T(x,x * y),z)
    ]]></literal>
    <justification jstring="[para(711(a,1),20(a,2,1))].">
      <j1 rule="para" parents="711 20"/>
    </justification>
  </clause>

  <clause id="714">
    <literal><![CDATA[
      L(R(T(x,y),z,u),y,x) = R(T(x,x * y),z,u)
    ]]></literal>
    <justification jstring="[para(711(a,1),24(a,1,1)),flip(a)].">
      <j1 rule="para" parents="711 24"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="715">
    <literal><![CDATA[
      x * T(y,y * x) = L(y,x,y) * x
    ]]></literal>
    <justification jstring="[para(711(a,1),237(a,1,2))].">
      <j1 rule="para" parents="711 237"/>
    </justification>
  </clause>

  <clause id="716">
    <literal><![CDATA[
      (x * y) * R(L(T(x,y),y,x),z,u) = R(x,z,u) * (x * y)
    ]]></literal>
    <justification jstring="[para(711(a,2),238(a,1,2,1))].">
      <j1 rule="para" parents="711 238"/>
    </justification>
  </clause>

  <clause id="717">
    <literal><![CDATA[
      (x * T(y,y * x)) / x = L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(271,a,712,a)].">
      <j1 rule="hyper" parents="271 712"/>
    </justification>
  </clause>

  <clause id="718">
    <literal><![CDATA[
      T((x * y) / x,y * x) = L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(35,a,270,a,b,712,a)].">
      <j1 rule="hyper" parents="35 270 712"/>
    </justification>
  </clause>

  <clause id="719">
    <literal><![CDATA[
      T(L(L(x,y,x),z,u),y) = L(T(x,x * y),z,u)
    ]]></literal>
    <justification jstring="[para(712(a,1),20(a,1,1)),flip(a)].">
      <j1 rule="para" parents="712 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="720">
    <literal><![CDATA[
      x * L(T(y,y * x),z,u) = L(L(y,x,y),z,u) * x
    ]]></literal>
    <justification jstring="[para(712(a,1),237(a,1,2,1))].">
      <j1 rule="para" parents="712 237"/>
    </justification>
  </clause>

  <clause id="721">
    <literal><![CDATA[
      L(x,x \ y,x) * (x \ y) = (x \ y) * T(x,y)
    ]]></literal>
    <justification jstring="[para(5(a,1),715(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5 715"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="722">
    <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),715(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="105 715"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="723">
    <literal><![CDATA[
      T(((x \ y) * x) / (x \ y),y) = L(x,x \ y,x)
    ]]></literal>
    <justification jstring="[para(5(a,1),718(a,1,2))].">
      <j1 rule="para" parents="5 718"/>
    </justification>
  </clause>

  <clause id="724">
    <literal><![CDATA[
      T(T((x * y) / x,z),y * x) = T(L(y,x,y),z)
    ]]></literal>
    <justification jstring="[para(718(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="718 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="725">
    <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="726">
    <literal><![CDATA[
      T(R(x / y,y,y \ z),z) = z \ (x * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(439,a,147,a(flip),b,368,a)].">
      <j1 rule="hyper" parents="439 147 368"/>
    </justification>
  </clause>

  <clause id="727">
    <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="728">
    <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="729">
    <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="730">
    <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="731">
    <literal><![CDATA[
      L(x \ 1,x,y) * z != u
    ]]></literal>
    <literal><![CDATA[
      ((y * x) \ y) \ u = z
    ]]></literal>
    <justification jstring="[para(391(a,1),38(a,1)),flip(a)].">
      <j1 rule="para" parents="391 38"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="732">
    <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="733">
    <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="734">
    <literal><![CDATA[
      x * (y * L(z \ 1,z,u)) = x * (y * ((u * z) \ u))
    ]]></literal>
    <justification jstring="[hyper(119,a,394,a,b,4,a)].">
      <j1 rule="hyper" parents="119 394 4"/>
    </justification>
  </clause>

  <clause id="735">
    <literal><![CDATA[
      x * L(y \ 1,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      u / ((z * y) \ z) = x
    ]]></literal>
    <justification jstring="[para(394(a,2),131(a,1))].">
      <j1 rule="para" parents="394 131"/>
    </justification>
  </clause>

  <clause id="736">
    <literal><![CDATA[
      (x * y) * T((x * y) \ x,z) = x * (y * T(y \ 1,z))
    ]]></literal>
    <justification jstring="[hyper(119,a,399,a,b,13,a(flip))].">
      <j1 rule="hyper" parents="119 399 13"/>
    </justification>
  </clause>

  <clause id="737">
    <literal><![CDATA[
      R(1 / x,x,y) != z
    ]]></literal>
    <literal><![CDATA[
      y / (x * y) = z
    ]]></literal>
    <justification jstring="[para(405(a,1),208(a,1))].">
      <j1 rule="para" parents="405 208"/>
    </justification>
  </clause>

  <clause id="738">
    <literal><![CDATA[
      R(T(1 / x,x * y),x,y) = (x * y) \ y
    ]]></literal>
    <justification jstring="[hyper(420,a,409,a),flip(a)].">
      <j1 rule="hyper" parents="420 409"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="739">
    <literal><![CDATA[
      T(x / (y * x),z) * (y * x) = (T(1 / y,z) * y) * x
    ]]></literal>
    <justification jstring="[para(409(a,2),101(a,1,1))].">
      <j1 rule="para" parents="409 101"/>
    </justification>
  </clause>

  <clause id="740">
    <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),412(a,1,2))].">
      <j1 rule="para" parents="106 412"/>
    </justification>
  </clause>

  <clause id="741">
    <literal><![CDATA[
      x * T(x \ (y * x),z) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,z) * x = u
    ]]></literal>
    <justification jstring="[para(17(a,1),417(a,1,2,1))].">
      <j1 rule="para" parents="17 417"/>
    </justification>
  </clause>

  <clause id="742">
    <literal><![CDATA[
      L(T(x \ 1,x),x,1 / x) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(320,a,107,a(flip),b,421,a),flip(a)].">
      <j1 rule="hyper" parents="320 107 421"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="743">
    <literal><![CDATA[
      (1 / x) \ T(1 / x,y) = x * T(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(116,a,421,a(flip),b,259,a)].">
      <j1 rule="hyper" parents="116 421 259"/>
    </justification>
  </clause>

  <clause id="744">
    <literal><![CDATA[
      x / L(y \ 1,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x / ((z * y) \ z) = u
    ]]></literal>
    <justification jstring="[para(444(a,1),327(a,1,1)),flip(b)].">
      <j1 rule="para" parents="444 327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="745">
    <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="746">
    <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="747">
    <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="748">
    <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="749">
    <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="750">
    <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="751">
    <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="752">
    <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="753">
    <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="754">
    <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="755">
    <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="756">
    <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="757">
    <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="758">
    <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="759">
    <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="760">
    <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="761">
    <literal><![CDATA[
      L(x \ y,x,y / x) != z
    ]]></literal>
    <literal><![CDATA[
      T(y / x,y) = z
    ]]></literal>
    <justification jstring="[para(493(a,2),288(a,1))].">
      <j1 rule="para" parents="493 288"/>
    </justification>
  </clause>

  <clause id="762">
    <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="763">
    <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="764">
    <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="765">
    <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="766">
    <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="767">
    <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="768">
    <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="769">
    <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="770">
    <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="771">
    <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),420(a,1,1))].">
      <j1 rule="para" parents="544 420"/>
    </justification>
  </clause>

  <clause id="772">
    <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="773">
    <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="774">
    <literal><![CDATA[
      (1 / x) * ((x \ 1) * x) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(58,a,742,a(flip),b,554,a),flip(a)].">
      <j1 rule="hyper" parents="58 742 554"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="775">
    <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="776">
    <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="777">
    <literal><![CDATA[
      (1 / (1 / x)) * (x * (1 / x)) = (1 / x) \ 1
    ]]></literal>
    <justification jstring="[para(75(a,1),774(a,1,2,1))].">
      <j1 rule="para" parents="75 774"/>
    </justification>
  </clause>

  <clause id="778">
    <literal><![CDATA[
      (1 / x) * K(x \ 1,x) = x \ 1
    ]]></literal>
    <justification jstring="[para(258(a,2),774(a,1,2))].">
      <j1 rule="para" parents="258 774"/>
    </justification>
  </clause>

  <clause id="779">
    <literal><![CDATA[
      (1 / x) \ (x \ 1) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(123,a,778,a)].">
      <j1 rule="hyper" parents="123 778"/>
    </justification>
  </clause>

  <clause id="780">
    <literal><![CDATA[
      K((x \ 1) \ 1,x \ 1) = x \ ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(116,a,778,a(flip),b,183,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="116 778 183"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="781">
    <literal><![CDATA[
      (x \ 1) \ ((1 / x) * (K(x \ 1,x) * y)) = L(y,K(x \ 1,x),1 / x)
    ]]></literal>
    <justification jstring="[para(778(a,1),13(a,2,1)),flip(a)].">
      <j1 rule="para" parents="778 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="782">
    <literal><![CDATA[
      (x * (y \ 1)) / L(K(y \ 1,y),1 / y,x) = x * (1 / y)
    ]]></literal>
    <justification jstring="[para(778(a,1),186(a,1,1,2))].">
      <j1 rule="para" parents="778 186"/>
    </justification>
  </clause>

  <clause id="783">
    <literal><![CDATA[
      x / L(K(y \ 1,y),1 / y,x / (y \ 1)) = (x / (y \ 1)) * (1 / y)
    ]]></literal>
    <justification jstring="[para(779(a,1),498(a,1,2,1))].">
      <j1 rule="para" parents="779 498"/>
    </justification>
  </clause>

  <clause id="784">
    <literal><![CDATA[
      T(x / y,y) != z \ u
    ]]></literal>
    <literal><![CDATA[
      z * (y \ x) = u
    ]]></literal>
    <justification jstring="[para(457(a,1),629(a,2)),flip(a)].">
      <j1 rule="para" parents="457 629"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="785">
    <literal><![CDATA[
      R(x,y,z) = T(((y * x) * z) / (y * z),y)
    ]]></literal>
    <justification jstring="[para(4(a,1),648(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4 648"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="786">
    <literal><![CDATA[
      T(x / (y * z),y) * (y * z) = ((y \ (x / z)) * y) * z
    ]]></literal>
    <justification jstring="[para(649(a,1),101(a,1,1))].">
      <j1 rule="para" parents="649 101"/>
    </justification>
  </clause>

  <clause id="787">
    <literal><![CDATA[
      ((x \ y) * x) * (x \ 1) = T(y * (x \ 1),x)
    ]]></literal>
    <justification jstring="[hyper(58,a,261,a,b,651,a)].">
      <j1 rule="hyper" parents="58 261 651"/>
    </justification>
  </clause>

  <clause id="788">
    <literal><![CDATA[
      T((x * y) * (x \ 1),x) = R(y,x,x \ 1)
    ]]></literal>
    <justification jstring="[para(4(a,1),651(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4 651"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="789">
    <literal><![CDATA[
      (x / y) * R((x / y) \ 1,x / y,y) = (y / x) * (x / y)
    ]]></literal>
    <justification jstring="[para(7(a,1),652(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7 652"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="790">
    <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(652(a,1),307(a,1,1))].">
      <j1 rule="para" parents="652 307"/>
    </justification>
  </clause>

  <clause id="791">
    <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(648(a,1),678(a,1,1))].">
      <j1 rule="para" parents="648 678"/>
    </justification>
  </clause>

  <clause id="792">
    <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="793">
    <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="794">
    <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="795">
    <literal><![CDATA[
      T(L(x,y \ z,y),y \ z) = z \ (y * (x * (y \ z)))
    ]]></literal>
    <justification jstring="[hyper(350,a,710,a),flip(a)].">
      <j1 rule="hyper" parents="350 710"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="796">
    <literal><![CDATA[
      T(L(x,y,z / y),y) = z \ ((z / y) * (x * y))
    ]]></literal>
    <justification jstring="[para(7(a,1),710(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7 710"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="797">
    <literal><![CDATA[
      T(L(x,y \ z,y),y \ z) != u
    ]]></literal>
    <literal><![CDATA[
      z \ (y * (x * (y \ z))) = u
    ]]></literal>
    <justification jstring="[para(710(a,1),350(a,1))].">
      <j1 rule="para" parents="710 350"/>
    </justification>
  </clause>

  <clause id="798">
    <literal><![CDATA[
      (x * y) * T(T(x,x * y),z) = x * (y * T(T(x,y),z))
    ]]></literal>
    <justification jstring="[hyper(119,a,713,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="119 713 13"/>
    </justification>
  </clause>

  <clause id="799">
    <literal><![CDATA[
      T((1 / x) * (x * y),x) = (1 / x) * (y * x)
    ]]></literal>
    <justification jstring="[para(259(a,2),775(a,1,1))].">
      <j1 rule="para" parents="259 775"/>
    </justification>
  </clause>

  <clause id="800">
    <literal><![CDATA[
      (1 / x) * ((x \ y) * x) = T((1 / x) * y,x)
    ]]></literal>
    <justification jstring="[para(488(a,1),775(a,1,1)),flip(a)].">
      <j1 rule="para" parents="488 775"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="801">
    <literal><![CDATA[
      (1 / x) \ T((1 / x) * y,x) = (x \ y) * x
    ]]></literal>
    <justification jstring="[para(488(a,1),776(a,1,2,1))].">
      <j1 rule="para" parents="488 776"/>
    </justification>
  </clause>

  <clause id="802">
    <literal><![CDATA[
      (((x * y) * z) / (x * z)) * x = x * R(y,x,z)
    ]]></literal>
    <justification jstring="[hyper(119,a,785,a,b,17,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 785 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="803">
    <literal><![CDATA[
      T(x,y) != R(z,y,u)
    ]]></literal>
    <literal><![CDATA[
      ((y * z) * u) / (y * u) = x
    ]]></literal>
    <justification jstring="[para(785(a,2),44(a,1)),flip(a)].">
      <j1 rule="para" parents="785 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="804">
    <literal><![CDATA[
      T(((1 / x) * y) * x,1 / x) = R(y,1 / x,x)
    ]]></literal>
    <justification jstring="[para(170(a,1),785(a,2,1)),flip(a)].">
      <j1 rule="para" parents="170 785"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="805">
    <literal><![CDATA[
      T((x * y) \ ((x * z) * y),x) = T(R(z,x,y),x * y)
    ]]></literal>
    <justification jstring="[para(785(a,2),246(a,1,1)),flip(a)].">
      <j1 rule="para" parents="785 246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="806">
    <literal><![CDATA[
      T(R(x,y,x),y * x) = T(x,y)
    ]]></literal>
    <justification jstring="[para(785(a,2),270(a,1,1))].">
      <j1 rule="para" parents="785 270"/>
    </justification>
  </clause>

  <clause id="807">
    <literal><![CDATA[
      R(T(x,y * x),y,x) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,22,a,b,806,a)].">
      <j1 rule="hyper" parents="58 22 806"/>
    </justification>
  </clause>

  <clause id="808">
    <literal><![CDATA[
      L(R(x,y,x),z,u) * (y * x) = (y * x) * L(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(806(a,1),237(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="806 237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="809">
    <literal><![CDATA[
      R(R(x,y,x),z,u) * (y * x) = (y * x) * R(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(806(a,1),238(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="806 238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="810">
    <literal><![CDATA[
      R(x,y,z) != T(z,y)
    ]]></literal>
    <literal><![CDATA[
      T(z,y * z) = x
    ]]></literal>
    <justification jstring="[para(806(a,1),143(a,1)),flip(a)].">
      <j1 rule="para" parents="806 143"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="811">
    <literal><![CDATA[
      ((x * T(y,x * y)) * y) / (x * y) = y
    ]]></literal>
    <justification jstring="[hyper(35,a,785,a(flip),b,807,a(flip))].">
      <j1 rule="hyper" parents="35 785 807"/>
    </justification>
  </clause>

  <clause id="812">
    <literal><![CDATA[
      R(T(x,y),y / x,x) = T(x,y / x)
    ]]></literal>
    <justification jstring="[para(7(a,1),807(a,1,1,2))].">
      <j1 rule="para" parents="7 807"/>
    </justification>
  </clause>

  <clause id="813">
    <literal><![CDATA[
      (T(x,y * x) * y) * x = T(x,y) * (y * x)
    ]]></literal>
    <justification jstring="[para(807(a,1),101(a,1,1)),flip(a)].">
      <j1 rule="para" parents="807 101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="814">
    <literal><![CDATA[
      R(x,y / z,z) != T(z,y / z)
    ]]></literal>
    <literal><![CDATA[
      T(z,y) = x
    ]]></literal>
    <justification jstring="[para(812(a,1),46(a,1)),flip(a)].">
      <j1 rule="para" parents="812 46"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="815">
    <literal><![CDATA[
      R(x,1 / x,x) = T(x,1 / x)
    ]]></literal>
    <justification jstring="[para(198(a,1),812(a,1,1))].">
      <j1 rule="para" parents="198 812"/>
    </justification>
  </clause>

  <clause id="816">
    <literal><![CDATA[
      T(x,1 / x) / x = x * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(117,a,815,a(flip),b,262,a)].">
      <j1 rule="hyper" parents="117 815 262"/>
    </justification>
  </clause>

  <clause id="817">
    <literal><![CDATA[
      R(R(x,y,z),1 / x,x) = R(T(x,1 / x),y,z)
    ]]></literal>
    <justification jstring="[para(815(a,1),26(a,1,1)),flip(a)].">
      <j1 rule="para" parents="815 26"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="818">
    <literal><![CDATA[
      T(x,1 / x) / x = K(x,1 / x)
    ]]></literal>
    <justification jstring="[hyper(320,a,260,a,b,816,a),flip(a)].">
      <j1 rule="hyper" parents="320 260 816"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="819">
    <literal><![CDATA[
      K(x,1 / x) * x = T(x,1 / x)
    ]]></literal>
    <justification jstring="[hyper(133,a,818,a)].">
      <j1 rule="hyper" parents="133 818"/>
    </justification>
  </clause>

  <clause id="820">
    <literal><![CDATA[
      T(x * T(y,x * y),y) = x * y
    ]]></literal>
    <justification jstring="[hyper(266,a,811,a)].">
      <j1 rule="hyper" parents="266 811"/>
    </justification>
  </clause>

  <clause id="821">
    <literal><![CDATA[
      (x * (y * x)) / x = y * T(x,y * x)
    ]]></literal>
    <justification jstring="[para(811(a,1),78(a,1,1,1))].">
      <j1 rule="para" parents="811 78"/>
    </justification>
  </clause>

  <clause id="822">
    <literal><![CDATA[
      (x * R(y,x,x \ 1)) / x = (x * y) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(271,a,788,a)].">
      <j1 rule="hyper" parents="271 788"/>
    </justification>
  </clause>

  <clause id="823">
    <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="824">
    <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="825">
    <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="826">
    <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="827">
    <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="828">
    <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="829">
    <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="830">
    <literal><![CDATA[
      (x * y) * (K(y,x) * z) != (y * x) * u
    ]]></literal>
    <literal><![CDATA[
      L(z,K(y,x),x * y) = u
    ]]></literal>
    <justification jstring="[para(84(a,1),479(a,1,1)),flip(a)].">
      <j1 rule="para" parents="84 479"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="831">
    <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="832">
    <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="833">
    <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="834">
    <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="835">
    <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="836">
    <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="837">
    <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="838">
    <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="839">
    <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(778(a,1),515(a,2,2))].">
      <j1 rule="para" parents="778 515"/>
    </justification>
  </clause>

  <clause id="840">
    <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="841">
    <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="842">
    <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="843">
    <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),604(a,1,2))].">
      <j1 rule="para" parents="25 604"/>
    </justification>
  </clause>

  <clause id="844">
    <literal><![CDATA[
      R(x / y,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      (x * z) / (y * z) = u
    ]]></literal>
    <justification jstring="[para(6(a,1),622(a,1,1,1))].">
      <j1 rule="para" parents="6 622"/>
    </justification>
  </clause>

  <clause id="845">
    <literal><![CDATA[
      (x * ((y * x) \ y)) / x = L(1 / x,x,y)
    ]]></literal>
    <justification jstring="[hyper(117,a,394,a(flip),b,636,a)].">
      <j1 rule="hyper" parents="117 394 636"/>
    </justification>
  </clause>

  <clause id="846">
    <literal><![CDATA[
      L(1 / (x \ y),x \ y,x) * (x \ y) = (x \ y) * (y \ x)
    ]]></literal>
    <justification jstring="[para(390(a,1),636(a,2,2))].">
      <j1 rule="para" parents="390 636"/>
    </justification>
  </clause>

  <clause id="847">
    <literal><![CDATA[
      ((x \ y) * (y \ x)) / (x \ y) = L(1 / (x \ y),x \ y,x)
    ]]></literal>
    <justification jstring="[para(5(a,1),845(a,1,1,2,1))].">
      <j1 rule="para" parents="5 845"/>
    </justification>
  </clause>

  <clause id="848">
    <literal><![CDATA[
      L((x * y) / x,z,u) = (x * L(y,z,u)) / x
    ]]></literal>
    <justification jstring="[hyper(131,a,637,a),flip(a)].">
      <j1 rule="hyper" parents="131 637"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="849">
    <literal><![CDATA[
      L((x * (y \ 1)) / x,y,z) = (x * ((z * y) \ z)) / x
    ]]></literal>
    <justification jstring="[hyper(117,a,394,a(flip),b,637,a),flip(a)].">
      <j1 rule="hyper" parents="117 394 637"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="850">
    <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,637,a),flip(a)].">
      <j1 rule="hyper" parents="117 90 637"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="851">
    <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),640(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="305 640"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="852">
    <literal><![CDATA[
      (x * y) * R((x * y) \ z,x,y) != u
    ]]></literal>
    <literal><![CDATA[
      ((z / (x * y)) * x) * y = u
    ]]></literal>
    <justification jstring="[para(640(a,1),283(a,1))].">
      <j1 rule="para" parents="640 283"/>
    </justification>
  </clause>

  <clause id="853">
    <literal><![CDATA[
      ((((x * y) * z) / (x * y)) * x) * y = (x * y) * R(z,x,y)
    ]]></literal>
    <justification jstring="[hyper(283,a,641,a)].">
      <j1 rule="hyper" parents="283 641"/>
    </justification>
  </clause>

  <clause id="854">
    <literal><![CDATA[
      R((x * y) / x,z,u) = (x * R(y,z,u)) / x
    ]]></literal>
    <justification jstring="[hyper(131,a,641,a),flip(a)].">
      <j1 rule="hyper" parents="131 641"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="855">
    <literal><![CDATA[
      R((x * (1 / y)) / x,y,z) = (x * (z / (y * z))) / x
    ]]></literal>
    <justification jstring="[hyper(117,a,403,a(flip),b,641,a),flip(a)].">
      <j1 rule="hyper" parents="117 403 641"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="856">
    <literal><![CDATA[
      (((x * y) / x) * z) * (z \ x) = x * R(y,z,z \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,368,a(flip),b,641,a)].">
      <j1 rule="hyper" parents="58 368 641"/>
    </justification>
  </clause>

  <clause id="857">
    <literal><![CDATA[
      ((x * y) * R(z,x,y)) / y = (((x * y) * z) / (x * y)) * x
    ]]></literal>
    <justification jstring="[hyper(117,a,641,a(flip),b,101,a(flip))].">
      <j1 rule="hyper" parents="117 641 101"/>
    </justification>
  </clause>

  <clause id="858">
    <literal><![CDATA[
      ((x / y) * L(y,z,u)) / (x / y) = L(x / (x / y),z,u)
    ]]></literal>
    <justification jstring="[para(75(a,1),644(a,1,1,2,1))].">
      <j1 rule="para" parents="75 644"/>
    </justification>
  </clause>

  <clause id="859">
    <literal><![CDATA[
      L(x / y,z,u) * y != w
    ]]></literal>
    <literal><![CDATA[
      y * L(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="860">
    <literal><![CDATA[
      T(L(x / y,z,u),y) != w
    ]]></literal>
    <literal><![CDATA[
      L(y \ x,z,u) = w
    ]]></literal>
    <justification jstring="[para(644(a,1),292(a,1,1)),flip(b)].">
      <j1 rule="para" parents="644 292"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="861">
    <literal><![CDATA[
      (x * ((y * x) \ (y * z))) / x = L(z / x,x,y)
    ]]></literal>
    <justification jstring="[para(92(a,1),644(a,1,1,2))].">
      <j1 rule="para" parents="92 644"/>
    </justification>
  </clause>

  <clause id="862">
    <literal><![CDATA[
      L((x \ y) / z,z,x) = (z * ((x * z) \ y)) / z
    ]]></literal>
    <justification jstring="[para(298(a,1),644(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="298 644"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="863">
    <literal><![CDATA[
      (x * ((1 / x) * y)) / x = L(y / x,x,1 / x)
    ]]></literal>
    <justification jstring="[para(488(a,1),644(a,1,1,2))].">
      <j1 rule="para" parents="488 644"/>
    </justification>
  </clause>

  <clause id="864">
    <literal><![CDATA[
      ((x \ 1) * (x * y)) / (x \ 1) = L(y / (x \ 1),x \ 1,x)
    ]]></literal>
    <justification jstring="[para(489(a,1),644(a,1,1,2))].">
      <j1 rule="para" parents="489 644"/>
    </justification>
  </clause>

  <clause id="865">
    <literal><![CDATA[
      L(T(x,y) / x,x,y) = (x * K(x,y)) / x
    ]]></literal>
    <justification jstring="[para(749(a,2),644(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="749 644"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="866">
    <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),645(a,1,1,2,1))].">
      <j1 rule="para" parents="13 645"/>
    </justification>
  </clause>

  <clause id="867">
    <literal><![CDATA[
      R(x / y,z,u) * y != w
    ]]></literal>
    <literal><![CDATA[
      y * R(y \ x,z,u) = w
    ]]></literal>
    <justification jstring="[para(645(a,1),251(a,1,1)),flip(b)].">
      <j1 rule="para" parents="645 251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="868">
    <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="869">
    <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="870">
    <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="871">
    <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="872">
    <literal><![CDATA[
      (1 / (1 / x)) * (x * (1 / x)) = x
    ]]></literal>
    <justification jstring="[hyper(320,a,75,a(flip),b,777,a),flip(a)].">
      <j1 rule="hyper" parents="320 75 777"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="874">
    <literal><![CDATA[
      (1 / (1 / x)) * K(x,1 / x) = x
    ]]></literal>
    <justification jstring="[para(260(a,2),872(a,1,2))].">
      <j1 rule="para" parents="260 872"/>
    </justification>
  </clause>

  <clause id="875">
    <literal><![CDATA[
      (x \ ((1 / x) \ y)) * x = (1 / x) \ T(y,x)
    ]]></literal>
    <justification jstring="[para(5(a,1),801(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 801"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="876">
    <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),823(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="107 823"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="877">
    <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,828,a,b,309,a)].">
      <j1 rule="hyper" parents="116 828 309"/>
    </justification>
  </clause>

  <clause id="878">
    <literal><![CDATA[
      x \ R(T(y,y \ z),u,w) = x \ R((y \ z) \ z,u,w)
    ]]></literal>
    <justification jstring="[hyper(116,a,828,a,b,5,a)].">
      <j1 rule="hyper" parents="116 828 5"/>
    </justification>
  </clause>

  <clause id="879">
    <literal><![CDATA[
      R(x,x \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      (y * z) / ((x \ y) * z) = u
    ]]></literal>
    <justification jstring="[para(72(a,1),844(a,1,1))].">
      <j1 rule="para" parents="72 844"/>
    </justification>
  </clause>

  <clause id="880">
    <literal><![CDATA[
      (x * y) * ((z * L(u,y,x)) / z) = x * (y * ((z * u) / z))
    ]]></literal>
    <justification jstring="[hyper(119,a,848,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="119 848 13"/>
    </justification>
  </clause>

  <clause id="881">
    <literal><![CDATA[
      L((x * y) / x,z,u) != w / x
    ]]></literal>
    <literal><![CDATA[
      x * L(y,z,u) = w
    ]]></literal>
    <justification jstring="[para(848(a,2),41(a,1))].">
      <j1 rule="para" parents="848 41"/>
    </justification>
  </clause>

  <clause id="882">
    <literal><![CDATA[
      L((x * y) / x,z,u) * x != w
    ]]></literal>
    <literal><![CDATA[
      x * L(y,z,u) = w
    ]]></literal>
    <justification jstring="[para(848(a,2),251(a,1,1)),flip(b)].">
      <j1 rule="para" parents="848 251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="883">
    <literal><![CDATA[
      L((x * (y \ z)) / x,y,u) = (x * ((u * y) \ (u * z))) / x
    ]]></literal>
    <justification jstring="[para(92(a,1),848(a,2,1,2))].">
      <j1 rule="para" parents="92 848"/>
    </justification>
  </clause>

  <clause id="884">
    <literal><![CDATA[
      L((x * (y \ (z \ u))) / x,y,z) = (x * ((z * y) \ u)) / x
    ]]></literal>
    <justification jstring="[para(298(a,1),848(a,2,1,2))].">
      <j1 rule="para" parents="298 848"/>
    </justification>
  </clause>

  <clause id="885">
    <literal><![CDATA[
      L((x * (y \ 1)) / x,y,z / y) = (x * (z \ (z / y))) / x
    ]]></literal>
    <justification jstring="[para(398(a,1),848(a,2,1,2))].">
      <j1 rule="para" parents="398 848"/>
    </justification>
  </clause>

  <clause id="886">
    <literal><![CDATA[
      L((x * (y \ z)) / x,y,1 / y) = (x * ((1 / y) * z)) / x
    ]]></literal>
    <justification jstring="[para(488(a,1),848(a,2,1,2))].">
      <j1 rule="para" parents="488 848"/>
    </justification>
  </clause>

  <clause id="887">
    <literal><![CDATA[
      L((x * ((y \ z) \ u)) / x,y \ z,y) = (x * (z \ (y * u))) / x
    ]]></literal>
    <justification jstring="[para(490(a,1),848(a,2,1,2))].">
      <j1 rule="para" parents="490 848"/>
    </justification>
  </clause>

  <clause id="888">
    <literal><![CDATA[
      R((x * y) / x,z,u) * x != w
    ]]></literal>
    <literal><![CDATA[
      x * R(y,z,u) = w
    ]]></literal>
    <justification jstring="[para(854(a,2),251(a,1,1)),flip(b)].">
      <j1 rule="para" parents="854 251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="889">
    <literal><![CDATA[
      R((x * ((y / z) / u)) / x,u,z) = (x * (y / (u * z))) / x
    ]]></literal>
    <justification jstring="[para(301(a,1),854(a,2,1,2))].">
      <j1 rule="para" parents="301 854"/>
    </justification>
  </clause>

  <clause id="890">
    <literal><![CDATA[
      R((x * (y / (1 / z))) / x,1 / z,z) = (x * (y * z)) / x
    ]]></literal>
    <justification jstring="[para(522(a,1),854(a,2,1,2))].">
      <j1 rule="para" parents="522 854"/>
    </justification>
  </clause>

  <clause id="891">
    <literal><![CDATA[
      R((x * (y / z)) / x,z,z \ 1) = (x * (y * (z \ 1))) / x
    ]]></literal>
    <justification jstring="[para(523(a,1),854(a,2,1,2))].">
      <j1 rule="para" parents="523 854"/>
    </justification>
  </clause>

  <clause id="892">
    <literal><![CDATA[
      ((x * R(y,z,u)) / x) * (z * u) != w
    ]]></literal>
    <literal><![CDATA[
      (((x * y) / x) * z) * u = w
    ]]></literal>
    <justification jstring="[para(854(a,1),283(a,1,1))].">
      <j1 rule="para" parents="854 283"/>
    </justification>
  </clause>

  <clause id="893">
    <literal><![CDATA[
      ((1 / x) \ y) \ ((1 / x) \ T(y,x)) = K(x \ ((1 / x) \ y),x)
    ]]></literal>
    <justification jstring="[hyper(116,a,875,a(flip),b,302,a)].">
      <j1 rule="hyper" parents="116 875 302"/>
    </justification>
  </clause>

  <clause id="894">
    <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="895">
    <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="896">
    <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="897">
    <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="898">
    <literal><![CDATA[
      x \ (y * a(z,u,a(w,v5,v6))) = (x \ y) * a(z,u,a(w,v5,v6))
    ]]></literal>
    <justification jstring="[para(145(a,1),474(a,1,2,2))].">
      <j1 rule="para" parents="145 474"/>
    </justification>
  </clause>

  <clause id="899">
    <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="900">
    <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="901">
    <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="902">
    <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="903">
    <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="904">
    <literal><![CDATA[
      R(T(x,x * y),y,T(x,y)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,22,a,b,902,a)].">
      <j1 rule="hyper" parents="58 22 902"/>
    </justification>
  </clause>

  <clause id="905">
    <literal><![CDATA[
      T(x,y * z) != T(y,z)
    ]]></literal>
    <literal><![CDATA[
      R(y,z,T(y,z)) = x
    ]]></literal>
    <justification jstring="[para(902(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="902 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="906">
    <literal><![CDATA[
      (x * y) * T(y,x) = (y * x) * y
    ]]></literal>
    <justification jstring="[hyper(119,a,806,a(flip),b,245,a)].">
      <j1 rule="hyper" parents="119 806 245"/>
    </justification>
  </clause>

  <clause id="907">
    <literal><![CDATA[
      (x * (y / x)) * x = y * T(x,y / x)
    ]]></literal>
    <justification jstring="[hyper(326,a,906,a),flip(a)].">
      <j1 rule="hyper" parents="326 906"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="908">
    <literal><![CDATA[
      (x * (y / x)) \ (y * (y / x)) = T(y / x,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,147,a(flip),b,906,a)].">
      <j1 rule="hyper" parents="116 147 906"/>
    </justification>
  </clause>

  <clause id="909">
    <literal><![CDATA[
      ((x \ 1) * x) \ x = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(116,a,64,a(flip),b,906,a)].">
      <j1 rule="hyper" parents="116 64 906"/>
    </justification>
  </clause>

  <clause id="910">
    <literal><![CDATA[
      (T(x,y) * (y * x)) \ ((x * y) * x) = K(y * x,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(116,a,906,a(flip),b,84,a)].">
      <j1 rule="hyper" parents="116 906 84"/>
    </justification>
  </clause>

  <clause id="911">
    <literal><![CDATA[
      K(x \ 1,x) \ x = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(258(a,2),909(a,1,1))].">
      <j1 rule="para" parents="258 909"/>
    </justification>
  </clause>

  <clause id="912">
    <literal><![CDATA[
      K(x \ 1,x) * ((x \ 1) \ 1) = x
    ]]></literal>
    <justification jstring="[hyper(119,a,106,a(flip),b,911,a)].">
      <j1 rule="hyper" parents="119 106 911"/>
    </justification>
  </clause>

  <clause id="913">
    <literal><![CDATA[
      (x * y) \ (y * T(x,y / x)) = a(x,y / x,x)
    ]]></literal>
    <justification jstring="[para(907(a,1),82(a,1,2))].">
      <j1 rule="para" parents="907 82"/>
    </justification>
  </clause>

  <clause id="914">
    <literal><![CDATA[
      ((x / y) * (x / (x / y))) * y = x * (x / (x / y))
    ]]></literal>
    <justification jstring="[hyper(119,a,244,a(flip),b,908,a)].">
      <j1 rule="hyper" parents="119 244 908"/>
    </justification>
  </clause>

  <clause id="915">
    <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,400,a,b,231,a)].">
      <j1 rule="hyper" parents="119 400 231"/>
    </justification>
  </clause>

  <clause id="916">
    <literal><![CDATA[
      (x * y) * R((x * y) \ x,z,u) = x * (y * R(y \ 1,z,u))
    ]]></literal>
    <justification jstring="[hyper(119,a,400,a,b,13,a(flip))].">
      <j1 rule="hyper" parents="119 400 13"/>
    </justification>
  </clause>

  <clause id="917">
    <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,401,a),flip(a)].">
      <j1 rule="hyper" parents="320 92 401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="918">
    <literal><![CDATA[
      (x * y) * L((x * y) \ x,z,u) = x * (y * L(y \ 1,z,u))
    ]]></literal>
    <justification jstring="[hyper(119,a,401,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="119 401 13"/>
    </justification>
  </clause>

  <clause id="919">
    <literal><![CDATA[
      L((x * (y \ z)) \ x,y \ z,y) = L(z \ y,y \ z,x)
    ]]></literal>
    <justification jstring="[para(390(a,1),401(a,1,1)),flip(a)].">
      <j1 rule="para" parents="390 401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="920">
    <literal><![CDATA[
      R(x / (y * x),z,u) * (y * x) = (R(1 / y,z,u) * y) * x
    ]]></literal>
    <justification jstring="[para(410(a,1),101(a,1,1))].">
      <j1 rule="para" parents="410 101"/>
    </justification>
  </clause>

  <clause id="921">
    <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),418(a,1,2,1))].">
      <j1 rule="para" parents="17 418"/>
    </justification>
  </clause>

  <clause id="922">
    <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),419(a,1,2,1))].">
      <j1 rule="para" parents="244 419"/>
    </justification>
  </clause>

  <clause id="923">
    <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="924">
    <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="925">
    <literal><![CDATA[
      x * (T(y,x) * T(z,y * x)) = L(z,T(y,x),x) * (y * x)
    ]]></literal>
    <justification jstring="[hyper(418,a,481,a),flip(a)].">
      <j1 rule="hyper" parents="418 481"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="926">
    <literal><![CDATA[
      (L(x \ y,x,z) * u) \ (((z * x) \ (z * y)) * (u * w)) = L(w,u,L(x \ y,x,z))
    ]]></literal>
    <justification jstring="[hyper(116,a,492,a(flip),b,90,a)].">
      <j1 rule="hyper" parents="116 492 90"/>
    </justification>
  </clause>

  <clause id="927">
    <literal><![CDATA[
      (L(x \ y,x,z) * u) \ (((z * x) \ (z * y)) * (u * w)) = L(w,u,(z * x) \ (z * y))
    ]]></literal>
    <justification jstring="[para(492(a,2),13(a,2,1)),flip(a)].">
      <j1 rule="para" parents="492 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="928">
    <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),495(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="105 495"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="929">
    <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(495(a,2),286(a,1,2))].">
      <j1 rule="para" parents="495 286"/>
    </justification>
  </clause>

  <clause id="930">
    <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="931">
    <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="932">
    <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="933">
    <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="934">
    <literal><![CDATA[
      (T(x,x * y) * y) * T(x,y) = T(x,y) * (x * y)
    ]]></literal>
    <justification jstring="[para(904(a,1),516(a,1,1)),flip(a)].">
      <j1 rule="para" parents="904 516"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="935">
    <literal><![CDATA[
      R(T(x / y,y * z),y,z) = (y * z) \ (x * z)
    ]]></literal>
    <justification jstring="[hyper(420,a,526,a),flip(a)].">
      <j1 rule="hyper" parents="420 526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="936">
    <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),420(a,1))].">
      <j1 rule="para" parents="526 420"/>
    </justification>
  </clause>

  <clause id="937">
    <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),823(a,2,1))].">
      <j1 rule="para" parents="528 823"/>
    </justification>
  </clause>

  <clause id="938">
    <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="939">
    <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="940">
    <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="941">
    <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="942">
    <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="943">
    <literal><![CDATA[
      x \ y != z * (u \ (u * w))
    ]]></literal>
    <literal><![CDATA[
      x * (z * w) = y
    ]]></literal>
    <justification jstring="[para(4(a,1),579(a,2,2,2,2))].">
      <j1 rule="para" parents="4 579"/>
    </justification>
  </clause>

  <clause id="944">
    <literal><![CDATA[
      R(1 / x,x,x \ y) != z
    ]]></literal>
    <literal><![CDATA[
      (x \ y) / y = z
    ]]></literal>
    <justification jstring="[para(592(a,1),208(a,1))].">
      <j1 rule="para" parents="592 208"/>
    </justification>
  </clause>

  <clause id="945">
    <literal><![CDATA[
      T((x \ y) / y,z) * y = (T(1 / x,z) * x) * (x \ y)
    ]]></literal>
    <justification jstring="[para(593(a,2),368(a,1,1))].">
      <j1 rule="para" parents="593 368"/>
    </justification>
  </clause>

  <clause id="946">
    <literal><![CDATA[
      (1 / x) * (x * T(x \ y,z)) = T((1 / x) * y,z)
    ]]></literal>
    <justification jstring="[hyper(387,a,607,a)].">
      <j1 rule="hyper" parents="387 607"/>
    </justification>
  </clause>

  <clause id="947">
    <literal><![CDATA[
      (1 / x) \ T((1 / x) * y,z) = x * T(x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(116,a,607,a(flip),b,259,a)].">
      <j1 rule="hyper" parents="116 607 259"/>
    </justification>
  </clause>

  <clause id="948">
    <literal><![CDATA[
      x * (((x \ 1) \ y) * (x \ 1)) = T(x * y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,551,a(flip),b,608,a)].">
      <j1 rule="hyper" parents="58 551 608"/>
    </justification>
  </clause>

  <clause id="949">
    <literal><![CDATA[
      x \ T(x * y,x \ 1) = ((x \ 1) \ y) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(116,a,608,a(flip),b,551,a(flip))].">
      <j1 rule="hyper" parents="116 608 551"/>
    </justification>
  </clause>

  <clause id="950">
    <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),631(a,1,2)),flip(a)].">
      <j1 rule="para" parents="80 631"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="951">
    <literal><![CDATA[
      x \ (((x * y) \ x) * (x * y)) = y * T(y \ 1,x * y)
    ]]></literal>
    <justification jstring="[hyper(116,a,395,a(flip),b,632,a)].">
      <j1 rule="hyper" parents="116 395 632"/>
    </justification>
  </clause>

  <clause id="952">
    <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="953">
    <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="954">
    <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="955">
    <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="956">
    <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="957">
    <literal><![CDATA[
      (x / y) * ((y \ 1) * y) = x * T(x \ (x / y),y)
    ]]></literal>
    <justification jstring="[hyper(119,a,590,a,b,696,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 590 696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="958">
    <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),714(a,1,1))].">
      <j1 rule="para" parents="22 714"/>
    </justification>
  </clause>

  <clause id="959">
    <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,719,a),flip(a)].">
      <j1 rule="hyper" parents="320 20 719"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="960">
    <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,723,a)].">
      <j1 rule="hyper" parents="58 273 723"/>
    </justification>
  </clause>

  <clause id="961">
    <literal><![CDATA[
      L(x,x \ y,x) * (x \ y) != z
    ]]></literal>
    <literal><![CDATA[
      (x \ y) * T(x,y) = z
    ]]></literal>
    <justification jstring="[para(723(a,1),680(a,1,1))].">
      <j1 rule="para" parents="723 680"/>
    </justification>
  </clause>

  <clause id="962">
    <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,724,a),flip(a)].">
      <j1 rule="hyper" parents="320 20 724"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="963">
    <literal><![CDATA[
      R(T(x / y,z),y,y \ z) = z \ (x * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(58,a,22,a,b,726,a)].">
      <j1 rule="hyper" parents="58 22 726"/>
    </justification>
  </clause>

  <clause id="964">
    <literal><![CDATA[
      (x \ y) * T((x \ y) \ 1,y) = x \ ((y \ x) * y)
    ]]></literal>
    <justification jstring="[para(390(a,1),746(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="390 746"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="965">
    <literal><![CDATA[
      (x \ y) * T((x \ y) \ z,y) = x \ ((y \ (x * z)) * y)
    ]]></literal>
    <justification jstring="[para(490(a,1),746(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="490 746"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="966">
    <literal><![CDATA[
      (x / y) \ ((x \ (x / y)) * x) = y * T(y \ 1,x)
    ]]></literal>
    <justification jstring="[para(398(a,1),754(a,1,2,1))].">
      <j1 rule="para" parents="398 754"/>
    </justification>
  </clause>

  <clause id="967">
    <literal><![CDATA[
      x \ ((x / y) * ((y \ z) * y)) = T(x \ ((x / y) * z),y)
    ]]></literal>
    <justification jstring="[para(493(a,1),796(a,1,1)),flip(a)].">
      <j1 rule="para" parents="493 796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="968">
    <literal><![CDATA[
      (x * y) * ((y * ((x * y) \ z)) / y) = x * (y * ((x \ z) / y))
    ]]></literal>
    <justification jstring="[hyper(119,a,862,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="119 862 13"/>
    </justification>
  </clause>

  <clause id="969">
    <literal><![CDATA[
      L((x \ (y * (x * z))) / z,z,x) = (z * T(y,x * z)) / z
    ]]></literal>
    <justification jstring="[para(17(a,2),862(a,2,1,2))].">
      <j1 rule="para" parents="17 862"/>
    </justification>
  </clause>

  <clause id="970">
    <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),862(a,2,1,2))].">
      <j1 rule="para" parents="230 862"/>
    </justification>
  </clause>

  <clause id="971">
    <literal><![CDATA[
      (x * y) * ((y * ((x * y) \ z)) / y) != u
    ]]></literal>
    <literal><![CDATA[
      x * (y * ((x \ z) / y)) = u
    ]]></literal>
    <justification jstring="[para(862(a,1),286(a,1,2))].">
      <j1 rule="para" parents="862 286"/>
    </justification>
  </clause>

  <clause id="972">
    <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(958(a,2),46(a,1)),flip(a)].">
      <j1 rule="para" parents="958 46"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="973">
    <literal><![CDATA[
      x * R(T(y,y * x),z,u) = L(R(y,z,u),x,y) * x
    ]]></literal>
    <justification jstring="[para(958(a,1),237(a,1,2))].">
      <j1 rule="para" parents="958 237"/>
    </justification>
  </clause>

  <clause id="974">
    <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),959(a,1,1))].">
      <j1 rule="para" parents="25 959"/>
    </justification>
  </clause>

  <clause id="975">
    <literal><![CDATA[
      (x \ (y * (z \ x))) * x = (T(y / z,x) * z) * (z \ x)
    ]]></literal>
    <justification jstring="[para(963(a,1),368(a,1,1))].">
      <j1 rule="para" parents="963 368"/>
    </justification>
  </clause>

  <clause id="976">
    <literal><![CDATA[
      (x * y) * T(L(x,z,u),x * y) = x * (y * T(L(x,z,u),y))
    ]]></literal>
    <justification jstring="[para(974(a,1),449(a,1,2))].">
      <j1 rule="para" parents="974 449"/>
    </justification>
  </clause>

  <clause id="977">
    <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="978">
    <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="979">
    <literal><![CDATA[
      (x * ((y * z) / y)) / x = (y * ((x * z) / x)) / y
    ]]></literal>
    <justification jstring="[para(4(a,1),868(a,1,1,2,1,2))].">
      <j1 rule="para" parents="4 868"/>
    </justification>
  </clause>

  <clause id="980">
    <literal><![CDATA[
      ((x * (y / z)) / x) * z != u
    ]]></literal>
    <literal><![CDATA[
      z * ((x * (z \ y)) / x) = u
    ]]></literal>
    <justification jstring="[para(868(a,1),251(a,1,1)),flip(b)].">
      <j1 rule="para" parents="868 251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="981">
    <literal><![CDATA[
      (x \ y) * ((z * ((x \ y) \ y)) / z) = ((z * x) / z) * (x \ y)
    ]]></literal>
    <justification jstring="[para(72(a,1),869(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="72 869"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="982">
    <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),869(a,1,1,1,2))].">
      <j1 rule="para" parents="102 869"/>
    </justification>
  </clause>

  <clause id="983">
    <literal><![CDATA[
      ((x * (y / (y / z))) / x) \ ((y / z) * ((x * z) / x)) = y / z
    ]]></literal>
    <justification jstring="[para(75(a,1),870(a,1,2,2,1,2))].">
      <j1 rule="para" parents="75 870"/>
    </justification>
  </clause>

  <clause id="984">
    <literal><![CDATA[
      T(T((x * y) / (z * y),u),z) = R(T(z \ x,u),z,y)
    ]]></literal>
    <justification jstring="[para(102(a,1),876(a,1,1,1))].">
      <j1 rule="para" parents="102 876"/>
    </justification>
  </clause>

  <clause id="985">
    <literal><![CDATA[
      R(T(x \ y,z),x,x \ z) = T(z \ (y * (x \ z)),x)
    ]]></literal>
    <justification jstring="[para(726(a,1),876(a,1,1)),flip(a)].">
      <j1 rule="para" parents="726 876"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="986">
    <literal><![CDATA[
      T(T(x,x * y) * y,T(x,y)) = x * y
    ]]></literal>
    <justification jstring="[hyper(239,a,934,a,b,xx)].">
      <j1 rule="hyper" parents="239 934"/>
    </justification>
  </clause>

  <clause id="987">
    <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,986,a),flip(a)].">
      <j1 rule="hyper" parents="320 7 986"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="988">
    <literal><![CDATA[
      x \ T(x * (y * (x \ 1)),z) = T(y,z) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(741,a,939,a),flip(a)].">
      <j1 rule="hyper" parents="741 939"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="989">
    <literal><![CDATA[
      (x \ 1) \ (x \ T(x * y,z)) = T((x \ 1) \ y,z)
    ]]></literal>
    <justification jstring="[hyper(123,a,939,a)].">
      <j1 rule="hyper" parents="123 939"/>
    </justification>
  </clause>

  <clause id="990">
    <literal><![CDATA[
      T(x * (y * (x \ 1)),z) = x * (T(y,z) * (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(119,a,451,a(flip),b,939,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 451 939"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="991">
    <literal><![CDATA[
      (x \ 1) * T((x \ 1) \ 1,y) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[para(3(a,1),939(a,2,2,1))].">
      <j1 rule="para" parents="3 939"/>
    </justification>
  </clause>

  <clause id="992">
    <literal><![CDATA[
      (x \ 1) * T((x \ 1) \ (x \ y),z) = x \ T(y,z)
    ]]></literal>
    <justification jstring="[para(5(a,1),939(a,2,2,1))].">
      <j1 rule="para" parents="5 939"/>
    </justification>
  </clause>

  <clause id="993">
    <literal><![CDATA[
      T(x,y) * (x \ 1) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,455,a(flip),b,991,a)].">
      <j1 rule="hyper" parents="58 455 991"/>
    </justification>
  </clause>

  <clause id="994">
    <literal><![CDATA[
      T(x,y) \ (x \ T(x,y)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(116,a,991,a(flip),b,455,a(flip))].">
      <j1 rule="hyper" parents="116 991 455"/>
    </justification>
  </clause>

  <clause id="995">
    <literal><![CDATA[
      (x * y) \ (y * (x \ T(x,y))) = L(x \ 1,T(x,y),y)
    ]]></literal>
    <justification jstring="[para(993(a,1),231(a,1,2,2))].">
      <j1 rule="para" parents="993 231"/>
    </justification>
  </clause>

  <clause id="996">
    <literal><![CDATA[
      T(x,y) * (x \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      x \ T(x,y) = z
    ]]></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="997">
    <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),996(a,1))].">
      <j1 rule="para" parents="455 996"/>
    </justification>
  </clause>

  <clause id="998">
    <literal><![CDATA[
      T(x * (y \ 1),z) / (y \ 1) = y * T(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,453,a(flip),b,940,a),flip(a)].">
      <j1 rule="hyper" parents="320 453 940"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="999">
    <literal><![CDATA[
      T(x * (y \ 1),z) / (y \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      y * T(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(940(a,2),677(a,1))].">
      <j1 rule="para" parents="940 677"/>
    </justification>
  </clause>

  <clause id="1000">
    <literal><![CDATA[
      T(((1 / x) * y) * x,z) / x = (1 / x) * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(680,a,941,a),flip(a)].">
      <j1 rule="hyper" parents="680 941"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1001">
    <literal><![CDATA[
      (1 / x) * T((1 / x) \ y,z) = T(y * x,z) / x
    ]]></literal>
    <justification jstring="[hyper(677,a,941,a)].">
      <j1 rule="hyper" parents="677 941"/>
    </justification>
  </clause>

  <clause id="1002">
    <literal><![CDATA[
      (1 / x) \ (T(y * x,z) / x) = T((1 / x) \ y,z)
    ]]></literal>
    <justification jstring="[hyper(116,a,941,a(flip),b,453,a(flip))].">
      <j1 rule="hyper" parents="116 941 453"/>
    </justification>
  </clause>

  <clause id="1003">
    <literal><![CDATA[
      T(1 / (1 / x),y) * (1 / x) = T(x,y) / x
    ]]></literal>
    <justification jstring="[para(2(a,1),941(a,2,1,1))].">
      <j1 rule="para" parents="2 941"/>
    </justification>
  </clause>

  <clause id="1004">
    <literal><![CDATA[
      x / y != T(z / (1 / y),u) * (1 / y)
    ]]></literal>
    <literal><![CDATA[
      T(z * y,u) = x
    ]]></literal>
    <justification jstring="[para(941(a,2),41(a,1)),flip(a)].">
      <j1 rule="para" parents="941 41"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1005">
    <literal><![CDATA[
      T(x * y,1 / y) / y = ((1 / y) \ x) * (1 / y)
    ]]></literal>
    <justification jstring="[para(107(a,1),941(a,1,1)),flip(a)].">
      <j1 rule="para" parents="107 941"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1006">
    <literal><![CDATA[
      T(x * y,z) / y != u
    ]]></literal>
    <literal><![CDATA[
      (1 / y) * T((1 / y) \ x,z) = u
    ]]></literal>
    <justification jstring="[para(941(a,1),677(a,1))].">
      <j1 rule="para" parents="941 677"/>
    </justification>
  </clause>

  <clause id="1007">
    <literal><![CDATA[
      (1 / x) * T((1 / x) \ 1,y) = T(x,y) / x
    ]]></literal>
    <justification jstring="[hyper(677,a,1003,a)].">
      <j1 rule="hyper" parents="677 1003"/>
    </justification>
  </clause>

  <clause id="1008">
    <literal><![CDATA[
      (1 / x) * T(x,y) = T(x,y) / x
    ]]></literal>
    <justification jstring="[hyper(58,a,456,a(flip),b,1003,a)].">
      <j1 rule="hyper" parents="58 456 1003"/>
    </justification>
  </clause>

  <clause id="1009">
    <literal><![CDATA[
      T(x,y) \ (T(x,y) / x) = T(1 / x,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(439,a,1003,a(flip),b,456,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="439 1003 456"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1010">
    <literal><![CDATA[
      (T(x,y) / x) / T(x,y) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(117,a,1003,a(flip),b,456,a(flip))].">
      <j1 rule="hyper" parents="117 1003 456"/>
    </justification>
  </clause>

  <clause id="1011">
    <literal><![CDATA[
      T(x,y) / x != z
    ]]></literal>
    <literal><![CDATA[
      (1 / x) * T((1 / x) \ 1,y) = z
    ]]></literal>
    <justification jstring="[para(1003(a,1),677(a,1))].">
      <j1 rule="para" parents="1003 677"/>
    </justification>
  </clause>

  <clause id="1012">
    <literal><![CDATA[
      T(x \ 1,y) / (x \ 1) = x * T(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(348,a,1008,a),flip(a)].">
      <j1 rule="hyper" parents="348 1008"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1013">
    <literal><![CDATA[
      T(x,x \ y) / x = (1 / x) * ((x \ y) \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,313,a(flip),b,1008,a),flip(a)].">
      <j1 rule="hyper" parents="58 313 1008"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1014">
    <literal><![CDATA[
      T(x / y,y) / (x / y) = (1 / (x / y)) * (y \ x)
    ]]></literal>
    <justification jstring="[para(107(a,1),1008(a,1,2)),flip(a)].">
      <j1 rule="para" parents="107 1008"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1015">
    <literal><![CDATA[
      T(x \ 1,y) / (x \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      x * T(x \ 1,y) = z
    ]]></literal>
    <justification jstring="[para(1008(a,1),348(a,1))].">
      <j1 rule="para" parents="1008 348"/>
    </justification>
  </clause>

  <clause id="1016">
    <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(1008(a,1),718(a,1,2))].">
      <j1 rule="para" parents="1008 718"/>
    </justification>
  </clause>

  <clause id="1017">
    <literal><![CDATA[
      L(x \ 1,x,T(x,y) / x) = T(1 / x,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(669,a,1009,a)].">
      <j1 rule="hyper" parents="669 1009"/>
    </justification>
  </clause>

  <clause id="1018">
    <literal><![CDATA[
      T(x * T(x \ 1,y),x \ 1) = (x \ 1) \ T(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(1012(a,1),107(a,1,1))].">
      <j1 rule="para" parents="1012 107"/>
    </justification>
  </clause>

  <clause id="1019">
    <literal><![CDATA[
      (1 / x) * ((x \ y) \ y) = ((x \ y) \ y) / x
    ]]></literal>
    <justification jstring="[para(106(a,1),1013(a,1,1)),flip(a)].">
      <j1 rule="para" parents="106 1013"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1020">
    <literal><![CDATA[
      ((x \ 1) \ (x \ y)) * (x \ 1) = x \ T(y,x \ 1)
    ]]></literal>
    <justification jstring="[para(5(a,1),949(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 949"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1021">
    <literal><![CDATA[
      (x / y) \ T(x,(x / y) \ 1) = (((x / y) \ 1) \ y) * ((x / y) \ 1)
    ]]></literal>
    <justification jstring="[para(7(a,1),949(a,1,2,1))].">
      <j1 rule="para" parents="7 949"/>
    </justification>
  </clause>

  <clause id="1022">
    <literal><![CDATA[
      (x / y) * K(y \ 1,y) = x * T(x \ (x / y),y)
    ]]></literal>
    <justification jstring="[para(258(a,2),957(a,1,2))].">
      <j1 rule="para" parents="258 957"/>
    </justification>
  </clause>

  <clause id="1023">
    <literal><![CDATA[
      K(x,y) = ((y * x) \ y) * T(((y * x) \ y) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,430,a,b,964,a)].">
      <j1 rule="hyper" parents="320 430 964"/>
    </justification>
  </clause>

  <clause id="1024">
    <literal><![CDATA[
      T(((x * y) \ x) \ 1,x) = ((x * y) \ x) \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,430,a,b,964,a),flip(a)].">
      <j1 rule="hyper" parents="116 430 964"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1025">
    <literal><![CDATA[
      K(x \ (x / y),x) = y * T(y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(465,a,966,a)].">
      <j1 rule="hyper" parents="465 966"/>
    </justification>
  </clause>

  <clause id="1026">
    <literal><![CDATA[
      x \ K(y \ (y / x),y) = T(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(116,a,85,a(flip),b,966,a(flip))].">
      <j1 rule="hyper" parents="116 85 966"/>
    </justification>
  </clause>

  <clause id="1027">
    <literal><![CDATA[
      K(x \ (x / (1 / y)),x) = T(y,x) / y
    ]]></literal>
    <justification jstring="[hyper(320,a,1007,a(flip),b,1025,a),flip(a)].">
      <j1 rule="hyper" parents="320 1007 1025"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1028">
    <literal><![CDATA[
      K(x \ (x / (y \ 1)),x) = y \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,991,a(flip),b,1025,a),flip(a)].">
      <j1 rule="hyper" parents="320 991 1025"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1029">
    <literal><![CDATA[
      T(x,y) = x * K(y \ (y / (x \ 1)),y)
    ]]></literal>
    <justification jstring="[hyper(119,a,1025,a,b,991,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 1025 991"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1030">
    <literal><![CDATA[
      K(x \ (x / y),x) / y = T(1 / y,x)
    ]]></literal>
    <justification jstring="[hyper(117,a,1025,a,b,453,a)].">
      <j1 rule="hyper" parents="117 1025 453"/>
    </justification>
  </clause>

  <clause id="1031">
    <literal><![CDATA[
      K(T(1 / x,T(x,y)),T(x,y)) = x * T(x \ 1,T(x,y))
    ]]></literal>
    <justification jstring="[para(1009(a,1),1025(a,1,1))].">
      <j1 rule="para" parents="1009 1025"/>
    </justification>
  </clause>

  <clause id="1032">
    <literal><![CDATA[
      T(x,y) = K(y \ (y / (1 / x)),y) * x
    ]]></literal>
    <justification jstring="[hyper(133,a,1027,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="133 1027"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1033">
    <literal><![CDATA[
      K(x \ (x / (1 / (y / (x * y)))),x) = R(x \ 1,x,y) / (y / (x * y))
    ]]></literal>
    <justification jstring="[para(646(a,1),1027(a,2,1))].">
      <j1 rule="para" parents="646 1027"/>
    </justification>
  </clause>

  <clause id="1034">
    <literal><![CDATA[
      K(x \ (x / (((x * y) / x) \ 1)),x) = ((x * y) / x) \ y
    ]]></literal>
    <justification jstring="[para(224(a,1),1028(a,2,2))].">
      <j1 rule="para" parents="224 1028"/>
    </justification>
  </clause>

  <clause id="1035">
    <literal><![CDATA[
      K((x * y) \ x,x * y) / y = T(1 / y,x * y)
    ]]></literal>
    <justification jstring="[para(6(a,1),1030(a,1,1,1,2))].">
      <j1 rule="para" parents="6 1030"/>
    </justification>
  </clause>

  <clause id="1036">
    <literal><![CDATA[
      T((x \ 1) \ (x \ y),z) = (x \ 1) \ (x \ T(y,z))
    ]]></literal>
    <justification jstring="[para(5(a,1),989(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5 989"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1037">
    <literal><![CDATA[
      (x \ 1) * T((x \ 1) \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x \ T(x * y,z) = u
    ]]></literal>
    <justification jstring="[para(989(a,1),255(a,1,2)),flip(b)].">
      <j1 rule="para" parents="989 255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1038">
    <literal><![CDATA[
      (x \ T(y,z)) / (x \ 1) = T((x \ y) / (x \ 1),z)
    ]]></literal>
    <justification jstring="[hyper(117,a,992,a(flip),b,453,a)].">
      <j1 rule="hyper" parents="117 992 453"/>
    </justification>
  </clause>

  <clause id="1039">
    <literal><![CDATA[
      (x * T(x \ y,z)) * (x \ 1) = T(y * (x \ 1),z)
    ]]></literal>
    <justification jstring="[hyper(133,a,998,a)].">
      <j1 rule="hyper" parents="133 998"/>
    </justification>
  </clause>

  <clause id="1040">
    <literal><![CDATA[
      T(x * y,1 / y) / y != z
    ]]></literal>
    <literal><![CDATA[
      ((1 / y) \ x) * (1 / y) = z
    ]]></literal>
    <justification jstring="[para(1001(a,1),284(a,1))].">
      <j1 rule="para" parents="1001 284"/>
    </justification>
  </clause>

  <clause id="1041">
    <literal><![CDATA[
      T((1 / x) \ (y / x),z) = (1 / x) \ (T(y,z) / x)
    ]]></literal>
    <justification jstring="[para(7(a,1),1002(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="7 1002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1042">
    <literal><![CDATA[
      (1 / x) * T((1 / x) \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      T(y * x,z) / x = u
    ]]></literal>
    <justification jstring="[para(1002(a,1),255(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1002 255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1043">
    <literal><![CDATA[
      ((1 / x) \ (y / x)) * (1 / x) = T(y,1 / x) / x
    ]]></literal>
    <justification jstring="[para(7(a,1),1005(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7 1005"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1044">
    <literal><![CDATA[
      (1 / (x / y)) * (y \ x) = (y \ x) / (x / y)
    ]]></literal>
    <justification jstring="[para(107(a,1),1014(a,1,1)),flip(a)].">
      <j1 rule="para" parents="107 1014"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1045">
    <literal><![CDATA[
      (x \ y) \ ((x \ y) / (y / x)) = T(1 / (y / x),x \ y)
    ]]></literal>
    <justification jstring="[hyper(439,a,xx,b,1044,a),flip(a)].">
      <j1 rule="hyper" parents="439 1044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1046">
    <literal><![CDATA[
      (x \ y) / (y / x) != (x \ y) * z
    ]]></literal>
    <literal><![CDATA[
      T(1 / (y / x),x \ y) = z
    ]]></literal>
    <justification jstring="[para(1044(a,1),240(a,2)),flip(a)].">
      <j1 rule="para" parents="1044 240"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1047">
    <literal><![CDATA[
      ((x * y) \ x) * T(((x * y) \ x) \ 1,x) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(1024(a,2),255(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1024 255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1048">
    <literal><![CDATA[
      T(L(x \ 1,x,y) \ 1,y) = ((y * x) \ y) \ K(x,y)
    ]]></literal>
    <justification jstring="[para(217(a,2),1024(a,1,1,1))].">
      <j1 rule="para" parents="217 1024"/>
    </justification>
  </clause>

  <clause id="1049">
    <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(1024(a,1),1012(a,1,1))].">
      <j1 rule="para" parents="1024 1012"/>
    </justification>
  </clause>

  <clause id="1050">
    <literal><![CDATA[
      (x \ 1) * T((x \ 1) \ (x \ y),z) != u
    ]]></literal>
    <literal><![CDATA[
      x \ T(y,z) = u
    ]]></literal>
    <justification jstring="[para(1036(a,2),255(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1036 255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1051">
    <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(1036(a,2),340(a,2,2))].">
      <j1 rule="para" parents="1036 340"/>
    </justification>
  </clause>

  <clause id="1052">
    <literal><![CDATA[
      T((x * y) * (x \ 1),z) = (x * T(y,z)) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(4(a,1),1039(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4 1039"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1053">
    <literal><![CDATA[
      K(1 / x,(1 / x) \ (y / x)) = (T(y,1 / x) / x) \ (y / x)
    ]]></literal>
    <justification jstring="[para(1043(a,1),86(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1043 86"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1054">
    <literal><![CDATA[
      T((x * y) * (x \ 1),y) = (x * y) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(104(a,1),1052(a,2,1,2))].">
      <j1 rule="para" parents="104 1052"/>
    </justification>
  </clause>

  <clause id="1055">
    <literal><![CDATA[
      K((x * y) * (x \ 1),y) = 1
    ]]></literal>
    <justification jstring="[hyper(50,a,1054,a)].">
      <j1 rule="hyper" parents="50 1054"/>
    </justification>
  </clause>

  <clause id="1056">
    <literal><![CDATA[
      K(((1 / x) * y) * x,y) = 1
    ]]></literal>
    <justification jstring="[para(75(a,1),1055(a,1,1,2))].">
      <j1 rule="para" parents="75 1055"/>
    </justification>
  </clause>

  <clause id="1057">
    <literal><![CDATA[
      K(x * y,(1 / y) \ x) = 1
    ]]></literal>
    <justification jstring="[para(5(a,1),1056(a,1,1,1))].">
      <j1 rule="para" parents="5 1056"/>
    </justification>
  </clause>

  <clause id="1058">
    <literal><![CDATA[
      T(x * y,(1 / y) \ x) = x * y
    ]]></literal>
    <justification jstring="[hyper(51,a,1057,a)].">
      <j1 rule="hyper" parents="51 1057"/>
    </justification>
  </clause>

  <clause id="1059">
    <literal><![CDATA[
      K(x,1 / x) \ (x * (T(x,y) / x)) = L(T(x,y),1 / x,x)
    ]]></literal>
    <justification jstring="[para(1008(a,1),363(a,1,2,2))].">
      <j1 rule="para" parents="1008 363"/>
    </justification>
  </clause>

  <clause id="1060">
    <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="1061">
    <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="1062">
    <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="1063">
    <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="1064">
    <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="1065">
    <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="1066">
    <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="1067">
    <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="1068">
    <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="1069">
    <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="1070">
    <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="1071">
    <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="1072">
    <literal><![CDATA[
      (1 / x) \ L(x \ 1,y,z) = x * L(T(x \ 1,x),y,z)
    ]]></literal>
    <justification jstring="[para(742(a,1),553(a,1,2,1))].">
      <j1 rule="para" parents="742 553"/>
    </justification>
  </clause>

  <clause id="1073">
    <literal><![CDATA[
      L(x \ 1,y,z) / (x \ 1) = L(1 / x,y,z) * x
    ]]></literal>
    <justification jstring="[para(402(a,1),557(a,1,1,1))].">
      <j1 rule="para" parents="402 557"/>
    </justification>
  </clause>

  <clause id="1074">
    <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="1075">
    <literal><![CDATA[
      L(x \ 1,y,z) / (x \ 1) = x * L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,636,a(flip),b,1073,a),flip(a)].">
      <j1 rule="hyper" parents="320 636 1073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1076">
    <literal><![CDATA[
      L(x \ 1,x,y) / (x \ 1) = x * ((y * x) \ y)
    ]]></literal>
    <justification jstring="[hyper(320,a,394,a(flip),b,1075,a),flip(a)].">
      <j1 rule="hyper" parents="320 394 1075"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1077">
    <literal><![CDATA[
      (x * ((y * x) \ y)) * (x \ 1) = L(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[hyper(133,a,1076,a)].">
      <j1 rule="hyper" parents="133 1076"/>
    </justification>
  </clause>

  <clause id="1078">
    <literal><![CDATA[
      (x \ y) * ((x * (x \ y)) \ x) = (y \ x) / ((x \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(390(a,1),1076(a,1,1)),flip(a)].">
      <j1 rule="para" parents="390 1076"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1079">
    <literal><![CDATA[
      L(x \ 1,x,y) \ ((x \ 1) * (x * ((y * x) \ y))) = K(x \ 1,x * ((y * x) \ y))
    ]]></literal>
    <justification jstring="[para(1077(a,1),11(a,2,1)),flip(a)].">
      <j1 rule="para" parents="1077 11"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1080">
    <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="1081">
    <literal><![CDATA[
      L(T(x,1 / x),y,z) / x = L(x,y,z) * (1 / x)
    ]]></literal>
    <justification jstring="[para(815(a,1),562(a,1,1,1))].">
      <j1 rule="para" parents="815 562"/>
    </justification>
  </clause>

  <clause id="1082">
    <literal><![CDATA[
      T(L(x,y,z),1 / x) / x = L(x,y,z) * (1 / x)
    ]]></literal>
    <justification jstring="[para(20(a,1),1081(a,1,1))].">
      <j1 rule="para" parents="20 1081"/>
    </justification>
  </clause>

  <clause id="1083">
    <literal><![CDATA[
      (1 / x) \ (L(x,y,z) / x) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(30,a,1043,a,b,1082,a(flip))].">
      <j1 rule="hyper" parents="30 1043 1082"/>
    </justification>
  </clause>

  <clause id="1084">
    <literal><![CDATA[
      (L(x,y,z) / x) / L(x,y,z) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(197,a,1083,a)].">
      <j1 rule="hyper" parents="197 1083"/>
    </justification>
  </clause>

  <clause id="1085">
    <literal><![CDATA[
      (1 / x) * L(x,y,z) = L(x,y,z) / x
    ]]></literal>
    <justification jstring="[hyper(134,a,1083,a)].">
      <j1 rule="hyper" parents="134 1083"/>
    </justification>
  </clause>

  <clause id="1086">
    <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(1085(a,1),718(a,1,2))].">
      <j1 rule="para" parents="1085 718"/>
    </justification>
  </clause>

  <clause id="1087">
    <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="1088">
    <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="1089">
    <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="1090">
    <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="1091">
    <literal><![CDATA[
      (x \ 1) * R((x \ 1) \ y,z,u) = x \ R(x * y,z,u)
    ]]></literal>
    <justification jstring="[hyper(116,a,609,a(flip),b,257,a),flip(a)].">
      <j1 rule="hyper" parents="116 609 257"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1092">
    <literal><![CDATA[
      (R(x / y,z,u) * y) * (y \ 1) = R(x * (y \ 1),z,u)
    ]]></literal>
    <justification jstring="[hyper(388,a,613,a)].">
      <j1 rule="hyper" parents="388 613"/>
    </justification>
  </clause>

  <clause id="1093">
    <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(722(a,2),38(a,1)),flip(a)].">
      <j1 rule="para" parents="722 38"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1094">
    <literal><![CDATA[
      x * ((x \ y) * T((x \ y) \ z,u)) = y * T(y \ (x * z),u)
    ]]></literal>
    <justification jstring="[hyper(119,a,757,a(flip),b,91,a),flip(a)].">
      <j1 rule="hyper" parents="119 757 91"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1095">
    <literal><![CDATA[
      (T(x / (y / z),u) * (y / z)) * z = T((x * z) / y,u) * y
    ]]></literal>
    <justification jstring="[para(765(a,1),508(a,1,1)),flip(a)].">
      <j1 rule="para" parents="765 508"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1096">
    <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,805,a),flip(a)].">
      <j1 rule="hyper" parents="320 22 805"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1097">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ x)) / z) = x * (y * ((z * (y \ 1)) / z))
    ]]></literal>
    <justification jstring="[hyper(119,a,849,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="119 849 13"/>
    </justification>
  </clause>

  <clause id="1098">
    <literal><![CDATA[
      ((x * (y / (z * y))) / x) * (z * y) = (((x * (1 / z)) / x) * z) * y
    ]]></literal>
    <justification jstring="[para(855(a,1),101(a,1,1))].">
      <j1 rule="para" parents="855 101"/>
    </justification>
  </clause>

  <clause id="1099">
    <literal><![CDATA[
      ((x * ((y \ z) / (y * (y \ z)))) / x) * z = (((x * (1 / y)) / x) * y) * (y \ z)
    ]]></literal>
    <justification jstring="[para(855(a,1),368(a,1,1))].">
      <j1 rule="para" parents="855 368"/>
    </justification>
  </clause>

  <clause id="1100">
    <literal><![CDATA[
      (x * ((y \ x) / x)) / (y \ x) = ((x * (1 / y)) / x) * y
    ]]></literal>
    <justification jstring="[hyper(117,a,591,a(flip),b,856,a)].">
      <j1 rule="hyper" parents="117 591 856"/>
    </justification>
  </clause>

  <clause id="1101">
    <literal><![CDATA[
      ((x \ y) * x) * (x \ z) = z * T(z \ (y * (x \ z)),x)
    ]]></literal>
    <justification jstring="[hyper(119,a,985,a(flip),b,728,a),flip(a)].">
      <j1 rule="hyper" parents="119 985 728"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1102">
    <literal><![CDATA[
      K(x,y) = L(x \ 1,x,y) * T(L(x \ 1,x,y) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,1048,a,b,393,a),flip(a)].">
      <j1 rule="hyper" parents="119 1048 393"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1103">
    <literal><![CDATA[
      K(x \ 1,x) * y != (x \ 1) * z
    ]]></literal>
    <literal><![CDATA[
      L(x \ z,x,x \ 1) = y
    ]]></literal>
    <justification jstring="[para(1063(a,1),38(a,1)),flip(a)].">
      <j1 rule="para" parents="1063 38"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1104">
    <literal><![CDATA[
      (x * y) * T((x * y) \ y,z) = (T(1 / x,z) * x) * y
    ]]></literal>
    <justification jstring="[hyper(677,a,739,a)].">
      <j1 rule="hyper" parents="677 739"/>
    </justification>
  </clause>

  <clause id="1105">
    <literal><![CDATA[
      (x * y) * T((x * y) \ z,x) = ((x \ (z / y)) * x) * y
    ]]></literal>
    <justification jstring="[hyper(677,a,786,a)].">
      <j1 rule="hyper" parents="677 786"/>
    </justification>
  </clause>

  <clause id="1106">
    <literal><![CDATA[
      ((x \ (y / z)) * x) * z != u
    ]]></literal>
    <literal><![CDATA[
      (x * z) * T((x * z) \ y,x) = u
    ]]></literal>
    <justification jstring="[para(786(a,1),677(a,1))].">
      <j1 rule="para" parents="786 677"/>
    </justification>
  </clause>

  <clause id="1107">
    <literal><![CDATA[
      x * (y * T(T(x,y),z)) = T(x,z) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(417,a,798,a),flip(a)].">
      <j1 rule="hyper" parents="417 798"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1108">
    <literal><![CDATA[
      T(x,y) * (x * z) = x * (T(x,y) * z)
    ]]></literal>
    <justification jstring="[para(236(a,1),1107(a,1,2)),flip(a)].">
      <j1 rule="para" parents="236 1107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1109">
    <literal><![CDATA[
      x \ (T(x,y) * z) = T(x,y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(599,a,1108,a)].">
      <j1 rule="hyper" parents="599 1108"/>
    </justification>
  </clause>

  <clause id="1110">
    <literal><![CDATA[
      T(x,y) * (x \ (T(x,y) \ z)) = x \ z
    ]]></literal>
    <justification jstring="[hyper(598,a,1108,a),flip(a)].">
      <j1 rule="hyper" parents="598 1108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1111">
    <literal><![CDATA[
      (T(x,y) * z) / (T(x,y) * (x \ z)) = x
    ]]></literal>
    <justification jstring="[hyper(574,a,1108,a)].">
      <j1 rule="hyper" parents="574 1108"/>
    </justification>
  </clause>

  <clause id="1112">
    <literal><![CDATA[
      T(T(x,y),x * (T(x,y) \ z)) = (x * (T(x,y) \ z)) \ (x * z)
    ]]></literal>
    <justification jstring="[hyper(439,a,151,a(flip),b,1108,a)].">
      <j1 rule="hyper" parents="439 151 1108"/>
    </justification>
  </clause>

  <clause id="1113">
    <literal><![CDATA[
      x * (T(x,y) * (x \ z)) = T(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(342,a,1108,a),flip(a)].">
      <j1 rule="hyper" parents="342 1108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1114">
    <literal><![CDATA[
      T(x,y) * (x * (T(x,y) \ z)) = x * z
    ]]></literal>
    <justification jstring="[hyper(320,a,151,a(flip),b,1108,a),flip(a)].">
      <j1 rule="hyper" parents="320 151 1108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1115">
    <literal><![CDATA[
      (x * (T(x,y) * z)) / (x * z) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(131,a,1108,a)].">
      <j1 rule="hyper" parents="131 1108"/>
    </justification>
  </clause>

  <clause id="1116">
    <literal><![CDATA[
      T(x,y) \ (x * z) = x * (T(x,y) \ z)
    ]]></literal>
    <justification jstring="[hyper(116,a,151,a(flip),b,1108,a)].">
      <j1 rule="hyper" parents="116 151 1108"/>
    </justification>
  </clause>

  <clause id="1117">
    <literal><![CDATA[
      x * (T(x,y) \ (x \ z)) = T(x,y) \ z
    ]]></literal>
    <justification jstring="[hyper(116,a,68,a(flip),b,1108,a),flip(a)].">
      <j1 rule="hyper" parents="116 68 1108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1118">
    <literal><![CDATA[
      x * (T(x,y) \ 1) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(116,a,65,a(flip),b,1108,a),flip(a)].">
      <j1 rule="hyper" parents="116 65 1108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1119">
    <literal><![CDATA[
      (x / y) * (T(x / y,z) * y) = T(x / y,z) * x
    ]]></literal>
    <justification jstring="[para(7(a,1),1108(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7 1108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1120">
    <literal><![CDATA[
      T(x,y) * (x * z) != x * u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) * z = u
    ]]></literal>
    <justification jstring="[para(1108(a,2),38(a,1))].">
      <j1 rule="para" parents="1108 38"/>
    </justification>
  </clause>

  <clause id="1121">
    <literal><![CDATA[
      x * (T(x,y) * T(z,x)) = T(x,y) * (z * x)
    ]]></literal>
    <justification jstring="[para(105(a,1),1108(a,1,2)),flip(a)].">
      <j1 rule="para" parents="105 1108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1122">
    <literal><![CDATA[
      (x / y) * (T(x / y,y) * z) = (y \ x) * ((x / y) * z)
    ]]></literal>
    <justification jstring="[para(107(a,1),1108(a,1,1)),flip(a)].">
      <j1 rule="para" parents="107 1108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1123">
    <literal><![CDATA[
      T((T(x,y) \ x) / x,x) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(268,a,1118,a)].">
      <j1 rule="hyper" parents="268 1118"/>
    </justification>
  </clause>

  <clause id="1124">
    <literal><![CDATA[
      (T(x,y) \ x) / (T(x,y) \ 1) = x
    ]]></literal>
    <justification jstring="[hyper(131,a,1118,a)].">
      <j1 rule="hyper" parents="131 1118"/>
    </justification>
  </clause>

  <clause id="1125">
    <literal><![CDATA[
      x \ (T(x,y) \ x) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(123,a,1118,a)].">
      <j1 rule="hyper" parents="123 1118"/>
    </justification>
  </clause>

  <clause id="1126">
    <literal><![CDATA[
      L(T(x,y) \ 1,x,1 / x) = (1 / x) * (T(x,y) \ x)
    ]]></literal>
    <justification jstring="[hyper(119,a,1118,a(flip),b,436,a),flip(a)].">
      <j1 rule="hyper" parents="119 1118 436"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1127">
    <literal><![CDATA[
      T((T(x,y) \ x) / x,x) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) \ 1 = z
    ]]></literal>
    <justification jstring="[para(1118(a,1),292(a,1,1,1)),flip(b)].">
      <j1 rule="para" parents="1118 292"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1128">
    <literal><![CDATA[
      T((1 / x) * (T(x,y) \ x),x) = (1 / x) * ((T(x,y) \ 1) * x)
    ]]></literal>
    <justification jstring="[para(1118(a,1),799(a,1,1,2))].">
      <j1 rule="para" parents="1118 799"/>
    </justification>
  </clause>

  <clause id="1129">
    <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(1124(a,1),420(a,1,1))].">
      <j1 rule="para" parents="1124 420"/>
    </justification>
  </clause>

  <clause id="1130">
    <literal><![CDATA[
      (T(x,y) \ T(x,z)) / (T(x,y) \ 1) = T(x,z)
    ]]></literal>
    <justification jstring="[para(1124(a,1),1038(a,2,1))].">
      <j1 rule="para" parents="1124 1038"/>
    </justification>
  </clause>

  <clause id="1131">
    <literal><![CDATA[
      T(x,y) \ (x \ z) = x \ (T(x,y) \ z)
    ]]></literal>
    <justification jstring="[hyper(123,a,1110,a)].">
      <j1 rule="hyper" parents="123 1110"/>
    </justification>
  </clause>

  <clause id="1132">
    <literal><![CDATA[
      x * (T(x,y) \ (x \ z)) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (T(x,y) \ z) = w
    ]]></literal>
    <justification jstring="[para(1110(a,1),597(a,1,2,2))].">
      <j1 rule="para" parents="1110 597"/>
    </justification>
  </clause>

  <clause id="1133">
    <literal><![CDATA[
      (T(x,y) * z) / u != x
    ]]></literal>
    <literal><![CDATA[
      T(x,y) * (x \ z) = u
    ]]></literal>
    <justification jstring="[para(1111(a,1),40(a,1)),flip(a)].">
      <j1 rule="para" parents="1111 40"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1134">
    <literal><![CDATA[
      T(x,y) * z != x * u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) * (x \ z) = u
    ]]></literal>
    <justification jstring="[para(1111(a,1),125(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1111 125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1135">
    <literal><![CDATA[
      x \ (T(x,y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) * (x \ z) = u
    ]]></literal>
    <justification jstring="[para(1111(a,1),267(a,1,1)),flip(b)].">
      <j1 rule="para" parents="1111 267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1136">
    <literal><![CDATA[
      x * (T(x,y) \ y) = T(y,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(411,a,1114,a),flip(a)].">
      <j1 rule="hyper" parents="411 1114"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1137">
    <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,1114,a),flip(a)].">
      <j1 rule="hyper" parents="29 448 1114"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1138">
    <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,1114,a),flip(a)].">
      <j1 rule="hyper" parents="29 303 1114"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1139">
    <literal><![CDATA[
      T(x,y) \ (x * z) != u
    ]]></literal>
    <literal><![CDATA[
      x * (T(x,y) \ z) = u
    ]]></literal>
    <justification jstring="[para(1114(a,1),287(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1114 287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1140">
    <literal><![CDATA[
      (x / y) * ((y \ x) \ y) = T(y,T(x / y,y))
    ]]></literal>
    <justification jstring="[para(107(a,1),1136(a,1,2,1))].">
      <j1 rule="para" parents="107 1136"/>
    </justification>
  </clause>

  <clause id="1141">
    <literal><![CDATA[
      x \ y != T(z,u) * (z \ (T(z,u) \ w))
    ]]></literal>
    <literal><![CDATA[
      x * (z \ w) = y
    ]]></literal>
    <justification jstring="[para(1117(a,1),579(a,2,2,2))].">
      <j1 rule="para" parents="1117 579"/>
    </justification>
  </clause>

  <clause id="1142">
    <literal><![CDATA[
      T(x,y) * (x \ (T(x,y) \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      x \ z = u
    ]]></literal>
    <justification jstring="[para(1131(a,1),255(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1131 255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1143">
    <literal><![CDATA[
      x * (T(x,y) \ (x \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) \ z = u
    ]]></literal>
    <justification jstring="[para(1131(a,2),255(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1131 255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1144">
    <literal><![CDATA[
      T(T(x,y * x) * y,x) = T(x,y) * T(y,x)
    ]]></literal>
    <justification jstring="[hyper(239,a,813,a,b,1121,a)].">
      <j1 rule="hyper" parents="239 813 1121"/>
    </justification>
  </clause>

  <clause id="1145">
    <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,1121,a),flip(a)].">
      <j1 rule="hyper" parents="29 448 1121"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1146">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) \ 1) * x) = x * K(x \ (x / T(x,y)),x)
    ]]></literal>
    <justification jstring="[para(1025(a,2),1121(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1025 1121"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1147">
    <literal><![CDATA[
      T(x,y) * (T(x,z) \ 1) = T(x,z) \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(133,a,1130,a)].">
      <j1 rule="hyper" parents="133 1130"/>
    </justification>
  </clause>

  <clause id="1148">
    <literal><![CDATA[
      (x / y) * ((y \ x) \ y) = T(y,y \ x)
    ]]></literal>
    <justification jstring="[para(107(a,1),1140(a,2,2))].">
      <j1 rule="para" parents="107 1140"/>
    </justification>
  </clause>

  <clause id="1149">
    <literal><![CDATA[
      ((x * y) / x) * (y \ x) = T(x,x \ (x * y))
    ]]></literal>
    <justification jstring="[para(4(a,1),1148(a,1,2,1))].">
      <j1 rule="para" parents="4 1148"/>
    </justification>
  </clause>

  <clause id="1150">
    <literal><![CDATA[
      T(x / y,z) \ T(x / y,y) = (y \ x) * (T(x / y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(107(a,1),1147(a,1,1)),flip(a)].">
      <j1 rule="para" parents="107 1147"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1151">
    <literal><![CDATA[
      T(x,y) = ((x * y) / x) * (y \ x)
    ]]></literal>
    <justification jstring="[para(4(a,1),1149(a,2,2)),flip(a)].">
      <j1 rule="para" parents="4 1149"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1152">
    <literal><![CDATA[
      ((x * y) / x) \ T(x,y) = y \ x
    ]]></literal>
    <justification jstring="[hyper(770,a,1151,a)].">
      <j1 rule="hyper" parents="770 1151"/>
    </justification>
  </clause>

  <clause id="1153">
    <literal><![CDATA[
      T((x * y) / x,y \ x) = (y \ x) \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(439,a,1151,a,b,xx)].">
      <j1 rule="hyper" parents="439 1151"/>
    </justification>
  </clause>

  <clause id="1154">
    <literal><![CDATA[
      ((x * (x / y)) / x) * y = T(x,x / y)
    ]]></literal>
    <justification jstring="[hyper(320,a,193,a(flip),b,1151,a)].">
      <j1 rule="hyper" parents="320 193 1151"/>
    </justification>
  </clause>

  <clause id="1155">
    <literal><![CDATA[
      T(x,x / y) / y = (x * (x / y)) / x
    ]]></literal>
    <justification jstring="[hyper(117,a,1151,a,b,193,a(flip))].">
      <j1 rule="hyper" parents="117 1151 193"/>
    </justification>
  </clause>

  <clause id="1156">
    <literal><![CDATA[
      ((x * y) * x) / (x * y) = T(x * y,x) / y
    ]]></literal>
    <justification jstring="[hyper(117,a,1151,a,b,152,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="117 1151 152"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1157">
    <literal><![CDATA[
      T(x,y) / (y \ x) = (x * y) / x
    ]]></literal>
    <justification jstring="[hyper(117,a,1151,a,b,xx)].">
      <j1 rule="hyper" parents="117 1151"/>
    </justification>
  </clause>

  <clause id="1158">
    <literal><![CDATA[
      (x / (x / y)) * (y \ (x / y)) = T(x / y,y)
    ]]></literal>
    <justification jstring="[para(7(a,1),1151(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="7 1151"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1159">
    <literal><![CDATA[
      ((x * R(y,y \ 1,x)) / x) * ((y \ 1) * x) = T(x,R(y,y \ 1,x))
    ]]></literal>
    <justification jstring="[para(425(a,1),1151(a,2,2)),flip(a)].">
      <j1 rule="para" parents="425 1151"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1160">
    <literal><![CDATA[
      T(T(x,y) / (y \ x),x) = y
    ]]></literal>
    <justification jstring="[para(1157(a,2),224(a,1,1))].">
      <j1 rule="para" parents="1157 224"/>
    </justification>
  </clause>

  <clause id="1161">
    <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(1157(a,1),1026(a,1,2,1,2))].">
      <j1 rule="para" parents="1157 1026"/>
    </justification>
  </clause>

  <clause id="1162">
    <literal><![CDATA[
      T((x \ y) \ T(y,x),y) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(1160(a,1),246(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1160 246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1163">
    <literal><![CDATA[
      T(T(R(x,y,y \ 1),x * y) / (y \ 1),R(x,y,y \ 1)) = x * y
    ]]></literal>
    <justification jstring="[para(435(a,1),1160(a,1,1,2))].">
      <j1 rule="para" parents="435 1160"/>
    </justification>
  </clause>

  <clause id="1164">
    <literal><![CDATA[
      x * ((y * (x \ y)) / y) = T(y,y / x)
    ]]></literal>
    <justification jstring="[hyper(58,a,869,a(flip),b,1154,a)].">
      <j1 rule="hyper" parents="58 869 1154"/>
    </justification>
  </clause>

  <clause id="1165">
    <literal><![CDATA[
      x \ T(y,y / x) = (y * (x \ y)) / y
    ]]></literal>
    <justification jstring="[hyper(116,a,1154,a(flip),b,869,a(flip))].">
      <j1 rule="hyper" parents="116 1154 869"/>
    </justification>
  </clause>

  <clause id="1166">
    <literal><![CDATA[
      ((x * (x / y)) / x) * y != z
    ]]></literal>
    <literal><![CDATA[
      T(x,x / y) = z
    ]]></literal>
    <justification jstring="[para(1155(a,1),251(a,1,1)),flip(b)].">
      <j1 rule="para" parents="1155 251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1167">
    <literal><![CDATA[
      T((x \ y) \ T(y,x),y) = (x \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(320,a,106,a(flip),b,1162,a),flip(a)].">
      <j1 rule="hyper" parents="320 106 1162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1168">
    <literal><![CDATA[
      (x / y) * ((x * y) / x) = T(x,x / (x / y))
    ]]></literal>
    <justification jstring="[para(75(a,1),1164(a,1,2,1,2))].">
      <j1 rule="para" parents="75 1164"/>
    </justification>
  </clause>

  <clause id="1169">
    <literal><![CDATA[
      x * ((y * (x \ y)) / y) != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ T(y,y / x) = u
    ]]></literal>
    <justification jstring="[para(1164(a,2),770(a,1))].">
      <j1 rule="para" parents="1164 770"/>
    </justification>
  </clause>

  <clause id="1170">
    <literal><![CDATA[
      (x * y) * L((x \ y) / y,y,x) = T(y,y / (x * y))
    ]]></literal>
    <justification jstring="[para(862(a,2),1164(a,1,2))].">
      <j1 rule="para" parents="862 1164"/>
    </justification>
  </clause>

  <clause id="1171">
    <literal><![CDATA[
      x * ((y * (x \ y)) / y) != z
    ]]></literal>
    <literal><![CDATA[
      T(y,y / x) = z
    ]]></literal>
    <justification jstring="[para(1165(a,1),255(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1165 255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1172">
    <literal><![CDATA[
      T((x \ y) \ T(y,x),x * y) = L(T(x,x \ y),y,x)
    ]]></literal>
    <justification jstring="[para(1153(a,1),962(a,1,1))].">
      <j1 rule="para" parents="1153 962"/>
    </justification>
  </clause>

  <clause id="1173">
    <literal><![CDATA[
      T(T(x * y,x) / y,y) = R(x,y,T(x,y))
    ]]></literal>
    <justification jstring="[para(1156(a,1),901(a,1,1))].">
      <j1 rule="para" parents="1156 901"/>
    </justification>
  </clause>

  <clause id="1174">
    <literal><![CDATA[
      x \ T(y * x,y) = R(y,x,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(420,a,1173,a)].">
      <j1 rule="hyper" parents="420 1173"/>
    </justification>
  </clause>

  <clause id="1175">
    <literal><![CDATA[
      R(x,y,T(x,y)) != z
    ]]></literal>
    <literal><![CDATA[
      y \ T(x * y,x) = z
    ]]></literal>
    <justification jstring="[para(1173(a,1),420(a,1))].">
      <j1 rule="para" parents="1173 420"/>
    </justification>
  </clause>

  <clause id="1176">
    <literal><![CDATA[
      L(R(x,y,T(x,y)),y,x) = x
    ]]></literal>
    <justification jstring="[para(1174(a,1),473(a,1,1))].">
      <j1 rule="para" parents="1174 473"/>
    </justification>
  </clause>

  <clause id="1177">
    <literal><![CDATA[
      (x * y) / ((x * y) / x) = y / (x \ ((x * y) / x))
    ]]></literal>
    <justification jstring="[hyper(117,a,224,a(flip),b,1158,a),flip(a)].">
      <j1 rule="hyper" parents="117 224 1158"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1178">
    <literal><![CDATA[
      T(x,x / (x / T(y,x))) = (x / T(y,x)) * y
    ]]></literal>
    <justification jstring="[para(225(a,1),1168(a,1,2)),flip(a)].">
      <j1 rule="para" parents="225 1168"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1179">
    <literal><![CDATA[
      T(x,T(y,x)) != z
    ]]></literal>
    <literal><![CDATA[
      y * (T(y,x) \ x) = z
    ]]></literal>
    <justification jstring="[para(235(a,1),1139(a,1))].">
      <j1 rule="para" parents="235 1139"/>
    </justification>
  </clause>

  <clause id="1180">
    <literal><![CDATA[
      x * (T(x,y) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) \ (x * z) = u
    ]]></literal>
    <justification jstring="[para(4(a,1),1143(a,1,2,2))].">
      <j1 rule="para" parents="4 1143"/>
    </justification>
  </clause>

  <clause id="1181">
    <literal><![CDATA[
      (x / y) * (y * T(y \ x,z)) = T(x / y,z) * x
    ]]></literal>
    <justification jstring="[para(453(a,1),1119(a,1,2))].">
      <j1 rule="para" parents="453 1119"/>
    </justification>
  </clause>

  <clause id="1182">
    <literal><![CDATA[
      x * T(1 / x,T(x,y)) = K(x,T(x,y) / x)
    ]]></literal>
    <justification jstring="[para(1009(a,1),1138(a,1,2))].">
      <j1 rule="para" parents="1009 1138"/>
    </justification>
  </clause>

  <clause id="1183">
    <literal><![CDATA[
      x * (y * ((x \ y) / y)) = T(y,y / (x * y))
    ]]></literal>
    <justification jstring="[hyper(286,a,1170,a)].">
      <j1 rule="hyper" parents="286 1170"/>
    </justification>
  </clause>

  <clause id="1184">
    <literal><![CDATA[
      T(x,x / (y * x)) != z
    ]]></literal>
    <literal><![CDATA[
      y * (x * ((y \ x) / x)) = z
    ]]></literal>
    <justification jstring="[para(1170(a,1),286(a,1))].">
      <j1 rule="para" parents="1170 286"/>
    </justification>
  </clause>

  <clause id="1185">
    <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(878(a,2),657(a,1))].">
      <j1 rule="para" parents="878 657"/>
    </justification>
  </clause>

  <clause id="1186">
    <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(919(a,1),45(a,1))].">
      <j1 rule="para" parents="919 45"/>
    </justification>
  </clause>

  <clause id="1187">
    <literal><![CDATA[
      (T(1 / x,y) * x) * (x \ z) = z * T(z \ (x \ z),y)
    ]]></literal>
    <justification jstring="[hyper(677,a,945,a),flip(a)].">
      <j1 rule="hyper" parents="677 945"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1188">
    <literal><![CDATA[
      (x \ (y * (z \ x))) * x = (z * T(z \ y,x)) * (z \ x)
    ]]></literal>
    <justification jstring="[para(453(a,1),975(a,2,1))].">
      <j1 rule="para" parents="453 975"/>
    </justification>
  </clause>

  <clause id="1189">
    <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,1018,a(flip),b,946,a)].">
      <j1 rule="hyper" parents="116 1018 946"/>
    </justification>
  </clause>

  <clause id="1190">
    <literal><![CDATA[
      T((x * y) / x,K(x \ (x / (((x * y) / x) \ 1)),x)) = (((x * y) / x) \ y) \ y
    ]]></literal>
    <justification jstring="[para(1034(a,2),106(a,1,2))].">
      <j1 rule="para" parents="1034 106"/>
    </justification>
  </clause>

  <clause id="1191">
    <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(1034(a,2),427(a,1,2))].">
      <j1 rule="para" parents="1034 427"/>
    </justification>
  </clause>

  <clause id="1192">
    <literal><![CDATA[
      K(T(1 / (1 / x),x \ 1),x \ 1) = T(x,x \ 1) / x
    ]]></literal>
    <justification jstring="[para(1045(a,1),1027(a,1,1))].">
      <j1 rule="para" parents="1045 1027"/>
    </justification>
  </clause>

  <clause id="1193">
    <literal><![CDATA[
      (x \ 1) * L((x \ 1) \ 1,y,z) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[para(3(a,1),1069(a,2,2,1))].">
      <j1 rule="para" parents="3 1069"/>
    </justification>
  </clause>

  <clause id="1194">
    <literal><![CDATA[
      L(x,y,z) * (x \ 1) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,638,a(flip),b,1193,a)].">
      <j1 rule="hyper" parents="58 638 1193"/>
    </justification>
  </clause>

  <clause id="1195">
    <literal><![CDATA[
      L(x,y,z) \ (x \ L(x,y,z)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(116,a,1193,a(flip),b,638,a(flip))].">
      <j1 rule="hyper" parents="116 1193 638"/>
    </justification>
  </clause>

  <clause id="1196">
    <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(1194(a,1),652(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1194 652"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1197">
    <literal><![CDATA[
      x \ T(x * (x \ L(x,y,z)),u) = T(L(x,y,z),u) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(1194(a,1),988(a,1,2,1,2))].">
      <j1 rule="para" parents="1194 988"/>
    </justification>
  </clause>

  <clause id="1198">
    <literal><![CDATA[
      x * L(x \ ((1 / x) \ y),z,u) = (1 / x) \ L(y,z,u)
    ]]></literal>
    <justification jstring="[para(5(a,1),1071(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 1071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1199">
    <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,1072,a),flip(a)].">
      <j1 rule="hyper" parents="320 237 1072"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1200">
    <literal><![CDATA[
      (x * y) \ x = (1 / y) * (L(y \ 1,y,x) * y)
    ]]></literal>
    <justification jstring="[hyper(119,a,1199,a(flip),b,392,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 1199 392"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1201">
    <literal><![CDATA[
      L((x \ y) \ 1,x \ y,x) * (x \ y) = (1 / (x \ y)) \ (y \ x)
    ]]></literal>
    <justification jstring="[para(390(a,1),1199(a,1,2)),flip(a)].">
      <j1 rule="para" parents="390 1199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1202">
    <literal><![CDATA[
      (1 / x) * (((y * x) \ y) * x) = (y * x) \ y
    ]]></literal>
    <justification jstring="[para(217(a,1),1200(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="217 1200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1203">
    <literal><![CDATA[
      x * L(x \ (((y * x) \ y) * x),z,u) = (1 / x) \ L((y * x) \ y,z,u)
    ]]></literal>
    <justification jstring="[para(1202(a,1),1071(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1202 1071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1204">
    <literal><![CDATA[
      L(x * (y \ 1),z,u) / (y \ 1) = y * L(y \ x,z,u)
    ]]></literal>
    <justification jstring="[hyper(320,a,636,a(flip),b,1074,a),flip(a)].">
      <j1 rule="hyper" parents="320 636 1074"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1205">
    <literal><![CDATA[
      (x \ y) / ((y \ x) \ 1) = (y \ x) * (x \ y)
    ]]></literal>
    <justification jstring="[para(5(a,1),1078(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 1078"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1207">
    <literal><![CDATA[
      (x \ 1) * R((x \ 1) \ 1,y,z) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(3(a,1),1091(a,2,2,1))].">
      <j1 rule="para" parents="3 1091"/>
    </justification>
  </clause>

  <clause id="1208">
    <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),1091(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="17 1091"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1209">
    <literal><![CDATA[
      R(x,y,z) * (x \ 1) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,642,a(flip),b,1207,a)].">
      <j1 rule="hyper" parents="58 642 1207"/>
    </justification>
  </clause>

  <clause id="1210">
    <literal><![CDATA[
      (1 / x) \ R(1 / x,y,z) = R(1 / x,y,z) * x
    ]]></literal>
    <justification jstring="[hyper(586,a,1209,a),flip(a)].">
      <j1 rule="hyper" parents="586 1209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1211">
    <literal><![CDATA[
      (x \ R(x,y,z)) / R(T(x,x \ 1),y,z) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(117,a,1209,a(flip),b,238,a)].">
      <j1 rule="hyper" parents="117 1209 238"/>
    </justification>
  </clause>

  <clause id="1212">
    <literal><![CDATA[
      (x \ R(x,y,z)) * K(x \ 1,R(x,y,z)) = (x \ 1) * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(1209(a,1),84(a,1,1))].">
      <j1 rule="para" parents="1209 84"/>
    </justification>
  </clause>

  <clause id="1213">
    <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(1209(a,1),652(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1209 652"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1214">
    <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(1209(a,1),679(a,2,1))].">
      <j1 rule="para" parents="1209 679"/>
    </justification>
  </clause>

  <clause id="1215">
    <literal><![CDATA[
      (1 / x) \ R(1 / x,y,z) = x * R(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,640,a(flip),b,1210,a),flip(a)].">
      <j1 rule="hyper" parents="320 640 1210"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1216">
    <literal><![CDATA[
      (1 / x) * ((y / (x * y)) * x) = R(1 / x,x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,404,a(flip),b,1210,a)].">
      <j1 rule="hyper" parents="119 404 1210"/>
    </justification>
  </clause>

  <clause id="1217">
    <literal><![CDATA[
      ((x / (y * x)) * y) \ (x / (y * x)) = T(1 / y,(x / (y * x)) * y)
    ]]></literal>
    <justification jstring="[hyper(439,a,219,a(flip),b,1216,a),flip(a)].">
      <j1 rule="hyper" parents="439 219 1216"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1218">
    <literal><![CDATA[
      (x / y) * R((x / y) \ 1,x / y,y) = (1 / (x / y)) \ (y / x)
    ]]></literal>
    <justification jstring="[para(408(a,1),1215(a,1,2)),flip(a)].">
      <j1 rule="para" parents="408 1215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1219">
    <literal><![CDATA[
      x * R(x \ 1,y,y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      a(1 / x,y,y \ 1) = z
    ]]></literal>
    <justification jstring="[para(1215(a,1),708(a,1))].">
      <j1 rule="para" parents="1215 708"/>
    </justification>
  </clause>

  <clause id="1220">
    <literal><![CDATA[
      (x * R(x \ y,z,u)) * (x \ 1) = R(y * (x \ 1),z,u)
    ]]></literal>
    <justification jstring="[para(640(a,1),1092(a,1,1))].">
      <j1 rule="para" parents="640 1092"/>
    </justification>
  </clause>

  <clause id="1221">
    <literal><![CDATA[
      (x * ((y \ x) / x)) / (y \ x) = y * ((x * (y \ 1)) / x)
    ]]></literal>
    <justification jstring="[hyper(320,a,869,a(flip),b,1100,a),flip(a)].">
      <j1 rule="hyper" parents="320 869 1100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1222">
    <literal><![CDATA[
      ((x \ 1) * x) * (x \ y) = y * T(y \ (x \ y),x)
    ]]></literal>
    <justification jstring="[para(2(a,1),1101(a,2,2,1,2))].">
      <j1 rule="para" parents="2 1101"/>
    </justification>
  </clause>

  <clause id="1223">
    <literal><![CDATA[
      K(x \ 1,x) * (x \ y) = y * T(y \ (x \ y),x)
    ]]></literal>
    <justification jstring="[hyper(570,a,1222,a)].">
      <j1 rule="hyper" parents="570 1222"/>
    </justification>
  </clause>

  <clause id="1224">
    <literal><![CDATA[
      (x * T(x \ (y \ x),y)) / (y \ x) = K(y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(131,a,1223,a)].">
      <j1 rule="hyper" parents="131 1223"/>
    </justification>
  </clause>

  <clause id="1225">
    <literal><![CDATA[
      K(x \ 1,x) * (x \ y) != z
    ]]></literal>
    <literal><![CDATA[
      y * T(y \ (x \ y),x) = z
    ]]></literal>
    <justification jstring="[para(1224(a,1),251(a,1,1)),flip(b)].">
      <j1 rule="para" parents="1224 251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1226">
    <literal><![CDATA[
      (x * y) * T((x * y) \ y,z) = (x * T(x \ 1,z)) * y
    ]]></literal>
    <justification jstring="[para(453(a,1),1104(a,2,1))].">
      <j1 rule="para" parents="453 1104"/>
    </justification>
  </clause>

  <clause id="1227">
    <literal><![CDATA[
      ((x \ (x / y)) * x) * y = x * (y * T(y \ 1,x))
    ]]></literal>
    <justification jstring="[hyper(58,a,736,a(flip),b,1105,a),flip(a)].">
      <j1 rule="hyper" parents="58 736 1105"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1228">
    <literal><![CDATA[
      x * ((y \ x) * T((y \ x) \ 1,x)) = ((x \ y) * x) * (y \ x)
    ]]></literal>
    <justification jstring="[para(72(a,1),1227(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="72 1227"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1229">
    <literal><![CDATA[
      (x / y) * ((y \ x) * z) = (y \ x) * ((x / y) * z)
    ]]></literal>
    <justification jstring="[para(107(a,1),1122(a,1,2,1))].">
      <j1 rule="para" parents="107 1122"/>
    </justification>
  </clause>

  <clause id="1230">
    <literal><![CDATA[
      (x \ (x * y)) * (((x * y) / x) * z) = ((x * y) / x) * (y * z)
    ]]></literal>
    <justification jstring="[para(224(a,1),1122(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="224 1122"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1231">
    <literal><![CDATA[
      ((x / y) \ x) * ((x / (x / y)) * z) = (x / (x / y)) * (y * z)
    ]]></literal>
    <justification jstring="[para(244(a,1),1122(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="244 1122"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1232">
    <literal><![CDATA[
      (x / y) * ((y \ x) \ 1) = (y \ x) \ (x / y)
    ]]></literal>
    <justification jstring="[hyper(415,a,1229,a),flip(a)].">
      <j1 rule="hyper" parents="415 1229"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1233">
    <literal><![CDATA[
      ((x \ 1) \ 1) / x = (x \ 1) \ (1 / x)
    ]]></literal>
    <justification jstring="[hyper(58,a,1019,a(flip),b,1232,a)].">
      <j1 rule="hyper" parents="58 1019 1232"/>
    </justification>
  </clause>

  <clause id="1234">
    <literal><![CDATA[
      (x \ (x * y)) \ ((x * y) / x) = ((x * y) / x) * (y \ 1)
    ]]></literal>
    <justification jstring="[para(4(a,1),1232(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4 1232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1235">
    <literal><![CDATA[
      (x * T(x \ 1,y)) * (x \ z) = z * T(z \ (x \ z),y)
    ]]></literal>
    <justification jstring="[para(453(a,1),1187(a,1,1))].">
      <j1 rule="para" parents="453 1187"/>
    </justification>
  </clause>

  <clause id="1236">
    <literal><![CDATA[
      (x \ (y \ x)) * x = (y * T(y \ 1,x)) * (y \ x)
    ]]></literal>
    <justification jstring="[para(2(a,1),1188(a,1,1,2))].">
      <j1 rule="para" parents="2 1188"/>
    </justification>
  </clause>

  <clause id="1237">
    <literal><![CDATA[
      T(x * T(x \ 1,y),x \ y) = K(y \ (x \ y),y)
    ]]></literal>
    <justification jstring="[hyper(239,a,1236,a(flip),b,302,a)].">
      <j1 rule="hyper" parents="239 1236 302"/>
    </justification>
  </clause>

  <clause id="1238">
    <literal><![CDATA[
      L(x \ ((1 / x) \ y),z,u) = x \ ((1 / x) \ L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(123,a,1198,a),flip(a)].">
      <j1 rule="hyper" parents="123 1198"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1239">
    <literal><![CDATA[
      (x * L(x \ y,z,u)) * (x \ 1) = L(y * (x \ 1),z,u)
    ]]></literal>
    <justification jstring="[hyper(133,a,1204,a)].">
      <j1 rule="hyper" parents="133 1204"/>
    </justification>
  </clause>

  <clause id="1240">
    <literal><![CDATA[
      x * L(x \ (y / (x \ 1)),z,u) = L(y,z,u) / (x \ 1)
    ]]></literal>
    <justification jstring="[para(7(a,1),1204(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7 1204"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1241">
    <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),1204(a,1,1,1,2))].">
      <j1 rule="para" parents="75 1204"/>
    </justification>
  </clause>

  <clause id="1242">
    <literal><![CDATA[
      (x * R(x \ 1,y,z)) * (x \ 1) = R(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(2(a,1),1220(a,2,1))].">
      <j1 rule="para" parents="2 1220"/>
    </justification>
  </clause>

  <clause id="1243">
    <literal><![CDATA[
      R(x \ 1,y,z) / (x \ 1) = x * R(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(131,a,1242,a)].">
      <j1 rule="hyper" parents="131 1242"/>
    </justification>
  </clause>

  <clause id="1244">
    <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(1243(a,1),1028(a,1,1,2))].">
      <j1 rule="para" parents="1243 1028"/>
    </justification>
  </clause>

  <clause id="1245">
    <literal><![CDATA[
      T(x,x * T(x \ 1,y)) = x
    ]]></literal>
    <justification jstring="[hyper(239,a,736,a(flip),b,1226,a(flip))].">
      <j1 rule="hyper" parents="239 736 1226"/>
    </justification>
  </clause>

  <clause id="1246">
    <literal><![CDATA[
      T(x,(x \ 1) * x) = x
    ]]></literal>
    <justification jstring="[para(105(a,1),1245(a,1,2))].">
      <j1 rule="para" parents="105 1245"/>
    </justification>
  </clause>

  <clause id="1247">
    <literal><![CDATA[
      R(x,(x * T(x \ 1,y)) / x,x) = T(x,(x * T(x \ 1,y)) / x)
    ]]></literal>
    <justification jstring="[para(1245(a,1),812(a,1,1))].">
      <j1 rule="para" parents="1245 812"/>
    </justification>
  </clause>

  <clause id="1248">
    <literal><![CDATA[
      T(x \ 1,T(x,y) * (x \ 1)) = x \ 1
    ]]></literal>
    <justification jstring="[para(455(a,1),1245(a,1,2))].">
      <j1 rule="para" parents="455 1245"/>
    </justification>
  </clause>

  <clause id="1249">
    <literal><![CDATA[
      T(x \ 1,x \ T(x,y)) = x \ 1
    ]]></literal>
    <justification jstring="[para(991(a,1),1245(a,1,2))].">
      <j1 rule="para" parents="991 1245"/>
    </justification>
  </clause>

  <clause id="1250">
    <literal><![CDATA[
      T(1 / x,T(x,y) / x) = 1 / x
    ]]></literal>
    <justification jstring="[para(1007(a,1),1245(a,1,2))].">
      <j1 rule="para" parents="1007 1245"/>
    </justification>
  </clause>

  <clause id="1251">
    <literal><![CDATA[
      R(x,x \ 1,x) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(1246(a,1),807(a,1,1))].">
      <j1 rule="para" parents="1246 807"/>
    </justification>
  </clause>

  <clause id="1252">
    <literal><![CDATA[
      T(x,x \ 1) \ x = (x \ 1) * x
    ]]></literal>
    <justification jstring="[para(1251(a,1),425(a,1,1))].">
      <j1 rule="para" parents="1251 425"/>
    </justification>
  </clause>

  <clause id="1253">
    <literal><![CDATA[
      T(x \ T(x,y),x \ 1) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(49,a,1249,a)].">
      <j1 rule="hyper" parents="49 1249"/>
    </justification>
  </clause>

  <clause id="1254">
    <literal><![CDATA[
      (x \ T(x,y)) * (x \ 1) = (x \ 1) * (x \ T(x,y))
    ]]></literal>
    <justification jstring="[hyper(119,a,1249,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 1249 17"/>
    </justification>
  </clause>

  <clause id="1255">
    <literal><![CDATA[
      T((x * (1 / y)) / x,T(y,z) / y) = (x * (1 / y)) / x
    ]]></literal>
    <justification jstring="[para(1250(a,1),460(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1250 460"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1256">
    <literal><![CDATA[
      ((x \ 1) \ 1) \ x = (x \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(657,a,1252,a)].">
      <j1 rule="hyper" parents="657 1252"/>
    </justification>
  </clause>

  <clause id="1257">
    <literal><![CDATA[
      T(x,x \ 1) \ 1 = T(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(239,a,1252,a(flip),b,1118,a),flip(a)].">
      <j1 rule="hyper" parents="239 1252 1118"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1258">
    <literal><![CDATA[
      ((x \ 1) \ 1) * K(x \ 1,x) = x
    ]]></literal>
    <justification jstring="[hyper(584,a,1256,a)].">
      <j1 rule="hyper" parents="584 1256"/>
    </justification>
  </clause>

  <clause id="1259">
    <literal><![CDATA[
      ((x \ 1) \ 1) \ x != y
    ]]></literal>
    <literal><![CDATA[
      K(x \ 1,x) = y
    ]]></literal>
    <justification jstring="[para(1256(a,2),370(a,1))].">
      <j1 rule="para" parents="1256 370"/>
    </justification>
  </clause>

  <clause id="1260">
    <literal><![CDATA[
      T(x \ 1,x) = ((x \ 1) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(657,a,1257,a),flip(a)].">
      <j1 rule="hyper" parents="657 1257"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1261">
    <literal><![CDATA[
      1 / T(x \ 1,x) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(197,a,1257,a)].">
      <j1 rule="hyper" parents="197 1257"/>
    </justification>
  </clause>

  <clause id="1262">
    <literal><![CDATA[
      T((1 / x) \ 1,1 / x) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(643(a,1),1257(a,1,1)),flip(a)].">
      <j1 rule="para" parents="643 1257"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1263">
    <literal><![CDATA[
      T(x \ 1,(x \ 1) \ 1) = T(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,106,a,b,1260,a)].">
      <j1 rule="hyper" parents="320 106 1260"/>
    </justification>
  </clause>

  <clause id="1264">
    <literal><![CDATA[
      T((x \ 1) \ 1,x \ 1) = T(x \ 1,x) \ 1
    ]]></literal>
    <justification jstring="[para(1260(a,2),1260(a,2,1))].">
      <j1 rule="para" parents="1260 1260"/>
    </justification>
  </clause>

  <clause id="1265">
    <literal><![CDATA[
      R(x \ 1,T(x,y),x \ 1) = T(x \ 1,T(x,y))
    ]]></literal>
    <justification jstring="[para(1248(a,1),807(a,1,1))].">
      <j1 rule="para" parents="1248 807"/>
    </justification>
  </clause>

  <clause id="1266">
    <literal><![CDATA[
      T((x * y) \ (y * x),y \ 1) = L(y \ T(y,x),y,x)
    ]]></literal>
    <justification jstring="[para(1253(a,1),750(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1253 750"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1267">
    <literal><![CDATA[
      T(x,1 / x) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(75(a,1),1262(a,1,1))].">
      <j1 rule="para" parents="75 1262"/>
    </justification>
  </clause>

  <clause id="1268">
    <literal><![CDATA[
      T(x,1 / x) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,106,a,b,1267,a),flip(a)].">
      <j1 rule="hyper" parents="320 106 1267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1269">
    <literal><![CDATA[
      ((x \ 1) \ 1) / x = K(x,1 / x)
    ]]></literal>
    <justification jstring="[hyper(117,a,1267,a(flip),b,819,a)].">
      <j1 rule="hyper" parents="117 1267 819"/>
    </justification>
  </clause>

  <clause id="1270">
    <literal><![CDATA[
      L((x \ 1) \ 1,y,z) / x = L(x,y,z) * (1 / x)
    ]]></literal>
    <justification jstring="[para(1267(a,1),1081(a,1,1,1))].">
      <j1 rule="para" parents="1267 1081"/>
    </justification>
  </clause>

  <clause id="1271">
    <literal><![CDATA[
      K(x,1 / x) * x = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,819,a,b,1268,a)].">
      <j1 rule="hyper" parents="58 819 1268"/>
    </justification>
  </clause>

  <clause id="1272">
    <literal><![CDATA[
      (x * T(y,y \ 1)) / x = T((x * y) / x,1 / y)
    ]]></literal>
    <justification jstring="[para(1268(a,1),460(a,1,1,2))].">
      <j1 rule="para" parents="1268 460"/>
    </justification>
  </clause>

  <clause id="1273">
    <literal><![CDATA[
      R(R(x,y,z),1 / x,x) = R(T(x,x \ 1),y,z)
    ]]></literal>
    <justification jstring="[para(1268(a,1),817(a,2,1))].">
      <j1 rule="para" parents="1268 817"/>
    </justification>
  </clause>

  <clause id="1274">
    <literal><![CDATA[
      (x \ 1) \ (1 / x) = K(x,1 / x)
    ]]></literal>
    <justification jstring="[hyper(58,a,1233,a(flip),b,1269,a)].">
      <j1 rule="hyper" parents="58 1233 1269"/>
    </justification>
  </clause>

  <clause id="1275">
    <literal><![CDATA[
      T(x,x \ 1) / x != y
    ]]></literal>
    <literal><![CDATA[
      K(x,1 / x) = y
    ]]></literal>
    <justification jstring="[para(1271(a,1),327(a,1,1)),flip(b)].">
      <j1 rule="para" parents="1271 327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1276">
    <literal><![CDATA[
      (1 / x) / K(x,1 / x) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(197,a,1274,a)].">
      <j1 rule="hyper" parents="197 1274"/>
    </justification>
  </clause>

  <clause id="1277">
    <literal><![CDATA[
      R(1 / x,x,1 / x) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(671,a,1276,a)].">
      <j1 rule="hyper" parents="671 1276"/>
    </justification>
  </clause>

  <clause id="1278">
    <literal><![CDATA[
      R(x / (y * x),y,1 / y) = R(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(1277(a,1),410(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1277 410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1279">
    <literal><![CDATA[
      ((x \ 1) \ 1) / x != y
    ]]></literal>
    <literal><![CDATA[
      K(x,1 / x) = y
    ]]></literal>
    <justification jstring="[para(106(a,1),1275(a,1,1))].">
      <j1 rule="para" parents="106 1275"/>
    </justification>
  </clause>

  <clause id="1280">
    <literal><![CDATA[
      (x \ 1) / (1 / x) != y
    ]]></literal>
    <literal><![CDATA[
      K(1 / x,1 / (1 / x)) = y
    ]]></literal>
    <justification jstring="[para(643(a,1),1275(a,1,1))].">
      <j1 rule="para" parents="643 1275"/>
    </justification>
  </clause>

  <clause id="1281">
    <literal><![CDATA[
      R(x \ 1,x,y) \ (((y / (x * y)) * x) * (1 / x)) = x * (1 / x)
    ]]></literal>
    <justification jstring="[para(1278(a,1),184(a,1,1))].">
      <j1 rule="para" parents="1278 184"/>
    </justification>
  </clause>

  <clause id="1282">
    <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(1273(a,1),709(a,1,2))].">
      <j1 rule="para" parents="1273 709"/>
    </justification>
  </clause>

  <clause id="1283">
    <literal><![CDATA[
      L(1 / x,y,z) * (1 / (1 / x)) = L(x \ 1,y,z) / (1 / x)
    ]]></literal>
    <justification jstring="[para(75(a,1),1270(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="75 1270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1284">
    <literal><![CDATA[
      T(L(x,y,z) * (1 / x),x) = x \ L((x \ 1) \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(1270(a,1),107(a,1,1))].">
      <j1 rule="para" parents="1270 107"/>
    </justification>
  </clause>

  <clause id="1285">
    <literal><![CDATA[
      T((x * y) / x,1 / y) = T((x * y) / x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(462,a,1272,a),flip(a)].">
      <j1 rule="hyper" parents="462 1272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1286">
    <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),1285(a,1,1)),flip(a)].">
      <j1 rule="para" parents="225 1285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1287">
    <literal><![CDATA[
      K(x,y) = T((y * x) \ (x * y),x \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,749,a,b,1266,a)].">
      <j1 rule="hyper" parents="320 749 1266"/>
    </justification>
  </clause>

  <clause id="1288">
    <literal><![CDATA[
      T(K(x,y),x \ 1) = K(x,y)
    ]]></literal>
    <justification jstring="[para(11(a,2),1287(a,2,1)),flip(a)].">
      <j1 rule="para" parents="11 1287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1289">
    <literal><![CDATA[
      T(x \ 1,K(x,y)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(49,a,1288,a)].">
      <j1 rule="hyper" parents="49 1288"/>
    </justification>
  </clause>

  <clause id="1290">
    <literal><![CDATA[
      K(x,y) * (x \ 1) = (x \ 1) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,1288,a(flip),b,17,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 1288 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1291">
    <literal><![CDATA[
      (x \ 1) * K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * (x \ 1) = z
    ]]></literal>
    <justification jstring="[para(1288(a,1),284(a,1,2))].">
      <j1 rule="para" parents="1288 284"/>
    </justification>
  </clause>

  <clause id="1292">
    <literal><![CDATA[
      T((x * y) \ x,K(y,z)) = L(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(1289(a,1),399(a,2,1))].">
      <j1 rule="para" parents="1289 399"/>
    </justification>
  </clause>

  <clause id="1293">
    <literal><![CDATA[
      T((x * y) \ x,K(y,z)) = (x * y) \ x
    ]]></literal>
    <justification jstring="[hyper(320,a,217,a(flip),b,1292,a),flip(a)].">
      <j1 rule="hyper" parents="320 217 1292"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1294">
    <literal><![CDATA[
      T(K(x,y),(z * x) \ z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(49,a,1293,a)].">
      <j1 rule="hyper" parents="49 1293"/>
    </justification>
  </clause>

  <clause id="1295">
    <literal><![CDATA[
      T(K(x \ 1,y),x) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(163(a,1),1294(a,1,2))].">
      <j1 rule="para" parents="163 1294"/>
    </justification>
  </clause>

  <clause id="1296">
    <literal><![CDATA[
      T(K(x,y),1 / x) = K(x,y)
    ]]></literal>
    <justification jstring="[para(164(a,1),1294(a,1,2))].">
      <j1 rule="para" parents="164 1294"/>
    </justification>
  </clause>

  <clause id="1297">
    <literal><![CDATA[
      T(1 / x,K(x,y)) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(49,a,1296,a)].">
      <j1 rule="hyper" parents="49 1296"/>
    </justification>
  </clause>

  <clause id="1298">
    <literal><![CDATA[
      (1 / x) * K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * (1 / x) = z
    ]]></literal>
    <justification jstring="[para(1296(a,1),284(a,1,2))].">
      <j1 rule="para" parents="1296 284"/>
    </justification>
  </clause>

  <clause id="1299">
    <literal><![CDATA[
      T((1 * x) / y,K(y / x,z)) = R(1 / (y / x),y / x,x)
    ]]></literal>
    <justification jstring="[para(1297(a,1),765(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1297 765"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1300">
    <literal><![CDATA[
      T(x,K(x \ 1,y)) = x
    ]]></literal>
    <justification jstring="[hyper(49,a,1295,a)].">
      <j1 rule="hyper" parents="49 1295"/>
    </justification>
  </clause>

  <clause id="1301">
    <literal><![CDATA[
      x * K(x \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x \ 1,y) * x = z
    ]]></literal>
    <justification jstring="[para(1295(a,1),284(a,1,2))].">
      <j1 rule="para" parents="1295 284"/>
    </justification>
  </clause>

  <clause id="1302">
    <literal><![CDATA[
      ((x * y) / x) * (y \ 1) = y \ ((x * y) / x)
    ]]></literal>
    <justification jstring="[para(4(a,1),1234(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4 1234"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1303">
    <literal><![CDATA[
      (x * T(x \ (y \ x),z)) / (y \ x) != u
    ]]></literal>
    <literal><![CDATA[
      y * T(y \ 1,z) = u
    ]]></literal>
    <justification jstring="[para(1235(a,1),327(a,1,1)),flip(b)].">
      <j1 rule="para" parents="1235 327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1304">
    <literal><![CDATA[
      (x \ T(x,y)) * ((x \ 1) \ z) = z * T(z \ ((x \ 1) \ z),y)
    ]]></literal>
    <justification jstring="[para(991(a,1),1235(a,1,1))].">
      <j1 rule="para" parents="991 1235"/>
    </justification>
  </clause>

  <clause id="1305">
    <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),1238(a,2,2,1))].">
      <j1 rule="para" parents="72 1238"/>
    </justification>
  </clause>

  <clause id="1306">
    <literal><![CDATA[
      T(x,1 / T(x,y)) = T(x,T(x,y) \ 1)
    ]]></literal>
    <justification jstring="[para(225(a,1),1286(a,1,1)),flip(a)].">
      <j1 rule="para" parents="225 1286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1307">
    <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),695(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="490 695"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1308">
    <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,716,a)].">
      <j1 rule="hyper" parents="58 447 716"/>
    </justification>
  </clause>

  <clause id="1309">
    <literal><![CDATA[
      R(x,y,z) * (x * u) = x * (R(x,y,z) * u)
    ]]></literal>
    <justification jstring="[para(238(a,1),1308(a,1,2)),flip(a)].">
      <j1 rule="para" parents="238 1308"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1310">
    <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(654,a,1309,a),flip(a)].">
      <j1 rule="hyper" parents="654 1309"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1311">
    <literal><![CDATA[
      x \ (R(x,y,z) * u) = R(x,y,z) * (x \ u)
    ]]></literal>
    <justification jstring="[hyper(599,a,1309,a)].">
      <j1 rule="hyper" parents="599 1309"/>
    </justification>
  </clause>

  <clause id="1312">
    <literal><![CDATA[
      R(x,y,z) * (x \ (R(x,y,z) \ u)) = x \ u
    ]]></literal>
    <justification jstring="[hyper(598,a,1309,a),flip(a)].">
      <j1 rule="hyper" parents="598 1309"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1313">
    <literal><![CDATA[
      (R(x,y,z) * u) / (R(x,y,z) * (x \ u)) = x
    ]]></literal>
    <justification jstring="[hyper(574,a,1309,a)].">
      <j1 rule="hyper" parents="574 1309"/>
    </justification>
  </clause>

  <clause id="1314">
    <literal><![CDATA[
      x * (R(x,y,z) * (x \ u)) = R(x,y,z) * u
    ]]></literal>
    <justification jstring="[hyper(342,a,1309,a),flip(a)].">
      <j1 rule="hyper" parents="342 1309"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1315">
    <literal><![CDATA[
      R(x,y,z) \ (x * (R(x,y,z) * u)) = x * u
    ]]></literal>
    <justification jstring="[hyper(123,a,1309,a)].">
      <j1 rule="hyper" parents="123 1309"/>
    </justification>
  </clause>

  <clause id="1316">
    <literal><![CDATA[
      x * (R(x,y,z) \ 1) = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(116,a,65,a(flip),b,1309,a),flip(a)].">
      <j1 rule="hyper" parents="116 65 1309"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1317">
    <literal><![CDATA[
      x * (R(x,y,z) * T(u,x)) = R(x,y,z) * (u * x)
    ]]></literal>
    <justification jstring="[para(105(a,1),1309(a,1,2)),flip(a)].">
      <j1 rule="para" parents="105 1309"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1318">
    <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,1316,a)].">
      <j1 rule="hyper" parents="285 1316"/>
    </justification>
  </clause>

  <clause id="1319">
    <literal><![CDATA[
      L(R(x,y,z) \ 1,x,1 / x) = (1 / x) * (R(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(119,a,1316,a(flip),b,436,a),flip(a)].">
      <j1 rule="hyper" parents="119 1316 436"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1320">
    <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(1316(a,1),988(a,1,2,1,2))].">
      <j1 rule="para" parents="1316 988"/>
    </justification>
  </clause>

  <clause id="1321">
    <literal><![CDATA[
      R(x,y,z) * (x \ (y * z)) = x \ ((x * y) * z)
    ]]></literal>
    <justification jstring="[para(101(a,1),1311(a,1,2)),flip(a)].">
      <j1 rule="para" parents="101 1311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1322">
    <literal><![CDATA[
      R(x,y,y \ z) * (x \ z) = x \ ((x * y) * (y \ z))
    ]]></literal>
    <justification jstring="[para(368(a,1),1311(a,1,2)),flip(a)].">
      <j1 rule="para" parents="368 1311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1323">
    <literal><![CDATA[
      x \ (R(x,y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) * (x \ u) = w
    ]]></literal>
    <justification jstring="[para(1313(a,1),267(a,1,1)),flip(b)].">
      <j1 rule="para" parents="1313 267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1324">
    <literal><![CDATA[
      R(x,y,x) * (x \ (y * x)) = T(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(239,a,101,a(flip),b,1314,a),flip(a)].">
      <j1 rule="hyper" parents="239 101 1314"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1325">
    <literal><![CDATA[
      R(x,y,x) * T(y,x) = T(x * y,x)
    ]]></literal>
    <justification jstring="[para(17(a,2),1324(a,1,2))].">
      <j1 rule="para" parents="17 1324"/>
    </justification>
  </clause>

  <clause id="1326">
    <literal><![CDATA[
      R(x,y,x) \ T(x * y,x) = T(y,x)
    ]]></literal>
    <justification jstring="[hyper(123,a,1325,a)].">
      <j1 rule="hyper" parents="123 1325"/>
    </justification>
  </clause>

  <clause id="1327">
    <literal><![CDATA[
      x \ T(y * z,y) != T(z,y)
    ]]></literal>
    <literal><![CDATA[
      R(y,z,y) = x
    ]]></literal>
    <justification jstring="[para(1326(a,1),43(a,1)),flip(a)].">
      <j1 rule="para" parents="1326 43"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1328">
    <literal><![CDATA[
      R(x,y,z) = (x \ ((x * y) * z)) / (x \ (y * z))
    ]]></literal>
    <justification jstring="[hyper(131,a,1321,a),flip(a)].">
      <j1 rule="hyper" parents="131 1321"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1329">
    <literal><![CDATA[
      x \ ((x * (x \ y)) * ((x \ y) \ z)) = ((y * ((x \ y) \ z)) / z) * (x \ z)
    ]]></literal>
    <justification jstring="[para(699(a,1),1322(a,1,1)),flip(a)].">
      <j1 rule="para" parents="699 1322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1330">
    <literal><![CDATA[
      L((x \ y) / y,z,u) * y = (L(1 / x,z,u) * x) * (x \ y)
    ]]></literal>
    <justification jstring="[para(407(a,1),729(a,1,1,1))].">
      <j1 rule="para" parents="407 729"/>
    </justification>
  </clause>

  <clause id="1331">
    <literal><![CDATA[
      x * ((x \ y) * R((x \ y) \ z,u,w)) = y * R(y \ (x * z),u,w)
    ]]></literal>
    <justification jstring="[hyper(119,a,758,a(flip),b,91,a),flip(a)].">
      <j1 rule="hyper" parents="119 758 91"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1332">
    <literal><![CDATA[
      x \ (y * R(y \ (x * z),u,w)) = (x \ y) * R((x \ y) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(758(a,1),474(a,1,2,2))].">
      <j1 rule="para" parents="758 474"/>
    </justification>
  </clause>

  <clause id="1333">
    <literal><![CDATA[
      x \ (y * L(y \ (x * z),u,w)) = (x \ y) * L((x \ y) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(759(a,1),474(a,1,2,2))].">
      <j1 rule="para" parents="759 474"/>
    </justification>
  </clause>

  <clause id="1334">
    <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),764(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="525 764"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1335">
    <literal><![CDATA[
      (R(x / (y / z),u,w) * (y / z)) * z = R((x * z) / y,u,w) * y
    ]]></literal>
    <justification jstring="[para(766(a,1),508(a,1,1)),flip(a)].">
      <j1 rule="para" parents="766 508"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1336">
    <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,808,a),flip(a)].">
      <j1 rule="hyper" parents="58 513 808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1337">
    <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,809,a),flip(a)].">
      <j1 rule="hyper" parents="58 514 809"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1338">
    <literal><![CDATA[
      L(((x * y) * z) / (x * y),y,x) != u / (x * y)
    ]]></literal>
    <literal><![CDATA[
      x * (y * z) = u
    ]]></literal>
    <justification jstring="[para(850(a,2),41(a,1))].">
      <j1 rule="para" parents="850 41"/>
    </justification>
  </clause>

  <clause id="1339">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ (x * u))) / z) = x * (y * ((z * (y \ u)) / z))
    ]]></literal>
    <justification jstring="[para(92(a,1),880(a,1,2,1,2))].">
      <j1 rule="para" parents="92 880"/>
    </justification>
  </clause>

  <clause id="1340">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ u)) / z) = x * (y * ((z * (y \ (x \ u))) / z))
    ]]></literal>
    <justification jstring="[para(298(a,1),880(a,1,2,1,2))].">
      <j1 rule="para" parents="298 880"/>
    </justification>
  </clause>

  <clause id="1341">
    <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(883(a,1),286(a,1,2))].">
      <j1 rule="para" parents="883 286"/>
    </justification>
  </clause>

  <clause id="1342">
    <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(884(a,1),286(a,1,2))].">
      <j1 rule="para" parents="884 286"/>
    </justification>
  </clause>

  <clause id="1343">
    <literal><![CDATA[
      (x / y) * (y * ((z * (y \ 1)) / z)) = x * ((z * (x \ (x / y))) / z)
    ]]></literal>
    <justification jstring="[hyper(119,a,885,a(flip),b,93,a),flip(a)].">
      <j1 rule="hyper" parents="119 885 93"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1344">
    <literal><![CDATA[
      (1 / x) \ ((y * ((1 / x) * z)) / y) = x * ((y * (x \ z)) / y)
    ]]></literal>
    <justification jstring="[hyper(116,a,886,a(flip),b,259,a)].">
      <j1 rule="hyper" parents="116 886 259"/>
    </justification>
  </clause>

  <clause id="1345">
    <literal><![CDATA[
      ((x * (y / (1 / z))) / x) * (1 / z) = ((x * (y * z)) / x) / z
    ]]></literal>
    <justification jstring="[hyper(117,a,890,a(flip),b,262,a),flip(a)].">
      <j1 rule="hyper" parents="117 890 262"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1346">
    <literal><![CDATA[
      ((x * (y * (z \ 1))) / x) / (z \ 1) = ((x * (y / z)) / x) * z
    ]]></literal>
    <justification jstring="[hyper(117,a,891,a(flip),b,261,a)].">
      <j1 rule="hyper" parents="117 891 261"/>
    </justification>
  </clause>

  <clause id="1347">
    <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,928,a(flip),b,231,a)].">
      <j1 rule="hyper" parents="119 928 231"/>
    </justification>
  </clause>

  <clause id="1348">
    <literal><![CDATA[
      (T(x,y) * z) * T(x,z) = (x * z) * T(T(x,z),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,903,a(flip),b,932,a),flip(a)].">
      <j1 rule="hyper" parents="58 903 932"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1349">
    <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,1348,a)].">
      <j1 rule="hyper" parents="117 64 1348"/>
    </justification>
  </clause>

  <clause id="1350">
    <literal><![CDATA[
      T(T(x,x \ 1),y) / T(x,x \ 1) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,993,a(flip),b,1349,a),flip(a)].">
      <j1 rule="hyper" parents="320 993 1349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1351">
    <literal><![CDATA[
      (x * y) * T((x * y) \ (z * y),u) = (T(z / x,u) * x) * y
    ]]></literal>
    <justification jstring="[hyper(119,a,937,a(flip),b,631,a)].">
      <j1 rule="hyper" parents="119 937 631"/>
    </justification>
  </clause>

  <clause id="1352">
    <literal><![CDATA[
      T(x,y) / x != z
    ]]></literal>
    <literal><![CDATA[
      (1 / x) * T(x,y) = z
    ]]></literal>
    <justification jstring="[para(1003(a,1),954(a,1))].">
      <j1 rule="para" parents="1003 954"/>
    </justification>
  </clause>

  <clause id="1353">
    <literal><![CDATA[
      (x * y) / a(z,z \ y,T(x,y)) = L(x,z \ y,z) * y
    ]]></literal>
    <justification jstring="[hyper(320,a,745,a(flip),b,955,a),flip(a)].">
      <j1 rule="hyper" parents="320 745 955"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1354">
    <literal><![CDATA[
      (L(x,y \ z,y) * z) \ (x * z) = a(y,y \ z,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(188,a,1353,a)].">
      <j1 rule="hyper" parents="188 1353"/>
    </justification>
  </clause>

  <clause id="1355">
    <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,969,a),flip(a)].">
      <j1 rule="hyper" parents="320 460 969"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1356">
    <literal><![CDATA[
      L((T(x,y) * (x \ y)) / y,y,x) = (y * K(T(x,y),y)) / y
    ]]></literal>
    <justification jstring="[para(1109(a,1),970(a,1,1,1))].">
      <j1 rule="para" parents="1109 970"/>
    </justification>
  </clause>

  <clause id="1357">
    <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),980(a,1,1,1,2))].">
      <j1 rule="para" parents="72 980"/>
    </justification>
  </clause>

  <clause id="1358">
    <literal><![CDATA[
      (x * y) \ ((x \ (x * y)) * x) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(964(a,1),1047(a,1))].">
      <j1 rule="para" parents="964 1047"/>
    </justification>
  </clause>

  <clause id="1359">
    <literal><![CDATA[
      K(x \ (x * y),x) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(85(a,1),1358(a,1))].">
      <j1 rule="para" parents="85 1358"/>
    </justification>
  </clause>

  <clause id="1360">
    <literal><![CDATA[
      T((1 * x) / y,K(y / x,z)) = x / y
    ]]></literal>
    <justification jstring="[hyper(320,a,408,a(flip),b,1299,a),flip(a)].">
      <j1 rule="hyper" parents="320 408 1299"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1361">
    <literal><![CDATA[
      T(x / y,K(y / x,z)) = x / y
    ]]></literal>
    <justification jstring="[para(2(a,1),1360(a,1,1,1))].">
      <j1 rule="para" parents="2 1360"/>
    </justification>
  </clause>

  <clause id="1362">
    <literal><![CDATA[
      T(x \ y,K(x / y,z)) = T(y / x,x)
    ]]></literal>
    <justification jstring="[para(1361(a,1),246(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1361 246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1363">
    <literal><![CDATA[
      T(x \ y,K(x / y,z)) = x \ y
    ]]></literal>
    <justification jstring="[hyper(320,a,107,a(flip),b,1362,a),flip(a)].">
      <j1 rule="hyper" parents="320 107 1362"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1364">
    <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="1365">
    <literal><![CDATA[
      x \ ((x * y) * a(z,u,w)) = (y * a(z,u,w)) * a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(116,a,80,a(flip),b,346,a(flip))].">
      <j1 rule="hyper" parents="116 80 346"/>
    </justification>
  </clause>

  <clause id="1366">
    <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="1367">
    <literal><![CDATA[
      R(x,y,a(z,u,a(w,v5,v6))) != v7
    ]]></literal>
    <literal><![CDATA[
      x = v7
    ]]></literal>
    <justification jstring="[para(1364(a,1),46(a,2))].">
      <j1 rule="para" parents="1364 46"/>
    </justification>
  </clause>

  <clause id="1368">
    <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="1369">
    <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="1370">
    <literal><![CDATA[
      T(x,L(y \ 1,y,z)) = T(x,(z * y) \ z)
    ]]></literal>
    <justification jstring="[hyper(239,a,394,a(flip),b,732,a),flip(a)].">
      <j1 rule="hyper" parents="239 394 732"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1371">
    <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),825(a,1,2,1))].">
      <j1 rule="para" parents="92 825"/>
    </justification>
  </clause>

  <clause id="1372">
    <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,894,a)].">
      <j1 rule="hyper" parents="116 346 894"/>
    </justification>
  </clause>

  <clause id="1373">
    <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),916(a,1,1))].">
      <j1 rule="para" parents="90 916"/>
    </justification>
  </clause>

  <clause id="1374">
    <literal><![CDATA[
      (x * y) * R((x * y) \ y,z,u) = (R(1 / x,z,u) * x) * y
    ]]></literal>
    <justification jstring="[hyper(867,a,920,a)].">
      <j1 rule="hyper" parents="867 920"/>
    </justification>
  </clause>

  <clause id="1375">
    <literal><![CDATA[
      ((x \ ((x * y) / z)) * x) * z = x * (z * T(z \ y,x))
    ]]></literal>
    <justification jstring="[hyper(58,a,1105,a(flip),b,923,a)].">
      <j1 rule="hyper" parents="58 1105 923"/>
    </justification>
  </clause>

  <clause id="1376">
    <literal><![CDATA[
      x * (y * T(y \ (x \ z),x)) = ((x \ (z / y)) * x) * y
    ]]></literal>
    <justification jstring="[para(5(a,1),1375(a,1,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 1375"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1377">
    <literal><![CDATA[
      x * (x * T(x \ T(y,x),x)) = ((x \ y) * x) * x
    ]]></literal>
    <justification jstring="[para(225(a,1),1375(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="225 1375"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1378">
    <literal><![CDATA[
      x * T(x \ T(y,x),x) = T((x \ y) * x,x)
    ]]></literal>
    <justification jstring="[hyper(240,a,1377,a),flip(a)].">
      <j1 rule="hyper" parents="240 1377"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1379">
    <literal><![CDATA[
      T((x \ y) * x,x) = (x \ T(y,x)) * x
    ]]></literal>
    <justification jstring="[hyper(284,a,1378,a),flip(a)].">
      <j1 rule="hyper" parents="284 1378"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1380">
    <literal><![CDATA[
      T((x \ y) * x,x) / x = x \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(117,a,1378,a(flip),b,105,a(flip))].">
      <j1 rule="hyper" parents="117 1378 105"/>
    </justification>
  </clause>

  <clause id="1381">
    <literal><![CDATA[
      T(x,y) \ T((y \ x) * y,y) = K(y \ T(x,y),y)
    ]]></literal>
    <justification jstring="[para(1378(a,1),431(a,1,2))].">
      <j1 rule="para" parents="1378 431"/>
    </justification>
  </clause>

  <clause id="1382">
    <literal><![CDATA[
      x * (T((x \ y) * x,x) / x) = T(y,x)
    ]]></literal>
    <justification jstring="[para(1379(a,2),71(a,1,2,1))].">
      <j1 rule="para" parents="1379 71"/>
    </justification>
  </clause>

  <clause id="1383">
    <literal><![CDATA[
      T(x * y,y) / y = y \ T(y * x,y)
    ]]></literal>
    <justification jstring="[para(4(a,1),1380(a,1,1,1,1))].">
      <j1 rule="para" parents="4 1380"/>
    </justification>
  </clause>

  <clause id="1384">
    <literal><![CDATA[
      (x \ T(y,x)) * x != z
    ]]></literal>
    <literal><![CDATA[
      T((x \ y) * x,x) = z
    ]]></literal>
    <justification jstring="[para(1380(a,1),251(a,1,1)),flip(b)].">
      <j1 rule="para" parents="1380 251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1385">
    <literal><![CDATA[
      x \ T(x * (y / x),x) = T(y,x) / x
    ]]></literal>
    <justification jstring="[para(76(a,1),1380(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="76 1380"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1386">
    <literal><![CDATA[
      T(x * (y / x),x) = x * (T(y,x) / x)
    ]]></literal>
    <justification jstring="[para(76(a,1),1382(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="76 1382"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1387">
    <literal><![CDATA[
      T(x * ((1 / x) * y),x) = x * ((1 / x) * T(y,x))
    ]]></literal>
    <justification jstring="[hyper(119,a,1000,a(flip),b,1383,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 1000 1383"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1388">
    <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),1383(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="454 1383"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1389">
    <literal><![CDATA[
      x \ T(x * L((x * y) / x,z,u),x) = T(x * L(y,z,u),x) / x
    ]]></literal>
    <justification jstring="[para(637(a,1),1383(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="637 1383"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1390">
    <literal><![CDATA[
      T(x * y,x) \ T(y * x,x) = K(x \ T(x * y,x),x)
    ]]></literal>
    <justification jstring="[para(4(a,1),1381(a,1,2,1,1))].">
      <j1 rule="para" parents="4 1381"/>
    </justification>
  </clause>

  <clause id="1391">
    <literal><![CDATA[
      ((x \ (y / (1 / z))) * x) * (1 / z) = x * (T((x \ y) * z,x) / z)
    ]]></literal>
    <justification jstring="[para(1001(a,1),1376(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1001 1376"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1392">
    <literal><![CDATA[
      ((x \ (y / y)) * x) * y = x * (K(x \ 1,x) * (x \ y))
    ]]></literal>
    <justification jstring="[para(1223(a,2),1376(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1223 1376"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1393">
    <literal><![CDATA[
      x * (K(x \ 1,x) * (x \ y)) = ((x \ 1) * x) * y
    ]]></literal>
    <justification jstring="[para(69(a,1),1392(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="69 1392"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1394">
    <literal><![CDATA[
      x * (K(x \ 1,x) * (x \ y)) = K(x \ 1,x) * y
    ]]></literal>
    <justification jstring="[hyper(570,a,1393,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="570 1393"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1396">
    <literal><![CDATA[
      K(x \ 1,x) * (x * y) = x * (K(x \ 1,x) * y)
    ]]></literal>
    <justification jstring="[para(4(a,1),1394(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 1394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1397">
    <literal><![CDATA[
      x * (K(x \ 1,x) * T(y,x)) = K(x \ 1,x) * (y * x)
    ]]></literal>
    <justification jstring="[para(17(a,2),1394(a,1,2,2))].">
      <j1 rule="para" parents="17 1394"/>
    </justification>
  </clause>

  <clause id="1398">
    <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(1396(a,1),232(a,1,2))].">
      <j1 rule="para" parents="1396 232"/>
    </justification>
  </clause>

  <clause id="1399">
    <literal><![CDATA[
      x * (y * T(y \ (x \ y),z)) = (x * T(x \ 1,z)) * y
    ]]></literal>
    <justification jstring="[hyper(58,a,1226,a(flip),b,924,a),flip(a)].">
      <j1 rule="hyper" parents="58 1226 924"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1400">
    <literal><![CDATA[
      (x * T(x \ 1,y)) * y = x * ((y \ (x \ y)) * y)
    ]]></literal>
    <justification jstring="[para(105(a,1),1399(a,1,2)),flip(a)].">
      <j1 rule="para" parents="105 1399"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1401">
    <literal><![CDATA[
      x * T(y * T(y \ 1,x),x) = y * ((x \ (y \ x)) * x)
    ]]></literal>
    <justification jstring="[hyper(285,a,1400,a)].">
      <j1 rule="hyper" parents="285 1400"/>
    </justification>
  </clause>

  <clause id="1402">
    <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,933,a),flip(a)].">
      <j1 rule="hyper" parents="320 453 933"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1403">
    <literal><![CDATA[
      x * (y * T(L(x,z,u),y)) = L(x,z,u) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(284,a,976,a),flip(a)].">
      <j1 rule="hyper" parents="284 976"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1404">
    <literal><![CDATA[
      L(x,y,z) * (x * u) = x * (L(x,y,z) * u)
    ]]></literal>
    <justification jstring="[para(105(a,1),1403(a,1,2)),flip(a)].">
      <j1 rule="para" parents="105 1403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1405">
    <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(654,a,1404,a),flip(a)].">
      <j1 rule="hyper" parents="654 1404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1406">
    <literal><![CDATA[
      x \ (L(x,y,z) * u) = L(x,y,z) * (x \ u)
    ]]></literal>
    <justification jstring="[hyper(599,a,1404,a)].">
      <j1 rule="hyper" parents="599 1404"/>
    </justification>
  </clause>

  <clause id="1407">
    <literal><![CDATA[
      L(x,y,z) * (x \ (L(x,y,z) \ u)) = x \ u
    ]]></literal>
    <justification jstring="[hyper(598,a,1404,a),flip(a)].">
      <j1 rule="hyper" parents="598 1404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1408">
    <literal><![CDATA[
      x * (L(x,y,z) * (x \ u)) = L(x,y,z) * u
    ]]></literal>
    <justification jstring="[hyper(342,a,1404,a),flip(a)].">
      <j1 rule="hyper" parents="342 1404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1409">
    <literal><![CDATA[
      (x * (L(x,y,z) * u)) / (x * u) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(131,a,1404,a)].">
      <j1 rule="hyper" parents="131 1404"/>
    </justification>
  </clause>

  <clause id="1410">
    <literal><![CDATA[
      L(x,y,z) \ (x * (L(x,y,z) * u)) = x * u
    ]]></literal>
    <justification jstring="[hyper(123,a,1404,a)].">
      <j1 rule="hyper" parents="123 1404"/>
    </justification>
  </clause>

  <clause id="1411">
    <literal><![CDATA[
      (x * y) / (x * (L(x,z,u) \ y)) = L(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(117,a,151,a(flip),b,1404,a)].">
      <j1 rule="hyper" parents="117 151 1404"/>
    </justification>
  </clause>

  <clause id="1412">
    <literal><![CDATA[
      L(x,y,z) \ (x * u) = x * (L(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(116,a,151,a(flip),b,1404,a)].">
      <j1 rule="hyper" parents="116 151 1404"/>
    </justification>
  </clause>

  <clause id="1413">
    <literal><![CDATA[
      x * (L(x,y,z) \ 1) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(116,a,65,a(flip),b,1404,a),flip(a)].">
      <j1 rule="hyper" parents="116 65 1404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1414">
    <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,1404,a(flip),b,84,a)].">
      <j1 rule="hyper" parents="116 1404 84"/>
    </justification>
  </clause>

  <clause id="1415">
    <literal><![CDATA[
      x \ (L(x,y,z) \ x) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(123,a,1413,a)].">
      <j1 rule="hyper" parents="123 1413"/>
    </justification>
  </clause>

  <clause id="1416">
    <literal><![CDATA[
      L(L(x,y,z) \ 1,x,1 / x) = (1 / x) * (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(119,a,1413,a(flip),b,436,a),flip(a)].">
      <j1 rule="hyper" parents="119 1413 436"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1417">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ (x * ((L(x,y,z) \ 1) * u)) = L(u,L(x,y,z) \ 1,x)
    ]]></literal>
    <justification jstring="[para(1413(a,1),13(a,2,1)),flip(a)].">
      <j1 rule="para" parents="1413 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1418">
    <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(1413(a,1),307(a,1,1))].">
      <j1 rule="para" parents="1413 307"/>
    </justification>
  </clause>

  <clause id="1419">
    <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(1413(a,2),1237(a,1,2))].">
      <j1 rule="para" parents="1413 1237"/>
    </justification>
  </clause>

  <clause id="1420">
    <literal><![CDATA[
      x \ (L(x,y,z) * (u * x)) = L(x,y,z) * T(u,x)
    ]]></literal>
    <justification jstring="[para(17(a,2),1406(a,2,2))].">
      <j1 rule="para" parents="17 1406"/>
    </justification>
  </clause>

  <clause id="1421">
    <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,1407,a),flip(a)].">
      <j1 rule="hyper" parents="116 17 1407"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1422">
    <literal><![CDATA[
      T((x * y) / x,L(y,z,u) * x) = L((y * x) / x,x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(1410(a,1),1355(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="1410 1355"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1423">
    <literal><![CDATA[
      L(x,y,z) \ (x * u) != w
    ]]></literal>
    <literal><![CDATA[
      x * (L(x,y,z) \ u) = w
    ]]></literal>
    <justification jstring="[para(1411(a,1),267(a,1,1)),flip(b)].">
      <j1 rule="para" parents="1411 267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1424">
    <literal><![CDATA[
      (x \ 1) * ((y * ((x \ 1) \ 1)) / y) = x \ ((y * x) / y)
    ]]></literal>
    <justification jstring="[hyper(320,a,1302,a(flip),b,981,a),flip(a)].">
      <j1 rule="hyper" parents="320 1302 981"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1425">
    <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),983(a,1,2,2))].">
      <j1 rule="para" parents="225 983"/>
    </justification>
  </clause>

  <clause id="1426">
    <literal><![CDATA[
      x * ((x \ y) * T((x \ y) \ 1,z)) = y * T(y \ x,z)
    ]]></literal>
    <justification jstring="[para(3(a,1),1094(a,2,2,1,2))].">
      <j1 rule="para" parents="3 1094"/>
    </justification>
  </clause>

  <clause id="1427">
    <literal><![CDATA[
      (x \ y) * T((x \ y) \ 1,z) = x \ (y * T(y \ x,z))
    ]]></literal>
    <justification jstring="[hyper(123,a,1426,a),flip(a)].">
      <j1 rule="hyper" parents="123 1426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1428">
    <literal><![CDATA[
      x * T(x \ y,y \ x) = y * K((y \ x) \ 1,y \ x)
    ]]></literal>
    <justification jstring="[para(358(a,1),1426(a,1,2)),flip(a)].">
      <j1 rule="para" parents="358 1426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1429">
    <literal><![CDATA[
      x * T(x \ y,z) = y * K(z \ (z / (y \ x)),z)
    ]]></literal>
    <justification jstring="[para(1025(a,2),1426(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1025 1426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1430">
    <literal><![CDATA[
      (x \ y) * K(z \ (z / ((x \ y) \ (x \ 1))),z) = x \ T(y,z)
    ]]></literal>
    <justification jstring="[hyper(1050,a,1429,a),flip(a)].">
      <j1 rule="hyper" parents="1050 1429"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1431">
    <literal><![CDATA[
      T(x * y,z) / y = x * K(z \ (z / (x \ (1 / y))),z)
    ]]></literal>
    <justification jstring="[hyper(1042,a,1429,a)].">
      <j1 rule="hyper" parents="1042 1429"/>
    </justification>
  </clause>

  <clause id="1432">
    <literal><![CDATA[
      K(x \ (x / (y \ z)),x) = y \ (z * T(z \ y,x))
    ]]></literal>
    <justification jstring="[hyper(536,a,1429,a),flip(a)].">
      <j1 rule="hyper" parents="536 1429"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1433">
    <literal><![CDATA[
      (x * y) * K(z \ (z / ((x * y) \ x)),z) = x * T(y,z)
    ]]></literal>
    <justification jstring="[para(4(a,1),1429(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4 1429"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1434">
    <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),1429(a,2,2,1,2,2))].">
      <j1 rule="para" parents="13 1429"/>
    </justification>
  </clause>

  <clause id="1435">
    <literal><![CDATA[
      K(x \ (x / T(y,z)),x) = z \ ((y * z) * T((y * z) \ z,x))
    ]]></literal>
    <justification jstring="[para(17(a,2),1432(a,1,1,2,2))].">
      <j1 rule="para" parents="17 1432"/>
    </justification>
  </clause>

  <clause id="1436">
    <literal><![CDATA[
      K(x \ (x / (y \ (y / z))),x) = y \ ((y / z) * T(z,x))
    ]]></literal>
    <justification jstring="[para(75(a,1),1432(a,2,2,2,1))].">
      <j1 rule="para" parents="75 1432"/>
    </justification>
  </clause>

  <clause id="1437">
    <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,1427,a)].">
      <j1 rule="hyper" parents="116 92 1427"/>
    </justification>
  </clause>

  <clause id="1438">
    <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),1428(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4 1428"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1439">
    <literal><![CDATA[
      (x / y) * K(z \ (z / ((x / y) \ (1 / y))),z) = T(x,z) / y
    ]]></literal>
    <justification jstring="[para(7(a,1),1431(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7 1431"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1440">
    <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,1095,a),flip(a)].">
      <j1 rule="hyper" parents="320 453 1095"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1441">
    <literal><![CDATA[
      (x \ y) * (T(y / x,z) \ 1) = T(y / x,z) \ (x \ y)
    ]]></literal>
    <justification jstring="[para(107(a,1),1150(a,1,2)),flip(a)].">
      <j1 rule="para" parents="107 1150"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1442">
    <literal><![CDATA[
      T(x / (y \ x),z) \ ((y \ x) \ x) = ((y \ x) \ x) * (T(y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(72(a,1),1441(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="72 1441"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1443">
    <literal><![CDATA[
      T(L(x,y,z),u) * (x \ 1) = x \ T(L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(5(a,1),1197(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 1197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1445">
    <literal><![CDATA[
      T(L(x,y,z),u) * (x \ 1) = x \ L(T(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(20(a,2),1443(a,2,2))].">
      <j1 rule="para" parents="20 1443"/>
    </justification>
  </clause>

  <clause id="1446">
    <literal><![CDATA[
      L(T(x,y),z,u) * (x \ 1) = x \ L(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(20(a,2),1445(a,1,1))].">
      <j1 rule="para" parents="20 1445"/>
    </justification>
  </clause>

  <clause id="1447">
    <literal><![CDATA[
      ((x \ y) * x) * (y \ x) = x * (y \ ((x \ y) * x))
    ]]></literal>
    <justification jstring="[para(964(a,1),1228(a,1,2)),flip(a)].">
      <j1 rule="para" parents="964 1228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1448">
    <literal><![CDATA[
      ((x \ y) * x) * (y \ x) = x * K(x \ y,x)
    ]]></literal>
    <justification jstring="[para(85(a,1),1447(a,2,2))].">
      <j1 rule="para" parents="85 1447"/>
    </justification>
  </clause>

  <clause id="1449">
    <literal><![CDATA[
      (x * y) * ((y * x) \ y) = y * K(y \ (y * x),y)
    ]]></literal>
    <justification jstring="[para(4(a,1),1448(a,1,1,1))].">
      <j1 rule="para" parents="4 1448"/>
    </justification>
  </clause>

  <clause id="1450">
    <literal><![CDATA[
      (x * y) * ((y * x) \ y) = y * K(x,y)
    ]]></literal>
    <justification jstring="[para(4(a,1),1449(a,2,2,1))].">
      <j1 rule="para" parents="4 1449"/>
    </justification>
  </clause>

  <clause id="1451">
    <literal><![CDATA[
      (x * y) * L(x \ 1,x,y) = y * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(627,a,1450,a)].">
      <j1 rule="hyper" parents="627 1450"/>
    </justification>
  </clause>

  <clause id="1452">
    <literal><![CDATA[
      x \ (y * K(x / y,y)) = (y * (x / y)) \ y
    ]]></literal>
    <justification jstring="[hyper(321,a,1450,a)].">
      <j1 rule="hyper" parents="321 1450"/>
    </justification>
  </clause>

  <clause id="1454">
    <literal><![CDATA[
      ((x * y) / x) * (y * z) = y * (((x * y) / x) * z)
    ]]></literal>
    <justification jstring="[para(4(a,1),1230(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4 1230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1455">
    <literal><![CDATA[
      x \ (((y * x) / y) * z) = ((y * x) / y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(599,a,1454,a)].">
      <j1 rule="hyper" parents="599 1454"/>
    </justification>
  </clause>

  <clause id="1456">
    <literal><![CDATA[
      x * (((y * x) / y) * (x \ z)) = ((y * x) / y) * z
    ]]></literal>
    <justification jstring="[hyper(342,a,1454,a),flip(a)].">
      <j1 rule="hyper" parents="342 1454"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1457">
    <literal><![CDATA[
      ((x * y) / x) \ (y * z) = y * (((x * y) / x) \ z)
    ]]></literal>
    <justification jstring="[hyper(116,a,151,a(flip),b,1454,a)].">
      <j1 rule="hyper" parents="116 151 1454"/>
    </justification>
  </clause>

  <clause id="1458">
    <literal><![CDATA[
      ((x * y) / x) * (y \ ((((x * y) / x) \ y) * z)) = L(z,((x * y) / x) \ y,(x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(747,a,1455,a),flip(a)].">
      <j1 rule="hyper" parents="747 1455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1459">
    <literal><![CDATA[
      ((x * y) / x) * z != y * u
    ]]></literal>
    <literal><![CDATA[
      ((x * y) / x) * (y \ z) = u
    ]]></literal>
    <justification jstring="[para(1456(a,1),38(a,1))].">
      <j1 rule="para" parents="1456 38"/>
    </justification>
  </clause>

  <clause id="1460">
    <literal><![CDATA[
      (x / (x / y)) * (y * z) = y * ((x / (x / y)) * z)
    ]]></literal>
    <justification jstring="[hyper(620,a,1231,a),flip(a)].">
      <j1 rule="hyper" parents="620 1231"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1461">
    <literal><![CDATA[
      (x / (x / y)) * (y \ 1) = y \ (x / (x / y))
    ]]></literal>
    <justification jstring="[hyper(415,a,1460,a),flip(a)].">
      <j1 rule="hyper" parents="415 1460"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1463">
    <literal><![CDATA[
      (x / (x / y)) * z != y * ((x / (x / y)) * u)
    ]]></literal>
    <literal><![CDATA[
      y * u = z
    ]]></literal>
    <justification jstring="[para(1460(a,1),38(a,1)),flip(a)].">
      <j1 rule="para" parents="1460 38"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1464">
    <literal><![CDATA[
      (x \ 1) / (1 / x) = x \ (1 / (1 / x))
    ]]></literal>
    <justification jstring="[hyper(58,a,1044,a(flip),b,1461,a)].">
      <j1 rule="hyper" parents="58 1044 1461"/>
    </justification>
  </clause>

  <clause id="1465">
    <literal><![CDATA[
      (L(1 / x,y,z) * x) * (x \ u) = u * L(u \ (x \ u),y,z)
    ]]></literal>
    <justification jstring="[hyper(859,a,1330,a),flip(a)].">
      <j1 rule="hyper" parents="859 1330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1466">
    <literal><![CDATA[
      (1 / x) \ ((y * (1 / x)) / y) = x * ((y * (x \ 1)) / y)
    ]]></literal>
    <justification jstring="[para(3(a,1),1344(a,1,2,1,2))].">
      <j1 rule="para" parents="3 1344"/>
    </justification>
  </clause>

  <clause id="1467">
    <literal><![CDATA[
      ((x * (x * y)) / x) / y = T(x,x / (1 / y))
    ]]></literal>
    <justification jstring="[hyper(1166,a,1345,a),flip(a)].">
      <j1 rule="hyper" parents="1166 1345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1468">
    <literal><![CDATA[
      (1 / x) * ((y * ((1 / x) \ z)) / y) = ((y * (z * x)) / y) / x
    ]]></literal>
    <justification jstring="[hyper(980,a,1345,a)].">
      <j1 rule="hyper" parents="980 1345"/>
    </justification>
  </clause>

  <clause id="1469">
    <literal><![CDATA[
      ((x * (1 / (1 / y))) / x) * (1 / y) = ((x * y) / x) / y
    ]]></literal>
    <justification jstring="[para(2(a,1),1345(a,2,1,1,2))].">
      <j1 rule="para" parents="2 1345"/>
    </justification>
  </clause>

  <clause id="1470">
    <literal><![CDATA[
      T(x,x / (1 / (x \ y))) = ((x * y) / x) / (x \ y)
    ]]></literal>
    <justification jstring="[para(5(a,1),1467(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5 1467"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1471">
    <literal><![CDATA[
      (1 / x) * ((y * ((1 / x) \ 1)) / y) = ((y * x) / y) / x
    ]]></literal>
    <justification jstring="[hyper(980,a,1469,a)].">
      <j1 rule="hyper" parents="980 1469"/>
    </justification>
  </clause>

  <clause id="1472">
    <literal><![CDATA[
      (1 / x) * ((y * x) / y) = ((y * x) / y) / x
    ]]></literal>
    <justification jstring="[para(75(a,1),1471(a,1,2,1,2))].">
      <j1 rule="para" parents="75 1471"/>
    </justification>
  </clause>

  <clause id="1473">
    <literal><![CDATA[
      ((x * T(y,x)) / x) / T(y,x) = (1 / T(y,x)) * y
    ]]></literal>
    <justification jstring="[para(225(a,1),1472(a,1,2)),flip(a)].">
      <j1 rule="para" parents="225 1472"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1475">
    <literal><![CDATA[
      x \ y != ((z * (u \ 1)) / z) / (u \ 1)
    ]]></literal>
    <literal><![CDATA[
      x * (u * ((z * (u \ 1)) / z)) = y
    ]]></literal>
    <justification jstring="[para(1472(a,1),624(a,2))].">
      <j1 rule="para" parents="1472 624"/>
    </justification>
  </clause>

  <clause id="1476">
    <literal><![CDATA[
      (1 / T(x,y)) * x = x / T(x,y)
    ]]></literal>
    <justification jstring="[para(225(a,1),1473(a,1,1)),flip(a)].">
      <j1 rule="para" parents="225 1473"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1477">
    <literal><![CDATA[
      (x / T(x,y)) / x = 1 / T(x,y)
    ]]></literal>
    <justification jstring="[hyper(131,a,1476,a)].">
      <j1 rule="hyper" parents="131 1476"/>
    </justification>
  </clause>

  <clause id="1478">
    <literal><![CDATA[
      (1 / T(x,y)) \ (x / T(x,y)) = x
    ]]></literal>
    <justification jstring="[hyper(123,a,1476,a)].">
      <j1 rule="hyper" parents="123 1476"/>
    </justification>
  </clause>

  <clause id="1479">
    <literal><![CDATA[
      (1 / T(x,y)) \ (T(x,z) / T(x,y)) = T(x,z)
    ]]></literal>
    <justification jstring="[para(1478(a,1),1041(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1478 1041"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1480">
    <literal><![CDATA[
      T(x,1 / T(x,y)) / T(x,y) = x * (1 / T(x,y))
    ]]></literal>
    <justification jstring="[para(1478(a,1),1043(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1478 1043"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1481">
    <literal><![CDATA[
      (T(x,y) / T(x,z)) / T(x,y) = 1 / T(x,z)
    ]]></literal>
    <justification jstring="[hyper(197,a,1479,a)].">
      <j1 rule="hyper" parents="197 1479"/>
    </justification>
  </clause>

  <clause id="1482">
    <literal><![CDATA[
      T(x,T(x,y) \ 1) / T(x,y) = x * (1 / T(x,y))
    ]]></literal>
    <justification jstring="[para(1306(a,1),1480(a,1,1))].">
      <j1 rule="para" parents="1306 1480"/>
    </justification>
  </clause>

  <clause id="1483">
    <literal><![CDATA[
      ((x * (y * (z \ 1))) / x) / (z \ 1) = z * ((x * (z \ y)) / x)
    ]]></literal>
    <justification jstring="[hyper(320,a,869,a(flip),b,1346,a),flip(a)].">
      <j1 rule="hyper" parents="320 869 1346"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1484">
    <literal><![CDATA[
      x * (y * T(y \ (x \ (z * y)),u)) = (T(z / x,u) * x) * y
    ]]></literal>
    <justification jstring="[hyper(58,a,924,a(flip),b,1351,a)].">
      <j1 rule="hyper" parents="58 924 1351"/>
    </justification>
  </clause>

  <clause id="1485">
    <literal><![CDATA[
      (T((x * y) / x,z) * x) * y = (x * y) * T(y,z)
    ]]></literal>
    <justification jstring="[para(4(a,1),1351(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4 1351"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1486">
    <literal><![CDATA[
      (x * y) * T((x * y) \ (z * y),u) = (x * T(x \ z,u)) * y
    ]]></literal>
    <justification jstring="[para(453(a,1),1351(a,2,1))].">
      <j1 rule="para" parents="453 1351"/>
    </justification>
  </clause>

  <clause id="1487">
    <literal><![CDATA[
      (x * T(y,z)) * y = (x * y) * T(y,z)
    ]]></literal>
    <justification jstring="[para(454(a,1),1485(a,1,1))].">
      <j1 rule="para" parents="454 1485"/>
    </justification>
  </clause>

  <clause id="1488">
    <literal><![CDATA[
      (x * y) / T(y,z) = (x / T(y,z)) * y
    ]]></literal>
    <justification jstring="[hyper(596,a,1487,a)].">
      <j1 rule="hyper" parents="596 1487"/>
    </justification>
  </clause>

  <clause id="1489">
    <literal><![CDATA[
      T((x / y) * T(y,z),y) = y \ (x * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(439,a,147,a(flip),b,1487,a)].">
      <j1 rule="hyper" parents="439 147 1487"/>
    </justification>
  </clause>

  <clause id="1490">
    <literal><![CDATA[
      ((x / T(y,z)) * y) * T(y,z) = x * y
    ]]></literal>
    <justification jstring="[hyper(326,a,1487,a),flip(a)].">
      <j1 rule="hyper" parents="326 1487"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1491">
    <literal><![CDATA[
      ((x / y) * T(y,z)) * y = x * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,147,a(flip),b,1487,a),flip(a)].">
      <j1 rule="hyper" parents="320 147 1487"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1492">
    <literal><![CDATA[
      (x * T(y,z)) \ ((x * y) * T(y,z)) = y
    ]]></literal>
    <justification jstring="[hyper(123,a,1487,a)].">
      <j1 rule="hyper" parents="123 1487"/>
    </justification>
  </clause>

  <clause id="1493">
    <literal><![CDATA[
      (x * T(y,z)) / y = (x / y) * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(117,a,147,a(flip),b,1487,a)].">
      <j1 rule="hyper" parents="117 147 1487"/>
    </justification>
  </clause>

  <clause id="1494">
    <literal><![CDATA[
      ((x / T(y,z)) / y) * T(y,z) = x / y
    ]]></literal>
    <justification jstring="[hyper(117,a,79,a(flip),b,1487,a),flip(a)].">
      <j1 rule="hyper" parents="117 79 1487"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1495">
    <literal><![CDATA[
      (x * (y / z)) * T(y / z,z) = (x * (z \ y)) * (y / z)
    ]]></literal>
    <justification jstring="[para(107(a,1),1487(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="107 1487"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1496">
    <literal><![CDATA[
      (x / T(y,z)) / y = (x / y) / T(y,z)
    ]]></literal>
    <justification jstring="[hyper(117,a,153,a(flip),b,1488,a(flip))].">
      <j1 rule="hyper" parents="117 153 1488"/>
    </justification>
  </clause>

  <clause id="1497">
    <literal><![CDATA[
      (x * y) / T(y,z) != y * u
    ]]></literal>
    <literal><![CDATA[
      T(x / T(y,z),y) = u
    ]]></literal>
    <justification jstring="[para(1488(a,2),240(a,2)),flip(a)].">
      <j1 rule="para" parents="1488 240"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1498">
    <literal><![CDATA[
      x * T(y,z) != u * y
    ]]></literal>
    <literal><![CDATA[
      (u / T(y,z)) * y = x
    ]]></literal>
    <justification jstring="[para(1490(a,1),39(a,1)),flip(a)].">
      <j1 rule="para" parents="1490 39"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1499">
    <literal><![CDATA[
      T(x,x / (x / T(y,x))) * T(y,x) = x * y
    ]]></literal>
    <justification jstring="[para(1178(a,2),1490(a,1,1))].">
      <j1 rule="para" parents="1178 1490"/>
    </justification>
  </clause>

  <clause id="1500">
    <literal><![CDATA[
      (x / y) * T(y,x) = (y * x) / y
    ]]></literal>
    <justification jstring="[hyper(117,a,105,a(flip),b,1491,a),flip(a)].">
      <j1 rule="hyper" parents="117 105 1491"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1501">
    <literal><![CDATA[
      T(x,y) \ ((x * y) / x) = T(y / x,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(439,a,xx,b,1500,a),flip(a)].">
      <j1 rule="hyper" parents="439 1500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1502">
    <literal><![CDATA[
      ((x \ y) * y) / (x \ y) = x * T(x \ y,y)
    ]]></literal>
    <justification jstring="[hyper(348,a,1500,a),flip(a)].">
      <j1 rule="hyper" parents="348 1500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1503">
    <literal><![CDATA[
      ((x * y) / x) / T(x,y) = y / x
    ]]></literal>
    <justification jstring="[hyper(131,a,1500,a)].">
      <j1 rule="hyper" parents="131 1500"/>
    </justification>
  </clause>

  <clause id="1504">
    <literal><![CDATA[
      T(x,y) = (y / x) \ ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(123,a,1500,a),flip(a)].">
      <j1 rule="hyper" parents="123 1500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1505">
    <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(396(a,1),1500(a,1,1)),flip(a)].">
      <j1 rule="para" parents="396 1500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1506">
    <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(422(a,1),1500(a,1,1)),flip(a)].">
      <j1 rule="para" parents="422 1500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1507">
    <literal><![CDATA[
      K(x \ (x / (x \ (x / y))),x) = x \ ((y * x) / y)
    ]]></literal>
    <justification jstring="[para(1500(a,1),1436(a,2,2))].">
      <j1 rule="para" parents="1500 1436"/>
    </justification>
  </clause>

  <clause id="1508">
    <literal><![CDATA[
      R(T(x,y * T(x,z)),y,T(x,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(1492(a,1),1096(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1492 1096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1509">
    <literal><![CDATA[
      ((x / T(y,z)) / y) * T(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x / y = u
    ]]></literal>
    <justification jstring="[para(1493(a,1),576(a,1))].">
      <j1 rule="para" parents="1493 576"/>
    </justification>
  </clause>

  <clause id="1510">
    <literal><![CDATA[
      ((x * (1 / T(x,y))) / x) * T(x,y) = T(x,T(x,y) \ 1) / x
    ]]></literal>
    <justification jstring="[para(1482(a,1),1494(a,1,1,1))].">
      <j1 rule="para" parents="1482 1494"/>
    </justification>
  </clause>

  <clause id="1511">
    <literal><![CDATA[
      R(T(x,L(x,y,x) * y),y,T(x,x * y)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(715(a,1),1508(a,1,1,2))].">
      <j1 rule="para" parents="715 1508"/>
    </justification>
  </clause>

  <clause id="1512">
    <literal><![CDATA[
      T(x,x / (x / T(y,x))) * (y * x) = x * (x * y)
    ]]></literal>
    <justification jstring="[para(1499(a,1),1121(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1499 1121"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1513">
    <literal><![CDATA[
      (x / y) * T(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      (x * T(y,z)) / y = u
    ]]></literal>
    <justification jstring="[para(6(a,1),1509(a,1,1,1))].">
      <j1 rule="para" parents="6 1509"/>
    </justification>
  </clause>

  <clause id="1514">
    <literal><![CDATA[
      T(x,x / (x / T(y,x))) = (x * (x * y)) / (y * x)
    ]]></literal>
    <justification jstring="[hyper(131,a,1512,a),flip(a)].">
      <j1 rule="hyper" parents="131 1512"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1515">
    <literal><![CDATA[
      (x * (x * y)) / (y * x) = (x / T(y,x)) * y
    ]]></literal>
    <justification jstring="[hyper(58,a,1178,a(flip),b,1514,a),flip(a)].">
      <j1 rule="hyper" parents="58 1178 1514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1516">
    <literal><![CDATA[
      R(((x * (x * y)) / x) / y,y,x) = (x / T(y,x)) * y
    ]]></literal>
    <justification jstring="[hyper(840,a,1515,a)].">
      <j1 rule="hyper" parents="840 1515"/>
    </justification>
  </clause>

  <clause id="1517">
    <literal><![CDATA[
      R(T(x,x / (1 / y)),y,x) = (x / T(y,x)) * y
    ]]></literal>
    <justification jstring="[para(1467(a,1),1516(a,1,1))].">
      <j1 rule="para" parents="1467 1516"/>
    </justification>
  </clause>

  <clause id="1518">
    <literal><![CDATA[
      (x * (y / z)) * (z \ y) = (x * (z \ y)) * (y / z)
    ]]></literal>
    <justification jstring="[para(107(a,1),1495(a,1,2))].">
      <j1 rule="para" parents="107 1495"/>
    </justification>
  </clause>

  <clause id="1519">
    <literal><![CDATA[
      (x * (y \ (y * z))) * ((y * z) / y) = (x * ((y * z) / y)) * z
    ]]></literal>
    <justification jstring="[para(224(a,1),1495(a,1,2)),flip(a)].">
      <j1 rule="para" parents="224 1495"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1520">
    <literal><![CDATA[
      (x * (y \ z)) / (z / y) = (x / (z / y)) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(596,a,1518,a)].">
      <j1 rule="hyper" parents="596 1518"/>
    </justification>
  </clause>

  <clause id="1521">
    <literal><![CDATA[
      (x * (y / z)) / (z \ y) = (x / (z \ y)) * (y / z)
    ]]></literal>
    <justification jstring="[hyper(117,a,147,a(flip),b,1518,a)].">
      <j1 rule="hyper" parents="117 147 1518"/>
    </justification>
  </clause>

  <clause id="1522">
    <literal><![CDATA[
      ((x / (y \ z)) / (z / y)) * (y \ z) != u
    ]]></literal>
    <literal><![CDATA[
      x / (z / y) = u
    ]]></literal>
    <justification jstring="[para(1520(a,1),576(a,1))].">
      <j1 rule="para" parents="1520 576"/>
    </justification>
  </clause>

  <clause id="1523">
    <literal><![CDATA[
      (x / (y / z)) * (z \ y) != u
    ]]></literal>
    <literal><![CDATA[
      (x * (z \ y)) / (y / z) = u
    ]]></literal>
    <justification jstring="[para(6(a,1),1522(a,1,1,1))].">
      <j1 rule="para" parents="6 1522"/>
    </justification>
  </clause>

  <clause id="1524">
    <literal><![CDATA[
      (x * y) * R((x * y) \ y,z,u) = (x * R(x \ 1,z,u)) * y
    ]]></literal>
    <justification jstring="[para(640(a,1),1374(a,2,1))].">
      <j1 rule="para" parents="640 1374"/>
    </justification>
  </clause>

  <clause id="1525">
    <literal><![CDATA[
      (x * T(x \ (y / z),u)) * z = (x * z) * T((x * z) \ y,u)
    ]]></literal>
    <justification jstring="[para(453(a,1),1402(a,1,1))].">
      <j1 rule="para" parents="453 1402"/>
    </justification>
  </clause>

  <clause id="1526">
    <literal><![CDATA[
      K(x \ (x / T(y,z)),x) = z \ ((y * T(y \ 1,x)) * z)
    ]]></literal>
    <justification jstring="[para(1226(a,1),1435(a,2,2))].">
      <j1 rule="para" parents="1226 1435"/>
    </justification>
  </clause>

  <clause id="1527">
    <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,1526,a)].">
      <j1 rule="hyper" parents="320 17 1526"/>
    </justification>
  </clause>

  <clause id="1528">
    <literal><![CDATA[
      (x * T(x \ 1,y)) * z = z * K(y \ (y / T(x,z)),y)
    ]]></literal>
    <justification jstring="[hyper(119,a,1526,a,b,xx),flip(a)].">
      <j1 rule="hyper" parents="119 1526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1529">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ 1,z) = T(x * T(x \ 1,z),y)
    ]]></literal>
    <justification jstring="[hyper(320,a,1025,a(flip),b,1527,a)].">
      <j1 rule="hyper" parents="320 1025 1527"/>
    </justification>
  </clause>

  <clause id="1530">
    <literal><![CDATA[
      T(x,y) \ T(x * T(x \ 1,z),y) = T(T(x,y) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(116,a,1527,a,b,1025,a(flip))].">
      <j1 rule="hyper" parents="116 1527 1025"/>
    </justification>
  </clause>

  <clause id="1531">
    <literal><![CDATA[
      K(x \ (x / T(x,y)),x) = T(K(x \ 1,x),y)
    ]]></literal>
    <justification jstring="[para(358(a,1),1527(a,1,1)),flip(a)].">
      <j1 rule="para" parents="358 1527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1532">
    <literal><![CDATA[
      K(x \ (x / T(y,z)),x) = T(K(x \ (x / y),x),z)
    ]]></literal>
    <justification jstring="[para(1025(a,2),1527(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1025 1527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1533">
    <literal><![CDATA[
      K(x \ (x / T(L(y \ 1,y,x),z)),x) = T(K(y,x),z)
    ]]></literal>
    <justification jstring="[para(1102(a,2),1527(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1102 1527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1534">
    <literal><![CDATA[
      T(K(x \ 1,x),y) / T(x,y) = T(1 / T(x,y),x)
    ]]></literal>
    <justification jstring="[para(1531(a,1),1030(a,1,1))].">
      <j1 rule="para" parents="1531 1030"/>
    </justification>
  </clause>

  <clause id="1535">
    <literal><![CDATA[
      K(x \ (x / T(y \ x,z)),x) = T(K(x \ y,x),z)
    ]]></literal>
    <justification jstring="[para(72(a,1),1532(a,2,1,1,2))].">
      <j1 rule="para" parents="72 1532"/>
    </justification>
  </clause>

  <clause id="1536">
    <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),1535(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="106 1535"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1537">
    <literal><![CDATA[
      T(x * T(x \ 1,T(x,y)),y) = (T(x,y) \ 1) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(284,a,1529,a),flip(a)].">
      <j1 rule="hyper" parents="284 1529"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1538">
    <literal><![CDATA[
      T(T(x,y) \ 1,x \ T(x,z)) = T(x,y) \ T(x * (x \ 1),y)
    ]]></literal>
    <justification jstring="[para(1249(a,1),1530(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="1249 1530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1539">
    <literal><![CDATA[
      ((x / y) * T((x / y) \ z,u)) * y = x * T(x \ (z * y),u)
    ]]></literal>
    <justification jstring="[para(453(a,1),1440(a,1,1))].">
      <j1 rule="para" parents="453 1440"/>
    </justification>
  </clause>

  <clause id="1540">
    <literal><![CDATA[
      (x * L(x \ 1,y,z)) * (x \ u) = u * L(u \ (x \ u),y,z)
    ]]></literal>
    <justification jstring="[para(636(a,1),1465(a,1,1))].">
      <j1 rule="para" parents="636 1465"/>
    </justification>
  </clause>

  <clause id="1541">
    <literal><![CDATA[
      (x \ 1) * ((y * ((x \ 1) \ K(x \ 1,x))) / y) = ((y * x) / y) / ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(912(a,1),1483(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="912 1483"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1542">
    <literal><![CDATA[
      x * (y * T(y \ (x \ (z * y)),u)) = (x * T(x \ z,u)) * y
    ]]></literal>
    <justification jstring="[para(453(a,1),1484(a,2,1))].">
      <j1 rule="para" parents="453 1484"/>
    </justification>
  </clause>

  <clause id="1543">
    <literal><![CDATA[
      (x * y) \ ((x * T(x \ z,u)) * y) = T((x * y) \ (z * y),u)
    ]]></literal>
    <justification jstring="[hyper(123,a,1486,a)].">
      <j1 rule="hyper" parents="123 1486"/>
    </justification>
  </clause>

  <clause id="1544">
    <literal><![CDATA[
      ((x * y) * T((x * y) \ x,z)) * y = (x * y) * (y * T(y \ 1,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,736,a(flip),b,1486,a),flip(a)].">
      <j1 rule="hyper" parents="58 736 1486"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1545">
    <literal><![CDATA[
      x * T(x \ (x \ (y * x)),z) = T(x * T(x \ y,z),x)
    ]]></literal>
    <justification jstring="[hyper(239,a,1486,a(flip),b,924,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="239 1486 924"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1546">
    <literal><![CDATA[
      T(x * T(x \ y,z),x) = x * T(x \ T(y,x),z)
    ]]></literal>
    <justification jstring="[para(17(a,2),1545(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="17 1545"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1547">
    <literal><![CDATA[
      x \ T(x * T(x \ y,z),x) = T(x \ T(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(770,a,1546,a)].">
      <j1 rule="hyper" parents="770 1546"/>
    </justification>
  </clause>

  <clause id="1548">
    <literal><![CDATA[
      T(x \ T(x * y,x),z) = x \ T(x * T(y,z),x)
    ]]></literal>
    <justification jstring="[para(4(a,1),1547(a,1,2,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4 1547"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1549">
    <literal><![CDATA[
      x \ T(x * T(y / x,z),x) = T(T(y,x) / x,z)
    ]]></literal>
    <justification jstring="[para(1385(a,1),1548(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1385 1548"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1550">
    <literal><![CDATA[
      T(x * T(y / x,z),x) = x * T(T(y,x) / x,z)
    ]]></literal>
    <justification jstring="[hyper(134,a,1549,a),flip(a)].">
      <j1 rule="hyper" parents="134 1549"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1551">
    <literal><![CDATA[
      T(x * T(y,z),x) / x = T(T(x * y,x) / x,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,1388,a(flip),b,1549,a)].">
      <j1 rule="hyper" parents="58 1388 1549"/>
    </justification>
  </clause>

  <clause id="1552">
    <literal><![CDATA[
      T(x * T(1 / x,y),x) = x * T(1 / x,y)
    ]]></literal>
    <justification jstring="[para(200(a,1),1550(a,2,2,1,1))].">
      <j1 rule="para" parents="200 1550"/>
    </justification>
  </clause>

  <clause id="1553">
    <literal><![CDATA[
      T(x,y) * ((x * (T(x,y) \ 1)) / x) = T(x,T(x,y) \ 1) / x
    ]]></literal>
    <justification jstring="[hyper(980,a,1510,a)].">
      <j1 rule="hyper" parents="980 1510"/>
    </justification>
  </clause>

  <clause id="1554">
    <literal><![CDATA[
      (x * ((y * z) / y)) * z = (x * z) * ((y * z) / y)
    ]]></literal>
    <justification jstring="[para(4(a,1),1519(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4 1519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1555">
    <literal><![CDATA[
      (x * y) / ((z * y) / z) = (x / ((z * y) / z)) * y
    ]]></literal>
    <justification jstring="[hyper(596,a,1554,a)].">
      <j1 rule="hyper" parents="596 1554"/>
    </justification>
  </clause>

  <clause id="1556">
    <literal><![CDATA[
      (1 / ((x * y) / x)) * y = y / ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(414,a,1554,a),flip(a)].">
      <j1 rule="hyper" parents="414 1554"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1558">
    <literal><![CDATA[
      ((x / y) * y) * ((x * y) / x) = T(x,x / (x / y)) * y
    ]]></literal>
    <justification jstring="[para(1168(a,1),1554(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1168 1554"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1559">
    <literal><![CDATA[
      T(x,x / (x / y)) * y = x * ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(326,a,1558,a),flip(a)].">
      <j1 rule="hyper" parents="326 1558"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1560">
    <literal><![CDATA[
      T(x,x / (x / y)) * (x \ y) = (x * y) / x
    ]]></literal>
    <justification jstring="[hyper(1134,a,1559,a)].">
      <j1 rule="hyper" parents="1134 1559"/>
    </justification>
  </clause>

  <clause id="1562">
    <literal><![CDATA[
      ((x * y) / x) / (x \ y) = T(x,x / (x / y))
    ]]></literal>
    <justification jstring="[hyper(131,a,1560,a)].">
      <j1 rule="hyper" parents="131 1560"/>
    </justification>
  </clause>

  <clause id="1563">
    <literal><![CDATA[
      T(x,x / (1 / (x \ y))) = T(x,x / (x / y))
    ]]></literal>
    <justification jstring="[hyper(58,a,1470,a,b,1562,a)].">
      <j1 rule="hyper" parents="58 1470 1562"/>
    </justification>
  </clause>

  <clause id="1564">
    <literal><![CDATA[
      T(x,x / (x / (x * y))) = T(x,x / (1 / y))
    ]]></literal>
    <justification jstring="[para(4(a,1),1563(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="4 1563"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1565">
    <literal><![CDATA[
      T(x,x * R(x \ 1,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(239,a,916,a(flip),b,1524,a(flip))].">
      <j1 rule="hyper" parents="239 916 1524"/>
    </justification>
  </clause>

  <clause id="1566">
    <literal><![CDATA[
      T(x * R(x \ 1,y,z),x) = x * R(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(239,a,1524,a(flip),b,916,a(flip))].">
      <j1 rule="hyper" parents="239 1524 916"/>
    </justification>
  </clause>

  <clause id="1567">
    <literal><![CDATA[
      T(1 / x,(1 / x) * R(x,y,z)) = 1 / x
    ]]></literal>
    <justification jstring="[para(75(a,1),1565(a,1,2,2,1))].">
      <j1 rule="para" parents="75 1565"/>
    </justification>
  </clause>

  <clause id="1568">
    <literal><![CDATA[
      T(x,(y / (x * y)) * x) = x
    ]]></literal>
    <justification jstring="[para(652(a,2),1565(a,1,2))].">
      <j1 rule="para" parents="652 1565"/>
    </justification>
  </clause>

  <clause id="1569">
    <literal><![CDATA[
      T(x \ 1,R(x,y,z) * (x \ 1)) = x \ 1
    ]]></literal>
    <justification jstring="[para(642(a,1),1565(a,1,2))].">
      <j1 rule="para" parents="642 1565"/>
    </justification>
  </clause>

  <clause id="1570">
    <literal><![CDATA[
      T(x \ 1,x \ R(x,y,z)) = x \ 1
    ]]></literal>
    <justification jstring="[para(1207(a,1),1565(a,1,2))].">
      <j1 rule="para" parents="1207 1565"/>
    </justification>
  </clause>

  <clause id="1571">
    <literal><![CDATA[
      T(x,y / (x * y)) * T(y / (x * y),x) = T(x * (y / (x * y)),x)
    ]]></literal>
    <justification jstring="[para(1568(a,1),1144(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="1568 1144"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1572">
    <literal><![CDATA[
      T(T(x \ 1,y),x \ R(x,z,u)) = T(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(1570(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1570 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1573">
    <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(1567(a,1),717(a,1,1,2))].">
      <j1 rule="para" parents="1567 717"/>
    </justification>
  </clause>

  <clause id="1574">
    <literal><![CDATA[
      R(x \ 1,R(x,y,z),x \ 1) = T(x \ 1,R(x,y,z))
    ]]></literal>
    <justification jstring="[para(1569(a,1),807(a,1,1))].">
      <j1 rule="para" parents="1569 807"/>
    </justification>
  </clause>

  <clause id="1575">
    <literal><![CDATA[
      T(x * ((x * R(x \ 1,y,z)) / x),x) = x * ((x * R(x \ 1,y,z)) / x)
    ]]></literal>
    <justification jstring="[para(1566(a,1),1386(a,2,2,1))].">
      <j1 rule="para" parents="1566 1386"/>
    </justification>
  </clause>

  <clause id="1576">
    <literal><![CDATA[
      (x * T(x \ (y / z),u)) * z = x * (z * T(z \ (x \ y),u))
    ]]></literal>
    <justification jstring="[hyper(320,a,924,a(flip),b,1525,a),flip(a)].">
      <j1 rule="hyper" parents="320 924 1525"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1577">
    <literal><![CDATA[
      (x * y) * T((x * y) \ z,x) != u
    ]]></literal>
    <literal><![CDATA[
      ((x \ (z / y)) * x) * y = u
    ]]></literal>
    <justification jstring="[para(1525(a,1),569(a,1))].">
      <j1 rule="para" parents="1525 569"/>
    </justification>
  </clause>

  <clause id="1578">
    <literal><![CDATA[
      T(T(x,y) \ 1,x \ T(x,z)) = T(x,y) \ T(1,y)
    ]]></literal>
    <justification jstring="[para(5(a,1),1538(a,2,2,1))].">
      <j1 rule="para" parents="5 1538"/>
    </justification>
  </clause>

  <clause id="1580">
    <literal><![CDATA[
      T(T(x,y) \ 1,x \ T(x,z)) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[para(200(a,1),1578(a,2,2))].">
      <j1 rule="para" parents="200 1578"/>
    </justification>
  </clause>

  <clause id="1582">
    <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,924,a(flip),b,1539,a)].">
      <j1 rule="hyper" parents="117 924 1539"/>
    </justification>
  </clause>

  <clause id="1583">
    <literal><![CDATA[
      (x / y) * T((x / y) \ z,x) = ((x \ (z * y)) * x) / y
    ]]></literal>
    <justification jstring="[hyper(117,a,105,a(flip),b,1539,a),flip(a)].">
      <j1 rule="hyper" parents="117 105 1539"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1584">
    <literal><![CDATA[
      ((x / y) * T((x / y) \ 1,z)) * y = x * T(x \ y,z)
    ]]></literal>
    <justification jstring="[para(2(a,1),1539(a,2,2,1,2))].">
      <j1 rule="para" parents="2 1539"/>
    </justification>
  </clause>

  <clause id="1585">
    <literal><![CDATA[
      (x / y) * T((x / y) \ 1,z) = (x * T(x \ y,z)) / y
    ]]></literal>
    <justification jstring="[hyper(131,a,1584,a),flip(a)].">
      <j1 rule="hyper" parents="131 1584"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1586">
    <literal><![CDATA[
      K((x / y) \ 1,x / y) * y = x * T(x \ y,x / y)
    ]]></literal>
    <justification jstring="[para(358(a,1),1584(a,1,1))].">
      <j1 rule="para" parents="358 1584"/>
    </justification>
  </clause>

  <clause id="1587">
    <literal><![CDATA[
      K(x \ (x / (y / z)),x) * z = y * T(y \ z,x)
    ]]></literal>
    <justification jstring="[para(1025(a,2),1584(a,1,1))].">
      <j1 rule="para" parents="1025 1584"/>
    </justification>
  </clause>

  <clause id="1588">
    <literal><![CDATA[
      K(x \ (x / (y / z)),x) = (y * T(y \ z,x)) / z
    ]]></literal>
    <justification jstring="[hyper(131,a,1587,a),flip(a)].">
      <j1 rule="hyper" parents="131 1587"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1589">
    <literal><![CDATA[
      K(x \ (x / ((y * z) / y)),x) = (y * (z * T(z \ 1,x))) / y
    ]]></literal>
    <justification jstring="[hyper(117,a,736,a(flip),b,1587,a),flip(a)].">
      <j1 rule="hyper" parents="117 736 1587"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1590">
    <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),1588(a,1,1,2))].">
      <j1 rule="para" parents="6 1588"/>
    </justification>
  </clause>

  <clause id="1591">
    <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),1588(a,1,1,2,2))].">
      <j1 rule="para" parents="15 1588"/>
    </justification>
  </clause>

  <clause id="1592">
    <literal><![CDATA[
      K(x \ (x / ((y \ x) / T(x,y))),x) = ((y \ x) * ((y \ x) \ x)) / T(x,y)
    ]]></literal>
    <justification jstring="[para(1167(a,1),1588(a,2,1,2))].">
      <j1 rule="para" parents="1167 1588"/>
    </justification>
  </clause>

  <clause id="1593">
    <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,1586,a),flip(a)].">
      <j1 rule="hyper" parents="320 451 1586"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1594">
    <literal><![CDATA[
      (x \ L(x,y,z)) * ((x \ 1) \ u) = u * L(u \ ((x \ 1) \ u),y,z)
    ]]></literal>
    <justification jstring="[para(1193(a,1),1540(a,1,1))].">
      <j1 rule="para" parents="1193 1540"/>
    </justification>
  </clause>

  <clause id="1595">
    <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,1387,a,b,1542,a)].">
      <j1 rule="hyper" parents="58 1387 1542"/>
    </justification>
  </clause>

  <clause id="1596">
    <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),1542(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="92 1542"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1597">
    <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(1543(a,1),255(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1543 255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1598">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) \ x) / x) = T(x,T(x,y) \ 1) / x
    ]]></literal>
    <justification jstring="[para(1118(a,1),1553(a,1,2,1))].">
      <j1 rule="para" parents="1118 1553"/>
    </justification>
  </clause>

  <clause id="1599">
    <literal><![CDATA[
      x * (y * T(y \ (x \ z),x)) != u
    ]]></literal>
    <literal><![CDATA[
      ((x \ (z / y)) * x) * y = u
    ]]></literal>
    <justification jstring="[para(1576(a,1),569(a,1))].">
      <j1 rule="para" parents="1576 569"/>
    </justification>
  </clause>

  <clause id="1600">
    <literal><![CDATA[
      (x \ 1) * (y * T(y \ ((x \ 1) \ z),u)) = (x \ T(x * (z / y),u)) * y
    ]]></literal>
    <justification jstring="[para(939(a,1),1576(a,1,1)),flip(a)].">
      <j1 rule="para" parents="939 1576"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1601">
    <literal><![CDATA[
      ((x / y) * K(y \ 1,y)) * y = x * (y * T(y \ (x \ x),y))
    ]]></literal>
    <justification jstring="[para(1022(a,2),1576(a,1,1))].">
      <j1 rule="para" parents="1022 1576"/>
    </justification>
  </clause>

  <clause id="1602">
    <literal><![CDATA[
      K(x \ (x / ((y * x) / y)),x) = (y * K(x \ 1,x)) / y
    ]]></literal>
    <justification jstring="[para(358(a,1),1589(a,2,1,2))].">
      <j1 rule="para" parents="358 1589"/>
    </justification>
  </clause>

  <clause id="1603">
    <literal><![CDATA[
      ((x * y) / x) \ ((x * K(y \ 1,y)) / x) = T(((x * y) / x) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(116,a,1602,a(flip),b,1025,a(flip))].">
      <j1 rule="hyper" parents="116 1602 1025"/>
    </justification>
  </clause>

  <clause id="1604">
    <literal><![CDATA[
      ((x / y) * K(y \ 1,y)) * y = x * (y * T(y \ 1,y))
    ]]></literal>
    <justification jstring="[para(61(a,1),1601(a,2,2,2,1,2))].">
      <j1 rule="para" parents="61 1601"/>
    </justification>
  </clause>

  <clause id="1606">
    <literal><![CDATA[
      ((x / y) * K(y \ 1,y)) * y = x * ((y \ 1) * y)
    ]]></literal>
    <justification jstring="[para(105(a,1),1604(a,2,2))].">
      <j1 rule="para" parents="105 1604"/>
    </justification>
  </clause>

  <clause id="1607">
    <literal><![CDATA[
      ((x / y) * K(y \ 1,y)) * y = x * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[para(358(a,1),1604(a,2,2))].">
      <j1 rule="para" parents="358 1604"/>
    </justification>
  </clause>

  <clause id="1608">
    <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,1606,a),flip(a)].">
      <j1 rule="hyper" parents="30 101 1606"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1609">
    <literal><![CDATA[
      (x * K(y \ 1,y)) * y = (x * y) * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[para(6(a,1),1607(a,1,1,1))].">
      <j1 rule="para" parents="6 1607"/>
    </justification>
  </clause>

  <clause id="1610">
    <literal><![CDATA[
      (L(1 / x,x,y) * K(x \ 1,x)) * x = (x * ((y * x) \ y)) * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(845(a,1),1607(a,1,1,1))].">
      <j1 rule="para" parents="845 1607"/>
    </justification>
  </clause>

  <clause id="1611">
    <literal><![CDATA[
      ((x / K(y \ 1,y)) * y) * K(y \ 1,y) = x * y
    ]]></literal>
    <justification jstring="[hyper(326,a,1609,a),flip(a)].">
      <j1 rule="hyper" parents="326 1609"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1612">
    <literal><![CDATA[
      ((x * (y \ 1)) / K(y \ 1,y)) * y = R(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(30,a,520,a,b,1611,a),flip(a)].">
      <j1 rule="hyper" parents="30 520 1611"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1613">
    <literal><![CDATA[
      (x * (y \ 1)) / K(y \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      R(x,y \ 1,y) / y = z
    ]]></literal>
    <justification jstring="[para(1608(a,1),327(a,1,1)),flip(b)].">
      <j1 rule="para" parents="1608 327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1614">
    <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,748,a),flip(a)].">
      <j1 rule="hyper" parents="29 448 748"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1615">
    <literal><![CDATA[
      x * ((x \ y) * ((z * ((x \ y) \ u)) / z)) = y * ((z * (y \ (x * u))) / z)
    ]]></literal>
    <justification jstring="[hyper(119,a,887,a(flip),b,91,a),flip(a)].">
      <j1 rule="hyper" parents="119 887 91"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1616">
    <literal><![CDATA[
      x \ (y * ((z * (y \ (x * u))) / z)) = (x \ y) * ((z * ((x \ y) \ u)) / z)
    ]]></literal>
    <justification jstring="[para(887(a,1),474(a,1,2,2))].">
      <j1 rule="para" parents="887 474"/>
    </justification>
  </clause>

  <clause id="1617">
    <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),900(a,1,2,1))].">
      <j1 rule="para" parents="496 900"/>
    </justification>
  </clause>

  <clause id="1618">
    <literal><![CDATA[
      (1 / (x \ y)) \ (y \ x) = (y \ x) * (x \ y)
    ]]></literal>
    <justification jstring="[para(390(a,1),1201(a,1,1)),flip(a)].">
      <j1 rule="para" parents="390 1201"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1619">
    <literal><![CDATA[
      (x \ (x * y)) * ((x * y) \ x) = (1 / ((x * y) \ x)) \ y
    ]]></literal>
    <justification jstring="[para(4(a,1),1618(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4 1618"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1620">
    <literal><![CDATA[
      (1 / ((x * y) \ x)) \ y = y * ((x * y) \ x)
    ]]></literal>
    <justification jstring="[para(4(a,1),1619(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4 1619"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1621">
    <literal><![CDATA[
      (1 / ((x * y) \ x)) * (y * ((x * y) \ x)) = y
    ]]></literal>
    <justification jstring="[hyper(134,a,1620,a)].">
      <j1 rule="hyper" parents="134 1620"/>
    </justification>
  </clause>

  <clause id="1622">
    <literal><![CDATA[
      (1 / (x / y)) * ((y / x) * (x / y)) = y / x
    ]]></literal>
    <justification jstring="[hyper(119,a,789,a(flip),b,1218,a(flip))].">
      <j1 rule="hyper" parents="119 789 1218"/>
    </justification>
  </clause>

  <clause id="1623">
    <literal><![CDATA[
      T(1 / (x / y),(y / x) * (x / y)) = ((y / x) * (x / y)) \ (y / x)
    ]]></literal>
    <justification jstring="[hyper(439,a,xx,b,1622,a)].">
      <j1 rule="hyper" parents="439 1622"/>
    </justification>
  </clause>

  <clause id="1624">
    <literal><![CDATA[
      T(x,(x * T(x \ 1,y)) / x) = R(x,T(1 / x,y),x)
    ]]></literal>
    <justification jstring="[para(457(a,1),1247(a,1,2)),flip(a)].">
      <j1 rule="para" parents="457 1247"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1625">
    <literal><![CDATA[
      R(x,T(1 / x,y),x) = T(x,T(1 / x,y))
    ]]></literal>
    <justification jstring="[para(457(a,1),1624(a,1,2)),flip(a)].">
      <j1 rule="para" parents="457 1624"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1626">
    <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(1625(a,1),1325(a,1,1))].">
      <j1 rule="para" parents="1625 1325"/>
    </justification>
  </clause>

  <clause id="1627">
    <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),1422(a,2,1))].">
      <j1 rule="para" parents="6 1422"/>
    </justification>
  </clause>

  <clause id="1628">
    <literal><![CDATA[
      x * T(y,L(y,z,u) * x) = L(y,x,L(y,z,u)) * x
    ]]></literal>
    <justification jstring="[para(1627(a,1),454(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1627 454"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1629">
    <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,1628,a)].">
      <j1 rule="hyper" parents="29 237 1628"/>
    </justification>
  </clause>

  <clause id="1630">
    <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(939(a,1),1599(a,1,2))].">
      <j1 rule="para" parents="939 1599"/>
    </justification>
  </clause>

  <clause id="1631">
    <literal><![CDATA[
      R((x * y) / (x * z),u,w) * (x * z) = x * (z * R(z \ y,u,w))
    ]]></literal>
    <justification jstring="[hyper(647,a,1061,a)].">
      <j1 rule="hyper" parents="647 1061"/>
    </justification>
  </clause>

  <clause id="1632">
    <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,1524,a(flip),b,1061,a),flip(a)].">
      <j1 rule="hyper" parents="58 1524 1061"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1633">
    <literal><![CDATA[
      x * (y * R(y \ (x \ z),x,y)) = ((z / (x * y)) * x) * y
    ]]></literal>
    <justification jstring="[hyper(852,a,1062,a),flip(a)].">
      <j1 rule="hyper" parents="852 1062"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1634">
    <literal><![CDATA[
      x * (y * R(y \ (x \ y),z,u)) = (x * R(x \ 1,z,u)) * y
    ]]></literal>
    <justification jstring="[hyper(58,a,1524,a(flip),b,1062,a),flip(a)].">
      <j1 rule="hyper" parents="58 1524 1062"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1635">
    <literal><![CDATA[
      (((x * (y * z)) / (x * y)) * x) * y = x * (y * R(z,x,y))
    ]]></literal>
    <justification jstring="[para(62(a,1),1633(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="62 1633"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1636">
    <literal><![CDATA[
      (((x * (y * z)) / (x * z)) * x) * z = x * (z * R(T(y,z),x,z))
    ]]></literal>
    <justification jstring="[para(105(a,1),1635(a,1,1,1,1,2))].">
      <j1 rule="para" parents="105 1635"/>
    </justification>
  </clause>

  <clause id="1637">
    <literal><![CDATA[
      (((x * (y * z)) / (x * z)) * x) * z = x * (R(y,x,z) * z)
    ]]></literal>
    <justification jstring="[para(238(a,1),1636(a,2,2))].">
      <j1 rule="para" parents="238 1636"/>
    </justification>
  </clause>

  <clause id="1638">
    <literal><![CDATA[
      (L((x * y) / x,z,u) * x) * y = (x * y) * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(882,a,1065,a),flip(a)].">
      <j1 rule="hyper" parents="882 1065"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1639">
    <literal><![CDATA[
      (x * y) * L((x * y) \ (z * y),u,w) = (L(z / x,u,w) * x) * y
    ]]></literal>
    <justification jstring="[hyper(859,a,1065,a)].">
      <j1 rule="hyper" parents="859 1065"/>
    </justification>
  </clause>

  <clause id="1640">
    <literal><![CDATA[
      (x * L(y,z,u)) * y = (x * y) * L(y,z,u)
    ]]></literal>
    <justification jstring="[para(637(a,1),1638(a,1,1))].">
      <j1 rule="para" parents="637 1638"/>
    </justification>
  </clause>

  <clause id="1641">
    <literal><![CDATA[
      (x * y) / L(y,z,u) = (x / L(y,z,u)) * y
    ]]></literal>
    <justification jstring="[hyper(596,a,1640,a)].">
      <j1 rule="hyper" parents="596 1640"/>
    </justification>
  </clause>

  <clause id="1642">
    <literal><![CDATA[
      ((x / L(y,z,u)) * y) \ (x * y) = L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(571,a,1640,a)].">
      <j1 rule="hyper" parents="571 1640"/>
    </justification>
  </clause>

  <clause id="1643">
    <literal><![CDATA[
      (1 / L(x,y,z)) * x = x / L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(414,a,1640,a),flip(a)].">
      <j1 rule="hyper" parents="414 1640"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1644">
    <literal><![CDATA[
      ((x / y) * L(y,z,u)) * y = x * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(320,a,147,a(flip),b,1640,a),flip(a)].">
      <j1 rule="hyper" parents="320 147 1640"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1645">
    <literal><![CDATA[
      ((1 / L(x,y,z)) * x) * L(x,y,z) = x
    ]]></literal>
    <justification jstring="[hyper(204,a,1640,a),flip(a)].">
      <j1 rule="hyper" parents="204 1640"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1646">
    <literal><![CDATA[
      (x * L(y,z,u)) \ ((x * y) * L(y,z,u)) = y
    ]]></literal>
    <justification jstring="[hyper(123,a,1640,a)].">
      <j1 rule="hyper" parents="123 1640"/>
    </justification>
  </clause>

  <clause id="1647">
    <literal><![CDATA[
      ((x / y) * L(y,z,u)) \ (x * L(y,z,u)) = y
    ]]></literal>
    <justification jstring="[hyper(116,a,147,a(flip),b,1640,a)].">
      <j1 rule="hyper" parents="116 147 1640"/>
    </justification>
  </clause>

  <clause id="1648">
    <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(1640(a,1),307(a,1,1))].">
      <j1 rule="para" parents="1640 307"/>
    </justification>
  </clause>

  <clause id="1649">
    <literal><![CDATA[
      (x / L(y,z,u)) / y = (x / y) / L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(117,a,153,a(flip),b,1641,a(flip))].">
      <j1 rule="hyper" parents="117 153 1641"/>
    </justification>
  </clause>

  <clause id="1650">
    <literal><![CDATA[
      (x * y) / L(y,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      (x / L(y,z,u)) * y = w
    ]]></literal>
    <justification jstring="[para(1642(a,1),330(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1642 330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1651">
    <literal><![CDATA[
      ((x * y) / z) * L(z,y,x) = (x * (y * z)) / z
    ]]></literal>
    <justification jstring="[hyper(117,a,90,a(flip),b,1644,a),flip(a)].">
      <j1 rule="hyper" parents="117 90 1644"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1652">
    <literal><![CDATA[
      R(T(x,y * L(x,z,u)),y,L(x,z,u)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(1646(a,1),1096(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1646 1096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1653">
    <literal><![CDATA[
      ((x * (y * z)) / z) / L(z,y,x) = (x * y) / z
    ]]></literal>
    <justification jstring="[para(186(a,1),1649(a,1,1)),flip(a)].">
      <j1 rule="para" parents="186 1649"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1654">
    <literal><![CDATA[
      L(x,y,z) \ ((z * (y * x)) / x) = T((z * y) / x,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(439,a,xx,b,1651,a),flip(a)].">
      <j1 rule="hyper" parents="439 1651"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1655">
    <literal><![CDATA[
      L(x,y,z) = ((z * y) / x) \ ((z * (y * x)) / x)
    ]]></literal>
    <justification jstring="[hyper(123,a,1651,a),flip(a)].">
      <j1 rule="hyper" parents="123 1651"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1656">
    <literal><![CDATA[
      (x * L(y,z,u)) * T(y,x) = (y * x) * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(119,a,1652,a(flip),b,631,a)].">
      <j1 rule="hyper" parents="119 1652 631"/>
    </justification>
  </clause>

  <clause id="1657">
    <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(1653(a,1),420(a,1,1))].">
      <j1 rule="para" parents="1653 420"/>
    </justification>
  </clause>

  <clause id="1658">
    <literal><![CDATA[
      ((x * (y / z)) / z) \ ((x * y) / z) = L(z,y / z,x)
    ]]></literal>
    <justification jstring="[para(7(a,1),1655(a,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="7 1655"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1659">
    <literal><![CDATA[
      (L((x / y) / z,u,w) * z) * y = (z * y) * L((z * y) \ x,u,w)
    ]]></literal>
    <justification jstring="[hyper(320,a,636,a(flip),b,1066,a),flip(a)].">
      <j1 rule="hyper" parents="320 636 1066"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1660">
    <literal><![CDATA[
      (x * y) * R((x * y) \ (z * y),u,w) = (R(z / x,u,w) * x) * y
    ]]></literal>
    <justification jstring="[hyper(867,a,1067,a)].">
      <j1 rule="hyper" parents="867 1067"/>
    </justification>
  </clause>

  <clause id="1661">
    <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(1194(a,1),1088(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="1194 1088"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1662">
    <literal><![CDATA[
      x * (y * ((x * (y \ 1)) / x)) = T(x,x / (x * y))
    ]]></literal>
    <justification jstring="[hyper(1171,a,1097,a),flip(a)].">
      <j1 rule="hyper" parents="1171 1097"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1663">
    <literal><![CDATA[
      x \ T(x,x / (x * y)) = y * ((x * (y \ 1)) / x)
    ]]></literal>
    <justification jstring="[hyper(1169,a,1097,a)].">
      <j1 rule="hyper" parents="1169 1097"/>
    </justification>
  </clause>

  <clause id="1664">
    <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),1097(a,1,1))].">
      <j1 rule="para" parents="90 1097"/>
    </justification>
  </clause>

  <clause id="1665">
    <literal><![CDATA[
      x * (T(x,T(x,y) \ 1) / x) = T(x,x / (x * T(x,y)))
    ]]></literal>
    <justification jstring="[para(1553(a,1),1662(a,1,2))].">
      <j1 rule="para" parents="1553 1662"/>
    </justification>
  </clause>

  <clause id="1666">
    <literal><![CDATA[
      (x * ((y * (x \ 1)) / y)) / (y \ 1) = T(y,y / (y * x))
    ]]></literal>
    <justification jstring="[hyper(117,a,1663,a(flip),b,993,a)].">
      <j1 rule="hyper" parents="117 1663 993"/>
    </justification>
  </clause>

  <clause id="1667">
    <literal><![CDATA[
      x \ y != z * ((x * (z \ 1)) / x)
    ]]></literal>
    <literal><![CDATA[
      T(x,x / (x * z)) = y
    ]]></literal>
    <justification jstring="[para(1663(a,1),42(a,1)),flip(a)].">
      <j1 rule="para" parents="1663 42"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1668">
    <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(1209(a,1),1666(a,1,1,2,1))].">
      <j1 rule="para" parents="1209 1666"/>
    </justification>
  </clause>

  <clause id="1669">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ y)) / z) = (((z * (1 / x)) / z) * x) * y
    ]]></literal>
    <justification jstring="[hyper(980,a,1098,a)].">
      <j1 rule="hyper" parents="980 1098"/>
    </justification>
  </clause>

  <clause id="1670">
    <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),1098(a,1,2))].">
      <j1 rule="para" parents="101 1098"/>
    </justification>
  </clause>

  <clause id="1671">
    <literal><![CDATA[
      (((x * y) / x) * (y \ 1)) * x = T(x,R(y,y \ 1,x))
    ]]></literal>
    <justification jstring="[hyper(892,a,1159,a)].">
      <j1 rule="hyper" parents="892 1159"/>
    </justification>
  </clause>

  <clause id="1672">
    <literal><![CDATA[
      (x \ ((y * x) / y)) * y = T(y,R(x,x \ 1,y))
    ]]></literal>
    <justification jstring="[para(1302(a,1),1671(a,1,1))].">
      <j1 rule="para" parents="1302 1671"/>
    </justification>
  </clause>

  <clause id="1673">
    <literal><![CDATA[
      T(x,R(y,y \ 1,x)) / x = y \ ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(131,a,1672,a)].">
      <j1 rule="hyper" parents="131 1672"/>
    </justification>
  </clause>

  <clause id="1674">
    <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),1672(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="225 1672"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1675">
    <literal><![CDATA[
      T(x,R(y,y \ 1,x)) / x != z
    ]]></literal>
    <literal><![CDATA[
      y \ ((x * y) / x) = z
    ]]></literal>
    <justification jstring="[para(1672(a,1),327(a,1,1)),flip(b)].">
      <j1 rule="para" parents="1672 327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1676">
    <literal><![CDATA[
      (1 / x) \ ((y * (1 / x)) / y) = T(y,R(1 / x,x,y)) / y
    ]]></literal>
    <justification jstring="[para(75(a,1),1673(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="75 1673"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1677">
    <literal><![CDATA[
      T(1 / x,T(x,R(y,y \ 1,x))) = L(x \ 1,x,y \ ((x * y) / x))
    ]]></literal>
    <justification jstring="[para(1673(a,1),1017(a,1,3)),flip(a)].">
      <j1 rule="para" parents="1673 1017"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1678">
    <literal><![CDATA[
      T(x,R(1 / y,y,x)) / x = y * ((x * (y \ 1)) / x)
    ]]></literal>
    <justification jstring="[hyper(58,a,1466,a(flip),b,1676,a),flip(a)].">
      <j1 rule="hyper" parents="58 1466 1676"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1679">
    <literal><![CDATA[
      (x * ((y * (x \ 1)) / y)) * y = T(y,R(1 / x,x,y))
    ]]></literal>
    <justification jstring="[hyper(133,a,1678,a)].">
      <j1 rule="hyper" parents="133 1678"/>
    </justification>
  </clause>

  <clause id="1680">
    <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(1118(a,1),1679(a,1,1,2,1))].">
      <j1 rule="para" parents="1118 1679"/>
    </justification>
  </clause>

  <clause id="1681">
    <literal><![CDATA[
      T(x,R(1 / y,y,x)) = (x \ T(x,x / (x * y))) * x
    ]]></literal>
    <justification jstring="[para(1663(a,2),1679(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1663 1679"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1682">
    <literal><![CDATA[
      T(T(x,x * y) * y,R(x,y,y \ 1)) = x * y
    ]]></literal>
    <justification jstring="[para(558(a,1),1163(a,1,1))].">
      <j1 rule="para" parents="558 1163"/>
    </justification>
  </clause>

  <clause id="1683">
    <literal><![CDATA[
      T(T(T(x,x * y) * y,z),R(x,y,y \ 1)) = T(x * y,z)
    ]]></literal>
    <justification jstring="[para(1682(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1682 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1684">
    <literal><![CDATA[
      T((x / y) * y,T(x / y,y)) = T(x,R(x / y,y,y \ 1))
    ]]></literal>
    <justification jstring="[para(987(a,1),1683(a,1,1)),flip(a)].">
      <j1 rule="para" parents="987 1683"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1685">
    <literal><![CDATA[
      T((x / y) * y,T(x / y,y)) = T(x,x * (y \ 1))
    ]]></literal>
    <justification jstring="[para(523(a,1),1684(a,2,2))].">
      <j1 rule="para" parents="523 1684"/>
    </justification>
  </clause>

  <clause id="1686">
    <literal><![CDATA[
      T(x,T(x / y,y)) = T(x,x * (y \ 1))
    ]]></literal>
    <justification jstring="[para(7(a,1),1685(a,1,1))].">
      <j1 rule="para" parents="7 1685"/>
    </justification>
  </clause>

  <clause id="1687">
    <literal><![CDATA[
      T(x,x * (y \ 1)) = T(x,y \ x)
    ]]></literal>
    <justification jstring="[para(107(a,1),1686(a,1,2)),flip(a)].">
      <j1 rule="para" parents="107 1686"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1688">
    <literal><![CDATA[
      T(x,(1 / y) \ x) = T(x,x * y)
    ]]></literal>
    <justification jstring="[para(75(a,1),1687(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="75 1687"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1689">
    <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,1208,a),flip(a)].">
      <j1 rule="hyper" parents="320 238 1208"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1690">
    <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(1118(a,1),1689(a,1,2,1,2))].">
      <j1 rule="para" parents="1118 1689"/>
    </justification>
  </clause>

  <clause id="1691">
    <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(1217(a,1),423(a,1))].">
      <j1 rule="para" parents="1217 423"/>
    </justification>
  </clause>

  <clause id="1692">
    <literal><![CDATA[
      (1 / x) * L((1 / x) \ y,z,u) = L(y * x,z,u) / x
    ]]></literal>
    <justification jstring="[para(75(a,1),1241(a,1,2)),flip(a)].">
      <j1 rule="para" parents="75 1241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1693">
    <literal><![CDATA[
      (1 / x) * L((1 / x) \ 1,y,z) = L(x,y,z) / x
    ]]></literal>
    <justification jstring="[para(2(a,1),1692(a,2,1,1))].">
      <j1 rule="para" parents="2 1692"/>
    </justification>
  </clause>

  <clause id="1694">
    <literal><![CDATA[
      L((x \ 1) \ (x \ y),z,u) = (x \ 1) \ (x \ L(y,z,u))
    ]]></literal>
    <justification jstring="[para(72(a,1),1305(a,1,1,2,1))].">
      <j1 rule="para" parents="72 1305"/>
    </justification>
  </clause>

  <clause id="1696">
    <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),1307(a,1,2,1))].">
      <j1 rule="para" parents="75 1307"/>
    </justification>
  </clause>

  <clause id="1697">
    <literal><![CDATA[
      (x \ y) * R((x \ y) \ 1,z,u) = x \ (y * R(y \ x,z,u))
    ]]></literal>
    <justification jstring="[para(3(a,1),1332(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="3 1332"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1698">
    <literal><![CDATA[
      (x \ y) * L((x \ y) \ 1,z,u) = x \ (y * L(y \ x,z,u))
    ]]></literal>
    <justification jstring="[para(3(a,1),1333(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="3 1333"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1699">
    <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),1333(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="5 1333"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1700">
    <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),1698(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13 1698"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1701">
    <literal><![CDATA[
      (L(x / (y / z),u,w) * (y / z)) * z = y * L(y \ (x * z),u,w)
    ]]></literal>
    <justification jstring="[hyper(320,a,636,a(flip),b,1334,a),flip(a)].">
      <j1 rule="hyper" parents="320 636 1334"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1702">
    <literal><![CDATA[
      (R(1 / (x / y),z,u) * (x / y)) * y = R(y / x,z,u) * x
    ]]></literal>
    <justification jstring="[para(2(a,1),1335(a,2,1,1,1))].">
      <j1 rule="para" parents="2 1335"/>
    </justification>
  </clause>

  <clause id="1703">
    <literal><![CDATA[
      (R(1 / (x / y),z,u) * (x / y)) * y = x * R(x \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(320,a,640,a(flip),b,1702,a),flip(a)].">
      <j1 rule="hyper" parents="320 640 1702"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1704">
    <literal><![CDATA[
      ((x / y) * R((x / y) \ 1,z,u)) * y = x * R(x \ y,z,u)
    ]]></literal>
    <justification jstring="[para(640(a,1),1703(a,1,1))].">
      <j1 rule="para" parents="640 1703"/>
    </justification>
  </clause>

  <clause id="1705">
    <literal><![CDATA[
      (x / y) * R((x / y) \ 1,z,u) = (x * R(x \ y,z,u)) / y
    ]]></literal>
    <justification jstring="[hyper(131,a,1704,a),flip(a)].">
      <j1 rule="hyper" parents="131 1704"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1706">
    <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),1705(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15 1705"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1707">
    <literal><![CDATA[
      (x / y) \ (x * ((z * (x \ (x / y))) / z)) = y * ((z * (y \ 1)) / z)
    ]]></literal>
    <justification jstring="[hyper(123,a,1343,a)].">
      <j1 rule="hyper" parents="123 1343"/>
    </justification>
  </clause>

  <clause id="1708">
    <literal><![CDATA[
      x \ ((x * y) * a(z,u,w)) = y * (a(z,u,w) * a(x,y,a(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(320,a,346,a(flip),b,1365,a),flip(a)].">
      <j1 rule="hyper" parents="320 346 1365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1709">
    <literal><![CDATA[
      (x \ (y / (1 / x))) * x = T(y,x) / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(117,a,1382,a(flip),b,1391,a),flip(a)].">
      <j1 rule="hyper" parents="117 1382 1391"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1710">
    <literal><![CDATA[
      ((x * (1 / (1 / T(y,x)))) / x) \ (y / T(y,x)) = 1 / T(y,x)
    ]]></literal>
    <justification jstring="[para(1476(a,1),1425(a,1,2))].">
      <j1 rule="para" parents="1476 1425"/>
    </justification>
  </clause>

  <clause id="1711">
    <literal><![CDATA[
      ((x \ y) \ y) * (T(x,z) \ 1) = T(x,z) \ ((x \ y) \ y)
    ]]></literal>
    <justification jstring="[para(72(a,1),1442(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="72 1442"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1713">
    <literal><![CDATA[
      (x * (y * T(y \ 1,z))) * y = (x * y) * (y * T(y \ 1,z))
    ]]></literal>
    <justification jstring="[para(736(a,1),1544(a,1,1))].">
      <j1 rule="para" parents="736 1544"/>
    </justification>
  </clause>

  <clause id="1714">
    <literal><![CDATA[
      T(x,y / (x * y)) * R(x \ 1,x,y) = T(x * (y / (x * y)),x)
    ]]></literal>
    <justification jstring="[para(646(a,1),1571(a,1,2))].">
      <j1 rule="para" parents="646 1571"/>
    </justification>
  </clause>

  <clause id="1715">
    <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),1626(a,1,2))].">
      <j1 rule="para" parents="246 1626"/>
    </justification>
  </clause>

  <clause id="1716">
    <literal><![CDATA[
      T(x,T(1 / x,y)) * T(x \ 1,y) = x * T(1 / x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,1552,a(flip),b,1715,a),flip(a)].">
      <j1 rule="hyper" parents="320 1552 1715"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1717">
    <literal><![CDATA[
      R((x * y) / (x * z),u,w) * (x * z) = x * (R(y / z,u,w) * z)
    ]]></literal>
    <justification jstring="[para(640(a,2),1631(a,2,2))].">
      <j1 rule="para" parents="640 1631"/>
    </justification>
  </clause>

  <clause id="1718">
    <literal><![CDATA[
      (x * y) * L((x * y) \ (z * y),u,w) = (x * L(x \ z,u,w)) * y
    ]]></literal>
    <justification jstring="[para(636(a,1),1639(a,2,1))].">
      <j1 rule="para" parents="636 1639"/>
    </justification>
  </clause>

  <clause id="1719">
    <literal><![CDATA[
      (x * L(x \ (y / z),u,w)) * z = (x * z) * L((x * z) \ y,u,w)
    ]]></literal>
    <justification jstring="[para(636(a,1),1659(a,1,1))].">
      <j1 rule="para" parents="636 1659"/>
    </justification>
  </clause>

  <clause id="1720">
    <literal><![CDATA[
      (x * y) * R((x * y) \ (z * y),u,w) = (x * R(x \ z,u,w)) * y
    ]]></literal>
    <justification jstring="[para(640(a,1),1660(a,2,1))].">
      <j1 rule="para" parents="640 1660"/>
    </justification>
  </clause>

  <clause id="1721">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ y)) / z) = (x * ((z * (x \ 1)) / z)) * y
    ]]></literal>
    <justification jstring="[para(869(a,1),1669(a,2,1))].">
      <j1 rule="para" parents="869 1669"/>
    </justification>
  </clause>

  <clause id="1722">
    <literal><![CDATA[
      (x \ y) \ (x \ (y * L(y \ z,u,w))) = L((x \ y) \ (x \ z),u,w)
    ]]></literal>
    <justification jstring="[hyper(123,a,1699,a)].">
      <j1 rule="hyper" parents="123 1699"/>
    </justification>
  </clause>

  <clause id="1723">
    <literal><![CDATA[
      ((x / y) * L((x / y) \ z,u,w)) * y = x * L(x \ (z * y),u,w)
    ]]></literal>
    <justification jstring="[para(636(a,1),1701(a,1,1))].">
      <j1 rule="para" parents="636 1701"/>
    </justification>
  </clause>

  <clause id="1724">
    <literal><![CDATA[
      (x / y) \ (x * ((x / y) / x)) = y * ((x * (y \ 1)) / x)
    ]]></literal>
    <justification jstring="[para(5(a,1),1707(a,1,2,2,1))].">
      <j1 rule="para" parents="5 1707"/>
    </justification>
  </clause>

  <clause id="1725">
    <literal><![CDATA[
      K(x,(x / y) / x) = y * ((x * (y \ 1)) / x)
    ]]></literal>
    <justification jstring="[hyper(467,a,1724,a)].">
      <j1 rule="hyper" parents="467 1724"/>
    </justification>
  </clause>

  <clause id="1726">
    <literal><![CDATA[
      (x / y) \ ((x / y) * K(x,(x / y) / x)) = y * ((x * (y \ 1)) / x)
    ]]></literal>
    <justification jstring="[para(303(a,2),1724(a,1,2))].">
      <j1 rule="para" parents="303 1724"/>
    </justification>
  </clause>

  <clause id="1727">
    <literal><![CDATA[
      x * ((y * (x \ 1)) / y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,(y / x) / y) = z
    ]]></literal>
    <justification jstring="[para(1724(a,1),467(a,1))].">
      <j1 rule="para" parents="1724 467"/>
    </justification>
  </clause>

  <clause id="1728">
    <literal><![CDATA[
      K(x,(x / (y \ 1)) / x) = y \ ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(320,a,1424,a(flip),b,1725,a),flip(a)].">
      <j1 rule="hyper" parents="320 1424 1725"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1729">
    <literal><![CDATA[
      x * K(x,(x / y) / x) = T(x,x / (x * y))
    ]]></literal>
    <justification jstring="[hyper(119,a,1725,a,b,1663,a)].">
      <j1 rule="hyper" parents="119 1725 1663"/>
    </justification>
  </clause>

  <clause id="1731">
    <literal><![CDATA[
      (x \ y) * ((y * ((x \ y) \ 1)) / y) = K(y,x / y)
    ]]></literal>
    <justification jstring="[para(72(a,1),1725(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="72 1725"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1732">
    <literal><![CDATA[
      x * ((T(x,y) * (x \ 1)) / T(x,y)) = K(T(x,y),1 / x)
    ]]></literal>
    <justification jstring="[para(1010(a,1),1725(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1010 1725"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1733">
    <literal><![CDATA[
      x * ((L(x,y,z) * (x \ 1)) / L(x,y,z)) = K(L(x,y,z),1 / x)
    ]]></literal>
    <justification jstring="[para(1084(a,1),1725(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1084 1725"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1734">
    <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(1205(a,1),1725(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1205 1725"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1735">
    <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(1481(a,1),1725(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1481 1725"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1736">
    <literal><![CDATA[
      K(x,(x / ((T(x,y) \ 1) \ 1)) / x) = (T(x,y) \ 1) \ ((T(x,y) \ x) / x)
    ]]></literal>
    <justification jstring="[para(1118(a,1),1728(a,2,2,1))].">
      <j1 rule="para" parents="1118 1728"/>
    </justification>
  </clause>

  <clause id="1737">
    <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(1209(a,1),1728(a,2,2,1))].">
      <j1 rule="para" parents="1209 1728"/>
    </justification>
  </clause>

  <clause id="1738">
    <literal><![CDATA[
      T(x,x / (x * (y \ x))) = x * K(x,y / x)
    ]]></literal>
    <justification jstring="[para(72(a,1),1729(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="72 1729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1739">
    <literal><![CDATA[
      T(x,R(y,x,(y * x) \ x)) = x * K(x,(y * x) / x)
    ]]></literal>
    <justification jstring="[para(99(a,2),1738(a,1,2))].">
      <j1 rule="para" parents="99 1738"/>
    </justification>
  </clause>

  <clause id="1740">
    <literal><![CDATA[
      T(x,R(y,x,(y * x) \ x)) = x * K(x,y)
    ]]></literal>
    <justification jstring="[para(6(a,1),1739(a,2,2,2))].">
      <j1 rule="para" parents="6 1739"/>
    </justification>
  </clause>

  <clause id="1741">
    <literal><![CDATA[
      T(x,R(y,x,(y * x) \ x)) * (x \ z) = x \ ((x * K(x,y)) * z)
    ]]></literal>
    <justification jstring="[para(1740(a,1),1109(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1740 1109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1742">
    <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),1732(a,1,2,1))].">
      <j1 rule="para" parents="455 1732"/>
    </justification>
  </clause>

  <clause id="1743">
    <literal><![CDATA[
      x \ ((x * K(x,y)) * z) = (x * K(x,y)) * (x \ z)
    ]]></literal>
    <justification jstring="[para(1740(a,1),1741(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1740 1741"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1744">
    <literal><![CDATA[
      (x * K(x,y)) * (x \ 1) = x \ (x * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(293,a,1743,a),flip(a)].">
      <j1 rule="hyper" parents="293 1743"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1745">
    <literal><![CDATA[
      (x * K(x,y)) * (x \ 1) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,4,a(flip),b,1744,a),flip(a)].">
      <j1 rule="hyper" parents="320 4 1744"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1746">
    <literal><![CDATA[
      K(x,y) / (x \ 1) = x * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(117,a,4,a(flip),b,1744,a)].">
      <j1 rule="hyper" parents="117 4 1744"/>
    </justification>
  </clause>

  <clause id="1748">
    <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),1717(a,2,2,1,1))].">
      <j1 rule="para" parents="6 1717"/>
    </justification>
  </clause>

  <clause id="1749">
    <literal><![CDATA[
      x * (y * L(y \ (x \ (z * y)),u,w)) = (x * L(x \ z,u,w)) * y
    ]]></literal>
    <justification jstring="[hyper(58,a,1060,a(flip),b,1718,a)].">
      <j1 rule="hyper" parents="58 1060 1718"/>
    </justification>
  </clause>

  <clause id="1750">
    <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,918,a(flip),b,1718,a),flip(a)].">
      <j1 rule="hyper" parents="58 918 1718"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1751">
    <literal><![CDATA[
      x * L(x \ (x \ (y * x)),z,u) = T(x * L(x \ y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(239,a,1718,a(flip),b,1060,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="239 1718 1060"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1752">
    <literal><![CDATA[
      (x * y) * L((x * y) \ y,z,u) = (x * L(x \ 1,z,u)) * y
    ]]></literal>
    <justification jstring="[para(2(a,1),1718(a,1,2,1,2))].">
      <j1 rule="para" parents="2 1718"/>
    </justification>
  </clause>

  <clause id="1753">
    <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),1751(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="17 1751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1754">
    <literal><![CDATA[
      x \ T(x * L(x \ y,z,u),x) = L(x \ T(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(770,a,1753,a)].">
      <j1 rule="hyper" parents="770 1753"/>
    </justification>
  </clause>

  <clause id="1755">
    <literal><![CDATA[
      T(x * L(x \ 1,y,z),x) = x * L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(200(a,1),1753(a,2,2,1,2))].">
      <j1 rule="para" parents="200 1753"/>
    </justification>
  </clause>

  <clause id="1756">
    <literal><![CDATA[
      T(x,x * L(x \ 1,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(49,a,1755,a)].">
      <j1 rule="hyper" parents="49 1755"/>
    </justification>
  </clause>

  <clause id="1757">
    <literal><![CDATA[
      K(x,x * L(x \ 1,y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(50,a,1756,a)].">
      <j1 rule="hyper" parents="50 1756"/>
    </justification>
  </clause>

  <clause id="1758">
    <literal><![CDATA[
      T(x \ y,(x \ y) * (y \ x)) = x \ y
    ]]></literal>
    <justification jstring="[para(390(a,1),1756(a,1,2,2))].">
      <j1 rule="para" parents="390 1756"/>
    </justification>
  </clause>

  <clause id="1759">
    <literal><![CDATA[
      T(x \ 1,L(x,y,z) * (x \ 1)) = x \ 1
    ]]></literal>
    <justification jstring="[para(638(a,1),1756(a,1,2))].">
      <j1 rule="para" parents="638 1756"/>
    </justification>
  </clause>

  <clause id="1760">
    <literal><![CDATA[
      T(1 / x,L(x,y,z) / x) = 1 / x
    ]]></literal>
    <justification jstring="[para(1693(a,1),1756(a,1,2))].">
      <j1 rule="para" parents="1693 1756"/>
    </justification>
  </clause>

  <clause id="1761">
    <literal><![CDATA[
      T((x * (1 / y)) / x,L(y,z,u) / y) = (x * (1 / y)) / x
    ]]></literal>
    <justification jstring="[para(1760(a,1),460(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1760 460"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1762">
    <literal><![CDATA[
      L(x \ y,y \ x,x \ y) * (y \ x) = (y \ x) * (x \ y)
    ]]></literal>
    <justification jstring="[para(1758(a,1),715(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1758 715"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1763">
    <literal><![CDATA[
      R(x \ 1,L(x,y,z),x \ 1) = T(x \ 1,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(1759(a,1),807(a,1,1))].">
      <j1 rule="para" parents="1759 807"/>
    </justification>
  </clause>

  <clause id="1764">
    <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),1754(a,1,2,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4 1754"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1765">
    <literal><![CDATA[
      x \ T(x * L(y / x,z,u),x) = L(T(y,x) / x,z,u)
    ]]></literal>
    <justification jstring="[para(1385(a,1),1764(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1385 1764"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1766">
    <literal><![CDATA[
      L(T(x * y,x) / x,z,u) = T(x * L(y,z,u),x) / x
    ]]></literal>
    <justification jstring="[hyper(58,a,1389,a(flip),b,1765,a),flip(a)].">
      <j1 rule="hyper" parents="58 1389 1765"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1767">
    <literal><![CDATA[
      L(x \ y,y \ x,x \ y) = L(1 / (y \ x),y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(30,a,846,a,b,1762,a),flip(a)].">
      <j1 rule="hyper" parents="30 846 1762"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1768">
    <literal><![CDATA[
      ((x \ y) * (y \ x)) \ (x \ y) = 1 / (y \ x)
    ]]></literal>
    <justification jstring="[hyper(1186,a,1767,a)].">
      <j1 rule="hyper" parents="1186 1767"/>
    </justification>
  </clause>

  <clause id="1769">
    <literal><![CDATA[
      x \ (y * L(y \ x,x \ y,y \ x)) = (x \ y) * (1 / (x \ y))
    ]]></literal>
    <justification jstring="[para(1767(a,2),474(a,1,2,2))].">
      <j1 rule="para" parents="1767 474"/>
    </justification>
  </clause>

  <clause id="1770">
    <literal><![CDATA[
      L((x \ y) \ 1,x \ y,y \ x) = 1 / (x \ y)
    ]]></literal>
    <justification jstring="[hyper(423,a,1768,a)].">
      <j1 rule="hyper" parents="423 1768"/>
    </justification>
  </clause>

  <clause id="1771">
    <literal><![CDATA[
      (((x * y) \ x) * y) \ ((x * y) \ x) = 1 / (x \ (x * y))
    ]]></literal>
    <justification jstring="[para(4(a,1),1768(a,1,1,2))].">
      <j1 rule="para" parents="4 1768"/>
    </justification>
  </clause>

  <clause id="1772">
    <literal><![CDATA[
      L(((x * y) \ x) \ 1,(x * y) \ x,y) = 1 / ((x * y) \ x)
    ]]></literal>
    <justification jstring="[para(4(a,1),1770(a,1,3))].">
      <j1 rule="para" parents="4 1770"/>
    </justification>
  </clause>

  <clause id="1773">
    <literal><![CDATA[
      (((x * y) \ x) * y) \ ((x * y) \ x) = 1 / y
    ]]></literal>
    <justification jstring="[para(4(a,1),1771(a,2,2))].">
      <j1 rule="para" parents="4 1771"/>
    </justification>
  </clause>

  <clause id="1774">
    <literal><![CDATA[
      L(x \ 1,x,(y * x) \ y) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(423,a,1773,a)].">
      <j1 rule="hyper" parents="423 1773"/>
    </justification>
  </clause>

  <clause id="1775">
    <literal><![CDATA[
      ((x * y) \ x) / (1 / y) = ((x * y) \ x) * y
    ]]></literal>
    <justification jstring="[hyper(197,a,1773,a)].">
      <j1 rule="hyper" parents="197 1773"/>
    </justification>
  </clause>

  <clause id="1776">
    <literal><![CDATA[
      (((x * y) \ x) * y) * (1 / y) = (x * y) \ x
    ]]></literal>
    <justification jstring="[hyper(134,a,1773,a)].">
      <j1 rule="hyper" parents="134 1773"/>
    </justification>
  </clause>

  <clause id="1777">
    <literal><![CDATA[
      L(x \ 1,x,x \ 1) = 1 / x
    ]]></literal>
    <justification jstring="[para(2(a,1),1774(a,1,3,1))].">
      <j1 rule="para" parents="2 1774"/>
    </justification>
  </clause>

  <clause id="1778">
    <literal><![CDATA[
      L(T(x \ 1,y),x,x \ 1) = T(1 / x,y)
    ]]></literal>
    <justification jstring="[para(1777(a,1),20(a,2,1))].">
      <j1 rule="para" parents="1777 20"/>
    </justification>
  </clause>

  <clause id="1779">
    <literal><![CDATA[
      L(L(x \ 1,y,z),x,x \ 1) = L(1 / x,y,z)
    ]]></literal>
    <justification jstring="[para(1777(a,1),25(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1777 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1780">
    <literal><![CDATA[
      (x \ 1) / (1 / x) = (x \ 1) * x
    ]]></literal>
    <justification jstring="[para(1777(a,1),396(a,1,2))].">
      <j1 rule="para" parents="1777 396"/>
    </justification>
  </clause>

  <clause id="1781">
    <literal><![CDATA[
      x * L(x \ (y \ x),y,y \ 1) = (y * (1 / y)) * (y \ x)
    ]]></literal>
    <justification jstring="[para(1777(a,1),1540(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1777 1540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1782">
    <literal><![CDATA[
      T(1 / (1 / x),x \ 1) = x
    ]]></literal>
    <justification jstring="[hyper(1046,a,1780,a)].">
      <j1 rule="hyper" parents="1046 1780"/>
    </justification>
  </clause>

  <clause id="1783">
    <literal><![CDATA[
      (x \ 1) / (1 / x) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,258,a,b,1780,a),flip(a)].">
      <j1 rule="hyper" parents="320 258 1780"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1784">
    <literal><![CDATA[
      T(T(1 / (1 / x),y),x \ 1) = T(x,y)
    ]]></literal>
    <justification jstring="[para(1782(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1782 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1785">
    <literal><![CDATA[
      T(x,y \ 1) != T(y,z)
    ]]></literal>
    <literal><![CDATA[
      T(1 / (1 / y),z) = x
    ]]></literal>
    <justification jstring="[para(1782(a,1),138(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1782 138"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1786">
    <literal><![CDATA[
      T(x,x \ 1) / x = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(1782(a,1),1192(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1782 1192"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1787">
    <literal><![CDATA[
      K(1 / x,1 / (1 / x)) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(1280,a,1783,a)].">
      <j1 rule="hyper" parents="1280 1783"/>
    </justification>
  </clause>

  <clause id="1788">
    <literal><![CDATA[
      K(x \ 1,x) * (1 / x) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(133,a,1783,a)].">
      <j1 rule="hyper" parents="133 1783"/>
    </justification>
  </clause>

  <clause id="1789">
    <literal><![CDATA[
      x \ (1 / (1 / x)) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,1464,a(flip),b,1783,a)].">
      <j1 rule="hyper" parents="58 1464 1783"/>
    </justification>
  </clause>

  <clause id="1790">
    <literal><![CDATA[
      x * K(x \ 1,x) = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(119,a,1783,a(flip),b,1464,a(flip))].">
      <j1 rule="hyper" parents="119 1783 1464"/>
    </justification>
  </clause>

  <clause id="1791">
    <literal><![CDATA[
      K(x,1 / x) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(1275,a,1786,a)].">
      <j1 rule="hyper" parents="1275 1786"/>
    </justification>
  </clause>

  <clause id="1792">
    <literal><![CDATA[
      K(x,x \ 1) * x = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(133,a,1786,a)].">
      <j1 rule="hyper" parents="133 1786"/>
    </justification>
  </clause>

  <clause id="1793">
    <literal><![CDATA[
      ((x \ 1) \ 1) / x = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(106(a,1),1786(a,1,1))].">
      <j1 rule="para" parents="106 1786"/>
    </justification>
  </clause>

  <clause id="1794">
    <literal><![CDATA[
      K(x,x \ 1) = x * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(386,a,1791,a),flip(a)].">
      <j1 rule="hyper" parents="386 1791"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1795">
    <literal><![CDATA[
      K((x / y) \ x,1 / y) = K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,674,a,b,1791,a)].">
      <j1 rule="hyper" parents="58 674 1791"/>
    </justification>
  </clause>

  <clause id="1796">
    <literal><![CDATA[
      (x \ 1) * K(x,x \ 1) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(119,a,1791,a(flip),b,1274,a)].">
      <j1 rule="hyper" parents="119 1791 1274"/>
    </justification>
  </clause>

  <clause id="1797">
    <literal><![CDATA[
      x \ K(x,x \ 1) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(116,a,1791,a(flip),b,260,a(flip))].">
      <j1 rule="hyper" parents="116 1791 260"/>
    </justification>
  </clause>

  <clause id="1798">
    <literal><![CDATA[
      K(x \ 1,(x \ 1) \ 1) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(72(a,1),1791(a,1,2)),flip(a)].">
      <j1 rule="para" parents="72 1791"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1799">
    <literal><![CDATA[
      K(x,x \ 1) \ 1 = K(1 / x,x)
    ]]></literal>
    <justification jstring="[para(1791(a,1),433(a,1,1))].">
      <j1 rule="para" parents="1791 433"/>
    </justification>
  </clause>

  <clause id="1800">
    <literal><![CDATA[
      K(x,x \ 1) != y
    ]]></literal>
    <literal><![CDATA[
      x * (1 / x) = y
    ]]></literal>
    <justification jstring="[para(1791(a,1),386(a,1))].">
      <j1 rule="para" parents="1791 386"/>
    </justification>
  </clause>

  <clause id="1801">
    <literal><![CDATA[
      (1 / (1 / x)) * K(x,x \ 1) = x
    ]]></literal>
    <justification jstring="[para(1791(a,1),874(a,1,2))].">
      <j1 rule="para" parents="1791 874"/>
    </justification>
  </clause>

  <clause id="1802">
    <literal><![CDATA[
      R(x \ 1,x,y) \ (((y / (x * y)) * x) * (1 / x)) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,1281,a,b,1794,a)].">
      <j1 rule="hyper" parents="320 1281 1794"/>
    </justification>
  </clause>

  <clause id="1803">
    <literal><![CDATA[
      L(x,y,z) * K(x,x \ 1) = x * (L(x,y,z) * (1 / x))
    ]]></literal>
    <justification jstring="[hyper(119,a,1794,a,b,1410,a)].">
      <j1 rule="hyper" parents="119 1794 1410"/>
    </justification>
  </clause>

  <clause id="1804">
    <literal><![CDATA[
      R(x,y,1 / y) * K(y,y \ 1) = (x * y) * (1 / y)
    ]]></literal>
    <justification jstring="[hyper(119,a,1794,a,b,184,a)].">
      <j1 rule="hyper" parents="119 1794 184"/>
    </justification>
  </clause>

  <clause id="1805">
    <literal><![CDATA[
      T(x,y) \ K(x,x \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      x * (T(x,y) \ (1 / x)) = z
    ]]></literal>
    <justification jstring="[para(1794(a,2),1139(a,1,2))].">
      <j1 rule="para" parents="1794 1139"/>
    </justification>
  </clause>

  <clause id="1806">
    <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(1794(a,2),924(a,1,1))].">
      <j1 rule="para" parents="1794 924"/>
    </justification>
  </clause>

  <clause id="1807">
    <literal><![CDATA[
      x * (1 / x) != y
    ]]></literal>
    <literal><![CDATA[
      K(x,x \ 1) = y
    ]]></literal>
    <justification jstring="[para(1797(a,1),255(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1797 255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1808">
    <literal><![CDATA[
      x \ y != z * (1 / z)
    ]]></literal>
    <literal><![CDATA[
      x * K(z,z \ 1) = y
    ]]></literal>
    <justification jstring="[para(1797(a,1),340(a,2,2))].">
      <j1 rule="para" parents="1797 340"/>
    </justification>
  </clause>

  <clause id="1809">
    <literal><![CDATA[
      (x \ 1) * L(y,1 / x,K(x \ 1,x)) = K(x \ 1,x) * ((1 / x) * y)
    ]]></literal>
    <justification jstring="[para(1788(a,1),90(a,1,1))].">
      <j1 rule="para" parents="1788 90"/>
    </justification>
  </clause>

  <clause id="1810">
    <literal><![CDATA[
      x * (T(x,y) \ K(x \ 1,x)) = T(x,y) \ (1 / (1 / x))
    ]]></literal>
    <justification jstring="[para(1789(a,1),1117(a,1,2,2))].">
      <j1 rule="para" parents="1789 1117"/>
    </justification>
  </clause>

  <clause id="1811">
    <literal><![CDATA[
      K(x \ 1,x) * x = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(1301,a,1790,a)].">
      <j1 rule="hyper" parents="1301 1790"/>
    </justification>
  </clause>

  <clause id="1812">
    <literal><![CDATA[
      L(x,x \ 1,x) = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(836,a,1790,a)].">
      <j1 rule="hyper" parents="836 1790"/>
    </justification>
  </clause>

  <clause id="1813">
    <literal><![CDATA[
      L(R(x,y,z),x \ 1,x) = R(1 / (1 / x),y,z)
    ]]></literal>
    <justification jstring="[para(1812(a,1),24(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1812 24"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1814">
    <literal><![CDATA[
      1 / (1 / x) != y
    ]]></literal>
    <literal><![CDATA[
      x * K(x \ 1,x) = y
    ]]></literal>
    <justification jstring="[para(1812(a,1),837(a,1))].">
      <j1 rule="para" parents="1812 837"/>
    </justification>
  </clause>

  <clause id="1815">
    <literal><![CDATA[
      K(x,x \ 1) * x = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(320,a,106,a(flip),b,1792,a),flip(a)].">
      <j1 rule="hyper" parents="320 106 1792"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1816">
    <literal><![CDATA[
      T(x,x \ 1) * L(y,x,K(x,x \ 1)) = K(x,x \ 1) * (x * y)
    ]]></literal>
    <justification jstring="[para(1792(a,1),90(a,1,1))].">
      <j1 rule="para" parents="1792 90"/>
    </justification>
  </clause>

  <clause id="1817">
    <literal><![CDATA[
      T(x,x \ 1) \ (K(x,x \ 1) * y) = L(x \ y,x,K(x,x \ 1))
    ]]></literal>
    <justification jstring="[para(1792(a,1),92(a,2,1)),flip(a)].">
      <j1 rule="para" parents="1792 92"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1818">
    <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(1792(a,1),479(a,1,1))].">
      <j1 rule="para" parents="1792 479"/>
    </justification>
  </clause>

  <clause id="1819">
    <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(1792(a,1),482(a,1,2,2))].">
      <j1 rule="para" parents="1792 482"/>
    </justification>
  </clause>

  <clause id="1820">
    <literal><![CDATA[
      K(x,x \ 1) * (x \ 1) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(1291,a,1796,a)].">
      <j1 rule="hyper" parents="1291 1796"/>
    </justification>
  </clause>

  <clause id="1821">
    <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,1801,a(flip),b,184,a)].">
      <j1 rule="hyper" parents="119 1801 184"/>
    </justification>
  </clause>

  <clause id="1822">
    <literal><![CDATA[
      x * L(y,K(x,x \ 1),1 / (1 / x)) = (1 / (1 / x)) * (K(x,x \ 1) * y)
    ]]></literal>
    <justification jstring="[para(1801(a,1),90(a,1,1))].">
      <j1 rule="para" parents="1801 90"/>
    </justification>
  </clause>

  <clause id="1823">
    <literal><![CDATA[
      R(x / (1 / (1 / y)),1 / (1 / y),K(y,y \ 1)) = (x * K(y,y \ 1)) / y
    ]]></literal>
    <justification jstring="[para(1801(a,1),102(a,2,2))].">
      <j1 rule="para" parents="1801 102"/>
    </justification>
  </clause>

  <clause id="1824">
    <literal><![CDATA[
      (1 / x) / L(y,(x \ 1) / y,K(x,x \ 1)) = K(x,x \ 1) * ((x \ 1) / y)
    ]]></literal>
    <justification jstring="[para(1820(a,1),544(a,1,1))].">
      <j1 rule="para" parents="1820 544"/>
    </justification>
  </clause>

  <clause id="1825">
    <literal><![CDATA[
      K(x,1 / x) != y
    ]]></literal>
    <literal><![CDATA[
      K(x,x \ 1) = y
    ]]></literal>
    <justification jstring="[para(260(a,2),1807(a,1))].">
      <j1 rule="para" parents="260 1807"/>
    </justification>
  </clause>

  <clause id="1826">
    <literal><![CDATA[
      K(1 / x,(1 / x) \ 1) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(1825,a,1787,a)].">
      <j1 rule="hyper" parents="1825 1787"/>
    </justification>
  </clause>

  <clause id="1827">
    <literal><![CDATA[
      K(1 / x,x) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(75(a,1),1826(a,1,2))].">
      <j1 rule="para" parents="75 1826"/>
    </justification>
  </clause>

  <clause id="1828">
    <literal><![CDATA[
      K(x,x \ 1) \ 1 = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,1799,a,b,1827,a)].">
      <j1 rule="hyper" parents="58 1799 1827"/>
    </justification>
  </clause>

  <clause id="1829">
    <literal><![CDATA[
      K((x \ 1) \ 1,x \ 1) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(72(a,1),1827(a,1,1)),flip(a)].">
      <j1 rule="para" parents="72 1827"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1830">
    <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(1261(a,1),1827(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1261 1827"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1831">
    <literal><![CDATA[
      K((x \ 1) \ 1,x \ 1) = K(x,1 / x)
    ]]></literal>
    <justification jstring="[hyper(320,a,1791,a,b,1829,a),flip(a)].">
      <j1 rule="hyper" parents="320 1791 1829"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1832">
    <literal><![CDATA[
      x \ ((x \ 1) \ 1) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,780,a(flip),b,1829,a)].">
      <j1 rule="hyper" parents="58 780 1829"/>
    </justification>
  </clause>

  <clause id="1833">
    <literal><![CDATA[
      x * K(x,x \ 1) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(119,a,1829,a(flip),b,780,a(flip))].">
      <j1 rule="hyper" parents="119 1829 780"/>
    </justification>
  </clause>

  <clause id="1834">
    <literal><![CDATA[
      x * K(x,x \ 1) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(119,a,1832,a(flip),b,310,a)].">
      <j1 rule="hyper" parents="119 1832 310"/>
    </justification>
  </clause>

  <clause id="1835">
    <literal><![CDATA[
      x \ ((x \ 1) \ 1) != y
    ]]></literal>
    <literal><![CDATA[
      K(x,x \ 1) = y
    ]]></literal>
    <justification jstring="[para(1833(a,1),287(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1833 287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1836">
    <literal><![CDATA[
      T(x,x \ 1) * L(y,K(x,x \ 1),x) = x * (K(x,x \ 1) * y)
    ]]></literal>
    <justification jstring="[para(1834(a,1),90(a,1,1))].">
      <j1 rule="para" parents="1834 90"/>
    </justification>
  </clause>

  <clause id="1837">
    <literal><![CDATA[
      K(T(x \ 1,x),(x \ 1) \ 1) = K(x \ 1,1 / (x \ 1))
    ]]></literal>
    <justification jstring="[para(1260(a,2),1831(a,1,1))].">
      <j1 rule="para" parents="1260 1831"/>
    </justification>
  </clause>

  <clause id="1838">
    <literal><![CDATA[
      K(x \ 1,x) * T(1 / x,y) = (x \ 1) * (x * T(x \ 1,y))
    ]]></literal>
    <justification jstring="[para(1778(a,1),484(a,1,2))].">
      <j1 rule="para" parents="1778 484"/>
    </justification>
  </clause>

  <clause id="1839">
    <literal><![CDATA[
      K(((x * y) \ x) \ (((x * y) \ x) * y),(x * y) \ x) * y = T(y,(x * y) \ x)
    ]]></literal>
    <justification jstring="[para(1775(a,1),1032(a,2,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1775 1032"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1840">
    <literal><![CDATA[
      (x * y) \ x = (L(y \ 1,y,x) * y) * (1 / y)
    ]]></literal>
    <justification jstring="[para(217(a,2),1776(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="217 1776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1841">
    <literal><![CDATA[
      K(x \ 1,x) * L(1 / x,y,z) = (x \ 1) * (x * L(x \ 1,y,z))
    ]]></literal>
    <justification jstring="[para(1779(a,1),484(a,1,2))].">
      <j1 rule="para" parents="1779 484"/>
    </justification>
  </clause>

  <clause id="1842">
    <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(1779(a,1),826(a,1,2))].">
      <j1 rule="para" parents="1779 826"/>
    </justification>
  </clause>

  <clause id="1843">
    <literal><![CDATA[
      L(x \ 1,x,y) / (1 / x) = L(x \ 1,x,y) * x
    ]]></literal>
    <justification jstring="[hyper(621,a,1840,a)].">
      <j1 rule="hyper" parents="621 1840"/>
    </justification>
  </clause>

  <clause id="1844">
    <literal><![CDATA[
      K(T(x \ 1,x),(x \ 1) \ 1) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(72(a,1),1837(a,2,2))].">
      <j1 rule="para" parents="72 1837"/>
    </justification>
  </clause>

  <clause id="1846">
    <literal><![CDATA[
      K(T(x \ 1,x),T(x,x \ 1)) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,1369,a,b,1844,a)].">
      <j1 rule="hyper" parents="58 1369 1844"/>
    </justification>
  </clause>

  <clause id="1847">
    <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,1829,a(flip),b,1846,a),flip(a)].">
      <j1 rule="hyper" parents="320 1829 1846"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1848">
    <literal><![CDATA[
      (x * ((y * x) \ y)) \ x = 1 / ((y * x) \ y)
    ]]></literal>
    <justification jstring="[hyper(500,a,1772,a)].">
      <j1 rule="hyper" parents="500 1772"/>
    </justification>
  </clause>

  <clause id="1849">
    <literal><![CDATA[
      x * L(x \ (y \ x),y,y \ 1) = K(y,y \ 1) * (y \ x)
    ]]></literal>
    <justification jstring="[para(1794(a,2),1781(a,2,1))].">
      <j1 rule="para" parents="1794 1781"/>
    </justification>
  </clause>

  <clause id="1850">
    <literal><![CDATA[
      x * (y * L(y \ (x \ y),z,u)) = (x * L(x \ 1,z,u)) * y
    ]]></literal>
    <justification jstring="[hyper(58,a,1060,a(flip),b,1752,a)].">
      <j1 rule="hyper" parents="58 1060 1752"/>
    </justification>
  </clause>

  <clause id="1851">
    <literal><![CDATA[
      T(x * L(x \ 1,T(x,y),y),y) = T(x,y) * ((x * y) \ y)
    ]]></literal>
    <justification jstring="[hyper(239,a,1752,a(flip),b,481,a(flip))].">
      <j1 rule="hyper" parents="239 1752 481"/>
    </justification>
  </clause>

  <clause id="1852">
    <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,1838,a(flip),b,633,a)].">
      <j1 rule="hyper" parents="119 1838 633"/>
    </justification>
  </clause>

  <clause id="1853">
    <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),1850(a,1,2,2,1,2))].">
      <j1 rule="para" parents="4 1850"/>
    </justification>
  </clause>

  <clause id="1854">
    <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(1594(a,2),1850(a,1,2))].">
      <j1 rule="para" parents="1594 1850"/>
    </justification>
  </clause>

  <clause id="1855">
    <literal><![CDATA[
      x * (y * L(y \ (x \ y),x,x \ 1)) = (x * (1 / x)) * y
    ]]></literal>
    <justification jstring="[para(1777(a,1),1850(a,2,1,2))].">
      <j1 rule="para" parents="1777 1850"/>
    </justification>
  </clause>

  <clause id="1856">
    <literal><![CDATA[
      x * (K(x,x \ 1) * (x \ y)) = (x * (1 / x)) * y
    ]]></literal>
    <justification jstring="[para(1849(a,1),1855(a,1,2))].">
      <j1 rule="para" parents="1849 1855"/>
    </justification>
  </clause>

  <clause id="1857">
    <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,1856,a),flip(a)].">
      <j1 rule="hyper" parents="29 90 1856"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1858">
    <literal><![CDATA[
      x * (K(x,x \ 1) * (x \ y)) = K(x,x \ 1) * y
    ]]></literal>
    <justification jstring="[para(1794(a,2),1856(a,2,1))].">
      <j1 rule="para" parents="1794 1856"/>
    </justification>
  </clause>

  <clause id="1859">
    <literal><![CDATA[
      x \ (K(x,x \ 1) * y) = K(x,x \ 1) * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(123,a,1858,a)].">
      <j1 rule="hyper" parents="123 1858"/>
    </justification>
  </clause>

  <clause id="1860">
    <literal><![CDATA[
      K(x,x \ 1) * (x * y) = x * (K(x,x \ 1) * y)
    ]]></literal>
    <justification jstring="[para(4(a,1),1858(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 1858"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1861">
    <literal><![CDATA[
      x * (K(x,x \ 1) * T(y,x)) = K(x,x \ 1) * (y * x)
    ]]></literal>
    <justification jstring="[para(17(a,2),1858(a,1,2,2))].">
      <j1 rule="para" parents="17 1858"/>
    </justification>
  </clause>

  <clause id="1862">
    <literal><![CDATA[
      K(x,x \ 1) * y != x * z
    ]]></literal>
    <literal><![CDATA[
      K(x,x \ 1) * (x \ y) = z
    ]]></literal>
    <justification jstring="[para(1858(a,1),38(a,1))].">
      <j1 rule="para" parents="1858 38"/>
    </justification>
  </clause>

  <clause id="1863">
    <literal><![CDATA[
      (1 / x) * (K(x \ 1,x) * ((1 / x) \ y)) = K(1 / x,(1 / x) \ 1) * y
    ]]></literal>
    <justification jstring="[para(1826(a,1),1858(a,1,2,1))].">
      <j1 rule="para" parents="1826 1858"/>
    </justification>
  </clause>

  <clause id="1864">
    <literal><![CDATA[
      K(x,x \ 1) * y != (1 / x) * z
    ]]></literal>
    <literal><![CDATA[
      x \ L(z,1 / x,x) = y
    ]]></literal>
    <justification jstring="[para(1857(a,1),38(a,1)),flip(a)].">
      <j1 rule="para" parents="1857 38"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1865">
    <literal><![CDATA[
      x * L(x \ y,y \ x,x \ y) = y * K(y \ x,(y \ x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(1808,a,1769,a),flip(a)].">
      <j1 rule="hyper" parents="1808 1769"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1866">
    <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,1860,a(flip),b,1816,a),flip(a)].">
      <j1 rule="hyper" parents="320 1860 1816"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1867">
    <literal><![CDATA[
      L(x,K(y,y \ 1),y) = L(x,y,K(y,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(29,a,1836,a,b,1866,a)].">
      <j1 rule="hyper" parents="29 1836 1866"/>
    </justification>
  </clause>

  <clause id="1868">
    <literal><![CDATA[
      L(x,1 / y,K(1 / y,(1 / y) \ 1)) = L(x,K(y \ 1,y),1 / y)
    ]]></literal>
    <justification jstring="[para(1826(a,1),1867(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1826 1867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1869">
    <literal><![CDATA[
      x * (y * R(y \ (x \ (z * y)),u,w)) = (x * R(x \ z,u,w)) * y
    ]]></literal>
    <justification jstring="[hyper(58,a,1062,a(flip),b,1720,a)].">
      <j1 rule="hyper" parents="58 1062 1720"/>
    </justification>
  </clause>

  <clause id="1870">
    <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,1720,a(flip),b,1331,a),flip(a)].">
      <j1 rule="hyper" parents="239 1720 1331"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1871">
    <literal><![CDATA[
      x * R(x \ (x \ (y * x)),z,u) = T(x * R(x \ y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(239,a,1720,a(flip),b,1062,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="239 1720 1062"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1872">
    <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,1720,a(flip),b,1331,a),flip(a)].">
      <j1 rule="hyper" parents="116 1720 1331"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1873">
    <literal><![CDATA[
      x \ ((x * R(x \ y,z,u)) * w) = w * R(w \ (x \ (y * w)),z,u)
    ]]></literal>
    <justification jstring="[hyper(116,a,1720,a(flip),b,1062,a(flip))].">
      <j1 rule="hyper" parents="116 1720 1062"/>
    </justification>
  </clause>

  <clause id="1874">
    <literal><![CDATA[
      (x * R(x \ (x * y),z,u)) * y = (x * y) * R(y,z,u)
    ]]></literal>
    <justification jstring="[para(4(a,1),1720(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4 1720"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1875">
    <literal><![CDATA[
      (x * R(y,z,u)) * y = (x * y) * R(y,z,u)
    ]]></literal>
    <justification jstring="[para(4(a,1),1874(a,1,1,2,1))].">
      <j1 rule="para" parents="4 1874"/>
    </justification>
  </clause>

  <clause id="1876">
    <literal><![CDATA[
      (1 / R(x,y,z)) * x = x / R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(414,a,1875,a),flip(a)].">
      <j1 rule="hyper" parents="414 1875"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1877">
    <literal><![CDATA[
      ((x / R(y,z,u)) * y) * R(y,z,u) = x * y
    ]]></literal>
    <justification jstring="[hyper(326,a,1875,a),flip(a)].">
      <j1 rule="hyper" parents="326 1875"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1878">
    <literal><![CDATA[
      (x * R(y,z,u)) \ ((x * y) * R(y,z,u)) = y
    ]]></literal>
    <justification jstring="[hyper(123,a,1875,a)].">
      <j1 rule="hyper" parents="123 1875"/>
    </justification>
  </clause>

  <clause id="1879">
    <literal><![CDATA[
      (x * R(y,z,u)) / y = (x / y) * R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(117,a,147,a(flip),b,1875,a)].">
      <j1 rule="hyper" parents="117 147 1875"/>
    </justification>
  </clause>

  <clause id="1880">
    <literal><![CDATA[
      (1 / x) * R(x,y,z) = R(x,y,z) / x
    ]]></literal>
    <justification jstring="[hyper(117,a,73,a(flip),b,1875,a),flip(a)].">
      <j1 rule="hyper" parents="117 73 1875"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1881">
    <literal><![CDATA[
      ((x / y) * R(y,z,u)) \ (x * R(y,z,u)) = y
    ]]></literal>
    <justification jstring="[hyper(116,a,147,a(flip),b,1875,a)].">
      <j1 rule="hyper" parents="116 147 1875"/>
    </justification>
  </clause>

  <clause id="1882">
    <literal><![CDATA[
      (x / R(x,y,z)) / x = 1 / R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(131,a,1876,a)].">
      <j1 rule="hyper" parents="131 1876"/>
    </justification>
  </clause>

  <clause id="1883">
    <literal><![CDATA[
      R(1 / (1 / x),y,z) * (1 / x) = R(x,y,z) / x
    ]]></literal>
    <justification jstring="[hyper(922,a,1880,a)].">
      <j1 rule="hyper" parents="922 1880"/>
    </justification>
  </clause>

  <clause id="1884">
    <literal><![CDATA[
      (R(x,y,z) / x) / R(x,y,z) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(131,a,1880,a)].">
      <j1 rule="hyper" parents="131 1880"/>
    </justification>
  </clause>

  <clause id="1885">
    <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(1880(a,1),240(a,2)),flip(a)].">
      <j1 rule="para" parents="1880 240"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1886">
    <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(1880(a,1),92(a,2,1))].">
      <j1 rule="para" parents="1880 92"/>
    </justification>
  </clause>

  <clause id="1887">
    <literal><![CDATA[
      (1 / R(x,y,z)) * x != u
    ]]></literal>
    <literal><![CDATA[
      x / R(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(1882(a,1),251(a,1,1)),flip(b)].">
      <j1 rule="para" parents="1882 251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1888">
    <literal><![CDATA[
      (1 / x) * R(x,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) / x = u
    ]]></literal>
    <justification jstring="[para(1884(a,1),251(a,1,1)),flip(b)].">
      <j1 rule="para" parents="1884 251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1889">
    <literal><![CDATA[
      (x * y) / R(y,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      (x / R(y,z,u)) * y = w
    ]]></literal>
    <justification jstring="[para(1877(a,1),327(a,1,1)),flip(b)].">
      <j1 rule="para" parents="1877 327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1890">
    <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(1877(a,1),804(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1877 804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1891">
    <literal><![CDATA[
      R(T(x,y * R(x,z,u)),y,R(x,z,u)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(1878(a,1),1096(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1878 1096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1892">
    <literal><![CDATA[
      (x * R(y / x,z,u)) \ (y * R(y / x,z,u)) = T(y / x,x)
    ]]></literal>
    <justification jstring="[hyper(936,a,1891,a)].">
      <j1 rule="hyper" parents="936 1891"/>
    </justification>
  </clause>

  <clause id="1893">
    <literal><![CDATA[
      (x * R(y,z,u)) * T(y,x) = (y * x) * R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(119,a,1891,a(flip),b,631,a)].">
      <j1 rule="hyper" parents="119 1891 631"/>
    </justification>
  </clause>

  <clause id="1894">
    <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,1891,a(flip),b,110,a),flip(a)].">
      <j1 rule="hyper" parents="119 1891 110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1895">
    <literal><![CDATA[
      (1 / x) * R((1 / x) \ 1,y,z) = R(x,y,z) / x
    ]]></literal>
    <justification jstring="[hyper(867,a,1883,a)].">
      <j1 rule="hyper" parents="867 1883"/>
    </justification>
  </clause>

  <clause id="1896">
    <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,1893,a)].">
      <j1 rule="hyper" parents="117 64 1893"/>
    </justification>
  </clause>

  <clause id="1897">
    <literal><![CDATA[
      R(x,y,z) / ((x \ 1) \ 1) = (x \ 1) * R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(675,a,1896,a)].">
      <j1 rule="hyper" parents="675 1896"/>
    </justification>
  </clause>

  <clause id="1898">
    <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),1871(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="17 1871"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1899">
    <literal><![CDATA[
      x \ T(x * R(x \ y,z,u),x) = R(x \ T(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(770,a,1898,a)].">
      <j1 rule="hyper" parents="770 1898"/>
    </justification>
  </clause>

  <clause id="1900">
    <literal><![CDATA[
      T(x * R(x \ y,z,u),x) / x = R(T(y,x) / x,z,u)
    ]]></literal>
    <justification jstring="[hyper(117,a,1898,a,b,640,a)].">
      <j1 rule="hyper" parents="117 1898 640"/>
    </justification>
  </clause>

  <clause id="1901">
    <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),1900(a,1,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4 1900"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1902">
    <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),1890(a,2,1))].">
      <j1 rule="para" parents="2 1890"/>
    </justification>
  </clause>

  <clause id="1903">
    <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,1892,a),flip(a)].">
      <j1 rule="hyper" parents="320 107 1892"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1904">
    <literal><![CDATA[
      (x * ((y * (x \ 1)) / y)) * x = x * (x * ((y * (x \ 1)) / y))
    ]]></literal>
    <justification jstring="[hyper(58,a,1097,a(flip),b,1721,a),flip(a)].">
      <j1 rule="hyper" parents="58 1097 1721"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1905">
    <literal><![CDATA[
      (x * (((x * y) * (x \ 1)) / (x * y))) * y = (x * y) * (y / (x * y))
    ]]></literal>
    <justification jstring="[para(5(a,1),1721(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 1721"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1906">
    <literal><![CDATA[
      (1 / x) * ((1 / x) * ((y * ((1 / x) \ 1)) / y)) = (((y * x) / y) / x) * (1 / x)
    ]]></literal>
    <justification jstring="[para(1471(a,1),1904(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1471 1904"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1907">
    <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(1722(a,2),45(a,1)),flip(a)].">
      <j1 rule="para" parents="1722 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1908">
    <literal><![CDATA[
      (x * L(x \ (y * z),u,w)) / z = (x / z) * L((x / z) \ y,u,w)
    ]]></literal>
    <justification jstring="[hyper(131,a,1723,a)].">
      <j1 rule="hyper" parents="131 1723"/>
    </justification>
  </clause>

  <clause id="1909">
    <literal><![CDATA[
      ((x / y) * L((x / y) \ 1,z,u)) * y = x * L(x \ y,z,u)
    ]]></literal>
    <justification jstring="[para(2(a,1),1723(a,2,2,1,2))].">
      <j1 rule="para" parents="2 1723"/>
    </justification>
  </clause>

  <clause id="1910">
    <literal><![CDATA[
      (x / y) * L((x / y) \ 1,z,u) = (x * L(x \ y,z,u)) / y
    ]]></literal>
    <justification jstring="[hyper(131,a,1909,a),flip(a)].">
      <j1 rule="hyper" parents="131 1909"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1911">
    <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),1910(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15 1910"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1912">
    <literal><![CDATA[
      x \ y != z * ((u * (z \ 1)) / u)
    ]]></literal>
    <literal><![CDATA[
      x * K(u,(u / z) / u) = y
    ]]></literal>
    <justification jstring="[para(1726(a,1),582(a,1)),flip(a)].">
      <j1 rule="para" parents="1726 582"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1913">
    <literal><![CDATA[
      R(T(x,y),z,u) * (x * w) = x * (R(T(x,y),z,u) * w)
    ]]></literal>
    <justification jstring="[para(1115(a,1),1748(a,1,1,1))].">
      <j1 rule="para" parents="1115 1748"/>
    </justification>
  </clause>

  <clause id="1914">
    <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,1913,a)].">
      <j1 rule="hyper" parents="116 151 1913"/>
    </justification>
  </clause>

  <clause id="1915">
    <literal><![CDATA[
      K(T(x \ 1,x) \ 1,T(x \ 1,(x \ 1) \ 1)) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(1264(a,1),1847(a,1,1))].">
      <j1 rule="para" parents="1264 1847"/>
    </justification>
  </clause>

  <clause id="1916">
    <literal><![CDATA[
      K(T(x \ 1,x) \ 1,T(x \ 1,x)) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(1263(a,1),1915(a,1,2))].">
      <j1 rule="para" parents="1263 1915"/>
    </justification>
  </clause>

  <clause id="1917">
    <literal><![CDATA[
      K(T(x,x \ 1),T(x \ 1,x)) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,1830,a(flip),b,1916,a)].">
      <j1 rule="hyper" parents="58 1830 1916"/>
    </justification>
  </clause>

  <clause id="1918">
    <literal><![CDATA[
      K(T(x,x \ 1),T(x,x \ 1) \ 1) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(1257(a,2),1917(a,1,2))].">
      <j1 rule="para" parents="1257 1917"/>
    </justification>
  </clause>

  <clause id="1919">
    <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(1918(a,1),1859(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1918 1859"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1920">
    <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(1795(a,1),1868(a,2,2))].">
      <j1 rule="para" parents="1795 1868"/>
    </justification>
  </clause>

  <clause id="1921">
    <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),1869(a,1,2,2,1,2))].">
      <j1 rule="para" parents="184 1869"/>
    </justification>
  </clause>

  <clause id="1922">
    <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(1873(a,1),255(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1873 255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1923">
    <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),1908(a,1,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="7 1908"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1924">
    <literal><![CDATA[
      (x * L(x \ (y * x),z,u)) / y = (x / y) * L(T(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(1504(a,2),1923(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1504 1923"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1925">
    <literal><![CDATA[
      (x / y) * L(T(y,x),z,u) = (L(y,z,u) * x) / y
    ]]></literal>
    <justification jstring="[para(634(a,1),1924(a,1,1)),flip(a)].">
      <j1 rule="para" parents="634 1924"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1926">
    <literal><![CDATA[
      (L(x,y,z) * (u * x)) / x = u * L(T(x,u * x),y,z)
    ]]></literal>
    <justification jstring="[para(6(a,1),1925(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6 1925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1927">
    <literal><![CDATA[
      T(x * L(T(y,x * y),z,u),y) = y \ (L(y,z,u) * (x * y))
    ]]></literal>
    <justification jstring="[para(1926(a,1),107(a,1,1))].">
      <j1 rule="para" parents="1926 107"/>
    </justification>
  </clause>

  <clause id="1928">
    <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,1420,a(flip),b,1927,a),flip(a)].">
      <j1 rule="hyper" parents="320 1420 1927"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1929">
    <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="1930">
    <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),401(a,1,1)),flip(a)].">
      <j1 rule="para" parents="501 401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1931">
    <literal><![CDATA[
      L(a(x,y,z),u,w) \ a(x,y,z) = a(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(897,a,1929,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="897 1929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1932">
    <literal><![CDATA[
      L(K(x,y),z,u) \ K(x,y) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(704,a,1929,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="704 1929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1933">
    <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),1929(a,2,2))].">
      <j1 rule="para" parents="13 1929"/>
    </justification>
  </clause>

  <clause id="1934">
    <literal><![CDATA[
      L(K(x,y),z,u) * a(u,z,K(x,y)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(134,a,1932,a)].">
      <j1 rule="hyper" parents="134 1932"/>
    </justification>
  </clause>

  <clause id="1935">
    <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(1932(a,1),340(a,2,2))].">
      <j1 rule="para" parents="1932 340"/>
    </justification>
  </clause>

  <clause id="1936">
    <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,1931,a)].">
      <j1 rule="hyper" parents="134 1931"/>
    </justification>
  </clause>

  <clause id="1937">
    <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(1931(a,1),503(a,1,1,1))].">
      <j1 rule="para" parents="1931 503"/>
    </justification>
  </clause>

  <clause id="1938">
    <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(1933(a,2),795(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1933 795"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1939">
    <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="1940">
    <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(924(a,1),1597(a,1))].">
      <j1 rule="para" parents="924 1597"/>
    </justification>
  </clause>

  <clause id="1941">
    <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),1680(a,2,2))].">
      <j1 rule="para" parents="529 1680"/>
    </justification>
  </clause>

  <clause id="1942">
    <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),1941(a,2,2,1))].">
      <j1 rule="para" parents="2 1941"/>
    </justification>
  </clause>

  <clause id="1943">
    <literal><![CDATA[
      (T(x,T(x,y) \ 1) / x) * x = T(x,x / (x * T(x,y)))
    ]]></literal>
    <justification jstring="[para(1598(a,1),1942(a,1,1))].">
      <j1 rule="para" parents="1598 1942"/>
    </justification>
  </clause>

  <clause id="1944">
    <literal><![CDATA[
      T(x,x / (x * T(x,y))) = T(x,T(x,y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(252,a,1943,a),flip(a)].">
      <j1 rule="hyper" parents="252 1943"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1946">
    <literal><![CDATA[
      x * (T(x,T(x,y) \ 1) / x) = T(x,T(x,y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,1665,a,b,1944,a)].">
      <j1 rule="hyper" parents="58 1665 1944"/>
    </justification>
  </clause>

  <clause id="1947">
    <literal><![CDATA[
      x * (T(x,y) * ((T(x,y) \ x) / x)) = T(x,T(x,y) \ 1)
    ]]></literal>
    <justification jstring="[para(1598(a,2),1946(a,1,2))].">
      <j1 rule="para" parents="1598 1946"/>
    </justification>
  </clause>

  <clause id="1948">
    <literal><![CDATA[
      L(x \ L(y,1 / x,K(x \ 1,x)),x,x \ 1) = (1 / x) * y
    ]]></literal>
    <justification jstring="[hyper(1103,a,1809,a(flip))].">
      <j1 rule="hyper" parents="1103 1809"/>
    </justification>
  </clause>

  <clause id="1949">
    <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),1940(a,1,2,2,1,2,2))].">
      <j1 rule="para" parents="5 1940"/>
    </justification>
  </clause>

  <clause id="1950">
    <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(1501(a,1),1161(a,1,2,1))].">
      <j1 rule="para" parents="1501 1161"/>
    </justification>
  </clause>

  <clause id="1951">
    <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,1950,a)].">
      <j1 rule="hyper" parents="134 1950"/>
    </justification>
  </clause>

  <clause id="1952">
    <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,1427,a(flip),b,1951,a),flip(a)].">
      <j1 rule="hyper" parents="58 1427 1951"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1953">
    <literal><![CDATA[
      (1 / x) \ L((y * x) \ y,z,u) = L((y * x) \ y,z,u) * x
    ]]></literal>
    <justification jstring="[hyper(921,a,1203,a),flip(a)].">
      <j1 rule="hyper" parents="921 1203"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1954">
    <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(1573(a,1),1214(a,1,1))].">
      <j1 rule="para" parents="1573 1214"/>
    </justification>
  </clause>

  <clause id="1955">
    <literal><![CDATA[
      L(x \ 1,R(x,y,z),1 / x) = (x \ R(x,y,z)) / R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(860,a,1954,a)].">
      <j1 rule="hyper" parents="860 1954"/>
    </justification>
  </clause>

  <clause id="1956">
    <literal><![CDATA[
      ((x * ((y \ x) \ z)) / z) * (y \ z) = y \ (x * ((y \ x) \ z))
    ]]></literal>
    <justification jstring="[para(5(a,1),1329(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 1329"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1958">
    <literal><![CDATA[
      x * ((x * y) * ((z * ((x * y) \ y)) / z)) = (x * ((z * (x \ 1)) / z)) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,1721,a(flip),b,1339,a),flip(a)].">
      <j1 rule="hyper" parents="58 1721 1339"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1959">
    <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,1525,a,b,1347,a(flip))].">
      <j1 rule="hyper" parents="239 1525 1347"/>
    </justification>
  </clause>

  <clause id="1960">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ y,z) = T(x * T(x \ y,z),y)
    ]]></literal>
    <justification jstring="[hyper(239,a,1486,a(flip),b,1347,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="239 1486 1347"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1961">
    <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),1347(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11 1347"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1962">
    <literal><![CDATA[
      x * L(y,T(y,x) \ y,T(y,x)) = (y * x) * T(K(x,y),y)
    ]]></literal>
    <justification jstring="[para(1145(a,1),1961(a,1,2))].">
      <j1 rule="para" parents="1145 1961"/>
    </justification>
  </clause>

  <clause id="1963">
    <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),1959(a,1,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="225 1959"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1964">
    <literal><![CDATA[
      L(L(x,L(y,z,u) \ 1,y),L(y,z,u) \ y,L(y,z,u)) = y \ (L(y,z,u) * (y * ((L(y,z,u) \ 1) * x)))
    ]]></literal>
    <justification jstring="[para(1417(a,1),490(a,1,1))].">
      <j1 rule="para" parents="1417 490"/>
    </justification>
  </clause>

  <clause id="1965">
    <literal><![CDATA[
      T(x * ((x * R(x \ 1,y,z)) / x),x) = x * R(1 / x,y,z)
    ]]></literal>
    <justification jstring="[para(645(a,1),1575(a,2,2))].">
      <j1 rule="para" parents="645 1575"/>
    </justification>
  </clause>

  <clause id="1966">
    <literal><![CDATA[
      T(x * R(1 / x,y,z),x) = x * R(1 / x,y,z)
    ]]></literal>
    <justification jstring="[para(645(a,1),1965(a,1,1,2))].">
      <j1 rule="para" parents="645 1965"/>
    </justification>
  </clause>

  <clause id="1967">
    <literal><![CDATA[
      T(x * (y / (x * y)),x) = x * R(1 / x,x,y)
    ]]></literal>
    <justification jstring="[para(219(a,1),1966(a,1,1,2))].">
      <j1 rule="para" parents="219 1966"/>
    </justification>
  </clause>

  <clause id="1968">
    <literal><![CDATA[
      T(x * (y / (x * y)),x) = x * (y / (x * y))
    ]]></literal>
    <justification jstring="[hyper(320,a,403,a(flip),b,1967,a),flip(a)].">
      <j1 rule="hyper" parents="320 403 1967"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1969">
    <literal><![CDATA[
      T(x,y / (x * y)) * R(x \ 1,x,y) = x * (y / (x * y))
    ]]></literal>
    <justification jstring="[hyper(58,a,1714,a,b,1968,a)].">
      <j1 rule="hyper" parents="58 1714 1968"/>
    </justification>
  </clause>

  <clause id="1970">
    <literal><![CDATA[
      T(x,x * (y / (x * y))) = x
    ]]></literal>
    <justification jstring="[hyper(49,a,1968,a)].">
      <j1 rule="hyper" parents="49 1968"/>
    </justification>
  </clause>

  <clause id="1971">
    <literal><![CDATA[
      T(x / y,(x / y) * (y / x)) = x / y
    ]]></literal>
    <justification jstring="[para(7(a,1),1970(a,1,2,2,2))].">
      <j1 rule="para" parents="7 1970"/>
    </justification>
  </clause>

  <clause id="1972">
    <literal><![CDATA[
      T(x \ y,(y / x) * (x / y)) = T(y / x,x)
    ]]></literal>
    <justification jstring="[para(1971(a,1),246(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1971 246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1973">
    <literal><![CDATA[
      T(x \ y,(y / x) * (x / y)) = x \ y
    ]]></literal>
    <justification jstring="[hyper(320,a,107,a(flip),b,1972,a),flip(a)].">
      <j1 rule="hyper" parents="320 107 1972"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1974">
    <literal><![CDATA[
      K(((x / y) * (y / x)) \ (x / y),(x / y) * (y / x)) = (y * (y \ x)) / x
    ]]></literal>
    <justification jstring="[para(1973(a,1),1590(a,2,1,2))].">
      <j1 rule="para" parents="1973 1590"/>
    </justification>
  </clause>

  <clause id="1975">
    <literal><![CDATA[
      K(x \ (x / ((y \ x) / T(x,y))),x) = x / T(x,y)
    ]]></literal>
    <justification jstring="[hyper(338,a,1592,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="338 1592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1976">
    <literal><![CDATA[
      (x \ T(x * (y / z),z)) * z = (x \ 1) * ((z \ ((x \ 1) \ y)) * z)
    ]]></literal>
    <justification jstring="[para(105(a,1),1600(a,1,2)),flip(a)].">
      <j1 rule="para" parents="105 1600"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1977">
    <literal><![CDATA[
      (x \ T(x * (y / y),z)) * y = (x \ 1) * ((x \ T(x,z)) * ((x \ 1) \ y))
    ]]></literal>
    <justification jstring="[para(1304(a,2),1600(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1304 1600"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1978">
    <literal><![CDATA[
      T((x \ (x * (y / x))) * x,x) = (x \ 1) * ((x \ ((x \ 1) \ y)) * x)
    ]]></literal>
    <justification jstring="[hyper(1384,a,1976,a)].">
      <j1 rule="hyper" parents="1384 1976"/>
    </justification>
  </clause>

  <clause id="1979">
    <literal><![CDATA[
      T(x,y) = (y \ 1) * ((y \ ((y \ 1) \ x)) * y)
    ]]></literal>
    <justification jstring="[para(76(a,1),1978(a,1,1))].">
      <j1 rule="para" parents="76 1978"/>
    </justification>
  </clause>

  <clause id="1980">
    <literal><![CDATA[
      (x \ ((x \ 1) \ y)) * x = (x \ 1) \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(770,a,1979,a),flip(a)].">
      <j1 rule="hyper" parents="770 1979"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1981">
    <literal><![CDATA[
      (x \ 1) * ((x \ y) * x) = T((x \ 1) * y,x)
    ]]></literal>
    <justification jstring="[para(4(a,1),1979(a,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="4 1979"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1982">
    <literal><![CDATA[
      T((x \ 1) * (x * y),x) = (x \ 1) * (y * x)
    ]]></literal>
    <justification jstring="[para(62(a,1),1979(a,2,2,1))].">
      <j1 rule="para" parents="62 1979"/>
    </justification>
  </clause>

  <clause id="1983">
    <literal><![CDATA[
      ((x \ 1) * y) \ T((x \ 1) * y,x) = L(K(x \ y,x),y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(116,a,1981,a(flip),b,487,a)].">
      <j1 rule="hyper" parents="116 1981 487"/>
    </justification>
  </clause>

  <clause id="1984">
    <literal><![CDATA[
      T(((x / y) \ 1) * x,x / y) = ((x / y) \ 1) * (y * (x / y))
    ]]></literal>
    <justification jstring="[para(75(a,1),1981(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="75 1981"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1985">
    <literal><![CDATA[
      T((x \ 1) * ((y \ x) * y),x) = (x \ 1) * (K(y \ x,y) * x)
    ]]></literal>
    <justification jstring="[para(85(a,1),1981(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="85 1981"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1986">
    <literal><![CDATA[
      ((x \ 1) * (x * y)) * x = x * ((x \ 1) * (y * x))
    ]]></literal>
    <justification jstring="[hyper(119,a,1982,a(flip),b,17,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 1982 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1987">
    <literal><![CDATA[
      ((x \ 1) * (x * y)) * x = L(y * x,x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,257,a(flip),b,1986,a),flip(a)].">
      <j1 rule="hyper" parents="320 257 1986"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1988">
    <literal><![CDATA[
      x * ((x \ y) * ((z * ((x \ y) \ 1)) / z)) = y * ((z * (y \ x)) / z)
    ]]></literal>
    <justification jstring="[para(3(a,1),1615(a,2,2,1,2,2))].">
      <j1 rule="para" parents="3 1615"/>
    </justification>
  </clause>

  <clause id="1989">
    <literal><![CDATA[
      (x \ y) * ((z * ((x \ y) \ 1)) / z) = x \ (y * ((z * (y \ x)) / z))
    ]]></literal>
    <justification jstring="[hyper(123,a,1988,a),flip(a)].">
      <j1 rule="hyper" parents="123 1988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1990">
    <literal><![CDATA[
      x * K(y,(y / (x \ z)) / y) = z * ((y * (z \ x)) / y)
    ]]></literal>
    <justification jstring="[para(1725(a,2),1988(a,1,2))].">
      <j1 rule="para" parents="1725 1988"/>
    </justification>
  </clause>

  <clause id="1991">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ y)) / z) = y * K(z,(z / T(x,y)) / z)
    ]]></literal>
    <justification jstring="[para(17(a,2),1990(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="17 1990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1992">
    <literal><![CDATA[
      T(x * ((y * (x \ 1)) / y),z) = K(y,(y / T(x,z)) / y)
    ]]></literal>
    <justification jstring="[hyper(239,a,1721,a(flip),b,1991,a(flip))].">
      <j1 rule="hyper" parents="239 1721 1991"/>
    </justification>
  </clause>

  <clause id="1993">
    <literal><![CDATA[
      T(x,y) * ((z * (T(x,y) \ 1)) / z) = T(x * ((z * (x \ 1)) / z),y)
    ]]></literal>
    <justification jstring="[hyper(320,a,1725,a(flip),b,1992,a)].">
      <j1 rule="hyper" parents="320 1725 1992"/>
    </justification>
  </clause>

  <clause id="1994">
    <literal><![CDATA[
      K(x,(x / T(y \ x,z)) / x) = T(K(x,y / x),z)
    ]]></literal>
    <justification jstring="[para(1731(a,1),1992(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1731 1992"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1995">
    <literal><![CDATA[
      T(K(x,y / x),K(y / x,z)) = K(x,(x / (y \ x)) / x)
    ]]></literal>
    <justification jstring="[para(1363(a,1),1994(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="1363 1994"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1996">
    <literal><![CDATA[
      T(K(x,y / x),K(y / x,z)) = K(x,y / x)
    ]]></literal>
    <justification jstring="[para(72(a,1),1995(a,2,2,1))].">
      <j1 rule="para" parents="72 1995"/>
    </justification>
  </clause>

  <clause id="1998">
    <literal><![CDATA[
      T(K(x,y),K((y * x) / x,z)) = K(x,(y * x) / x)
    ]]></literal>
    <justification jstring="[para(6(a,1),1996(a,1,1,2))].">
      <j1 rule="para" parents="6 1996"/>
    </justification>
  </clause>

  <clause id="1999">
    <literal><![CDATA[
      T(K(x,y),K(y,z)) = K(x,(y * x) / x)
    ]]></literal>
    <justification jstring="[para(6(a,1),1998(a,1,2,1))].">
      <j1 rule="para" parents="6 1998"/>
    </justification>
  </clause>

  <clause id="2000">
    <literal><![CDATA[
      T(K(x,y),K(y,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(6(a,1),1999(a,2,2))].">
      <j1 rule="para" parents="6 1999"/>
    </justification>
  </clause>

  <clause id="2001">
    <literal><![CDATA[
      K(K(x,y),K(y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(50,a,2000,a)].">
      <j1 rule="hyper" parents="50 2000"/>
    </justification>
  </clause>

  <clause id="2002">
    <literal><![CDATA[
      T(K(x,y),K(z,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(49,a,2000,a)].">
      <j1 rule="hyper" parents="49 2000"/>
    </justification>
  </clause>

  <clause id="2003">
    <literal><![CDATA[
      K(x,y) * K(z,x) = K(z,x) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,2000,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 2000 17"/>
    </justification>
  </clause>

  <clause id="2004">
    <literal><![CDATA[
      T(x,K(y,z)) != K(u,y)
    ]]></literal>
    <literal><![CDATA[
      K(u,y) = x
    ]]></literal>
    <justification jstring="[para(2000(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="2000 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2005">
    <literal><![CDATA[
      K(x,y) * K(z,x) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,x) * K(x,y) = u
    ]]></literal>
    <justification jstring="[para(2000(a,1),284(a,1,2))].">
      <j1 rule="para" parents="2000 284"/>
    </justification>
  </clause>

  <clause id="2006">
    <literal><![CDATA[
      L(K(x,y),z,u) * K(y,w) = K(y,w) * L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(2000(a,1),237(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2000 237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2007">
    <literal><![CDATA[
      R(K(x,y),z,u) * K(y,w) = K(y,w) * R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(2000(a,1),238(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2000 238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2008">
    <literal><![CDATA[
      T(x,K(y,z)) != K(z,u)
    ]]></literal>
    <literal><![CDATA[
      K(z,u) = x
    ]]></literal>
    <justification jstring="[para(2002(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="2002 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2009">
    <literal><![CDATA[
      K(x,y) * K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) * K(x,y) = u
    ]]></literal>
    <justification jstring="[para(2002(a,1),284(a,1,2))].">
      <j1 rule="para" parents="2002 284"/>
    </justification>
  </clause>

  <clause id="2010">
    <literal><![CDATA[
      L(K(x,y),z,u) * K(w,x) = K(w,x) * L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(2002(a,1),237(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2002 237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2011">
    <literal><![CDATA[
      R(K(x,y),z,u) * K(w,x) = K(w,x) * R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(2002(a,1),238(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2002 238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2012">
    <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(2002(a,1),580(a,2,2))].">
      <j1 rule="para" parents="2002 580"/>
    </justification>
  </clause>

  <clause id="2013">
    <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(2002(a,1),419(a,1,2,1))].">
      <j1 rule="para" parents="2002 419"/>
    </justification>
  </clause>

  <clause id="2014">
    <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),1993(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 1993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2015">
    <literal><![CDATA[
      T(x,y) * ((x * (T(x,y) \ 1)) / x) = T(x * (1 / x),y)
    ]]></literal>
    <justification jstring="[para(5(a,1),1993(a,2,1,2,1))].">
      <j1 rule="para" parents="5 1993"/>
    </justification>
  </clause>

  <clause id="2016">
    <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),1993(a,2,1,2,1)),flip(a)].">
      <j1 rule="para" parents="455 1993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2017">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) \ x) / x) = T(x * (1 / x),y)
    ]]></literal>
    <justification jstring="[para(1118(a,1),2015(a,1,2,1))].">
      <j1 rule="para" parents="1118 2015"/>
    </justification>
  </clause>

  <clause id="2018">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) \ x) / x) = T(K(x,x \ 1),y)
    ]]></literal>
    <justification jstring="[para(1794(a,2),2017(a,2,1))].">
      <j1 rule="para" parents="1794 2017"/>
    </justification>
  </clause>

  <clause id="2019">
    <literal><![CDATA[
      x * T(K(x,x \ 1),y) = T(x,T(x,y) \ 1)
    ]]></literal>
    <justification jstring="[para(2018(a,1),1947(a,1,2))].">
      <j1 rule="para" parents="2018 1947"/>
    </justification>
  </clause>

  <clause id="2020">
    <literal><![CDATA[
      T(x,T(x,y) \ 1) != x * z
    ]]></literal>
    <literal><![CDATA[
      T(K(x,x \ 1),y) = z
    ]]></literal>
    <justification jstring="[para(2019(a,1),38(a,1))].">
      <j1 rule="para" parents="2019 38"/>
    </justification>
  </clause>

  <clause id="2021">
    <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,1794,a,b,2014,a),flip(a)].">
      <j1 rule="hyper" parents="320 1794 2014"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2022">
    <literal><![CDATA[
      K(T(x,y),T(x,y) \ 1) = T(K(T(x,y),1 / x),y)
    ]]></literal>
    <justification jstring="[para(1732(a,1),2021(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1732 2021"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2023">
    <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(2022(a,2),44(a,1)),flip(a)].">
      <j1 rule="para" parents="2022 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2024">
    <literal><![CDATA[
      (x \ y) * ((z * ((x \ y) \ (x \ u))) / z) = x \ (y * ((z * (y \ u)) / z))
    ]]></literal>
    <justification jstring="[para(5(a,1),1616(a,1,2,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5 1616"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2025">
    <literal><![CDATA[
      (x * R(x \ 1,y,z)) * (x * u) = x * ((x * R(x \ 1,y,z)) * u)
    ]]></literal>
    <justification jstring="[para(1524(a,1),1632(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1524 1632"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2026">
    <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(1207(a,1),2025(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1207 2025"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2027">
    <literal><![CDATA[
      R(x,y,z) * (T(x,u) \ 1) = T(x,u) \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(5(a,1),1690(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 1690"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2028">
    <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(1147(a,1),1735(a,1,2,1))].">
      <j1 rule="para" parents="1147 1735"/>
    </justification>
  </clause>

  <clause id="2029">
    <literal><![CDATA[
      (x * (y * L(y \ 1,z,u))) * y = (x * y) * (y * L(y \ 1,z,u))
    ]]></literal>
    <justification jstring="[para(918(a,1),1750(a,1,1))].">
      <j1 rule="para" parents="918 1750"/>
    </justification>
  </clause>

  <clause id="2030">
    <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,2029,a)].">
      <j1 rule="hyper" parents="117 147 2029"/>
    </justification>
  </clause>

  <clause id="2031">
    <literal><![CDATA[
      (x * y) * (y * L(y \ 1,y,1 / y)) = (x * (y * (1 / y))) * y
    ]]></literal>
    <justification jstring="[para(389(a,1),2029(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="389 2029"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2032">
    <literal><![CDATA[
      (x * (y * (1 / y))) * y = (x * y) * (y * (1 / y))
    ]]></literal>
    <justification jstring="[para(389(a,1),2031(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="389 2031"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2033">
    <literal><![CDATA[
      (x * K(y,y \ 1)) * y = (x * y) * (y * (1 / y))
    ]]></literal>
    <justification jstring="[para(1794(a,2),2032(a,1,1,2))].">
      <j1 rule="para" parents="1794 2032"/>
    </justification>
  </clause>

  <clause id="2034">
    <literal><![CDATA[
      (x * K(y,y \ 1)) * y = (x * y) * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[para(1794(a,2),2033(a,2,2))].">
      <j1 rule="para" parents="1794 2033"/>
    </justification>
  </clause>

  <clause id="2035">
    <literal><![CDATA[
      T((x / y) * K(y,y \ 1),y) = y \ (x * K(y,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(439,a,147,a(flip),b,2034,a)].">
      <j1 rule="hyper" parents="439 147 2034"/>
    </justification>
  </clause>

  <clause id="2036">
    <literal><![CDATA[
      (x * K(y,y \ 1)) \ ((x * y) * K(y,y \ 1)) = y
    ]]></literal>
    <justification jstring="[hyper(123,a,2034,a)].">
      <j1 rule="hyper" parents="123 2034"/>
    </justification>
  </clause>

  <clause id="2037">
    <literal><![CDATA[
      (x * K(y,y \ 1)) / y = (x / y) * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(117,a,147,a(flip),b,2034,a)].">
      <j1 rule="hyper" parents="117 147 2034"/>
    </justification>
  </clause>

  <clause id="2038">
    <literal><![CDATA[
      R(T(x,y * K(x,x \ 1)),y,K(x,x \ 1)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(2036(a,1),1096(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2036 1096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2039">
    <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(2037(a,1),420(a,1,1))].">
      <j1 rule="para" parents="2037 420"/>
    </justification>
  </clause>

  <clause id="2040">
    <literal><![CDATA[
      (x * L(x \ 1,y,z)) * (x * u) = x * ((x * L(x \ 1,y,z)) * u)
    ]]></literal>
    <justification jstring="[para(1752(a,1),1853(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1752 1853"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2041">
    <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,2040,a)].">
      <j1 rule="hyper" parents="116 151 2040"/>
    </justification>
  </clause>

  <clause id="2042">
    <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(605,a,2041,a)].">
      <j1 rule="hyper" parents="605 2041"/>
    </justification>
  </clause>

  <clause id="2043">
    <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(436(a,1),1863(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="436 1863"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2044">
    <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),1870(a,1,1))].">
      <j1 rule="para" parents="17 1870"/>
    </justification>
  </clause>

  <clause id="2045">
    <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),2044(a,1,2,1,1))].">
      <j1 rule="para" parents="17 2044"/>
    </justification>
  </clause>

  <clause id="2046">
    <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),2045(a,2,1,2,1))].">
      <j1 rule="para" parents="4 2045"/>
    </justification>
  </clause>

  <clause id="2047">
    <literal><![CDATA[
      K(((x / y) * (y / x)) \ (x / y),(x / y) * (y / x)) = x / x
    ]]></literal>
    <justification jstring="[hyper(338,a,1974,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="338 1974"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2048">
    <literal><![CDATA[
      K(((x / y) * (y / x)) \ (x / y),(x / y) * (y / x)) = 1
    ]]></literal>
    <justification jstring="[hyper(320,a,69,a(flip),b,2047,a),flip(a)].">
      <j1 rule="hyper" parents="320 69 2047"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2050">
    <literal><![CDATA[
      T(1 / (x / y),(y / x) * (x / y)) = 1 / (x / y)
    ]]></literal>
    <justification jstring="[para(2048(a,1),1035(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2048 1035"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2051">
    <literal><![CDATA[
      ((x / y) * (y / x)) \ (x / y) = 1 / (y / x)
    ]]></literal>
    <justification jstring="[hyper(58,a,1623,a(flip),b,2050,a)].">
      <j1 rule="hyper" parents="58 1623 2050"/>
    </justification>
  </clause>

  <clause id="2052">
    <literal><![CDATA[
      K(1 / (x / y),(y / x) * (x / y)) = 1
    ]]></literal>
    <justification jstring="[hyper(50,a,2050,a)].">
      <j1 rule="hyper" parents="50 2050"/>
    </justification>
  </clause>

  <clause id="2053">
    <literal><![CDATA[
      ((x / y) * (y / x)) * (1 / (y / x)) = x / y
    ]]></literal>
    <justification jstring="[hyper(119,a,2050,a(flip),b,1623,a(flip))].">
      <j1 rule="hyper" parents="119 2050 1623"/>
    </justification>
  </clause>

  <clause id="2054">
    <literal><![CDATA[
      K(1 / x,(y / (x * y)) * ((x * y) / y)) = 1
    ]]></literal>
    <justification jstring="[para(6(a,1),2052(a,1,1,2))].">
      <j1 rule="para" parents="6 2052"/>
    </justification>
  </clause>

  <clause id="2055">
    <literal><![CDATA[
      ((x * y) / y) * (y / (x * y)) = x / (1 / (y / (x * y)))
    ]]></literal>
    <justification jstring="[hyper(117,a,6,a(flip),b,2053,a),flip(a)].">
      <j1 rule="hyper" parents="117 6 2053"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2056">
    <literal><![CDATA[
      K(1 / x,(y / (x * y)) * x) = 1
    ]]></literal>
    <justification jstring="[para(6(a,1),2054(a,1,2,2))].">
      <j1 rule="para" parents="6 2054"/>
    </justification>
  </clause>

  <clause id="2057">
    <literal><![CDATA[
      T(1 / x,(y / (x * y)) * x) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(51,a,2056,a)].">
      <j1 rule="hyper" parents="51 2056"/>
    </justification>
  </clause>

  <clause id="2058">
    <literal><![CDATA[
      L(x \ 1,x,y / (x * y)) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(1691,a,2057,a)].">
      <j1 rule="hyper" parents="1691 2057"/>
    </justification>
  </clause>

  <clause id="2059">
    <literal><![CDATA[
      ((x / (y * x)) * y) * (1 / y) = x / (y * x)
    ]]></literal>
    <justification jstring="[hyper(119,a,2057,a(flip),b,1217,a)].">
      <j1 rule="hyper" parents="119 2057 1217"/>
    </justification>
  </clause>

  <clause id="2060">
    <literal><![CDATA[
      L(x \ 1,x,R(1 / x,x,y)) = 1 / x
    ]]></literal>
    <justification jstring="[para(219(a,2),2058(a,1,3))].">
      <j1 rule="para" parents="219 2058"/>
    </justification>
  </clause>

  <clause id="2061">
    <literal><![CDATA[
      R(1 / x,x,y) / (1 / x) = R(1 / x,x,y) * x
    ]]></literal>
    <justification jstring="[para(2060(a,1),396(a,1,2))].">
      <j1 rule="para" parents="2060 396"/>
    </justification>
  </clause>

  <clause id="2062">
    <literal><![CDATA[
      R(x \ 1,x,y) \ (y / (x * y)) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(2059(a,1),1802(a,1,2))].">
      <j1 rule="para" parents="2059 1802"/>
    </justification>
  </clause>

  <clause id="2063">
    <literal><![CDATA[
      x / (y * x) = R(y \ 1,y,x) * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(134,a,2062,a),flip(a)].">
      <j1 rule="hyper" parents="134 2062"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2064">
    <literal><![CDATA[
      T(1 / (1 / x),R(1 / x,x,y)) = x
    ]]></literal>
    <justification jstring="[hyper(1885,a,2061,a)].">
      <j1 rule="hyper" parents="1885 2061"/>
    </justification>
  </clause>

  <clause id="2065">
    <literal><![CDATA[
      T(1 / (1 / x),y / (x * y)) = x
    ]]></literal>
    <justification jstring="[para(219(a,1),2064(a,1,2))].">
      <j1 rule="para" parents="219 2064"/>
    </justification>
  </clause>

  <clause id="2066">
    <literal><![CDATA[
      T(x,y / (x * y)) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(2065(a,1),1784(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2065 1784"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2067">
    <literal><![CDATA[
      T(x,y / (x * y)) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(320,a,106,a(flip),b,2066,a),flip(a)].">
      <j1 rule="hyper" parents="320 106 2066"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2068">
    <literal><![CDATA[
      K((x / (y * x)) \ 1,x / (y * x)) * (y * x) = T(y,y \ 1) * x
    ]]></literal>
    <justification jstring="[para(2066(a,1),1593(a,2,1))].">
      <j1 rule="para" parents="2066 1593"/>
    </justification>
  </clause>

  <clause id="2069">
    <literal><![CDATA[
      T(x / y,y / x) = ((x / y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(7(a,1),2067(a,1,2,2))].">
      <j1 rule="para" parents="7 2067"/>
    </justification>
  </clause>

  <clause id="2070">
    <literal><![CDATA[
      x \ T(x,y / (x * y)) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,x \ 1) = z
    ]]></literal>
    <justification jstring="[para(2067(a,2),1835(a,1,2))].">
      <j1 rule="para" parents="2067 1835"/>
    </justification>
  </clause>

  <clause id="2071">
    <literal><![CDATA[
      T(x / (y * x),y) = ((x / (y * x)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(6(a,1),2069(a,1,2))].">
      <j1 rule="para" parents="6 2069"/>
    </justification>
  </clause>

  <clause id="2072">
    <literal><![CDATA[
      ((((x * y) / x) \ 1) \ 1) * x = x * T(y,x / (x * y))
    ]]></literal>
    <justification jstring="[para(2069(a,1),454(a,1,1))].">
      <j1 rule="para" parents="2069 454"/>
    </justification>
  </clause>

  <clause id="2073">
    <literal><![CDATA[
      R(x \ 1,x,y) = ((y / (x * y)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(58,a,646,a(flip),b,2071,a)].">
      <j1 rule="hyper" parents="58 646 2071"/>
    </justification>
  </clause>

  <clause id="2074">
    <literal><![CDATA[
      (R(1 / x,x,y) \ 1) \ 1 = R(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[para(219(a,2),2073(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="219 2073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2075">
    <literal><![CDATA[
      x / (1 / (y / (x * y))) = x * (y / (x * y))
    ]]></literal>
    <justification jstring="[para(6(a,1),2055(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6 2055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2076">
    <literal><![CDATA[
      K(x \ (x * (y / (x * y))),x) = R(x \ 1,x,y) / (y / (x * y))
    ]]></literal>
    <justification jstring="[para(2075(a,1),1033(a,1,1,2))].">
      <j1 rule="para" parents="2075 1033"/>
    </justification>
  </clause>

  <clause id="2077">
    <literal><![CDATA[
      T(x,((y * x) / y) \ 1) = T(x,y / (y * x))
    ]]></literal>
    <justification jstring="[hyper(952,a,2072,a)].">
      <j1 rule="hyper" parents="952 2072"/>
    </justification>
  </clause>

  <clause id="2078">
    <literal><![CDATA[
      R(x \ 1,x,y) / (y / (x * y)) = K(y / (x * y),x)
    ]]></literal>
    <justification jstring="[hyper(1359,a,2076,a),flip(a)].">
      <j1 rule="hyper" parents="1359 2076"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2080">
    <literal><![CDATA[
      K(x / (y * x),y) * (x / (y * x)) = R(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[hyper(133,a,2078,a)].">
      <j1 rule="hyper" parents="133 2078"/>
    </justification>
  </clause>

  <clause id="2082">
    <literal><![CDATA[
      (x \ 1) * ((x \ T(x,y)) * ((x \ 1) \ z)) = (x \ T(x * 1,y)) * z
    ]]></literal>
    <justification jstring="[para(69(a,1),1977(a,1,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="69 1977"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2083">
    <literal><![CDATA[
      (x \ 1) * ((x \ T(x,y)) * ((x \ 1) \ z)) = (x \ T(x,y)) * z
    ]]></literal>
    <justification jstring="[para(3(a,1),2082(a,2,1,2,1))].">
      <j1 rule="para" parents="3 2082"/>
    </justification>
  </clause>

  <clause id="2085">
    <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,2083,a),flip(a)].">
      <j1 rule="hyper" parents="115 5 2083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2086">
    <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),866(a,1,1)),flip(a)].">
      <j1 rule="para" parents="447 866"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2087">
    <literal><![CDATA[
      (T(x,y) * (1 / x)) / T(x,y) = L(1 / x,T(x,y),1 / x)
    ]]></literal>
    <justification jstring="[hyper(58,a,1255,a(flip),b,1016,a)].">
      <j1 rule="hyper" parents="58 1255 1016"/>
    </justification>
  </clause>

  <clause id="2089">
    <literal><![CDATA[
      T(L(1 / x,T(x,y),1 / x),x) = (T(x,y) * (x \ 1)) / T(x,y)
    ]]></literal>
    <justification jstring="[para(2087(a,1),679(a,1,1))].">
      <j1 rule="para" parents="2087 679"/>
    </justification>
  </clause>

  <clause id="2090">
    <literal><![CDATA[
      (T(x,y) * (x \ 1)) / T(x,y) = L(x \ 1,T(x,y),1 / x)
    ]]></literal>
    <justification jstring="[hyper(860,a,2089,a),flip(a)].">
      <j1 rule="hyper" parents="860 2089"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2091">
    <literal><![CDATA[
      x * L(x \ 1,T(x,y),1 / x) = K(T(x,y),1 / x)
    ]]></literal>
    <justification jstring="[para(2090(a,1),1732(a,1,2))].">
      <j1 rule="para" parents="2090 1732"/>
    </justification>
  </clause>

  <clause id="2092">
    <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(1398(a,1),288(a,1))].">
      <j1 rule="para" parents="1398 288"/>
    </justification>
  </clause>

  <clause id="2093">
    <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),1437(a,1,2,1,2,1))].">
      <j1 rule="para" parents="4 1437"/>
    </justification>
  </clause>

  <clause id="2094">
    <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,2093,a),flip(a)].">
      <j1 rule="hyper" parents="33 362 2093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2095">
    <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,1505,a),flip(a)].">
      <j1 rule="hyper" parents="320 449 1505"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2096">
    <literal><![CDATA[
      T(x,x * (y * T(y \ 1,x))) = x
    ]]></literal>
    <justification jstring="[para(2095(a,1),276(a,1,2))].">
      <j1 rule="para" parents="2095 276"/>
    </justification>
  </clause>

  <clause id="2097">
    <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(2095(a,1),1302(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2095 1302"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2098">
    <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(2095(a,1),1472(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2095 1472"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2099">
    <literal><![CDATA[
      T(x,x * K(y,x)) = x
    ]]></literal>
    <justification jstring="[para(1023(a,2),2096(a,1,2,2))].">
      <j1 rule="para" parents="1023 2096"/>
    </justification>
  </clause>

  <clause id="2100">
    <literal><![CDATA[
      T(x,x * (y \ (z * T(z \ y,x)))) = x
    ]]></literal>
    <justification jstring="[para(1427(a,1),2096(a,1,2,2))].">
      <j1 rule="para" parents="1427 2096"/>
    </justification>
  </clause>

  <clause id="2101">
    <literal><![CDATA[
      T(x * K(y,x),x) = x * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(49,a,2099,a)].">
      <j1 rule="hyper" parents="49 2099"/>
    </justification>
  </clause>

  <clause id="2102">
    <literal><![CDATA[
      T(x,x * (T(x,y) \ ((y \ x) * ((y \ x) \ x)))) = x
    ]]></literal>
    <justification jstring="[para(1167(a,1),2100(a,1,2,2,2,2))].">
      <j1 rule="para" parents="1167 2100"/>
    </justification>
  </clause>

  <clause id="2103">
    <literal><![CDATA[
      T(x,x * (T(x,y) \ x)) = x
    ]]></literal>
    <justification jstring="[para(5(a,1),2102(a,1,2,2,2))].">
      <j1 rule="para" parents="5 2102"/>
    </justification>
  </clause>

  <clause id="2104">
    <literal><![CDATA[
      T(T(x,y),x * (T(x,z) \ x)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(2103(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2103 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2105">
    <literal><![CDATA[
      (x * (T(x,y) \ x)) \ (x * x) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,1112,a(flip),b,2104,a)].">
      <j1 rule="hyper" parents="58 1112 2104"/>
    </justification>
  </clause>

  <clause id="2106">
    <literal><![CDATA[
      (x * x) / T(x,y) = x * (T(x,y) \ x)
    ]]></literal>
    <justification jstring="[hyper(197,a,2105,a)].">
      <j1 rule="hyper" parents="197 2105"/>
    </justification>
  </clause>

  <clause id="2107">
    <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(1674(a,1),2105(a,1,1,2,1))].">
      <j1 rule="para" parents="1674 2105"/>
    </justification>
  </clause>

  <clause id="2108">
    <literal><![CDATA[
      T(x / T(x,y),x) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(1497,a,2106,a)].">
      <j1 rule="hyper" parents="1497 2106"/>
    </justification>
  </clause>

  <clause id="2109">
    <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(2106(a,2),718(a,1,2))].">
      <j1 rule="para" parents="2106 718"/>
    </justification>
  </clause>

  <clause id="2110">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ x,x) = (T(x,y) \ x) * T(x,y)
    ]]></literal>
    <justification jstring="[para(2108(a,1),453(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2108 453"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2111">
    <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(1062(a,2),1922(a,1))].">
      <j1 rule="para" parents="1062 1922"/>
    </justification>
  </clause>

  <clause id="2112">
    <literal><![CDATA[
      (x * (((T(y,x) \ y) * x) \ x)) \ (x * x) = (T(y,x) \ y) * x
    ]]></literal>
    <justification jstring="[hyper(320,a,1674,a(flip),b,2107,a),flip(a)].">
      <j1 rule="hyper" parents="320 1674 2107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2113">
    <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),834(a,1))].">
      <j1 rule="para" parents="664 834"/>
    </justification>
  </clause>

  <clause id="2114">
    <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),915(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="105 915"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2115">
    <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,1524,a(flip),b,2114,a),flip(a)].">
      <j1 rule="hyper" parents="239 1524 2114"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2116">
    <literal><![CDATA[
      T(x * R(x \ 1,T(x,y),z),y) = (z / (T(x,y) * z)) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(653,a,2115,a),flip(a)].">
      <j1 rule="hyper" parents="653 2115"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2117">
    <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(993(a,1),2116(a,2,1,2))].">
      <j1 rule="para" parents="993 2116"/>
    </justification>
  </clause>

  <clause id="2118">
    <literal><![CDATA[
      ((x \ 1) / (x \ T(x,y))) * T(x,y) = T(x * T(x \ 1,T(x,y)),y)
    ]]></literal>
    <justification jstring="[para(1265(a,1),2117(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1265 2117"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2119">
    <literal><![CDATA[
      (x \ 1) / (x \ T(x,y)) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(30,a,1537,a(flip),b,2118,a),flip(a)].">
      <j1 rule="hyper" parents="30 1537 2118"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2120">
    <literal><![CDATA[
      T(T(x,y) \ 1,x \ T(x,y)) = (x \ T(x,y)) \ (x \ 1)
    ]]></literal>
    <justification jstring="[para(2119(a,1),107(a,1,1))].">
      <j1 rule="para" parents="2119 107"/>
    </justification>
  </clause>

  <clause id="2121">
    <literal><![CDATA[
      (x \ T(x,y)) \ (x \ 1) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(58,a,1580,a(flip),b,2120,a),flip(a)].">
      <j1 rule="hyper" parents="58 1580 2120"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2123">
    <literal><![CDATA[
      (x \ T(x,y)) * ((x \ 1) \ (T(x,y) \ 1)) = 1
    ]]></literal>
    <justification jstring="[para(2121(a,1),2085(a,1,2,2))].">
      <j1 rule="para" parents="2121 2085"/>
    </justification>
  </clause>

  <clause id="2124">
    <literal><![CDATA[
      (x \ 1) \ (T(x,y) \ 1) = (x \ T(x,y)) \ 1
    ]]></literal>
    <justification jstring="[hyper(123,a,2123,a),flip(a)].">
      <j1 rule="hyper" parents="123 2123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2125">
    <literal><![CDATA[
      ((x * ((y \ z) / z)) / x) * z = (((x * (1 / y)) / x) * y) * (y \ z)
    ]]></literal>
    <justification jstring="[para(5(a,1),1099(a,1,1,1,2,2))].">
      <j1 rule="para" parents="5 1099"/>
    </justification>
  </clause>

  <clause id="2126">
    <literal><![CDATA[
      (((x * ((y \ z) / z)) / x) * z) / (y \ z) = ((x * (1 / y)) / x) * y
    ]]></literal>
    <justification jstring="[hyper(537,a,2125,a)].">
      <j1 rule="hyper" parents="537 2125"/>
    </justification>
  </clause>

  <clause id="2127">
    <literal><![CDATA[
      (((x * ((y \ z) / z)) / x) * z) / (y \ z) != u
    ]]></literal>
    <literal><![CDATA[
      ((x * (1 / y)) / x) * y = u
    ]]></literal>
    <justification jstring="[para(2125(a,2),327(a,1,1)),flip(b)].">
      <j1 rule="para" parents="2125 327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2128">
    <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,1879,a,b,2126,a),flip(a)].">
      <j1 rule="hyper" parents="320 1879 2126"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2129">
    <literal><![CDATA[
      T(x,y) * (R(x,z,u) \ 1) = R(x,z,u) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(5(a,1),1320(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 1320"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2130">
    <literal><![CDATA[
      ((x * y) / x) / ((y \ 1) \ 1) = (y \ 1) * ((x * y) / x)
    ]]></literal>
    <justification jstring="[para(360(a,1),1541(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="360 1541"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2131">
    <literal><![CDATA[
      (T(x,y) \ 1) * ((y * T(x,y)) / y) = x / ((T(x,y) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(225(a,1),2130(a,1,1)),flip(a)].">
      <j1 rule="para" parents="225 2130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2132">
    <literal><![CDATA[
      x / ((T(x,y) \ 1) \ 1) = (T(x,y) \ 1) * x
    ]]></literal>
    <justification jstring="[para(225(a,1),2131(a,1,2)),flip(a)].">
      <j1 rule="para" parents="225 2131"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2133">
    <literal><![CDATA[
      (T(x,y) \ 1) \ ((T(x,y) \ x) / x) = K(x,((T(x,y) \ 1) * x) / x)
    ]]></literal>
    <justification jstring="[para(2132(a,1),1736(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2132 1736"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2134">
    <literal><![CDATA[
      (T(x,y) \ 1) \ ((T(x,y) \ x) / x) = K(x,T(x,y) \ 1)
    ]]></literal>
    <justification jstring="[para(6(a,1),2133(a,2,2))].">
      <j1 rule="para" parents="6 2133"/>
    </justification>
  </clause>

  <clause id="2135">
    <literal><![CDATA[
      (T(x,y) \ 1) * K(x,T(x,y) \ 1) = (T(x,y) \ x) / x
    ]]></literal>
    <justification jstring="[hyper(134,a,2134,a)].">
      <j1 rule="hyper" parents="134 2134"/>
    </justification>
  </clause>

  <clause id="2137">
    <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,1719,a,b,1617,a(flip))].">
      <j1 rule="hyper" parents="239 1719 1617"/>
    </justification>
  </clause>

  <clause id="2138">
    <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,1718,a(flip),b,1617,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="239 1718 1617"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2139">
    <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),2138(a,2,1,2,1))].">
      <j1 rule="para" parents="4 2138"/>
    </justification>
  </clause>

  <clause id="2140">
    <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),2137(a,1,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="225 2137"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2141">
    <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),2140(a,1,2,1,2))].">
      <j1 rule="para" parents="200 2140"/>
    </justification>
  </clause>

  <clause id="2142">
    <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(2140(a,2),770(a,1))].">
      <j1 rule="para" parents="2140 770"/>
    </justification>
  </clause>

  <clause id="2143">
    <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,2141,a)].">
      <j1 rule="hyper" parents="123 2141"/>
    </justification>
  </clause>

  <clause id="2144">
    <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,394,a(flip),b,2141,a),flip(a)].">
      <j1 rule="hyper" parents="58 394 2141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2145">
    <literal><![CDATA[
      T(x,y) * L(T(x,y) \ 1,x,1 / x) = T(x * T(1 / x,1),y)
    ]]></literal>
    <justification jstring="[para(752(a,1),2141(a,2,1,2))].">
      <j1 rule="para" parents="752 2141"/>
    </justification>
  </clause>

  <clause id="2146">
    <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),2143(a,1,2,1,2))].">
      <j1 rule="para" parents="390 2143"/>
    </justification>
  </clause>

  <clause id="2147">
    <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(1008(a,1),2144(a,2,2,1))].">
      <j1 rule="para" parents="1008 2144"/>
    </justification>
  </clause>

  <clause id="2148">
    <literal><![CDATA[
      T(x,y) * ((1 / x) * (T(x,y) \ x)) = T(x * T(1 / x,1),y)
    ]]></literal>
    <justification jstring="[para(1126(a,1),2145(a,1,2))].">
      <j1 rule="para" parents="1126 2145"/>
    </justification>
  </clause>

  <clause id="2149">
    <literal><![CDATA[
      T(x,y) * ((1 / x) * (T(x,y) \ x)) = T(x * (1 / x),y)
    ]]></literal>
    <justification jstring="[para(198(a,1),2148(a,2,1,2))].">
      <j1 rule="para" parents="198 2148"/>
    </justification>
  </clause>

  <clause id="2150">
    <literal><![CDATA[
      (1 / x) * (T(x,y) \ x) = (T(x,y) \ x) / x
    ]]></literal>
    <justification jstring="[hyper(29,a,2017,a,b,2149,a),flip(a)].">
      <j1 rule="hyper" parents="29 2017 2149"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2151">
    <literal><![CDATA[
      (T(x,y) \ x) \ ((T(x,y) \ x) / x) = T(1 / x,T(x,y) \ x)
    ]]></literal>
    <justification jstring="[hyper(439,a,xx,b,2150,a),flip(a)].">
      <j1 rule="hyper" parents="439 2150"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2152">
    <literal><![CDATA[
      T((T(x,y) \ x) / x,x) = (1 / x) * ((T(x,y) \ 1) * x)
    ]]></literal>
    <justification jstring="[para(2150(a,1),1128(a,1,1))].">
      <j1 rule="para" parents="2150 1128"/>
    </justification>
  </clause>

  <clause id="2153">
    <literal><![CDATA[
      (1 / x) * ((T(x,y) \ 1) * x) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(1127,a,2152,a),flip(a)].">
      <j1 rule="hyper" parents="1127 2152"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2154">
    <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(2151(a,1),1022(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="2151 1022"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2155">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) / x) \ (1 / x)) = T(K(T(x,y),1 / x),y)
    ]]></literal>
    <justification jstring="[para(2091(a,1),2147(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2091 2147"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2156">
    <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,2022,a,b,2155,a),flip(a)].">
      <j1 rule="hyper" parents="320 2022 2155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2157">
    <literal><![CDATA[
      (T(x,y) / x) \ (1 / x) = 1 / T(x,y)
    ]]></literal>
    <justification jstring="[hyper(29,a,1794,a(flip),b,2156,a),flip(a)].">
      <j1 rule="hyper" parents="29 1794 2156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2158">
    <literal><![CDATA[
      (T(x,y) / x) * (1 / T(x,y)) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(134,a,2157,a)].">
      <j1 rule="hyper" parents="134 2157"/>
    </justification>
  </clause>

  <clause id="2159">
    <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),2157(a,1,2))].">
      <j1 rule="para" parents="265 2157"/>
    </justification>
  </clause>

  <clause id="2160">
    <literal><![CDATA[
      (x \ T(x,y)) \ (x \ 1) = 1 / T(T(x,x \ 1),y)
    ]]></literal>
    <justification jstring="[para(1350(a,1),2159(a,1,1))].">
      <j1 rule="para" parents="1350 2159"/>
    </justification>
  </clause>

  <clause id="2161">
    <literal><![CDATA[
      1 / T(T(x,x \ 1),y) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(58,a,2121,a(flip),b,2160,a),flip(a)].">
      <j1 rule="hyper" parents="58 2121 2160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2162">
    <literal><![CDATA[
      T(T(x,x \ 1),y) = (T(x,y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(188,a,2161,a),flip(a)].">
      <j1 rule="hyper" parents="188 2161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2163">
    <literal><![CDATA[
      T(1 / (1 / x),y) \ 1 = 1 / T(x,y)
    ]]></literal>
    <justification jstring="[para(357(a,1),2161(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="357 2161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2164">
    <literal><![CDATA[
      T((x \ 1) \ 1,y) = (T(x,y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(58,a,663,a(flip),b,2162,a)].">
      <j1 rule="hyper" parents="58 663 2162"/>
    </justification>
  </clause>

  <clause id="2165">
    <literal><![CDATA[
      (T(1 / x,y) \ 1) \ 1 = T(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(643(a,1),2162(a,1,1)),flip(a)].">
      <j1 rule="para" parents="643 2162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2166">
    <literal><![CDATA[
      1 / (1 / T(x,y)) = T(1 / (1 / x),y)
    ]]></literal>
    <justification jstring="[hyper(197,a,2163,a)].">
      <j1 rule="hyper" parents="197 2163"/>
    </justification>
  </clause>

  <clause id="2167">
    <literal><![CDATA[
      x * ((T(y,x) \ 1) \ 1) = ((y \ 1) \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(119,a,2164,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 2164 17"/>
    </justification>
  </clause>

  <clause id="2168">
    <literal><![CDATA[
      T(((x / y) \ 1) \ 1,y) = ((y \ x) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(107(a,1),2164(a,2,1,1))].">
      <j1 rule="para" parents="107 2164"/>
    </justification>
  </clause>

  <clause id="2169">
    <literal><![CDATA[
      T(x,y) * K(T(x,y) \ 1,T(x,y)) = T(1 / (1 / x),y)
    ]]></literal>
    <justification jstring="[hyper(1814,a,2166,a)].">
      <j1 rule="hyper" parents="1814 2166"/>
    </justification>
  </clause>

  <clause id="2170">
    <literal><![CDATA[
      T(1 / (1 / (x / y)),y) = 1 / (1 / (y \ x))
    ]]></literal>
    <justification jstring="[para(107(a,1),2166(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="107 2166"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2171">
    <literal><![CDATA[
      ((x * T(1 / (1 / y),x)) / x) \ (y / T(y,x)) = 1 / T(y,x)
    ]]></literal>
    <justification jstring="[para(2166(a,1),1710(a,1,1,1,2))].">
      <j1 rule="para" parents="2166 1710"/>
    </justification>
  </clause>

  <clause id="2172">
    <literal><![CDATA[
      T(x,T(x,y) \ 1) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(740,a,2167,a)].">
      <j1 rule="hyper" parents="740 2167"/>
    </justification>
  </clause>

  <clause id="2173">
    <literal><![CDATA[
      (((x / y) \ 1) \ 1) * y = y * (((y \ x) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(107(a,1),2167(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="107 2167"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2174">
    <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),2167(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="528 2167"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2175">
    <literal><![CDATA[
      (T(x,y) \ 1) \ (T(x,y) \ x) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(1129,a,2172,a)].">
      <j1 rule="hyper" parents="1129 2172"/>
    </justification>
  </clause>

  <clause id="2176">
    <literal><![CDATA[
      T(x,T(x,y) \ 1) = x * K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,1833,a,b,2172,a),flip(a)].">
      <j1 rule="hyper" parents="320 1833 2172"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2177">
    <literal><![CDATA[
      T(x,T(x,y) \ 1) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,106,a,b,2172,a),flip(a)].">
      <j1 rule="hyper" parents="320 106 2172"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2178">
    <literal><![CDATA[
      T(K(x,x \ 1),y) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(2020,a,2176,a)].">
      <j1 rule="hyper" parents="2020 2176"/>
    </justification>
  </clause>

  <clause id="2179">
    <literal><![CDATA[
      K(T(x,y),T(x,y) \ 1) = K(T(x,y),1 / x)
    ]]></literal>
    <justification jstring="[hyper(2023,a,2178,a),flip(a)].">
      <j1 rule="hyper" parents="2023 2178"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2180">
    <literal><![CDATA[
      T(x,K(y,y \ 1)) = x
    ]]></literal>
    <justification jstring="[hyper(49,a,2178,a)].">
      <j1 rule="hyper" parents="49 2178"/>
    </justification>
  </clause>

  <clause id="2181">
    <literal><![CDATA[
      K(x,x \ 1) * y = y * K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(119,a,2178,a(flip),b,17,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 2178 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2182">
    <literal><![CDATA[
      T(x,y) \ K(x,x \ 1) = (T(x,y) \ x) / x
    ]]></literal>
    <justification jstring="[hyper(116,a,2178,a(flip),b,2018,a)].">
      <j1 rule="hyper" parents="116 2178 2018"/>
    </justification>
  </clause>

  <clause id="2183">
    <literal><![CDATA[
      x * K(y,y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,y \ 1) * x = z
    ]]></literal>
    <justification jstring="[para(2178(a,1),284(a,1,2))].">
      <j1 rule="para" parents="2178 284"/>
    </justification>
  </clause>

  <clause id="2184">
    <literal><![CDATA[
      x \ y != z * K(u,u \ 1)
    ]]></literal>
    <literal><![CDATA[
      x * (K(u,u \ 1) * z) = y
    ]]></literal>
    <justification jstring="[para(2178(a,1),580(a,2,2))].">
      <j1 rule="para" parents="2178 580"/>
    </justification>
  </clause>

  <clause id="2186">
    <literal><![CDATA[
      T(x,K(y,y \ 1)) != z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(2180(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="2180 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2187">
    <literal><![CDATA[
      T(x,K(1 / y,y)) = x
    ]]></literal>
    <justification jstring="[para(75(a,1),2180(a,1,2,2))].">
      <j1 rule="para" parents="75 2180"/>
    </justification>
  </clause>

  <clause id="2188">
    <literal><![CDATA[
      K(x,x \ 1) * y != z * K(x,x \ 1)
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(2180(a,1),241(a,1,2))].">
      <j1 rule="para" parents="2180 241"/>
    </justification>
  </clause>

  <clause id="2189">
    <literal><![CDATA[
      K(x,x \ 1) * y != z
    ]]></literal>
    <literal><![CDATA[
      y * K(x,x \ 1) = z
    ]]></literal>
    <justification jstring="[para(2180(a,1),284(a,1,2))].">
      <j1 rule="para" parents="2180 284"/>
    </justification>
  </clause>

  <clause id="2190">
    <literal><![CDATA[
      T(x,K(y \ 1,y)) = x
    ]]></literal>
    <justification jstring="[para(1798(a,1),2180(a,1,2))].">
      <j1 rule="para" parents="1798 2180"/>
    </justification>
  </clause>

  <clause id="2191">
    <literal><![CDATA[
      T(K(x \ 1,x),y) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(49,a,2190,a)].">
      <j1 rule="hyper" parents="49 2190"/>
    </justification>
  </clause>

  <clause id="2192">
    <literal><![CDATA[
      K(x \ 1,x) * y = y * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,2190,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 2190 17"/>
    </justification>
  </clause>

  <clause id="2193">
    <literal><![CDATA[
      (x * K(y \ 1,y)) / x = K(y \ 1,y)
    ]]></literal>
    <justification jstring="[para(2190(a,1),187(a,1,2))].">
      <j1 rule="para" parents="2190 187"/>
    </justification>
  </clause>

  <clause id="2194">
    <literal><![CDATA[
      T(x,(y \ 1) * y) = x
    ]]></literal>
    <justification jstring="[para(258(a,1),2190(a,1,2))].">
      <j1 rule="para" parents="258 2190"/>
    </justification>
  </clause>

  <clause id="2195">
    <literal><![CDATA[
      K(x \ 1,x) * y != z * K(x \ 1,x)
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(2190(a,1),241(a,1,2))].">
      <j1 rule="para" parents="2190 241"/>
    </justification>
  </clause>

  <clause id="2196">
    <literal><![CDATA[
      K(x \ 1,x) * y != z
    ]]></literal>
    <literal><![CDATA[
      y * K(x \ 1,x) = z
    ]]></literal>
    <justification jstring="[para(2190(a,1),284(a,1,2))].">
      <j1 rule="para" parents="2190 284"/>
    </justification>
  </clause>

  <clause id="2197">
    <literal><![CDATA[
      R(x,y,z) * K(u \ 1,u) = K(u \ 1,u) * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(2190(a,1),238(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2190 238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2198">
    <literal><![CDATA[
      K(x \ 1,x) \ ((y * (x \ 1)) * x) = R(y,x \ 1,x)
    ]]></literal>
    <justification jstring="[para(2190(a,1),1068(a,2,1))].">
      <j1 rule="para" parents="2190 1068"/>
    </justification>
  </clause>

  <clause id="2199">
    <literal><![CDATA[
      ((x \ 1) * x) * y = y * ((x \ 1) * x)
    ]]></literal>
    <justification jstring="[hyper(119,a,2194,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 2194 17"/>
    </justification>
  </clause>

  <clause id="2200">
    <literal><![CDATA[
      K(x \ (x / T(x,y)),x) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,1531,a,b,2191,a)].">
      <j1 rule="hyper" parents="58 1531 2191"/>
    </justification>
  </clause>

  <clause id="2201">
    <literal><![CDATA[
      x * K(y \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y \ 1,y) * x = z
    ]]></literal>
    <justification jstring="[para(2191(a,1),284(a,1,2))].">
      <j1 rule="para" parents="2191 284"/>
    </justification>
  </clause>

  <clause id="2202">
    <literal><![CDATA[
      K(x \ 1,x) / T(x,y) = T(1 / T(x,y),x)
    ]]></literal>
    <justification jstring="[para(2191(a,1),1534(a,1,1))].">
      <j1 rule="para" parents="2191 1534"/>
    </justification>
  </clause>

  <clause id="2203">
    <literal><![CDATA[
      K(x,x \ 1) * L(x,y,z) = x * (L(x,y,z) * (1 / x))
    ]]></literal>
    <justification jstring="[hyper(320,a,1803,a(flip),b,2181,a),flip(a)].">
      <j1 rule="hyper" parents="320 1803 2181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2204">
    <literal><![CDATA[
      K(x,x \ 1) * (1 / (1 / x)) = x
    ]]></literal>
    <justification jstring="[hyper(320,a,1801,a(flip),b,2181,a),flip(a)].">
      <j1 rule="hyper" parents="320 1801 2181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2205">
    <literal><![CDATA[
      (K(x,x \ 1) * y) / z = (y * K(x,x \ 1)) / z
    ]]></literal>
    <justification jstring="[hyper(117,a,2181,a,b,7,a)].">
      <j1 rule="hyper" parents="117 2181 7"/>
    </justification>
  </clause>

  <clause id="2206">
    <literal><![CDATA[
      K(x,x \ 1) \ x = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(116,a,1801,a(flip),b,2181,a)].">
      <j1 rule="hyper" parents="116 1801 2181"/>
    </justification>
  </clause>

  <clause id="2207">
    <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(2181(a,2),505(a,1,2))].">
      <j1 rule="para" parents="2181 505"/>
    </justification>
  </clause>

  <clause id="2208">
    <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(2181(a,2),631(a,1,1))].">
      <j1 rule="para" parents="2181 631"/>
    </justification>
  </clause>

  <clause id="2209">
    <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(2181(a,1),773(a,1,2))].">
      <j1 rule="para" parents="2181 773"/>
    </justification>
  </clause>

  <clause id="2210">
    <literal><![CDATA[
      K(x,1 / x) * (1 / (1 / x)) = x
    ]]></literal>
    <justification jstring="[para(1791(a,2),2204(a,1,1))].">
      <j1 rule="para" parents="1791 2204"/>
    </justification>
  </clause>

  <clause id="2211">
    <literal><![CDATA[
      L(x,1 / x,x) = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(628,a,2210,a)].">
      <j1 rule="hyper" parents="628 2210"/>
    </justification>
  </clause>

  <clause id="2212">
    <literal><![CDATA[
      L(T(x,y),1 / x,x) = T(1 / (1 / x),y)
    ]]></literal>
    <justification jstring="[para(2211(a,1),20(a,2,1))].">
      <j1 rule="para" parents="2211 20"/>
    </justification>
  </clause>

  <clause id="2213">
    <literal><![CDATA[
      L(1 / x,y,z) * K(x \ 1,x) = (x \ 1) * (x * L(x \ 1,y,z))
    ]]></literal>
    <justification jstring="[hyper(1842,a,2192,a),flip(a)].">
      <j1 rule="hyper" parents="1842 2192"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2214">
    <literal><![CDATA[
      K(x \ 1,x) * (y / x) = y * T(y \ (y / x),x)
    ]]></literal>
    <justification jstring="[hyper(320,a,1022,a(flip),b,2192,a),flip(a)].">
      <j1 rule="hyper" parents="320 1022 2192"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2215">
    <literal><![CDATA[
      x * (K(y \ 1,y) * z) = x * (z * K(y \ 1,y))
    ]]></literal>
    <justification jstring="[hyper(119,a,2192,a,b,4,a)].">
      <j1 rule="hyper" parents="119 2192 4"/>
    </justification>
  </clause>

  <clause id="2216">
    <literal><![CDATA[
      R(K(x \ 1,x),y,z) * (y * z) = (y * K(x \ 1,x)) * z
    ]]></literal>
    <justification jstring="[para(2192(a,1),101(a,2,1))].">
      <j1 rule="para" parents="2192 101"/>
    </justification>
  </clause>

  <clause id="2217">
    <literal><![CDATA[
      L(x \ (K(y \ 1,y) \ z),x,K(y \ 1,y)) = (x * K(y \ 1,y)) \ z
    ]]></literal>
    <justification jstring="[para(2192(a,1),298(a,2,1))].">
      <j1 rule="para" parents="2192 298"/>
    </justification>
  </clause>

  <clause id="2218">
    <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(2192(a,2),505(a,1,2))].">
      <j1 rule="para" parents="2192 505"/>
    </justification>
  </clause>

  <clause id="2219">
    <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(2192(a,2),631(a,1,1))].">
      <j1 rule="para" parents="2192 631"/>
    </justification>
  </clause>

  <clause id="2220">
    <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(2192(a,1),773(a,1,2))].">
      <j1 rule="para" parents="2192 773"/>
    </justification>
  </clause>

  <clause id="2221">
    <literal><![CDATA[
      T(K(x \ 1,x),y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x \ 1,x) = z
    ]]></literal>
    <justification jstring="[para(2193(a,1),292(a,1,1)),flip(b)].">
      <j1 rule="para" parents="2193 292"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2222">
    <literal><![CDATA[
      ((x * y) / x) \ K(y \ 1,y) = T(((x * y) / x) \ 1,y)
    ]]></literal>
    <justification jstring="[para(2193(a,1),1603(a,1,2))].">
      <j1 rule="para" parents="2193 1603"/>
    </justification>
  </clause>

  <clause id="2223">
    <literal><![CDATA[
      a(x \ 1,x,x \ 1) = (x \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(793,a,2199,a)].">
      <j1 rule="hyper" parents="793 2199"/>
    </justification>
  </clause>

  <clause id="2225">
    <literal><![CDATA[
      x * K(x \ (x / T(x,y)),x) = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(119,a,2200,a,b,1789,a)].">
      <j1 rule="hyper" parents="119 2200 1789"/>
    </justification>
  </clause>

  <clause id="2226">
    <literal><![CDATA[
      K(x,1 / x) * T(1 / (1 / x),y) = x * (T(x,y) / x)
    ]]></literal>
    <justification jstring="[hyper(119,a,2212,a(flip),b,1059,a)].">
      <j1 rule="hyper" parents="119 2212 1059"/>
    </justification>
  </clause>

  <clause id="2227">
    <literal><![CDATA[
      T(x,((y * x) / y) \ 1) = ((y \ (y * x)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(792,a,2168,a)].">
      <j1 rule="hyper" parents="792 2168"/>
    </justification>
  </clause>

  <clause id="2228">
    <literal><![CDATA[
      (x * (((x \ y) \ 1) \ 1)) / x = ((y / x) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(271,a,2168,a)].">
      <j1 rule="hyper" parents="271 2168"/>
    </justification>
  </clause>

  <clause id="2229">
    <literal><![CDATA[
      T(T(x / y,y / x),y) = ((y \ x) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(2069(a,2),2168(a,1,1))].">
      <j1 rule="para" parents="2069 2168"/>
    </justification>
  </clause>

  <clause id="2230">
    <literal><![CDATA[
      (x * (1 / (1 / (x \ y)))) / x = 1 / (1 / (y / x))
    ]]></literal>
    <justification jstring="[hyper(271,a,2170,a)].">
      <j1 rule="hyper" parents="271 2170"/>
    </justification>
  </clause>

  <clause id="2231">
    <literal><![CDATA[
      (T(x,y) \ 1) * ((x \ 1) \ 1) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(134,a,2175,a)].">
      <j1 rule="hyper" parents="134 2175"/>
    </justification>
  </clause>

  <clause id="2234">
    <literal><![CDATA[
      T(x,y) \ (1 / (1 / x)) = (T(x,y) \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(116,a,2225,a(flip),b,1146,a)].">
      <j1 rule="hyper" parents="116 2225 1146"/>
    </justification>
  </clause>

  <clause id="2235">
    <literal><![CDATA[
      T(x \ y,x / y) = ((x \ y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(678,a,2229,a)].">
      <j1 rule="hyper" parents="678 2229"/>
    </justification>
  </clause>

  <clause id="2236">
    <literal><![CDATA[
      T((x * y) \ y,x) = (((x * y) \ y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(6(a,1),2235(a,1,2))].">
      <j1 rule="para" parents="6 2235"/>
    </justification>
  </clause>

  <clause id="2237">
    <literal><![CDATA[
      T(x \ (y \ x),y) = ((x \ (y \ x)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(72(a,1),2235(a,1,2))].">
      <j1 rule="para" parents="72 2235"/>
    </justification>
  </clause>

  <clause id="2238">
    <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(734(a,2),2196(a,1))].">
      <j1 rule="para" parents="734 2196"/>
    </justification>
  </clause>

  <clause id="2239">
    <literal><![CDATA[
      x * T(x \ (x / y),y) != z
    ]]></literal>
    <literal><![CDATA[
      (x / y) * K(y \ 1,y) = z
    ]]></literal>
    <justification jstring="[para(2214(a,1),2196(a,1))].">
      <j1 rule="para" parents="2214 2196"/>
    </justification>
  </clause>

  <clause id="2240">
    <literal><![CDATA[
      T(x,((y * x) / y) \ 1) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(4(a,1),2227(a,2,1,1))].">
      <j1 rule="para" parents="4 2227"/>
    </justification>
  </clause>

  <clause id="2241">
    <literal><![CDATA[
      T(x,y / (y * x)) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(58,a,2077,a(flip),b,2240,a)].">
      <j1 rule="hyper" parents="58 2077 2240"/>
    </justification>
  </clause>

  <clause id="2243">
    <literal><![CDATA[
      T(x,y / (y * x)) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,106,a,b,2241,a),flip(a)].">
      <j1 rule="hyper" parents="320 106 2241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2244">
    <literal><![CDATA[
      T(1 / (1 / x),y / (y * x)) = x
    ]]></literal>
    <justification jstring="[hyper(1785,a,2243,a(flip))].">
      <j1 rule="hyper" parents="1785 2243"/>
    </justification>
  </clause>

  <clause id="2245">
    <literal><![CDATA[
      T(1 / (1 / x),(y / x) / y) = x
    ]]></literal>
    <justification jstring="[para(7(a,1),2244(a,1,2,2))].">
      <j1 rule="para" parents="7 2244"/>
    </justification>
  </clause>

  <clause id="2246">
    <literal><![CDATA[
      (1 / (1 / x)) \ (((y / x) / y) * x) = (y / x) / y
    ]]></literal>
    <justification jstring="[para(2245(a,1),226(a,1,2,2))].">
      <j1 rule="para" parents="2245 226"/>
    </justification>
  </clause>

  <clause id="2247">
    <literal><![CDATA[
      (x * ((y \ 1) \ 1)) / x = (((x * y) / x) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(4(a,1),2228(a,1,1,2,1,1))].">
      <j1 rule="para" parents="4 2228"/>
    </justification>
  </clause>

  <clause id="2248">
    <literal><![CDATA[
      (x * (1 / (1 / y))) / x = 1 / (1 / ((x * y) / x))
    ]]></literal>
    <justification jstring="[para(4(a,1),2230(a,1,1,2,2,2))].">
      <j1 rule="para" parents="4 2230"/>
    </justification>
  </clause>

  <clause id="2249">
    <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(2030(a,2),2246(a,1,2))].">
      <j1 rule="para" parents="2030 2246"/>
    </justification>
  </clause>

  <clause id="2250">
    <literal><![CDATA[
      K(x,x \ 1) * (x \ L(x,y,z)) = L(x,y,z) * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(1862,a,2203,a)].">
      <j1 rule="hyper" parents="1862 2203"/>
    </justification>
  </clause>

  <clause id="2251">
    <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(2222(a,2),1237(a,1,1,2))].">
      <j1 rule="para" parents="2222 1237"/>
    </justification>
  </clause>

  <clause id="2253">
    <literal><![CDATA[
      K(x,x \ 1) * T(1 / (1 / x),y) = x * (T(x,y) / x)
    ]]></literal>
    <justification jstring="[para(1791(a,1),2226(a,1,1))].">
      <j1 rule="para" parents="1791 2226"/>
    </justification>
  </clause>

  <clause id="2254">
    <literal><![CDATA[
      (x \ L(x,y,z)) * K(x,x \ 1) = L(x,y,z) * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(2189,a,2250,a)].">
      <j1 rule="hyper" parents="2189 2250"/>
    </justification>
  </clause>

  <clause id="2255">
    <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,1283,a(flip),b,2250,a),flip(a)].">
      <j1 rule="hyper" parents="320 1283 2250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2256">
    <literal><![CDATA[
      K(x,x \ 1) * T(K(x,x \ 1) \ x,y) = x * (T(x,y) / x)
    ]]></literal>
    <justification jstring="[para(2206(a,2),2253(a,1,2,1))].">
      <j1 rule="para" parents="2206 2253"/>
    </justification>
  </clause>

  <clause id="2257">
    <literal><![CDATA[
      (1 / (1 / x)) \ (x / T(x,y)) = 1 / T(x,y)
    ]]></literal>
    <justification jstring="[para(225(a,1),2171(a,1,1))].">
      <j1 rule="para" parents="225 2171"/>
    </justification>
  </clause>

  <clause id="2259">
    <literal><![CDATA[
      (x * (T(x,y) / x)) * (K(x,x \ 1) \ 1) = T(x * (K(x,x \ 1) \ 1),y)
    ]]></literal>
    <justification jstring="[para(2256(a,1),1039(a,1,1))].">
      <j1 rule="para" parents="2256 1039"/>
    </justification>
  </clause>

  <clause id="2260">
    <literal><![CDATA[
      ((x \ 1) * (x * L(x \ 1,x,y))) * x = (x * ((y * x) \ y)) * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(2213(a,1),1610(a,1,1))].">
      <j1 rule="para" parents="2213 1610"/>
    </justification>
  </clause>

  <clause id="2261">
    <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,2217,a),flip(a)].">
      <j1 rule="hyper" parents="320 361 2217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2262">
    <literal><![CDATA[
      (x * (T(x,y) / x)) * K(x \ 1,x) = T(x * (K(x,x \ 1) \ 1),y)
    ]]></literal>
    <justification jstring="[para(1828(a,1),2259(a,1,2))].">
      <j1 rule="para" parents="1828 2259"/>
    </justification>
  </clause>

  <clause id="2263">
    <literal><![CDATA[
      (x * (T(x,y) / x)) * K(x \ 1,x) = T(x * K(x \ 1,x),y)
    ]]></literal>
    <justification jstring="[para(1828(a,1),2262(a,2,1,2))].">
      <j1 rule="para" parents="1828 2262"/>
    </justification>
  </clause>

  <clause id="2264">
    <literal><![CDATA[
      (x * (T(x,y) / x)) * K(x \ 1,x) = T(1 / (1 / x),y)
    ]]></literal>
    <justification jstring="[para(1790(a,1),2263(a,2,1))].">
      <j1 rule="para" parents="1790 2263"/>
    </justification>
  </clause>

  <clause id="2265">
    <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),1696(a,1,2,2,1,1))].">
      <j1 rule="para" parents="75 1696"/>
    </justification>
  </clause>

  <clause id="2266">
    <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),2265(a,2,2,1,2))].">
      <j1 rule="para" parents="5 2265"/>
    </justification>
  </clause>

  <clause id="2267">
    <literal><![CDATA[
      K(x,(y * x) \ y) * x = T(x,(y * x) \ y)
    ]]></literal>
    <justification jstring="[para(4(a,1),1839(a,1,1,1))].">
      <j1 rule="para" parents="4 1839"/>
    </justification>
  </clause>

  <clause id="2268">
    <literal><![CDATA[
      T(K(x,(y * x) \ y),x) = x \ T(x,(y * x) \ y)
    ]]></literal>
    <justification jstring="[hyper(439,a,xx,b,2267,a)].">
      <j1 rule="hyper" parents="439 2267"/>
    </justification>
  </clause>

  <clause id="2270">
    <literal><![CDATA[
      L(T(K(x,(y * x) \ y),x),x,y) = K(((y * x) \ y) \ 1,(y * x) \ y)
    ]]></literal>
    <justification jstring="[para(2268(a,2),2094(a,1,1))].">
      <j1 rule="para" parents="2268 2094"/>
    </justification>
  </clause>

  <clause id="2271">
    <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(642(a,1),1872(a,2,2,1))].">
      <j1 rule="para" parents="642 1872"/>
    </justification>
  </clause>

  <clause id="2272">
    <literal><![CDATA[
      (((x * y) / x) / y) * (1 / y) = (1 / y) * (((x * y) / x) / y)
    ]]></literal>
    <justification jstring="[para(1471(a,1),1906(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1471 1906"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2273">
    <literal><![CDATA[
      ((1 / x) * (((y * x) / y) / x)) / (1 / x) = ((y * x) / y) / x
    ]]></literal>
    <justification jstring="[hyper(131,a,2272,a)].">
      <j1 rule="hyper" parents="131 2272"/>
    </justification>
  </clause>

  <clause id="2274">
    <literal><![CDATA[
      R(((x * y) / x) / y,y,x) = ((1 / y) * ((x * y) / (y * x))) / (1 / y)
    ]]></literal>
    <justification jstring="[para(2273(a,1),889(a,1,1))].">
      <j1 rule="para" parents="2273 889"/>
    </justification>
  </clause>

  <clause id="2275">
    <literal><![CDATA[
      ((1 / x) * ((y * x) / (x * y))) / (1 / x) = (y * x) / (x * y)
    ]]></literal>
    <justification jstring="[hyper(622,a,2274,a),flip(a)].">
      <j1 rule="hyper" parents="622 2274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2276">
    <literal><![CDATA[
      T((x * y) / (y * x),y * x) = ((1 / y) * ((y * x) \ (x * y))) / (1 / y)
    ]]></literal>
    <justification jstring="[para(2275(a,1),679(a,1,1))].">
      <j1 rule="para" parents="2275 679"/>
    </justification>
  </clause>

  <clause id="2277">
    <literal><![CDATA[
      ((1 / x) * ((x * y) \ (y * x))) / (1 / x) = (x * y) \ (y * x)
    ]]></literal>
    <justification jstring="[hyper(420,a,2276,a),flip(a)].">
      <j1 rule="hyper" parents="420 2276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2278">
    <literal><![CDATA[
      K(x,y) = ((1 / y) * ((y * x) \ (x * y))) / (1 / y)
    ]]></literal>
    <justification jstring="[hyper(320,a,11,a,b,2277,a)].">
      <j1 rule="hyper" parents="320 11 2277"/>
    </justification>
  </clause>

  <clause id="2279">
    <literal><![CDATA[
      ((1 / x) * K(y,x)) / (1 / x) = K(y,x)
    ]]></literal>
    <justification jstring="[para(11(a,2),2278(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="11 2278"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2280">
    <literal><![CDATA[
      T(1 / x,K(y,x)) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(266,a,2279,a)].">
      <j1 rule="hyper" parents="266 2279"/>
    </justification>
  </clause>

  <clause id="2281">
    <literal><![CDATA[
      K(x,y) * (1 / y) = (1 / y) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(133,a,2279,a)].">
      <j1 rule="hyper" parents="133 2279"/>
    </justification>
  </clause>

  <clause id="2282">
    <literal><![CDATA[
      K(1 / x,K(y,x)) = 1
    ]]></literal>
    <justification jstring="[hyper(50,a,2280,a)].">
      <j1 rule="hyper" parents="50 2280"/>
    </justification>
  </clause>

  <clause id="2283">
    <literal><![CDATA[
      T(x \ 1,K(y,x)) = T(1 / x,x)
    ]]></literal>
    <justification jstring="[para(2280(a,1),246(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2280 246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2284">
    <literal><![CDATA[
      K(x,K(y,x \ 1)) = 1
    ]]></literal>
    <justification jstring="[para(72(a,1),2282(a,1,1))].">
      <j1 rule="para" parents="72 2282"/>
    </justification>
  </clause>

  <clause id="2285">
    <literal><![CDATA[
      K(x,y \ 1) * y = y * K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(538,a,2284,a)].">
      <j1 rule="hyper" parents="538 2284"/>
    </justification>
  </clause>

  <clause id="2286">
    <literal><![CDATA[
      T(x,K(y,x \ 1)) = x
    ]]></literal>
    <justification jstring="[hyper(51,a,2284,a)].">
      <j1 rule="hyper" parents="51 2284"/>
    </justification>
  </clause>

  <clause id="2287">
    <literal><![CDATA[
      L(x,y,z) * K(u,x \ 1) = K(u,x \ 1) * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(2286(a,1),237(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2286 237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2288">
    <literal><![CDATA[
      T(x \ 1,K(y,x)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(320,a,107,a(flip),b,2283,a),flip(a)].">
      <j1 rule="hyper" parents="320 107 2283"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2289">
    <literal><![CDATA[
      T((x * y) \ x,K(z,y)) = L(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(2288(a,1),399(a,2,1))].">
      <j1 rule="para" parents="2288 399"/>
    </justification>
  </clause>

  <clause id="2290">
    <literal><![CDATA[
      T(x \ y,K(z,y \ x)) = L((y \ x) \ 1,y \ x,y)
    ]]></literal>
    <justification jstring="[para(5(a,1),2289(a,1,1,1))].">
      <j1 rule="para" parents="5 2289"/>
    </justification>
  </clause>

  <clause id="2291">
    <literal><![CDATA[
      T(x \ y,K(z,y \ x)) = x \ y
    ]]></literal>
    <justification jstring="[hyper(320,a,390,a(flip),b,2290,a),flip(a)].">
      <j1 rule="hyper" parents="320 390 2290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2292">
    <literal><![CDATA[
      K(x,y \ z) * (z \ y) = (z \ y) * K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(119,a,2291,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 2291 17"/>
    </justification>
  </clause>

  <clause id="2293">
    <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(2287(a,2),39(a,1))].">
      <j1 rule="para" parents="2287 39"/>
    </justification>
  </clause>

  <clause id="2294">
    <literal><![CDATA[
      (x * ((y * (x \ 1)) / y)) * (x * z) = x * ((x * ((y * (x \ 1)) / y)) * z)
    ]]></literal>
    <justification jstring="[para(1721(a,1),1958(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1721 1958"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2295">
    <literal><![CDATA[
      L(x \ R(x,y \ 1,y),x,K(y \ 1,y)) = a(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[para(2198(a,1),2261(a,1,1,2))].">
      <j1 rule="para" parents="2198 2261"/>
    </justification>
  </clause>

  <clause id="2296">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ (u * y))) / z) = (((z * (u / x)) / z) * x) * y
    ]]></literal>
    <justification jstring="[hyper(892,a,982,a),flip(a)].">
      <j1 rule="hyper" parents="892 982"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2297">
    <literal><![CDATA[
      (((x * ((y / z) / u)) / x) * u) * z = (u * z) * ((x * ((u * z) \ y)) / x)
    ]]></literal>
    <justification jstring="[para(7(a,1),2296(a,1,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7 2296"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2298">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ (u * y))) / z) = (x * ((z * (x \ u)) / z)) * y
    ]]></literal>
    <justification jstring="[para(869(a,1),2296(a,2,1))].">
      <j1 rule="para" parents="869 2296"/>
    </justification>
  </clause>

  <clause id="2299">
    <literal><![CDATA[
      (x * y) * ((x * ((x * y) \ z)) / x) = (x * ((z / y) / x)) * y
    ]]></literal>
    <justification jstring="[hyper(326,a,2297,a),flip(a)].">
      <j1 rule="hyper" parents="326 2297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2300">
    <literal><![CDATA[
      (x * y) * ((x * ((x * y) \ z)) / x) != u
    ]]></literal>
    <literal><![CDATA[
      (x * ((z / y) / x)) * y = u
    ]]></literal>
    <justification jstring="[para(2297(a,1),326(a,1))].">
      <j1 rule="para" parents="2297 326"/>
    </justification>
  </clause>

  <clause id="2301">
    <literal><![CDATA[
      (x * ((x / y) / x)) * y = T(x,x / (x * y))
    ]]></literal>
    <justification jstring="[hyper(1171,a,2299,a),flip(a)].">
      <j1 rule="hyper" parents="1171 2299"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2302">
    <literal><![CDATA[
      x * (y * ((x * (y \ (x \ z))) / x)) = (x * ((z / y) / x)) * y
    ]]></literal>
    <justification jstring="[hyper(58,a,1340,a(flip),b,2299,a)].">
      <j1 rule="hyper" parents="58 1340 2299"/>
    </justification>
  </clause>

  <clause id="2303">
    <literal><![CDATA[
      T(x,x / (x * y)) != z
    ]]></literal>
    <literal><![CDATA[
      T(x * ((x / y) / x),y) = y \ z
    ]]></literal>
    <justification jstring="[para(2301(a,1),277(a,1))].">
      <j1 rule="para" parents="2301 277"/>
    </justification>
  </clause>

  <clause id="2304">
    <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),2302(a,2,1,2,1)),flip(a)].">
      <j1 rule="para" parents="365 2302"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2305">
    <literal><![CDATA[
      (x * ((y / (z * (x \ y))) / x)) * (z * (x \ y)) = x * ((z * ((x * (z \ 1)) / x)) * (x \ y))
    ]]></literal>
    <justification jstring="[para(1721(a,1),2302(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1721 2302"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2306">
    <literal><![CDATA[
      T(x,x / (x * y)) != z
    ]]></literal>
    <literal><![CDATA[
      (x * ((x / y) / x)) * y = z
    ]]></literal>
    <justification jstring="[para(1164(a,1),2300(a,1))].">
      <j1 rule="para" parents="1164 2300"/>
    </justification>
  </clause>

  <clause id="2307">
    <literal><![CDATA[
      ((x / y) * ((z * ((x / y) \ u)) / z)) * y = x * ((z * (((x / y) * y) \ (u * y))) / z)
    ]]></literal>
    <justification jstring="[hyper(326,a,2298,a),flip(a)].">
      <j1 rule="hyper" parents="326 2298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2308">
    <literal><![CDATA[
      (x \ (y * x)) * ((z * ((x \ (y * x)) \ x)) / z) = T(y * ((z * (y \ x)) / z),x)
    ]]></literal>
    <justification jstring="[hyper(239,a,2298,a(flip),b,1615,a),flip(a)].">
      <j1 rule="hyper" parents="239 2298 1615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2309">
    <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),2308(a,1,1))].">
      <j1 rule="para" parents="17 2308"/>
    </justification>
  </clause>

  <clause id="2310">
    <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),2309(a,1,2,1,2,1))].">
      <j1 rule="para" parents="17 2309"/>
    </justification>
  </clause>

  <clause id="2311">
    <literal><![CDATA[
      (x \ 1) * (L(x \ 1,x,y) \ (x * ((y * x) \ y))) = K(x \ 1,x * ((y * x) \ y))
    ]]></literal>
    <justification jstring="[hyper(1423,a,1079,a)].">
      <j1 rule="hyper" parents="1423 1079"/>
    </justification>
  </clause>

  <clause id="2312">
    <literal><![CDATA[
      ((x * y) \ x) * K(y \ 1,y * ((x * y) \ x)) = (y \ 1) * (y * ((x * y) \ x))
    ]]></literal>
    <justification jstring="[hyper(733,a,1079,a)].">
      <j1 rule="hyper" parents="733 1079"/>
    </justification>
  </clause>

  <clause id="2313">
    <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,1506,a),flip(a)].">
      <j1 rule="hyper" parents="320 449 1506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2314">
    <literal><![CDATA[
      (L(x,1 / x,y) * y) / L(x,1 / x,y) = y * (T(x,y) / x)
    ]]></literal>
    <justification jstring="[para(1008(a,1),2313(a,2,2))].">
      <j1 rule="para" parents="1008 2313"/>
    </justification>
  </clause>

  <clause id="2315">
    <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(2314(a,1),1457(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2314 1457"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2316">
    <literal><![CDATA[
      (x * y) * (z * T(z \ L(y \ z,y,x),u)) = (x * (y * T(y \ 1,u))) * z
    ]]></literal>
    <justification jstring="[para(736(a,1),1596(a,1,1)),flip(a)].">
      <j1 rule="para" parents="736 1596"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2317">
    <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),2316(a,1,2))].">
      <j1 rule="para" parents="105 2316"/>
    </justification>
  </clause>

  <clause id="2318">
    <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(1396(a,1),2043(a,2,2))].">
      <j1 rule="para" parents="1396 2043"/>
    </justification>
  </clause>

  <clause id="2319">
    <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(1502(a,1),2109(a,1,1))].">
      <j1 rule="para" parents="1502 2109"/>
    </justification>
  </clause>

  <clause id="2320">
    <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(1145(a,1),2319(a,1,1))].">
      <j1 rule="para" parents="1145 2319"/>
    </justification>
  </clause>

  <clause id="2321">
    <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(2106(a,1),2320(a,1,2))].">
      <j1 rule="para" parents="2106 2320"/>
    </justification>
  </clause>

  <clause id="2322">
    <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,2321,a)].">
      <j1 rule="hyper" parents="58 20 2321"/>
    </justification>
  </clause>

  <clause id="2323">
    <literal><![CDATA[
      L(x,T(x,y) \ x,T(x,y)) = L(x,T(x,y) \ x,x)
    ]]></literal>
    <justification jstring="[para(2103(a,1),2322(a,1,1))].">
      <j1 rule="para" parents="2103 2322"/>
    </justification>
  </clause>

  <clause id="2324">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ x,x) = L(x,T(x,y) \ x,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,1145,a,b,2323,a)].">
      <j1 rule="hyper" parents="58 1145 2323"/>
    </justification>
  </clause>

  <clause id="2325">
    <literal><![CDATA[
      x * L(y,T(y,x) \ y,y) = (y * x) * T(K(x,y),y)
    ]]></literal>
    <justification jstring="[para(2323(a,1),1962(a,1,2))].">
      <j1 rule="para" parents="2323 1962"/>
    </justification>
  </clause>

  <clause id="2326">
    <literal><![CDATA[
      L(x,T(x,y) \ x,x) = (T(x,y) \ x) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,2110,a(flip),b,2324,a),flip(a)].">
      <j1 rule="hyper" parents="58 2110 2324"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2327">
    <literal><![CDATA[
      K(x \ 1,x * ((y * x) \ y)) = (x \ 1) * T(x,(y * x) \ y)
    ]]></literal>
    <justification jstring="[para(730(a,1),2311(a,1,2)),flip(a)].">
      <j1 rule="para" parents="730 2311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2328">
    <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,2318,a),flip(a)].">
      <j1 rule="hyper" parents="320 259 2318"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2329">
    <literal><![CDATA[
      L(K(x \ 1,x) * y,x,1 / x) = K(x \ 1,x) * L(y,x,1 / x)
    ]]></literal>
    <justification jstring="[para(1826(a,1),2328(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1826 2328"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2330">
    <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),2329(a,1,1)),flip(a)].">
      <j1 rule="para" parents="105 2329"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2331">
    <literal><![CDATA[
      L(x,y,L(z \ u,z,w)) = L(x,y,(w * z) \ (w * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,926,a(flip),b,927,a)].">
      <j1 rule="hyper" parents="58 926 927"/>
    </justification>
  </clause>

  <clause id="2332">
    <literal><![CDATA[
      L(x,y,L(z \ 1,z,u)) = L(x,y,(u * z) \ u)
    ]]></literal>
    <justification jstring="[para(3(a,1),2331(a,2,3,2))].">
      <j1 rule="para" parents="3 2331"/>
    </justification>
  </clause>

  <clause id="2333">
    <literal><![CDATA[
      L((x * y) \ x,((x * y) \ x) \ 1,L(y \ 1,y,x)) = 1 / (1 / ((x * y) \ x))
    ]]></literal>
    <justification jstring="[hyper(320,a,1812,a(flip),b,2332,a),flip(a)].">
      <j1 rule="hyper" parents="320 1812 2332"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2334">
    <literal><![CDATA[
      x * (y * L(y \ 1,((x * y) \ x) \ 1,L(y \ 1,y,x))) = (x * y) * (1 / (1 / ((x * y) \ x)))
    ]]></literal>
    <justification jstring="[para(2333(a,1),918(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2333 918"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2335">
    <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),1064(a,1,2,1,1))].">
      <j1 rule="para" parents="258 1064"/>
    </justification>
  </clause>

  <clause id="2336">
    <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),1582(a,1,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="17 1582"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2337">
    <literal><![CDATA[
      (x * T(x \ y,x)) * (1 / x) = T(y * (1 / x),x)
    ]]></literal>
    <justification jstring="[para(68(a,1),1595(a,1,1)),flip(a)].">
      <j1 rule="para" parents="68 1595"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2338">
    <literal><![CDATA[
      ((x \ y) * x) * (1 / x) = T(y * (1 / x),x)
    ]]></literal>
    <justification jstring="[hyper(569,a,2337,a)].">
      <j1 rule="hyper" parents="569 2337"/>
    </justification>
  </clause>

  <clause id="2340">
    <literal><![CDATA[
      T((x * y) * (1 / x),x) = (y * x) * (1 / x)
    ]]></literal>
    <justification jstring="[para(4(a,1),2338(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4 2338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2341">
    <literal><![CDATA[
      T(x * (1 / y),y) != z * (1 / y)
    ]]></literal>
    <literal><![CDATA[
      (y \ x) * y = z
    ]]></literal>
    <justification jstring="[para(2338(a,1),39(a,1))].">
      <j1 rule="para" parents="2338 39"/>
    </justification>
  </clause>

  <clause id="2342">
    <literal><![CDATA[
      T((x * y) * (1 / x),x) != z * (1 / x)
    ]]></literal>
    <literal><![CDATA[
      y * x = z
    ]]></literal>
    <justification jstring="[para(2340(a,2),39(a,1))].">
      <j1 rule="para" parents="2340 39"/>
    </justification>
  </clause>

  <clause id="2343">
    <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(1794(a,2),1806(a,1,2,1,1))].">
      <j1 rule="para" parents="1794 1806"/>
    </justification>
  </clause>

  <clause id="2344">
    <literal><![CDATA[
      (x \ 1) * ((x \ L(x,y,z)) * ((x \ 1) \ u)) = (x \ L(x,y,z)) * u
    ]]></literal>
    <justification jstring="[para(1193(a,1),1854(a,2,1))].">
      <j1 rule="para" parents="1193 1854"/>
    </justification>
  </clause>

  <clause id="2345">
    <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),2344(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 2344"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2346">
    <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,2345,a),flip(a)].">
      <j1 rule="hyper" parents="116 65 2345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2347">
    <literal><![CDATA[
      (x \ R(x,y,z)) * ((x \ 1) * u) = (x \ 1) * ((x \ R(x,y,z)) * u)
    ]]></literal>
    <justification jstring="[para(1207(a,1),2026(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1207 2026"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2348">
    <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,2347,a),flip(a)].">
      <j1 rule="hyper" parents="116 65 2347"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2349">
    <literal><![CDATA[
      (x * (y * T(y \ 1,x))) * (x \ 1) = x \ (x * (y * T(y \ 1,x)))
    ]]></literal>
    <justification jstring="[para(2095(a,1),2097(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2095 2097"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2350">
    <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,2349,a),flip(a)].">
      <j1 rule="hyper" parents="320 4 2349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2352">
    <literal><![CDATA[
      (x \ 1) * T((x \ 1) \ 1,y) = (y * (x \ T(x,y))) * (y \ 1)
    ]]></literal>
    <justification jstring="[para(991(a,1),2350(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="991 2350"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2353">
    <literal><![CDATA[
      ((x * y) \ x) * T(((x * y) \ x) \ 1,x) = (x * K(y,x)) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(1023(a,2),2350(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1023 2350"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2354">
    <literal><![CDATA[
      (x * (y \ T(y,x))) * (x \ 1) = y \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(997,a,2352,a),flip(a)].">
      <j1 rule="hyper" parents="997 2352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2355">
    <literal><![CDATA[
      (x * K(y,x)) * (x \ 1) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(1047,a,2353,a),flip(a)].">
      <j1 rule="hyper" parents="1047 2353"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2356">
    <literal><![CDATA[
      (1 / x) * K(y,1 / x) = K(y,1 / x) / x
    ]]></literal>
    <justification jstring="[hyper(353,a,2355,a),flip(a)].">
      <j1 rule="hyper" parents="353 2355"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2357">
    <literal><![CDATA[
      (1 / x) * (x * (y * T(y \ 1,x))) = (x * (y * T(y \ 1,x))) / x
    ]]></literal>
    <justification jstring="[para(2095(a,1),2098(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2095 2098"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2358">
    <literal><![CDATA[
      L(x * T(x \ 1,y),y,1 / y) = (y * (x * T(x \ 1,y))) / y
    ]]></literal>
    <justification jstring="[hyper(486,a,2357,a)].">
      <j1 rule="hyper" parents="486 2357"/>
    </justification>
  </clause>

  <clause id="2359">
    <literal><![CDATA[
      (x * (((x * y) \ x) * T(((x * y) \ x) \ 1,x))) / x = L(K(y,x),x,1 / x)
    ]]></literal>
    <justification jstring="[para(1023(a,2),2358(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1023 2358"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2360">
    <literal><![CDATA[
      L(K(x,y),y,1 / y) = (y * K(x,y)) / y
    ]]></literal>
    <justification jstring="[para(1023(a,2),2359(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1023 2359"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2361">
    <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),2154(a,1,2))].">
      <j1 rule="para" parents="246 2154"/>
    </justification>
  </clause>

  <clause id="2362">
    <literal><![CDATA[
      ((T(x,y) \ x) / x) * K(x \ 1,x) = (x \ 1) * (T(x,y) \ x)
    ]]></literal>
    <justification jstring="[hyper(284,a,2361,a),flip(a)].">
      <j1 rule="hyper" parents="284 2361"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2363">
    <literal><![CDATA[
      K(x \ 1,x) * ((1 / x) \ L(1 / x,y,z)) = L(x \ 1,y,z) / (1 / x)
    ]]></literal>
    <justification jstring="[para(1826(a,1),2255(a,1,1))].">
      <j1 rule="para" parents="1826 2255"/>
    </justification>
  </clause>

  <clause id="2364">
    <literal><![CDATA[
      K(x \ 1,x) * (x * L(x \ 1,y,z)) = L(x \ 1,y,z) / (1 / x)
    ]]></literal>
    <justification jstring="[para(1070(a,1),2363(a,1,2))].">
      <j1 rule="para" parents="1070 2363"/>
    </justification>
  </clause>

  <clause id="2365">
    <literal><![CDATA[
      (x * ((y * x) \ y)) * K(x \ 1,x) = L(x \ 1,x,y) / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(2238,a,2364,a)].">
      <j1 rule="hyper" parents="2238 2364"/>
    </justification>
  </clause>

  <clause id="2366">
    <literal><![CDATA[
      (x * ((y * x) \ y)) * K(x \ 1,x) = L(x \ 1,x,y) * x
    ]]></literal>
    <justification jstring="[hyper(320,a,1843,a(flip),b,2365,a),flip(a)].">
      <j1 rule="hyper" parents="320 1843 2365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2367">
    <literal><![CDATA[
      (x \ 1) * (x * L(x \ 1,x,y)) = L(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[hyper(30,a,2260,a,b,2366,a(flip))].">
      <j1 rule="hyper" parents="30 2260 2366"/>
    </justification>
  </clause>

  <clause id="2368">
    <literal><![CDATA[
      (x * y) \ x = (y \ 1) * (y * L(y \ 1,y,x))
    ]]></literal>
    <justification jstring="[hyper(320,a,217,a(flip),b,2367,a)].">
      <j1 rule="hyper" parents="320 217 2367"/>
    </justification>
  </clause>

  <clause id="2369">
    <literal><![CDATA[
      (x \ 1) * (x * ((y * x) \ y)) = (y * x) \ y
    ]]></literal>
    <justification jstring="[hyper(320,a,734,a(flip),b,2368,a)].">
      <j1 rule="hyper" parents="320 734 2368"/>
    </justification>
  </clause>

  <clause id="2370">
    <literal><![CDATA[
      (x \ 1) \ ((y * x) \ y) = x * ((y * x) \ y)
    ]]></literal>
    <justification jstring="[hyper(116,a,2368,a,b,734,a(flip))].">
      <j1 rule="hyper" parents="116 2368 734"/>
    </justification>
  </clause>

  <clause id="2371">
    <literal><![CDATA[
      K(x \ 1,x * ((y * x) \ y)) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,2369,a(flip),b,2312,a),flip(a)].">
      <j1 rule="hyper" parents="115 2369 2312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2372">
    <literal><![CDATA[
      T(x,(y * x) \ y) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(116,a,2371,a(flip),b,2327,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="116 2371 2327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2373">
    <literal><![CDATA[
      T(x,(y * x) \ y) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,106,a,b,2372,a),flip(a)].">
      <j1 rule="hyper" parents="320 106 2372"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2374">
    <literal><![CDATA[
      K(x,(y * x) \ y) = ((x \ 1) \ 1) / x
    ]]></literal>
    <justification jstring="[hyper(117,a,2372,a(flip),b,2267,a),flip(a)].">
      <j1 rule="hyper" parents="117 2372 2267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2375">
    <literal><![CDATA[
      T(x \ y,y \ x) = ((x \ y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(5(a,1),2372(a,1,2,1))].">
      <j1 rule="para" parents="5 2372"/>
    </justification>
  </clause>

  <clause id="2376">
    <literal><![CDATA[
      T(1 / (1 / x),(y * x) \ y) = x
    ]]></literal>
    <justification jstring="[hyper(1785,a,2373,a(flip))].">
      <j1 rule="hyper" parents="1785 2373"/>
    </justification>
  </clause>

  <clause id="2377">
    <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),2373(a,1,2,1))].">
      <j1 rule="para" parents="84 2373"/>
    </justification>
  </clause>

  <clause id="2378">
    <literal><![CDATA[
      T(1 / (1 / (x \ y)),y \ x) = x \ y
    ]]></literal>
    <justification jstring="[para(5(a,1),2376(a,1,2,1))].">
      <j1 rule="para" parents="5 2376"/>
    </justification>
  </clause>

  <clause id="2379">
    <literal><![CDATA[
      K(x,(y * x) \ y) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,1793,a(flip),b,2374,a),flip(a)].">
      <j1 rule="hyper" parents="320 1793 2374"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2380">
    <literal><![CDATA[
      K(x,(y * x) \ y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,1 / x) = z
    ]]></literal>
    <justification jstring="[para(2374(a,2),1279(a,1))].">
      <j1 rule="para" parents="2374 1279"/>
    </justification>
  </clause>

  <clause id="2381">
    <literal><![CDATA[
      K(x \ y,(x \ y) \ 1) = K(x \ y,y \ x)
    ]]></literal>
    <justification jstring="[para(5(a,1),2379(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 2379"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2382">
    <literal><![CDATA[
      K(x,y \ (y / x)) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(7(a,1),2379(a,1,2,1))].">
      <j1 rule="para" parents="7 2379"/>
    </justification>
  </clause>

  <clause id="2383">
    <literal><![CDATA[
      K(x \ y,T(y,x) \ ((y * x) / y)) = K(x \ y,(x \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(1151(a,2),2379(a,1,2,1))].">
      <j1 rule="para" parents="1151 2379"/>
    </justification>
  </clause>

  <clause id="2384">
    <literal><![CDATA[
      K(x,(y * x) \ y) \ 1 = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(2379(a,2),1828(a,1,1))].">
      <j1 rule="para" parents="2379 1828"/>
    </justification>
  </clause>

  <clause id="2385">
    <literal><![CDATA[
      T(K(x,(y * x) \ y),z) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(2379(a,2),2178(a,1,1))].">
      <j1 rule="para" parents="2379 2178"/>
    </justification>
  </clause>

  <clause id="2386">
    <literal><![CDATA[
      K((x / y) \ x,z \ (z / y)) = K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,674,a,b,2382,a)].">
      <j1 rule="hyper" parents="58 674 2382"/>
    </justification>
  </clause>

  <clause id="2387">
    <literal><![CDATA[
      T(x \ y,x / y) = T(x \ y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(320,a,2235,a,b,2375,a)].">
      <j1 rule="hyper" parents="320 2235 2375"/>
    </justification>
  </clause>

  <clause id="2388">
    <literal><![CDATA[
      1 / T(x \ y,y \ x) = (x \ y) \ 1
    ]]></literal>
    <justification jstring="[hyper(197,a,2375,a(flip))].">
      <j1 rule="hyper" parents="197 2375"/>
    </justification>
  </clause>

  <clause id="2389">
    <literal><![CDATA[
      T(K(x \ (x / (y \ 1)),x),T(y,x) \ y) = ((y \ T(y,x)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(1028(a,2),2375(a,1,1))].">
      <j1 rule="para" parents="1028 2375"/>
    </justification>
  </clause>

  <clause id="2390">
    <literal><![CDATA[
      x * K((x \ y) \ 1,x \ y) = y * (((y \ x) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(2375(a,1),1428(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2375 1428"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2391">
    <literal><![CDATA[
      K(x \ (x / T(y \ x,x \ y)),x) = T(K(x \ y,x),(y \ x) \ 1)
    ]]></literal>
    <justification jstring="[para(2375(a,2),1536(a,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2375 1536"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2392">
    <literal><![CDATA[
      (1 / (1 / (x \ y))) * (y \ x) = (y \ x) * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(119,a,2378,a(flip),b,17,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 2378 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2393">
    <literal><![CDATA[
      T(1 / (1 / K(x \ (x / (y \ 1)),x)),T(y,x) \ y) = y \ T(y,x)
    ]]></literal>
    <justification jstring="[para(1028(a,2),2378(a,1,1,2,2))].">
      <j1 rule="para" parents="1028 2378"/>
    </justification>
  </clause>

  <clause id="2394">
    <literal><![CDATA[
      L(K(x,x \ 1),x,y) = K(((y * x) \ y) \ 1,(y * x) \ y)
    ]]></literal>
    <justification jstring="[para(2385(a,1),2270(a,1,1))].">
      <j1 rule="para" parents="2385 2270"/>
    </justification>
  </clause>

  <clause id="2395">
    <literal><![CDATA[
      T(T(x / y,x \ y),y) = T(y \ x,y / x)
    ]]></literal>
    <justification jstring="[hyper(320,a,246,a,b,2387,a)].">
      <j1 rule="hyper" parents="320 246 2387"/>
    </justification>
  </clause>

  <clause id="2396">
    <literal><![CDATA[
      1 / T(x \ (x / y),y) = (x \ (x / y)) \ 1
    ]]></literal>
    <justification jstring="[para(75(a,1),2388(a,1,2,2))].">
      <j1 rule="para" parents="75 2388"/>
    </justification>
  </clause>

  <clause id="2397">
    <literal><![CDATA[
      L(x * ((y * x) \ y),x \ 1,y * x) = ((y * x) * (x \ 1)) \ y
    ]]></literal>
    <justification jstring="[para(2370(a,1),298(a,1,1))].">
      <j1 rule="para" parents="2370 298"/>
    </justification>
  </clause>

  <clause id="2398">
    <literal><![CDATA[
      (x \ y) * (1 / (x \ y)) = K(x \ y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(1800,a,2381,a)].">
      <j1 rule="hyper" parents="1800 2381"/>
    </justification>
  </clause>

  <clause id="2399">
    <literal><![CDATA[
      K((x * y) \ x,((x * y) \ x) \ 1) = K((x * y) \ x,y)
    ]]></literal>
    <justification jstring="[para(4(a,1),2381(a,2,2))].">
      <j1 rule="para" parents="4 2381"/>
    </justification>
  </clause>

  <clause id="2400">
    <literal><![CDATA[
      T(x,K(y \ z,z \ y)) = x
    ]]></literal>
    <justification jstring="[para(2381(a,1),2180(a,1,2))].">
      <j1 rule="para" parents="2381 2180"/>
    </justification>
  </clause>

  <clause id="2401">
    <literal><![CDATA[
      K(x \ y,y \ x) * z = z * K(x \ y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(2342,a,2400,a),flip(a)].">
      <j1 rule="hyper" parents="2342 2400"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2402">
    <literal><![CDATA[
      T(x / y,y / x) = T(x / y,x \ y)
    ]]></literal>
    <justification jstring="[hyper(35,a,246,a,b,2395,a)].">
      <j1 rule="hyper" parents="35 246 2395"/>
    </justification>
  </clause>

  <clause id="2403">
    <literal><![CDATA[
      T(x / y,x \ y) = ((x / y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(58,a,2069,a(flip),b,2402,a),flip(a)].">
      <j1 rule="hyper" parents="58 2069 2402"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2404">
    <literal><![CDATA[
      T(x / (x * y),y) = ((x / (x * y)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(4(a,1),2403(a,1,2))].">
      <j1 rule="para" parents="4 2403"/>
    </justification>
  </clause>

  <clause id="2405">
    <literal><![CDATA[
      L(x \ y,y \ x,x \ y) = 1 / (1 / (x \ y))
    ]]></literal>
    <justification jstring="[hyper(30,a,1762,a,b,2392,a)].">
      <j1 rule="hyper" parents="30 1762 2392"/>
    </justification>
  </clause>

  <clause id="2406">
    <literal><![CDATA[
      L(1 / (x \ y),x \ y,x) = 1 / (1 / (y \ x))
    ]]></literal>
    <justification jstring="[hyper(30,a,846,a,b,2392,a)].">
      <j1 rule="hyper" parents="30 846 2392"/>
    </justification>
  </clause>

  <clause id="2407">
    <literal><![CDATA[
      x * K(x \ y,(x \ y) \ 1) = y * (1 / (1 / (y \ x)))
    ]]></literal>
    <justification jstring="[para(2405(a,1),1865(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2405 1865"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2408">
    <literal><![CDATA[
      T(K(x,y),K(x,y) \ 1) = T(K(x,y),K(y,x))
    ]]></literal>
    <justification jstring="[para(11(a,2),2377(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11 2377"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2409">
    <literal><![CDATA[
      T(K(x,y),K(y,x)) = (K(x,y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(427,a,2408,a),flip(a)].">
      <j1 rule="hyper" parents="427 2408"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2410">
    <literal><![CDATA[
      (K(x,y) \ 1) \ 1 = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,2002,a(flip),b,2409,a),flip(a)].">
      <j1 rule="hyper" parents="58 2002 2409"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2413">
    <literal><![CDATA[
      1 / (1 / K(x,y)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(2410(a,1),190(a,1,2,2))].">
      <j1 rule="para" parents="2410 190"/>
    </justification>
  </clause>

  <clause id="2414">
    <literal><![CDATA[
      K(x,y) \ 1 != z
    ]]></literal>
    <literal><![CDATA[
      1 / K(x,y) = z
    ]]></literal>
    <justification jstring="[para(2413(a,1),267(a,1,1)),flip(b)].">
      <j1 rule="para" parents="2413 267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2415">
    <literal><![CDATA[
      x * K(x \ y,y \ x) = y * (1 / (1 / (y \ x)))
    ]]></literal>
    <justification jstring="[para(2381(a,1),2407(a,1,2))].">
      <j1 rule="para" parents="2381 2407"/>
    </justification>
  </clause>

  <clause id="2416">
    <literal><![CDATA[
      (x / y) * K(y,y \ 1) = x * (1 / (1 / (x \ (x / y))))
    ]]></literal>
    <justification jstring="[para(2386(a,1),2415(a,1,2))].">
      <j1 rule="para" parents="2386 2415"/>
    </justification>
  </clause>

  <clause id="2417">
    <literal><![CDATA[
      K((x * y) \ x,((x * y) \ x) \ 1) = L(K(y,y \ 1),y,x) \ 1
    ]]></literal>
    <justification jstring="[para(2394(a,2),432(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2394 432"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2419">
    <literal><![CDATA[
      K(x \ y,T(x / y,T(y,x))) = K(x \ y,(x \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(1501(a,1),2383(a,1,2))].">
      <j1 rule="para" parents="1501 2383"/>
    </justification>
  </clause>

  <clause id="2420">
    <literal><![CDATA[
      K(x \ y,T(x / y,T(y,x))) = K(x \ y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(320,a,2381,a(flip),b,2419,a),flip(a)].">
      <j1 rule="hyper" parents="320 2381 2419"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2421">
    <literal><![CDATA[
      L(x * ((y * x) \ y),x \ 1,y * x) = R(y,x,x \ 1) \ y
    ]]></literal>
    <justification jstring="[para(261(a,1),2397(a,2,1))].">
      <j1 rule="para" parents="261 2397"/>
    </justification>
  </clause>

  <clause id="2422">
    <literal><![CDATA[
      K((x * y) \ x,y) = L(K(y,y \ 1),y,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(58,a,2399,a(flip),b,2417,a)].">
      <j1 rule="hyper" parents="58 2399 2417"/>
    </justification>
  </clause>

  <clause id="2423">
    <literal><![CDATA[
      T(K(x \ y,x),(y \ x) \ 1) = T(K(x \ y,x),x \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,1535,a(flip),b,2391,a),flip(a)].">
      <j1 rule="hyper" parents="58 1535 2391"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2424">
    <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),2423(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4 2423"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2425">
    <literal><![CDATA[
      T(K(x \ (x / (y \ 1)),x),T(y,x) \ y) = y \ T(y,x)
    ]]></literal>
    <justification jstring="[para(2413(a,1),2393(a,1,1))].">
      <j1 rule="para" parents="2413 2393"/>
    </justification>
  </clause>

  <clause id="2426">
    <literal><![CDATA[
      ((x \ T(x,y)) \ 1) \ 1 = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,2389,a(flip),b,2425,a)].">
      <j1 rule="hyper" parents="58 2389 2425"/>
    </justification>
  </clause>

  <clause id="2427">
    <literal><![CDATA[
      1 / (x \ T(x,y)) = (x \ T(x,y)) \ 1
    ]]></literal>
    <justification jstring="[hyper(197,a,2426,a)].">
      <j1 rule="hyper" parents="197 2426"/>
    </justification>
  </clause>

  <clause id="2428">
    <literal><![CDATA[
      T(K(x,y),((y * x) \ y) \ 1) = T(K(x,y),y \ (y * x))
    ]]></literal>
    <justification jstring="[para(4(a,1),2424(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4 2424"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2429">
    <literal><![CDATA[
      T(K(x,y),((y * x) \ y) \ 1) = T(K(x,y),x)
    ]]></literal>
    <justification jstring="[para(4(a,1),2428(a,2,2))].">
      <j1 rule="para" parents="4 2428"/>
    </justification>
  </clause>

  <clause id="2431">
    <literal><![CDATA[
      ((x / y) * ((z * ((x / y) \ u)) / z)) * y = x * ((z * (x \ (u * y))) / z)
    ]]></literal>
    <justification jstring="[para(7(a,1),2307(a,2,2,1,2,1))].">
      <j1 rule="para" parents="7 2307"/>
    </justification>
  </clause>

  <clause id="2432">
    <literal><![CDATA[
      (x * ((y * (x \ (z * u))) / y)) / u = (x / u) * ((y * ((x / u) \ z)) / y)
    ]]></literal>
    <justification jstring="[hyper(131,a,2431,a)].">
      <j1 rule="hyper" parents="131 2431"/>
    </justification>
  </clause>

  <clause id="2433">
    <literal><![CDATA[
      (x / y) * ((z * ((x / y) \ 1)) / z) = (x * ((z * (x \ y)) / z)) / y
    ]]></literal>
    <justification jstring="[para(2(a,1),2432(a,1,1,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2 2432"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2434">
    <literal><![CDATA[
      (x * (T(y,x) / y)) \ (x * z) = x * ((x * (T(y,x) / y)) \ z)
    ]]></literal>
    <justification jstring="[para(2314(a,1),2315(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2314 2315"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2435">
    <literal><![CDATA[
      L(x * K(y \ 1,y),y,1 / y) = L(x,y,1 / y) * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(418,a,2330,a),flip(a)].">
      <j1 rule="hyper" parents="418 2330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2436">
    <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,1600,a(flip),b,2335,a),flip(a)].">
      <j1 rule="hyper" parents="320 1600 2335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2437">
    <literal><![CDATA[
      K(x,x \ 1) * T(K(x,x \ 1) \ y,z) = x * (T((x \ y) * x,z) / x)
    ]]></literal>
    <justification jstring="[para(1001(a,1),2343(a,2,2))].">
      <j1 rule="para" parents="1001 2343"/>
    </justification>
  </clause>

  <clause id="2438">
    <literal><![CDATA[
      K(x,x \ 1) * T(K(x,x \ 1) \ y,x) = T(y,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,1382,a(flip),b,2437,a),flip(a)].">
      <j1 rule="hyper" parents="320 1382 2437"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2439">
    <literal><![CDATA[
      T(x * K(y,y \ 1),y) = T(x,y) * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(741,a,2438,a),flip(a)].">
      <j1 rule="hyper" parents="741 2438"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2440">
    <literal><![CDATA[
      T((1 / K(x,x \ 1)) * y,x) = (1 / K(x,x \ 1)) * T(y,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,2438,a(flip),b,947,a),flip(a)].">
      <j1 rule="hyper" parents="119 2438 947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2441">
    <literal><![CDATA[
      T(K(x,x \ 1) * y,x) = K(x,x \ 1) * T(y,x)
    ]]></literal>
    <justification jstring="[para(4(a,1),2438(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4 2438"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2442">
    <literal><![CDATA[
      T((x / y) * K(y,y \ 1),y) = (y \ x) * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[para(107(a,1),2439(a,2,1))].">
      <j1 rule="para" parents="107 2439"/>
    </justification>
  </clause>

  <clause id="2443">
    <literal><![CDATA[
      x * T(K(x,x \ 1) * y,x) = K(x,x \ 1) * (y * x)
    ]]></literal>
    <justification jstring="[para(2441(a,2),1861(a,1,2))].">
      <j1 rule="para" parents="2441 1861"/>
    </justification>
  </clause>

  <clause id="2444">
    <literal><![CDATA[
      x \ (y * K(x,x \ 1)) = (x \ y) * K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(2039,a,2442,a)].">
      <j1 rule="hyper" parents="2039 2442"/>
    </justification>
  </clause>

  <clause id="2445">
    <literal><![CDATA[
      x * ((x \ y) * K(x,x \ 1)) = y * K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(119,a,2442,a(flip),b,2035,a(flip))].">
      <j1 rule="hyper" parents="119 2442 2035"/>
    </justification>
  </clause>

  <clause id="2446">
    <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(2442(a,2),39(a,1))].">
      <j1 rule="para" parents="2442 39"/>
    </justification>
  </clause>

  <clause id="2447">
    <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),2444(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="75 2444"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2448">
    <literal><![CDATA[
      (x * y) * K(x,x \ 1) = x * (y * K(x,x \ 1))
    ]]></literal>
    <justification jstring="[para(4(a,1),2445(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4 2445"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2449">
    <literal><![CDATA[
      R(x,y,K(x,x \ 1)) = x
    ]]></literal>
    <justification jstring="[hyper(515,a,2448,a)].">
      <j1 rule="hyper" parents="515 2448"/>
    </justification>
  </clause>

  <clause id="2450">
    <literal><![CDATA[
      (1 / x) * (y * K(1 / x,(1 / x) \ 1)) = ((1 / x) * y) * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(1826(a,1),2448(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1826 2448"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2451">
    <literal><![CDATA[
      R(T(x,y),z,K(x,x \ 1)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(2449(a,1),22(a,2,1))].">
      <j1 rule="para" parents="2449 22"/>
    </justification>
  </clause>

  <clause id="2452">
    <literal><![CDATA[
      T(x,y * K(x,x \ 1)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,2038,a(flip),b,2451,a),flip(a)].">
      <j1 rule="hyper" parents="58 2038 2451"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2454">
    <literal><![CDATA[
      T(x \ 1,y * K(x \ 1,x)) = T(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(1798(a,1),2452(a,1,2,2))].">
      <j1 rule="para" parents="1798 2452"/>
    </justification>
  </clause>

  <clause id="2455">
    <literal><![CDATA[
      T(x,R(x \ 1,x,y)) = T(x,y / (x * y))
    ]]></literal>
    <justification jstring="[para(2063(a,2),2452(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2063 2452"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2456">
    <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(2455(a,1),230(a,1,2,1))].">
      <j1 rule="para" parents="2455 230"/>
    </justification>
  </clause>

  <clause id="2457">
    <literal><![CDATA[
      (K(x,x \ 1) * y) * x = K(x,x \ 1) * (y * x)
    ]]></literal>
    <justification jstring="[hyper(284,a,2443,a)].">
      <j1 rule="hyper" parents="284 2443"/>
    </justification>
  </clause>

  <clause id="2458">
    <literal><![CDATA[
      K(x,x \ 1) * (y * x) != z
    ]]></literal>
    <literal><![CDATA[
      (K(x,x \ 1) * y) * x = z
    ]]></literal>
    <justification jstring="[para(2443(a,1),284(a,1))].">
      <j1 rule="para" parents="2443 284"/>
    </justification>
  </clause>

  <clause id="2459">
    <literal><![CDATA[
      L(x,y,K(x,x \ 1)) = x
    ]]></literal>
    <justification jstring="[hyper(479,a,2457,a)].">
      <j1 rule="hyper" parents="479 2457"/>
    </justification>
  </clause>

  <clause id="2460">
    <literal><![CDATA[
      L(1 / x,y,K(x \ 1,x)) = 1 / x
    ]]></literal>
    <justification jstring="[para(1826(a,1),2459(a,1,3))].">
      <j1 rule="para" parents="1826 2459"/>
    </justification>
  </clause>

  <clause id="2461">
    <literal><![CDATA[
      L(T(1 / x,y),z,K(x \ 1,x)) = T(1 / x,y)
    ]]></literal>
    <justification jstring="[para(2460(a,1),20(a,2,1))].">
      <j1 rule="para" parents="2460 20"/>
    </justification>
  </clause>

  <clause id="2462">
    <literal><![CDATA[
      (1 / K(x,x \ 1)) * T(y,x) = T(K(x \ 1,x) * y,x)
    ]]></literal>
    <justification jstring="[para(468(a,1),2440(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="468 2440"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2463">
    <literal><![CDATA[
      T(K(x \ 1,x) * y,x) = K(x \ 1,x) * T(y,x)
    ]]></literal>
    <justification jstring="[para(468(a,1),2462(a,1,1)),flip(a)].">
      <j1 rule="para" parents="468 2462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2464">
    <literal><![CDATA[
      x * T(K(x \ 1,x) * y,x) = K(x \ 1,x) * (y * x)
    ]]></literal>
    <justification jstring="[para(2463(a,2),1397(a,1,2))].">
      <j1 rule="para" parents="2463 1397"/>
    </justification>
  </clause>

  <clause id="2465">
    <literal><![CDATA[
      (K(x \ 1,x) * y) * x = K(x \ 1,x) * (y * x)
    ]]></literal>
    <justification jstring="[hyper(284,a,2464,a)].">
      <j1 rule="hyper" parents="284 2464"/>
    </justification>
  </clause>

  <clause id="2466">
    <literal><![CDATA[
      L(x,y,K(x \ 1,x)) = x
    ]]></literal>
    <justification jstring="[hyper(479,a,2465,a)].">
      <j1 rule="hyper" parents="479 2465"/>
    </justification>
  </clause>

  <clause id="2467">
    <literal><![CDATA[
      L(T(x,y),z,K(x \ 1,x)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(2466(a,1),20(a,2,1))].">
      <j1 rule="para" parents="2466 20"/>
    </justification>
  </clause>

  <clause id="2468">
    <literal><![CDATA[
      T(x,K(x \ 1,x) * y) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(2092,a,2467,a)].">
      <j1 rule="hyper" parents="2092 2467"/>
    </justification>
  </clause>

  <clause id="2469">
    <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(436(a,1),2447(a,1,1)),flip(a)].">
      <j1 rule="para" parents="436 2447"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2470">
    <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(2150(a,1),2450(a,2,1))].">
      <j1 rule="para" parents="2150 2450"/>
    </justification>
  </clause>

  <clause id="2471">
    <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(1827(a,1),2469(a,1,2,2))].">
      <j1 rule="para" parents="1827 2469"/>
    </justification>
  </clause>

  <clause id="2472">
    <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(2435(a,2),2471(a,1,2))].">
      <j1 rule="para" parents="2435 2471"/>
    </justification>
  </clause>

  <clause id="2473">
    <literal><![CDATA[
      (x * y) * K(1 / x,(1 / x) \ 1) = x * (y * K(x \ 1,x))
    ]]></literal>
    <justification jstring="[hyper(555,a,2472,a),flip(a)].">
      <j1 rule="hyper" parents="555 2472"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2474">
    <literal><![CDATA[
      (x * y) * K(x \ 1,x) = x * (y * K(x \ 1,x))
    ]]></literal>
    <justification jstring="[para(1826(a,1),2473(a,1,2))].">
      <j1 rule="para" parents="1826 2473"/>
    </justification>
  </clause>

  <clause id="2475">
    <literal><![CDATA[
      R(x,y,K(x \ 1,x)) = x
    ]]></literal>
    <justification jstring="[hyper(515,a,2474,a)].">
      <j1 rule="hyper" parents="515 2474"/>
    </justification>
  </clause>

  <clause id="2476">
    <literal><![CDATA[
      x * ((T(x,y) \ 1) * K(x \ 1,x)) = (T(x,y) \ x) * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(1118(a,1),2474(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1118 2474"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2477">
    <literal><![CDATA[
      R(T(x,y),z,K(x \ 1,x)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(2475(a,1),22(a,2,1))].">
      <j1 rule="para" parents="2475 22"/>
    </justification>
  </clause>

  <clause id="2478">
    <literal><![CDATA[
      x * (y * K(x \ 1,x)) != z
    ]]></literal>
    <literal><![CDATA[
      (x * y) * K(x \ 1,x) = z
    ]]></literal>
    <justification jstring="[para(2475(a,1),283(a,1,1))].">
      <j1 rule="para" parents="2475 283"/>
    </justification>
  </clause>

  <clause id="2479">
    <literal><![CDATA[
      (T(x,y) \ 1) * K(x \ 1,x) = T(x,y) \ K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(2477(a,1),425(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2477 425"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2480">
    <literal><![CDATA[
      (T(x,y) \ x) * K(x \ 1,x) = x * (T(x,y) \ K(x \ 1,x))
    ]]></literal>
    <justification jstring="[para(2479(a,1),2476(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2479 2476"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2481">
    <literal><![CDATA[
      (T(x,y) \ x) * K(x \ 1,x) = T(x,y) \ (1 / (1 / x))
    ]]></literal>
    <justification jstring="[hyper(320,a,1810,a(flip),b,2480,a),flip(a)].">
      <j1 rule="hyper" parents="320 1810 2480"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2482">
    <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,725,a),flip(a)].">
      <j1 rule="hyper" parents="320 512 725"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2483">
    <literal><![CDATA[
      x * (K(x,y) * T(K(x,y) \ y,z)) = (T(y,z) * x) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(929,a,2482,a)].">
      <j1 rule="hyper" parents="929 2482"/>
    </justification>
  </clause>

  <clause id="2484">
    <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),2483(a,1,2)),flip(a)].">
      <j1 rule="para" parents="105 2483"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2485">
    <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,1761,a(flip),b,1086,a)].">
      <j1 rule="hyper" parents="58 1761 1086"/>
    </justification>
  </clause>

  <clause id="2487">
    <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(2485(a,1),869(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2485 869"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2488">
    <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,636,a(flip),b,2487,a),flip(a)].">
      <j1 rule="hyper" parents="320 636 2487"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2489">
    <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,1733,a(flip),b,2488,a),flip(a)].">
      <j1 rule="hyper" parents="58 1733 2488"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2490">
    <literal><![CDATA[
      (x * y) * K(z \ (z / L(u,y,x)),z) = x * ((y * u) * T((y * u) \ y,z))
    ]]></literal>
    <justification jstring="[hyper(929,a,1434,a),flip(a)].">
      <j1 rule="hyper" parents="929 1434"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2491">
    <literal><![CDATA[
      (x * y) * K(z \ (z / L(u,y,x)),z) = x * (y * (u * T(u \ 1,z)))
    ]]></literal>
    <justification jstring="[para(736(a,1),2490(a,2,2))].">
      <j1 rule="para" parents="736 2490"/>
    </justification>
  </clause>

  <clause id="2492">
    <literal><![CDATA[
      L(x * T(x \ 1,y),z,u) = K(y \ (y / L(x,z,u)),y)
    ]]></literal>
    <justification jstring="[hyper(479,a,2491,a)].">
      <j1 rule="hyper" parents="479 2491"/>
    </justification>
  </clause>

  <clause id="2493">
    <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,1025,a(flip),b,2492,a)].">
      <j1 rule="hyper" parents="320 1025 2492"/>
    </justification>
  </clause>

  <clause id="2494">
    <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),2492(a,2,1,2))].">
      <j1 rule="para" parents="69 2492"/>
    </justification>
  </clause>

  <clause id="2495">
    <literal><![CDATA[
      L(x \ T(x,y),z,u) = K(y \ (y / L(x \ 1,z,u)),y)
    ]]></literal>
    <justification jstring="[para(991(a,1),2492(a,1,1))].">
      <j1 rule="para" parents="991 2492"/>
    </justification>
  </clause>

  <clause id="2496">
    <literal><![CDATA[
      L(T(x,y) / x,z,u) = K(y \ (y / L(1 / x,z,u)),y)
    ]]></literal>
    <justification jstring="[para(1007(a,1),2492(a,1,1))].">
      <j1 rule="para" parents="1007 2492"/>
    </justification>
  </clause>

  <clause id="2497">
    <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),2495(a,2,1,2))].">
      <j1 rule="para" parents="6 2495"/>
    </justification>
  </clause>

  <clause id="2498">
    <literal><![CDATA[
      K(x \ (x / R(y,z,u)),x) = (((y * z) * T((y * z) \ z,x)) * u) / (z * u)
    ]]></literal>
    <justification jstring="[para(1486(a,1),1591(a,2,1))].">
      <j1 rule="para" parents="1486 1591"/>
    </justification>
  </clause>

  <clause id="2499">
    <literal><![CDATA[
      K(x \ (x / R(y,z,u)),x) = (((y * T(y \ 1,x)) * z) * u) / (z * u)
    ]]></literal>
    <justification jstring="[para(1226(a,1),2498(a,2,1,1))].">
      <j1 rule="para" parents="1226 2498"/>
    </justification>
  </clause>

  <clause id="2500">
    <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,2499,a)].">
      <j1 rule="hyper" parents="320 15 2499"/>
    </justification>
  </clause>

  <clause id="2501">
    <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(2499(a,2),518(a,1))].">
      <j1 rule="para" parents="2499 518"/>
    </justification>
  </clause>

  <clause id="2502">
    <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,1025,a(flip),b,2500,a)].">
      <j1 rule="hyper" parents="320 1025 2500"/>
    </justification>
  </clause>

  <clause id="2503">
    <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(1211(a,1),2500(a,2,1,2))].">
      <j1 rule="para" parents="1211 2500"/>
    </justification>
  </clause>

  <clause id="2504">
    <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(1025(a,1),2501(a,1))].">
      <j1 rule="para" parents="1025 2501"/>
    </justification>
  </clause>

  <clause id="2505">
    <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,2502,a),flip(a)].">
      <j1 rule="hyper" parents="284 2502"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2506">
    <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),1661(a,1,1))].">
      <j1 rule="para" parents="60 1661"/>
    </justification>
  </clause>

  <clause id="2507">
    <literal><![CDATA[
      (((x * y) \ x) \ K(y,x)) / (((x * y) \ x) \ 1) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,1023,a,b,1049,a),flip(a)].">
      <j1 rule="hyper" parents="320 1023 1049"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2508">
    <literal><![CDATA[
      (((x * y) \ x) \ 1) \ (((x * y) \ x) \ K(y,x)) = T(K(y,x),((x * y) \ x) \ 1)
    ]]></literal>
    <justification jstring="[para(2507(a,1),107(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2507 107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2509">
    <literal><![CDATA[
      (((x * y) \ x) \ 1) \ (((x * y) \ x) \ K(y,x)) = T(K(y,x),y)
    ]]></literal>
    <justification jstring="[hyper(320,a,2429,a(flip),b,2508,a),flip(a)].">
      <j1 rule="hyper" parents="320 2429 2508"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2510">
    <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),1087(a,1,2,1,1))].">
      <j1 rule="para" parents="258 1087"/>
    </justification>
  </clause>

  <clause id="2511">
    <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),1090(a,1,2,1,1))].">
      <j1 rule="para" parents="258 1090"/>
    </justification>
  </clause>

  <clause id="2512">
    <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),1244(a,1,1))].">
      <j1 rule="para" parents="17 1244"/>
    </justification>
  </clause>

  <clause id="2513">
    <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(2455(a,1),2512(a,2,2))].">
      <j1 rule="para" parents="2455 2512"/>
    </justification>
  </clause>

  <clause id="2514">
    <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(2493(a,1),1419(a,1,1))].">
      <j1 rule="para" parents="2493 1419"/>
    </justification>
  </clause>

  <clause id="2515">
    <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),2514(a,1,1,1))].">
      <j1 rule="para" parents="358 2514"/>
    </justification>
  </clause>

  <clause id="2516">
    <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(1413(a,1),2515(a,1,2))].">
      <j1 rule="para" parents="1413 2515"/>
    </justification>
  </clause>

  <clause id="2517">
    <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,2516,a)].">
      <j1 rule="hyper" parents="58 20 2516"/>
    </justification>
  </clause>

  <clause id="2518">
    <literal><![CDATA[
      L(T(K(x \ 1,x),L(x,y,z) \ x),y,z) = K(L(x,y,z) \ 1,x)
    ]]></literal>
    <justification jstring="[para(1415(a,1),2517(a,2,1))].">
      <j1 rule="para" parents="1415 2517"/>
    </justification>
  </clause>

  <clause id="2519">
    <literal><![CDATA[
      L(K(x \ 1,x),y,z) = K(L(x,y,z) \ 1,x)
    ]]></literal>
    <justification jstring="[para(2191(a,1),2518(a,1,1))].">
      <j1 rule="para" parents="2191 2518"/>
    </justification>
  </clause>

  <clause id="2520">
    <literal><![CDATA[
      (x * y) * K(L(z,y,x) \ 1,z) = x * (y * K(z \ 1,z))
    ]]></literal>
    <justification jstring="[hyper(119,a,2519,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="119 2519 13"/>
    </justification>
  </clause>

  <clause id="2522">
    <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),2271(a,1,1))].">
      <j1 rule="para" parents="85 2271"/>
    </justification>
  </clause>

  <clause id="2523">
    <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),2522(a,1,2,1,1))].">
      <j1 rule="para" parents="85 2522"/>
    </justification>
  </clause>

  <clause id="2524">
    <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,2362,a(flip),b,2470,a),flip(a)].">
      <j1 rule="hyper" parents="320 2362 2470"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2525">
    <literal><![CDATA[
      (1 / x) * ((T(x,y) \ x) * K(x \ 1,x)) = (x \ 1) * (T(x,y) \ x)
    ]]></literal>
    <justification jstring="[para(1826(a,1),2524(a,1,2,2))].">
      <j1 rule="para" parents="1826 2524"/>
    </justification>
  </clause>

  <clause id="2526">
    <literal><![CDATA[
      (1 / x) * (T(x,y) \ (1 / (1 / x))) = (x \ 1) * (T(x,y) \ x)
    ]]></literal>
    <justification jstring="[para(2481(a,1),2525(a,1,2))].">
      <j1 rule="para" parents="2481 2525"/>
    </justification>
  </clause>

  <clause id="2527">
    <literal><![CDATA[
      (1 / x) * ((T(x,y) \ 1) * x) = (x \ 1) * (T(x,y) \ x)
    ]]></literal>
    <justification jstring="[para(2234(a,1),2526(a,1,2))].">
      <j1 rule="para" parents="2234 2526"/>
    </justification>
  </clause>

  <clause id="2528">
    <literal><![CDATA[
      (x \ 1) \ (T(x,y) \ 1) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(116,a,2153,a(flip),b,2527,a(flip))].">
      <j1 rule="hyper" parents="116 2153 2527"/>
    </justification>
  </clause>

  <clause id="2529">
    <literal><![CDATA[
      (x \ T(x,y)) \ 1 = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(58,a,2124,a(flip),b,2528,a)].">
      <j1 rule="hyper" parents="58 2124 2528"/>
    </justification>
  </clause>

  <clause id="2530">
    <literal><![CDATA[
      1 / (x \ T(x,y)) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(58,a,2427,a,b,2529,a)].">
      <j1 rule="hyper" parents="58 2427 2529"/>
    </justification>
  </clause>

  <clause id="2531">
    <literal><![CDATA[
      T(x / y,y) \ (x / y) = ((x / y) \ (y \ x)) \ 1
    ]]></literal>
    <justification jstring="[para(107(a,1),2529(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="107 2529"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2532">
    <literal><![CDATA[
      T(x,R(y,x,(y * x) \ x)) \ x = (x \ (x * K(x,y))) \ 1
    ]]></literal>
    <justification jstring="[para(1740(a,1),2529(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1740 2529"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2533">
    <literal><![CDATA[
      ((x / y) \ (y \ x)) \ 1 = (y \ x) \ (x / y)
    ]]></literal>
    <justification jstring="[para(107(a,1),2531(a,1,1)),flip(a)].">
      <j1 rule="para" parents="107 2531"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2534">
    <literal><![CDATA[
      (x \ (x * y)) \ ((x * y) / x) = (((x * y) / x) \ y) \ 1
    ]]></literal>
    <justification jstring="[para(4(a,1),2533(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4 2533"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2535">
    <literal><![CDATA[
      (((x * y) / x) \ y) \ 1 = y \ ((x * y) / x)
    ]]></literal>
    <justification jstring="[para(4(a,1),2534(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4 2534"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2536">
    <literal><![CDATA[
      1 / (x \ ((y * x) / y)) = ((y * x) / y) \ x
    ]]></literal>
    <justification jstring="[hyper(197,a,2535,a)].">
      <j1 rule="hyper" parents="197 2535"/>
    </justification>
  </clause>

  <clause id="2537">
    <literal><![CDATA[
      T(x,R(y,x,(y * x) \ x)) \ x = K(x,y) \ 1
    ]]></literal>
    <justification jstring="[para(4(a,1),2532(a,2,1))].">
      <j1 rule="para" parents="4 2532"/>
    </justification>
  </clause>

  <clause id="2539">
    <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,1869,a(flip),b,2510,a),flip(a)].">
      <j1 rule="hyper" parents="320 1869 2510"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2540">
    <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,1749,a(flip),b,2511,a),flip(a)].">
      <j1 rule="hyper" parents="320 1749 2511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2541">
    <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(1091(a,1),2539(a,2,1))].">
      <j1 rule="para" parents="1091 2539"/>
    </justification>
  </clause>

  <clause id="2542">
    <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(1069(a,1),2540(a,2,1))].">
      <j1 rule="para" parents="1069 2540"/>
    </justification>
  </clause>

  <clause id="2543">
    <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,851,a),flip(a)].">
      <j1 rule="hyper" parents="320 514 851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2544">
    <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(1371,a,2543,a)].">
      <j1 rule="hyper" parents="1371 2543"/>
    </justification>
  </clause>

  <clause id="2545">
    <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(1251(a,1),2544(a,2,1,1))].">
      <j1 rule="para" parents="1251 2544"/>
    </justification>
  </clause>

  <clause id="2546">
    <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),1921(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="17 1921"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2547">
    <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),2546(a,2,2))].">
      <j1 rule="para" parents="238 2546"/>
    </justification>
  </clause>

  <clause id="2548">
    <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),1930(a,2,1,2))].">
      <j1 rule="para" parents="3 1930"/>
    </justification>
  </clause>

  <clause id="2549">
    <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(2209,a,2208,a),flip(a)].">
      <j1 rule="hyper" parents="2209 2208"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2550">
    <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(2220,a,2219,a),flip(a)].">
      <j1 rule="hyper" parents="2220 2219"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2551">
    <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),1189(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="75 1189"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2552">
    <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),2551(a,2,2,2,1))].">
      <j1 rule="para" parents="75 2551"/>
    </justification>
  </clause>

  <clause id="2553">
    <literal><![CDATA[
      x * T(x \ T(x,y),(1 / x) \ 1) = (1 / x) \ (x \ T(x,y))
    ]]></literal>
    <justification jstring="[para(75(a,1),2552(a,1,2,1,2,1))].">
      <j1 rule="para" parents="75 2552"/>
    </justification>
  </clause>

  <clause id="2554">
    <literal><![CDATA[
      (1 / x) \ (x \ T(x,y)) = x * T(x \ T(x,y),x)
    ]]></literal>
    <justification jstring="[para(75(a,1),2553(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="75 2553"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2555">
    <literal><![CDATA[
      (1 / x) \ (x \ T(x,y)) = (x \ T(x,y)) * x
    ]]></literal>
    <justification jstring="[hyper(320,a,105,a(flip),b,2554,a),flip(a)].">
      <j1 rule="hyper" parents="320 105 2554"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2556">
    <literal><![CDATA[
      (x \ T(x,R(y,x,(y * x) \ x))) * x = (1 / x) \ (x \ (x * K(x,y)))
    ]]></literal>
    <justification jstring="[para(1740(a,1),2555(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="1740 2555"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2557">
    <literal><![CDATA[
      (x \ T(x,R(y,x,(y * x) \ x))) * x = (1 / x) \ K(x,y)
    ]]></literal>
    <justification jstring="[para(4(a,1),2556(a,2,2))].">
      <j1 rule="para" parents="4 2556"/>
    </justification>
  </clause>

  <clause id="2559">
    <literal><![CDATA[
      (x \ (x * K(x,y))) * x = (1 / x) \ K(x,y)
    ]]></literal>
    <justification jstring="[para(1740(a,1),2557(a,1,1,2))].">
      <j1 rule="para" parents="1740 2557"/>
    </justification>
  </clause>

  <clause id="2560">
    <literal><![CDATA[
      (1 / x) \ K(x,y) = K(x,y) * x
    ]]></literal>
    <justification jstring="[para(4(a,1),2559(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4 2559"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2562">
    <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,1817,a(flip),b,1919,a),flip(a)].">
      <j1 rule="hyper" parents="320 1817 1919"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2563">
    <literal><![CDATA[
      K(x,x \ 1) * (T(x,x \ 1) \ y) = L(x \ y,x,K(x,x \ 1))
    ]]></literal>
    <justification jstring="[para(1918(a,1),2562(a,1,1))].">
      <j1 rule="para" parents="1918 2562"/>
    </justification>
  </clause>

  <clause id="2564">
    <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),2563(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="106 2563"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2565">
    <literal><![CDATA[
      (x * y) * (1 / (1 / ((x * y) \ x))) != x * z
    ]]></literal>
    <literal><![CDATA[
      y * L(y \ 1,((x * y) \ x) \ 1,L(y \ 1,y,x)) = z
    ]]></literal>
    <justification jstring="[para(2334(a,1),38(a,1))].">
      <j1 rule="para" parents="2334 38"/>
    </justification>
  </clause>

  <clause id="2566">
    <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(1756(a,1),2497(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1756 2497"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2567">
    <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),2566(a,2,1))].">
      <j1 rule="para" parents="61 2566"/>
    </justification>
  </clause>

  <clause id="2568">
    <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,2567,a),flip(a)].">
      <j1 rule="hyper" parents="320 179 2567"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2571">
    <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,2568,a(flip))].">
      <j1 rule="hyper" parents="167 85 2568"/>
    </justification>
  </clause>

  <clause id="2572">
    <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(2571(a,1),39(a,1)),flip(a)].">
      <j1 rule="para" parents="2571 39"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2573">
    <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(1897(a,1),1737(a,1,2,1))].">
      <j1 rule="para" parents="1897 1737"/>
    </justification>
  </clause>

  <clause id="2574">
    <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),2573(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6 2573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2576">
    <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(2574(a,1),340(a,2,2))].">
      <j1 rule="para" parents="2574 340"/>
    </justification>
  </clause>

  <clause id="2577">
    <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),1734(a,2,2))].">
      <j1 rule="para" parents="6 1734"/>
    </justification>
  </clause>

  <clause id="2578">
    <literal><![CDATA[
      (((x \ y) * (y \ x)) / (x \ y)) * ((y \ x) \ 1) = K(x \ y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,981,a(flip),b,2577,a)].">
      <j1 rule="hyper" parents="58 981 2577"/>
    </justification>
  </clause>

  <clause id="2580">
    <literal><![CDATA[
      L(1 / (x \ y),x \ y,x) * ((y \ x) \ 1) = K(x \ y,y \ x)
    ]]></literal>
    <justification jstring="[para(847(a,1),2578(a,1,1))].">
      <j1 rule="para" parents="847 2578"/>
    </justification>
  </clause>

  <clause id="2581">
    <literal><![CDATA[
      (x \ y) * K(y \ x,x \ y) = L(1 / (y \ x),y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(30,a,2355,a,b,2580,a)].">
      <j1 rule="hyper" parents="30 2355 2580"/>
    </justification>
  </clause>

  <clause id="2582">
    <literal><![CDATA[
      (x \ y) * K(y \ x,x \ y) = 1 / (1 / (x \ y))
    ]]></literal>
    <justification jstring="[hyper(320,a,2406,a(flip),b,2581,a),flip(a)].">
      <j1 rule="hyper" parents="320 2406 2581"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2583">
    <literal><![CDATA[
      K((x \ y) \ 1,x \ y) = K(y \ x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(29,a,1790,a,b,2582,a)].">
      <j1 rule="hyper" parents="29 1790 2582"/>
    </justification>
  </clause>

  <clause id="2584">
    <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,2583,a),flip(a)].">
      <j1 rule="hyper" parents="320 673 2583"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2585">
    <literal><![CDATA[
      K(1 / (x \ y),x \ y) = K(y \ x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,1827,a,b,2583,a)].">
      <j1 rule="hyper" parents="58 1827 2583"/>
    </justification>
  </clause>

  <clause id="2586">
    <literal><![CDATA[
      x * K(y \ x,x \ y) = y * (((y \ x) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(2583(a,1),2390(a,1,2))].">
      <j1 rule="para" parents="2583 2390"/>
    </justification>
  </clause>

  <clause id="2587">
    <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,2585,a),flip(a)].">
      <j1 rule="hyper" parents="320 673 2585"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2588">
    <literal><![CDATA[
      L(K(x,x \ 1),x,y) = K(x,(y * x) \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,2394,a,b,2584,a)].">
      <j1 rule="hyper" parents="58 2394 2584"/>
    </justification>
  </clause>

  <clause id="2589">
    <literal><![CDATA[
      (x * y) * K(y,(x * y) \ x) = x * T(y,(x * y) \ x)
    ]]></literal>
    <justification jstring="[para(2584(a,1),1438(a,1,2))].">
      <j1 rule="para" parents="2584 1438"/>
    </justification>
  </clause>

  <clause id="2590">
    <literal><![CDATA[
      L(K(x,x \ 1),x,y) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,2379,a(flip),b,2588,a),flip(a)].">
      <j1 rule="hyper" parents="320 2379 2588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2591">
    <literal><![CDATA[
      K(x,(y * x) \ y) \ 1 = K((y * x) \ y,x)
    ]]></literal>
    <justification jstring="[para(2588(a,1),2422(a,2,1)),flip(a)].">
      <j1 rule="para" parents="2588 2422"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2593">
    <literal><![CDATA[
      L(K(x \ 1,x),1 / x,y) = K(1 / x,(1 / x) \ 1)
    ]]></literal>
    <justification jstring="[para(1826(a,1),2590(a,1,1))].">
      <j1 rule="para" parents="1826 2590"/>
    </justification>
  </clause>

  <clause id="2594">
    <literal><![CDATA[
      K((x * y) \ x,y) = K(y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,2384,a(flip),b,2591,a),flip(a)].">
      <j1 rule="hyper" parents="58 2384 2591"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2596">
    <literal><![CDATA[
      K(T(x,y) \ 1,T(x,y)) = K((x * y) \ y,T(x,y))
    ]]></literal>
    <justification jstring="[para(105(a,1),2594(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="105 2594"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2597">
    <literal><![CDATA[
      K((x * y) \ y,y \ (x * y)) = K(T(x,y) \ 1,T(x,y))
    ]]></literal>
    <justification jstring="[para(17(a,1),2596(a,2,2)),flip(a)].">
      <j1 rule="para" parents="17 2596"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2598">
    <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(1500(a,1),2596(a,2,1,1))].">
      <j1 rule="para" parents="1500 2596"/>
    </justification>
  </clause>

  <clause id="2599">
    <literal><![CDATA[
      L(K(x \ 1,x),1 / x,y) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,1826,a(flip),b,2593,a),flip(a)].">
      <j1 rule="hyper" parents="320 1826 2593"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2600">
    <literal><![CDATA[
      (x * (y \ 1)) / K(y \ 1,y) = x * (1 / y)
    ]]></literal>
    <justification jstring="[para(2599(a,1),782(a,1,2))].">
      <j1 rule="para" parents="2599 782"/>
    </justification>
  </clause>

  <clause id="2601">
    <literal><![CDATA[
      (x / (y \ 1)) * (1 / y) = x / K(y \ 1,y)
    ]]></literal>
    <justification jstring="[para(2599(a,1),783(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2599 783"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2602">
    <literal><![CDATA[
      R(x,y \ 1,y) / y = x * (1 / y)
    ]]></literal>
    <justification jstring="[hyper(1613,a,2600,a)].">
      <j1 rule="hyper" parents="1613 2600"/>
    </justification>
  </clause>

  <clause id="2603">
    <literal><![CDATA[
      (x / (1 / y)) * (y \ 1) = x * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(325,a,2600,a),flip(a)].">
      <j1 rule="hyper" parents="325 2600"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2604">
    <literal><![CDATA[
      (x * (1 / y)) * K(y \ 1,y) = x * (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(133,a,2600,a)].">
      <j1 rule="hyper" parents="133 2600"/>
    </justification>
  </clause>

  <clause id="2605">
    <literal><![CDATA[
      (x * (1 / y)) * y = R(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[para(2600(a,1),1612(a,1,1))].">
      <j1 rule="para" parents="2600 1612"/>
    </justification>
  </clause>

  <clause id="2607">
    <literal><![CDATA[
      R(x,1 / y,y) = R(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(1080,a,2602,a),flip(a)].">
      <j1 rule="hyper" parents="1080 2602"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2608">
    <literal><![CDATA[
      R(T(x / (1 / y),z),y \ 1,y) = T(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(1004,a,2602,a),flip(a)].">
      <j1 rule="hyper" parents="1004 2602"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2609">
    <literal><![CDATA[
      R(x / (1 / y),y \ 1,y) = x * y
    ]]></literal>
    <justification jstring="[hyper(325,a,2602,a),flip(a)].">
      <j1 rule="hyper" parents="325 2602"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2610">
    <literal><![CDATA[
      x / y != z * (1 / y)
    ]]></literal>
    <literal><![CDATA[
      R(z,y \ 1,y) = x
    ]]></literal>
    <justification jstring="[para(2602(a,1),41(a,1)),flip(a)].">
      <j1 rule="para" parents="2602 41"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2611">
    <literal><![CDATA[
      x \ R(y,x \ 1,x) = T(y * (1 / x),x)
    ]]></literal>
    <justification jstring="[para(2602(a,1),107(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2602 107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2612">
    <literal><![CDATA[
      (x * (1 / y)) * y != z
    ]]></literal>
    <literal><![CDATA[
      R(x,y \ 1,y) = z
    ]]></literal>
    <justification jstring="[para(2602(a,1),251(a,1,1)),flip(b)].">
      <j1 rule="para" parents="2602 251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2613">
    <literal><![CDATA[
      R(x,(y \ 1) \ 1,y \ 1) = R(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[para(72(a,1),2607(a,1,2)),flip(a)].">
      <j1 rule="para" parents="72 2607"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2614">
    <literal><![CDATA[
      ((1 / x) * K(y,x)) * x = R(K(y,x),x \ 1,x)
    ]]></literal>
    <justification jstring="[para(2281(a,1),2605(a,1,1))].">
      <j1 rule="para" parents="2281 2605"/>
    </justification>
  </clause>

  <clause id="2615">
    <literal><![CDATA[
      ((1 / x) * (y * x)) \ (y * R(y / (1 / x),x \ 1,x)) = (1 / x) \ y
    ]]></literal>
    <justification jstring="[para(2609(a,1),1903(a,1,1,2))].">
      <j1 rule="para" parents="2609 1903"/>
    </justification>
  </clause>

  <clause id="2617">
    <literal><![CDATA[
      (x * (y \ 1)) / (1 / y) = x * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(1523,a,2603,a)].">
      <j1 rule="hyper" parents="1523 2603"/>
    </justification>
  </clause>

  <clause id="2618">
    <literal><![CDATA[
      (x / (y \ 1)) * K(y \ 1,y) = x / (1 / y)
    ]]></literal>
    <justification jstring="[hyper(1522,a,2603,a),flip(a)].">
      <j1 rule="hyper" parents="1522 2603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2619">
    <literal><![CDATA[
      K(x \ 1,x) * (y * (1 / x)) = y * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(2201,a,2604,a)].">
      <j1 rule="hyper" parents="2201 2604"/>
    </justification>
  </clause>

  <clause id="2620">
    <literal><![CDATA[
      R(x,1 / y,K(y \ 1,y)) = x
    ]]></literal>
    <justification jstring="[hyper(839,a,2604,a)].">
      <j1 rule="hyper" parents="839 2604"/>
    </justification>
  </clause>

  <clause id="2621">
    <literal><![CDATA[
      R(x,1 / (1 / y),K(y,y \ 1)) = x
    ]]></literal>
    <justification jstring="[para(1795(a,1),2620(a,1,3))].">
      <j1 rule="para" parents="1795 2620"/>
    </justification>
  </clause>

  <clause id="2622">
    <literal><![CDATA[
      (x * K(y,y \ 1)) / y = x / (1 / (1 / y))
    ]]></literal>
    <justification jstring="[hyper(58,a,1823,a(flip),b,2621,a)].">
      <j1 rule="hyper" parents="58 1823 2621"/>
    </justification>
  </clause>

  <clause id="2623">
    <literal><![CDATA[
      (x * (1 / (1 / y))) * K(y,y \ 1) = x * y
    ]]></literal>
    <justification jstring="[para(2621(a,1),1821(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2621 1821"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2624">
    <literal><![CDATA[
      (x * K(y \ 1,y)) * (1 / y) = x * (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(133,a,2617,a)].">
      <j1 rule="hyper" parents="133 2617"/>
    </justification>
  </clause>

  <clause id="2625">
    <literal><![CDATA[
      R(x * K(y \ 1,y),y \ 1,y) = (x * (y \ 1)) * y
    ]]></literal>
    <justification jstring="[para(2617(a,1),2609(a,1,1))].">
      <j1 rule="para" parents="2617 2609"/>
    </justification>
  </clause>

  <clause id="2626">
    <literal><![CDATA[
      K(x \ 1,x) * (y / (x \ 1)) = y / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(2201,a,2618,a)].">
      <j1 rule="hyper" parents="2201 2618"/>
    </justification>
  </clause>

  <clause id="2628">
    <literal><![CDATA[
      (x / y) * K(y,y \ 1) = x / (1 / (1 / y))
    ]]></literal>
    <justification jstring="[hyper(58,a,2037,a(flip),b,2622,a)].">
      <j1 rule="hyper" parents="58 2037 2622"/>
    </justification>
  </clause>

  <clause id="2629">
    <literal><![CDATA[
      x * K(y,y \ 1) != z * y
    ]]></literal>
    <literal><![CDATA[
      z * (1 / (1 / y)) = x
    ]]></literal>
    <justification jstring="[para(2623(a,1),39(a,1)),flip(a)].">
      <j1 rule="para" parents="2623 39"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2630">
    <literal><![CDATA[
      K(x,x \ 1) * (y / x) = y / (1 / (1 / x))
    ]]></literal>
    <justification jstring="[hyper(2183,a,2628,a)].">
      <j1 rule="hyper" parents="2183 2628"/>
    </justification>
  </clause>

  <clause id="2631">
    <literal><![CDATA[
      x * (1 / (1 / (x \ (x / y)))) = x / (1 / (1 / y))
    ]]></literal>
    <justification jstring="[hyper(58,a,2416,a(flip),b,2628,a)].">
      <j1 rule="hyper" parents="58 2416 2628"/>
    </justification>
  </clause>

  <clause id="2632">
    <literal><![CDATA[
      1 / (1 / (x \ (x / y))) = x \ (x / (1 / (1 / y)))
    ]]></literal>
    <justification jstring="[hyper(116,a,2628,a(flip),b,2416,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="116 2628 2416"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2633">
    <literal><![CDATA[
      K(x,1 / x) * (y / x) = y / (1 / (1 / x))
    ]]></literal>
    <justification jstring="[para(1791(a,2),2630(a,1,1))].">
      <j1 rule="para" parents="1791 2630"/>
    </justification>
  </clause>

  <clause id="2634">
    <literal><![CDATA[
      T(x * y,x \ (1 / y)) = R(((x / (1 / y)) \ 1) \ 1,y \ 1,y)
    ]]></literal>
    <justification jstring="[para(2403(a,1),2608(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2403 2608"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2635">
    <literal><![CDATA[
      x / (1 / (1 / (y \ x))) = x * (1 / (1 / (x \ y)))
    ]]></literal>
    <justification jstring="[para(72(a,1),2631(a,1,2,2,2,2)),flip(a)].">
      <j1 rule="para" parents="72 2631"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2636">
    <literal><![CDATA[
      (x / (1 / (1 / y))) / x = 1 / (1 / ((x / y) / x))
    ]]></literal>
    <justification jstring="[para(2631(a,1),2230(a,1,1))].">
      <j1 rule="para" parents="2631 2230"/>
    </justification>
  </clause>

  <clause id="2637">
    <literal><![CDATA[
      (x \ (x / (1 / (1 / y)))) \ 1 = 1 / (x \ (x / y))
    ]]></literal>
    <justification jstring="[hyper(188,a,2632,a)].">
      <j1 rule="hyper" parents="188 2632"/>
    </justification>
  </clause>

  <clause id="2638">
    <literal><![CDATA[
      1 / (1 / (x \ (x / (y \ 1)))) = x \ (x / (1 / y))
    ]]></literal>
    <justification jstring="[para(72(a,1),2632(a,2,2,2,2))].">
      <j1 rule="para" parents="72 2632"/>
    </justification>
  </clause>

  <clause id="2639">
    <literal><![CDATA[
      (x * (1 / (1 / (x \ y)))) \ x = 1 / (1 / (y \ x))
    ]]></literal>
    <justification jstring="[hyper(188,a,2635,a)].">
      <j1 rule="hyper" parents="188 2635"/>
    </justification>
  </clause>

  <clause id="2640">
    <literal><![CDATA[
      x / (1 / (1 / ((x * y) \ x))) = x * (1 / (1 / y))
    ]]></literal>
    <justification jstring="[para(4(a,1),2635(a,2,2,2,2))].">
      <j1 rule="para" parents="4 2635"/>
    </justification>
  </clause>

  <clause id="2641">
    <literal><![CDATA[
      1 / (1 / ((x / (y \ 1)) / x)) = (x / (1 / y)) / x
    ]]></literal>
    <justification jstring="[para(72(a,1),2636(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="72 2636"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2642">
    <literal><![CDATA[
      1 / (x \ (x / (y \ 1))) = (x \ (x / (1 / y))) \ 1
    ]]></literal>
    <justification jstring="[para(72(a,1),2637(a,1,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="72 2637"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2643">
    <literal><![CDATA[
      1 / (x \ (x / ((y \ 1) \ 1))) = (x \ (x / y)) \ 1
    ]]></literal>
    <justification jstring="[para(190(a,1),2637(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="190 2637"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2644">
    <literal><![CDATA[
      1 / (1 / ((x * y) \ x)) = (x * (1 / (1 / y))) \ x
    ]]></literal>
    <justification jstring="[para(4(a,1),2639(a,1,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="4 2639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2645">
    <literal><![CDATA[
      (x * (1 / (1 / T(y,x)))) \ x = 1 / (1 / ((y * x) \ x))
    ]]></literal>
    <justification jstring="[para(17(a,2),2639(a,1,1,2,2,2))].">
      <j1 rule="para" parents="17 2639"/>
    </justification>
  </clause>

  <clause id="2646">
    <literal><![CDATA[
      1 / ((x / (y \ 1)) / x) = ((x / (1 / y)) / x) \ 1
    ]]></literal>
    <justification jstring="[hyper(188,a,2641,a),flip(a)].">
      <j1 rule="hyper" parents="188 2641"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2647">
    <literal><![CDATA[
      T(x \ (x / (1 / y)),1 / y) = x \ (x / (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(31,a,2396,a,b,2642,a)].">
      <j1 rule="hyper" parents="31 2396 2642"/>
    </justification>
  </clause>

  <clause id="2648">
    <literal><![CDATA[
      ((x \ (x / y)) \ 1) \ 1 = x \ (x / ((y \ 1) \ 1))
    ]]></literal>
    <justification jstring="[hyper(188,a,2643,a)].">
      <j1 rule="hyper" parents="188 2643"/>
    </justification>
  </clause>

  <clause id="2649">
    <literal><![CDATA[
      T(x \ (x / y),y) = x \ (x / ((y \ 1) \ 1))
    ]]></literal>
    <justification jstring="[hyper(31,a,2396,a,b,2643,a)].">
      <j1 rule="hyper" parents="31 2396 2643"/>
    </justification>
  </clause>

  <clause id="2650">
    <literal><![CDATA[
      x * (((x \ (x / y)) \ 1) \ 1) = x / ((y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(2643(a,1),195(a,1,2,1))].">
      <j1 rule="para" parents="2643 195"/>
    </justification>
  </clause>

  <clause id="2651">
    <literal><![CDATA[
      x * T(x \ (x / y),y) = x / ((y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(119,a,2649,a,b,xx)].">
      <j1 rule="hyper" parents="119 2649"/>
    </justification>
  </clause>

  <clause id="2652">
    <literal><![CDATA[
      x * (y \ (y / ((x \ 1) \ 1))) = (y \ (y / x)) * x
    ]]></literal>
    <justification jstring="[hyper(119,a,2649,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 2649 17"/>
    </justification>
  </clause>

  <clause id="2653">
    <literal><![CDATA[
      (x / y) * K(y \ 1,y) = x / ((y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(2239,a,2651,a)].">
      <j1 rule="hyper" parents="2239 2651"/>
    </justification>
  </clause>

  <clause id="2654">
    <literal><![CDATA[
      (x * y) / ((y \ 1) \ 1) = x * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[para(6(a,1),2653(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6 2653"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2655">
    <literal><![CDATA[
      (x / ((y \ 1) \ 1)) * y = x * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[para(2653(a,1),1607(a,1,1))].">
      <j1 rule="para" parents="2653 1607"/>
    </justification>
  </clause>

  <clause id="2656">
    <literal><![CDATA[
      (x * K(y \ 1,y)) * ((y \ 1) \ 1) = x * y
    ]]></literal>
    <justification jstring="[hyper(133,a,2654,a)].">
      <j1 rule="hyper" parents="133 2654"/>
    </justification>
  </clause>

  <clause id="2657">
    <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(2162(a,2),2654(a,1,2))].">
      <j1 rule="para" parents="2162 2654"/>
    </justification>
  </clause>

  <clause id="2658">
    <literal><![CDATA[
      (x * ((y \ 1) \ 1)) * K(y \ 1,y) = x * y
    ]]></literal>
    <justification jstring="[para(6(a,1),2655(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6 2655"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2659">
    <literal><![CDATA[
      (x / T(y,y \ 1)) * y = x * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[para(106(a,2),2655(a,1,1,2))].">
      <j1 rule="para" parents="106 2655"/>
    </justification>
  </clause>

  <clause id="2660">
    <literal><![CDATA[
      (x * T(y,y \ 1)) * K(y \ 1,y) = x * y
    ]]></literal>
    <justification jstring="[para(660(a,1),2655(a,1,1)),flip(a)].">
      <j1 rule="para" parents="660 2655"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2661">
    <literal><![CDATA[
      (K(x \ 1,x) * y) * ((x \ 1) \ 1) = y * x
    ]]></literal>
    <justification jstring="[para(2192(a,2),2656(a,1,1))].">
      <j1 rule="para" parents="2192 2656"/>
    </justification>
  </clause>

  <clause id="2662">
    <literal><![CDATA[
      (x * (y \ 1)) * ((y \ 1) \ 1) = (x * (1 / y)) * y
    ]]></literal>
    <justification jstring="[para(2604(a,1),2656(a,1,1))].">
      <j1 rule="para" parents="2604 2656"/>
    </justification>
  </clause>

  <clause id="2663">
    <literal><![CDATA[
      (x * (y \ 1)) * ((y \ 1) \ 1) = R(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(30,a,520,a,b,2658,a),flip(a)].">
      <j1 rule="hyper" parents="30 520 2658"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2664">
    <literal><![CDATA[
      K(x \ 1,x) * (y * T(x,x \ 1)) = y * x
    ]]></literal>
    <justification jstring="[hyper(2201,a,2660,a)].">
      <j1 rule="hyper" parents="2201 2660"/>
    </justification>
  </clause>

  <clause id="2665">
    <literal><![CDATA[
      K(x \ 1,x) \ (y * x) = y * T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(116,a,2660,a(flip),b,2192,a)].">
      <j1 rule="hyper" parents="116 2660 2192"/>
    </justification>
  </clause>

  <clause id="2666">
    <literal><![CDATA[
      x * K(y \ 1,y) != z * y
    ]]></literal>
    <literal><![CDATA[
      z * T(y,y \ 1) = x
    ]]></literal>
    <justification jstring="[para(2660(a,1),39(a,1)),flip(a)].">
      <j1 rule="para" parents="2660 39"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2667">
    <literal><![CDATA[
      x * ((y \ 1) \ 1) != z * y
    ]]></literal>
    <literal><![CDATA[
      K(y \ 1,y) * z = x
    ]]></literal>
    <justification jstring="[para(2661(a,1),39(a,1)),flip(a)].">
      <j1 rule="para" parents="2661 39"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2668">
    <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(2665(a,1),2541(a,1,2,1))].">
      <j1 rule="para" parents="2665 2541"/>
    </justification>
  </clause>

  <clause id="2669">
    <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(2665(a,1),2542(a,1,2,1))].">
      <j1 rule="para" parents="2665 2542"/>
    </justification>
  </clause>

  <clause id="2670">
    <literal><![CDATA[
      R(x,y \ 1,(y \ 1) \ 1) = R(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(521,a,2663,a)].">
      <j1 rule="hyper" parents="521 2663"/>
    </justification>
  </clause>

  <clause id="2671">
    <literal><![CDATA[
      T(x * ((y \ 1) \ 1),y \ 1) = R((y \ 1) \ x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,787,a(flip),b,2663,a)].">
      <j1 rule="hyper" parents="58 787 2663"/>
    </justification>
  </clause>

  <clause id="2672">
    <literal><![CDATA[
      x \ R(x,y \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      a(x,y \ 1,(y \ 1) \ 1) = z
    ]]></literal>
    <justification jstring="[para(2663(a,1),794(a,1,2))].">
      <j1 rule="para" parents="2663 794"/>
    </justification>
  </clause>

  <clause id="2673">
    <literal><![CDATA[
      x / (((y \ x) \ 1) \ 1) = x * (((x \ y) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(72(a,1),2650(a,1,2,1,1,2)),flip(a)].">
      <j1 rule="para" parents="72 2650"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2674">
    <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(1227(a,1),2625(a,2,1))].">
      <j1 rule="para" parents="1227 2625"/>
    </justification>
  </clause>

  <clause id="2675">
    <literal><![CDATA[
      K(1 / ((x * y) \ x),(x * y) \ x) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,1 / y) = z
    ]]></literal>
    <justification jstring="[para(2587(a,2),2380(a,1))].">
      <j1 rule="para" parents="2587 2380"/>
    </justification>
  </clause>

  <clause id="2676">
    <literal><![CDATA[
      (x * y) * K(y,y \ 1) = x * T(y,(x * y) \ x)
    ]]></literal>
    <justification jstring="[para(2379(a,1),2589(a,1,2))].">
      <j1 rule="para" parents="2379 2589"/>
    </justification>
  </clause>

  <clause id="2677">
    <literal><![CDATA[
      (x * y) * K(y,y \ 1) = x * ((y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(2372(a,1),2676(a,2,2))].">
      <j1 rule="para" parents="2372 2676"/>
    </justification>
  </clause>

  <clause id="2678">
    <literal><![CDATA[
      (x * y) * K(y,y \ 1) = x * T(y,y \ 1)
    ]]></literal>
    <justification jstring="[para(2373(a,1),2676(a,2,2))].">
      <j1 rule="para" parents="2373 2676"/>
    </justification>
  </clause>

  <clause id="2680">
    <literal><![CDATA[
      K(x,x \ 1) * (y * x) = y * ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(2183,a,2677,a)].">
      <j1 rule="hyper" parents="2183 2677"/>
    </justification>
  </clause>

  <clause id="2681">
    <literal><![CDATA[
      (x * y) * K(T(x,y),T(x,y) \ 1) = y * ((T(x,y) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(569,a,2677,a)].">
      <j1 rule="hyper" parents="569 2677"/>
    </justification>
  </clause>

  <clause id="2682">
    <literal><![CDATA[
      (x / y) * ((y \ 1) \ 1) = x * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(326,a,2677,a),flip(a)].">
      <j1 rule="hyper" parents="326 2677"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2683">
    <literal><![CDATA[
      (x * K(y,y \ 1)) * y = x * ((y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,2034,a,b,2677,a)].">
      <j1 rule="hyper" parents="58 2034 2677"/>
    </justification>
  </clause>

  <clause id="2685">
    <literal><![CDATA[
      K(x,x \ 1) * (y * x) = y * T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(2183,a,2678,a)].">
      <j1 rule="hyper" parents="2183 2678"/>
    </justification>
  </clause>

  <clause id="2686">
    <literal><![CDATA[
      (x / y) * T(y,y \ 1) = x * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(326,a,2678,a),flip(a)].">
      <j1 rule="hyper" parents="326 2678"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2687">
    <literal><![CDATA[
      (x * K(y,y \ 1)) \ (x * T(y,y \ 1)) = y
    ]]></literal>
    <justification jstring="[hyper(116,a,2678,a(flip),b,2034,a)].">
      <j1 rule="hyper" parents="116 2678 2034"/>
    </justification>
  </clause>

  <clause id="2688">
    <literal><![CDATA[
      (K(x,x \ 1) * y) * x = y * ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(2458,a,2680,a)].">
      <j1 rule="hyper" parents="2458 2680"/>
    </justification>
  </clause>

  <clause id="2689">
    <literal><![CDATA[
      (T(x,y) \ 1) * K(x,x \ 1) = (T(x,y) \ x) / x
    ]]></literal>
    <justification jstring="[hyper(117,a,2231,a(flip),b,2683,a),flip(a)].">
      <j1 rule="hyper" parents="117 2231 2683"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2690">
    <literal><![CDATA[
      (x / T(y,y \ 1)) * K(y,y \ 1) = x / y
    ]]></literal>
    <justification jstring="[hyper(117,a,369,a(flip),b,2683,a),flip(a)].">
      <j1 rule="hyper" parents="117 369 2683"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2691">
    <literal><![CDATA[
      (x * (y \ 1)) * K(y,y \ 1) = x * (1 / y)
    ]]></literal>
    <justification jstring="[hyper(30,a,2662,a(flip),b,2683,a),flip(a)].">
      <j1 rule="hyper" parents="30 2662 2683"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2692">
    <literal><![CDATA[
      (K(x \ 1,x) * y) * K(x,x \ 1) = y
    ]]></literal>
    <justification jstring="[hyper(30,a,2661,a(flip),b,2683,a),flip(a)].">
      <j1 rule="hyper" parents="30 2661 2683"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2693">
    <literal><![CDATA[
      (x * K(y \ 1,y)) * K(y,y \ 1) = x
    ]]></literal>
    <justification jstring="[hyper(30,a,2656,a(flip),b,2683,a),flip(a)].">
      <j1 rule="hyper" parents="30 2656 2683"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2694">
    <literal><![CDATA[
      K(x \ 1,x) * (y * K(x,x \ 1)) = y
    ]]></literal>
    <justification jstring="[hyper(2667,a,2683,a(flip))].">
      <j1 rule="hyper" parents="2667 2683"/>
    </justification>
  </clause>

  <clause id="2695">
    <literal><![CDATA[
      K(x \ 1,x) * (y * x) = y * (1 / (1 / x))
    ]]></literal>
    <justification jstring="[hyper(2629,a,2692,a),flip(a)].">
      <j1 rule="hyper" parents="2629 2692"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2696">
    <literal><![CDATA[
      K(x,x \ 1) * (K(x \ 1,x) * y) = y
    ]]></literal>
    <justification jstring="[hyper(2183,a,2692,a)].">
      <j1 rule="hyper" parents="2183 2692"/>
    </justification>
  </clause>

  <clause id="2697">
    <literal><![CDATA[
      K(x \ 1,x) * (K(x,x \ 1) * y) = y
    ]]></literal>
    <justification jstring="[hyper(30,a,2181,a(flip),b,2692,a),flip(a)].">
      <j1 rule="hyper" parents="30 2181 2692"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2698">
    <literal><![CDATA[
      K(x \ 1,x) * (y / (x * y)) = R(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[hyper(30,a,2063,a(flip),b,2692,a),flip(a)].">
      <j1 rule="hyper" parents="30 2063 2692"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2699">
    <literal><![CDATA[
      ((x \ 1) * (x * y)) * K(x,x \ 1) = L(y,x,x \ 1)
    ]]></literal>
    <justification jstring="[para(484(a,1),2692(a,1,1))].">
      <j1 rule="para" parents="484 2692"/>
    </justification>
  </clause>

  <clause id="2700">
    <literal><![CDATA[
      K(x,x \ 1) * y != z
    ]]></literal>
    <literal><![CDATA[
      K(x \ 1,x) * z = y
    ]]></literal>
    <justification jstring="[para(2692(a,1),2188(a,2)),flip(b)].">
      <j1 rule="para" parents="2692 2188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2701">
    <literal><![CDATA[
      (x / (1 / y)) * K(y,y \ 1) = x / (y \ 1)
    ]]></literal>
    <justification jstring="[para(2626(a,1),2692(a,1,1))].">
      <j1 rule="para" parents="2626 2692"/>
    </justification>
  </clause>

  <clause id="2702">
    <literal><![CDATA[
      (x * y) * K(y \ 1,y) = x * (1 / (1 / y))
    ]]></literal>
    <justification jstring="[hyper(2629,a,2693,a),flip(a)].">
      <j1 rule="hyper" parents="2629 2693"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2703">
    <literal><![CDATA[
      K(x,x \ 1) * (y * K(x \ 1,x)) = y
    ]]></literal>
    <justification jstring="[hyper(2183,a,2693,a)].">
      <j1 rule="hyper" parents="2183 2693"/>
    </justification>
  </clause>

  <clause id="2704">
    <literal><![CDATA[
      x / K(y \ 1,y) = x * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(326,a,2693,a),flip(a)].">
      <j1 rule="hyper" parents="326 2693"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2705">
    <literal><![CDATA[
      (x / (1 / (1 / y))) * K(y \ 1,y) = x / y
    ]]></literal>
    <justification jstring="[hyper(30,a,2628,a,b,2693,a),flip(a)].">
      <j1 rule="hyper" parents="30 2628 2693"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2706">
    <literal><![CDATA[
      (K(x,x \ 1) * y) * K(x \ 1,x) = y
    ]]></literal>
    <justification jstring="[hyper(30,a,2181,a(flip),b,2693,a),flip(a)].">
      <j1 rule="hyper" parents="30 2181 2693"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2707">
    <literal><![CDATA[
      K(x,x \ 1) \ y = y * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,2693,a(flip),b,2181,a)].">
      <j1 rule="hyper" parents="116 2693 2181"/>
    </justification>
  </clause>

  <clause id="2708">
    <literal><![CDATA[
      K(x,x \ 1) * y != z
    ]]></literal>
    <literal><![CDATA[
      z * K(x \ 1,x) = y
    ]]></literal>
    <justification jstring="[para(2693(a,1),2188(a,2)),flip(b)].">
      <j1 rule="para" parents="2693 2188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2709">
    <literal><![CDATA[
      K(x \ 1,x) * y != z
    ]]></literal>
    <literal><![CDATA[
      z * K(x,x \ 1) = y
    ]]></literal>
    <justification jstring="[para(2694(a,1),38(a,1)),flip(a)].">
      <j1 rule="para" parents="2694 38"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2710">
    <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(2694(a,1),92(a,2,1))].">
      <j1 rule="para" parents="2694 92"/>
    </justification>
  </clause>

  <clause id="2711">
    <literal><![CDATA[
      x * K(y \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      z * K(y,y \ 1) = x
    ]]></literal>
    <justification jstring="[para(2694(a,1),2195(a,1)),flip(a)].">
      <j1 rule="para" parents="2694 2195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2712">
    <literal><![CDATA[
      K(x \ 1,x) \ y = K(x,x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(342,a,2696,a),flip(a)].">
      <j1 rule="hyper" parents="342 2696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2713">
    <literal><![CDATA[
      K(x,x \ 1) * ((x \ 1) * y) = L(x \ y,x,x \ 1)
    ]]></literal>
    <justification jstring="[para(1063(a,1),2696(a,1,2))].">
      <j1 rule="para" parents="1063 2696"/>
    </justification>
  </clause>

  <clause id="2714">
    <literal><![CDATA[
      K(x,x \ 1) * (y * (x \ 1)) = y * (1 / x)
    ]]></literal>
    <justification jstring="[para(2619(a,1),2696(a,1,2))].">
      <j1 rule="para" parents="2619 2696"/>
    </justification>
  </clause>

  <clause id="2715">
    <literal><![CDATA[
      K(x,x \ 1) * (y / (1 / x)) = y / (x \ 1)
    ]]></literal>
    <justification jstring="[para(2626(a,1),2696(a,1,2))].">
      <j1 rule="para" parents="2626 2696"/>
    </justification>
  </clause>

  <clause id="2716">
    <literal><![CDATA[
      K(x \ 1,x) * y != z
    ]]></literal>
    <literal><![CDATA[
      K(x,x \ 1) * z = y
    ]]></literal>
    <justification jstring="[para(2697(a,1),38(a,1)),flip(a)].">
      <j1 rule="para" parents="2697 38"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2717">
    <literal><![CDATA[
      x * K(y \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,y \ 1) * z = x
    ]]></literal>
    <justification jstring="[para(2697(a,1),2195(a,1)),flip(a)].">
      <j1 rule="para" parents="2697 2195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2718">
    <literal><![CDATA[
      (x / (y \ 1)) * (1 / y) = x * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,2601,a,b,2704,a)].">
      <j1 rule="hyper" parents="58 2601 2704"/>
    </justification>
  </clause>

  <clause id="2719">
    <literal><![CDATA[
      (x * K(y,y \ 1)) * K(y \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(2704(a,1),251(a,1,1))].">
      <j1 rule="para" parents="2704 251"/>
    </justification>
  </clause>

  <clause id="2720">
    <literal><![CDATA[
      (x * K(y \ 1,y)) * K(y,y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(2704(a,1),328(a,1))].">
      <j1 rule="para" parents="2704 328"/>
    </justification>
  </clause>

  <clause id="2721">
    <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(2704(a,1),622(a,1,1,1))].">
      <j1 rule="para" parents="2704 622"/>
    </justification>
  </clause>

  <clause id="2722">
    <literal><![CDATA[
      K(x \ 1,x) * T(K(x,x \ 1) * y,z) = (x \ T(x * (y / x),z)) * x
    ]]></literal>
    <justification jstring="[para(2712(a,1),2436(a,1,2,1))].">
      <j1 rule="para" parents="2712 2436"/>
    </justification>
  </clause>

  <clause id="2723">
    <literal><![CDATA[
      (K(x,x \ 1) * y) * x = y * T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(2458,a,2685,a)].">
      <j1 rule="hyper" parents="2458 2685"/>
    </justification>
  </clause>

  <clause id="2724">
    <literal><![CDATA[
      L(x,K(x,x \ 1),y) = x
    ]]></literal>
    <justification jstring="[hyper(1819,a,2687,a)].">
      <j1 rule="hyper" parents="1819 2687"/>
    </justification>
  </clause>

  <clause id="2725">
    <literal><![CDATA[
      L(1 / x,K(x \ 1,x),y) = 1 / x
    ]]></literal>
    <justification jstring="[para(1826(a,1),2724(a,1,2))].">
      <j1 rule="para" parents="1826 2724"/>
    </justification>
  </clause>

  <clause id="2726">
    <literal><![CDATA[
      (x * y) * (y \ 1) = R(x,y,1 / y)
    ]]></literal>
    <justification jstring="[hyper(30,a,1804,a,b,2691,a),flip(a)].">
      <j1 rule="hyper" parents="30 1804 2691"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2727">
    <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(2691(a,1),510(a,1,1))].">
      <j1 rule="para" parents="2691 510"/>
    </justification>
  </clause>

  <clause id="2728">
    <literal><![CDATA[
      R(x,y,1 / y) / (y \ 1) = x * y
    ]]></literal>
    <justification jstring="[hyper(131,a,2726,a)].">
      <j1 rule="hyper" parents="131 2726"/>
    </justification>
  </clause>

  <clause id="2729">
    <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,2726,a)].">
      <j1 rule="hyper" parents="117 22 2726"/>
    </justification>
  </clause>

  <clause id="2730">
    <literal><![CDATA[
      R(x \ y,x,1 / x) = T(y * (x \ 1),x)
    ]]></literal>
    <justification jstring="[hyper(58,a,787,a(flip),b,2726,a),flip(a)].">
      <j1 rule="hyper" parents="58 787 2726"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2731">
    <literal><![CDATA[
      R(1 / L(x,y,z),x,1 / x) = (x / L(x,y,z)) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(1643(a,1),2726(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1643 2726"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2732">
    <literal><![CDATA[
      (R(x,y,y \ 1) / (1 / y)) * K(y,y \ 1) = x * y
    ]]></literal>
    <justification jstring="[hyper(320,a,440,a(flip),b,2701,a),flip(a)].">
      <j1 rule="hyper" parents="320 440 2701"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2733">
    <literal><![CDATA[
      (x / (1 / (1 / y))) / (1 / y) = (x / y) / (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(117,a,2705,a(flip),b,2603,a),flip(a)].">
      <j1 rule="hyper" parents="117 2705 2603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2734">
    <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(2166(a,1),2715(a,1,2,2))].">
      <j1 rule="para" parents="2166 2715"/>
    </justification>
  </clause>

  <clause id="2735">
    <literal><![CDATA[
      K(x / (y * x),y) = K(y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(30,a,2080,a,b,2698,a)].">
      <j1 rule="hyper" parents="30 2080 2698"/>
    </justification>
  </clause>

  <clause id="2736">
    <literal><![CDATA[
      K((x / y) \ 1,x / y) = K(y / x,x / y)
    ]]></literal>
    <justification jstring="[para(7(a,1),2735(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7 2735"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2738">
    <literal><![CDATA[
      K((x / (y * x)) \ 1,x / (y * x)) = K(y,x / (y * x))
    ]]></literal>
    <justification jstring="[para(6(a,1),2736(a,2,1))].">
      <j1 rule="para" parents="6 2736"/>
    </justification>
  </clause>

  <clause id="2739">
    <literal><![CDATA[
      K(x,T(x,y) \ 1) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(29,a,2135,a,b,2689,a)].">
      <j1 rule="hyper" parents="29 2135 2689"/>
    </justification>
  </clause>

  <clause id="2740">
    <literal><![CDATA[
      T(K(x,x \ 1),y) = K(x,T(x,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,2178,a,b,2739,a)].">
      <j1 rule="hyper" parents="320 2178 2739"/>
    </justification>
  </clause>

  <clause id="2742">
    <literal><![CDATA[
      K(x,T(x,y) \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,x \ 1) = z
    ]]></literal>
    <justification jstring="[para(2740(a,1),177(a,1)),flip(b)].">
      <j1 rule="para" parents="2740 177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2743">
    <literal><![CDATA[
      T(K(T(x,y),1 / x),z) = K(T(x,y),T(T(x,y),u) \ 1)
    ]]></literal>
    <justification jstring="[para(2179(a,1),2740(a,1,1))].">
      <j1 rule="para" parents="2179 2740"/>
    </justification>
  </clause>

  <clause id="2744">
    <literal><![CDATA[
      R(x,y,y \ 1) / (1 / y) = x * (1 / (1 / y))
    ]]></literal>
    <justification jstring="[hyper(2629,a,2732,a),flip(a)].">
      <j1 rule="hyper" parents="2629 2732"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2745">
    <literal><![CDATA[
      x / (1 / y) != z * (1 / (1 / y))
    ]]></literal>
    <literal><![CDATA[
      R(z,y,y \ 1) = x
    ]]></literal>
    <justification jstring="[para(2744(a,1),41(a,1)),flip(a)].">
      <j1 rule="para" parents="2744 41"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2746">
    <literal><![CDATA[
      (x * T(1 / (1 / y),x)) \ x = 1 / (1 / ((y * x) \ x))
    ]]></literal>
    <justification jstring="[para(2166(a,1),2645(a,1,1,2))].">
      <j1 rule="para" parents="2166 2645"/>
    </justification>
  </clause>

  <clause id="2747">
    <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(2743(a,2),2742(a,1))].">
      <j1 rule="para" parents="2743 2742"/>
    </justification>
  </clause>

  <clause id="2748">
    <literal><![CDATA[
      1 / (1 / ((x * y) \ y)) = ((1 / (1 / x)) * y) \ y
    ]]></literal>
    <justification jstring="[para(105(a,1),2746(a,1,1)),flip(a)].">
      <j1 rule="para" parents="105 2746"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2749">
    <literal><![CDATA[
      (((1 / (1 / x)) * y) \ y) \ 1 = 1 / ((x * y) \ y)
    ]]></literal>
    <justification jstring="[hyper(188,a,2748,a)].">
      <j1 rule="hyper" parents="188 2748"/>
    </justification>
  </clause>

  <clause id="2750">
    <literal><![CDATA[
      1 / (((x \ 1) * y) \ y) = (((1 / x) * y) \ y) \ 1
    ]]></literal>
    <justification jstring="[para(72(a,1),2749(a,1,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="72 2749"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2751">
    <literal><![CDATA[
      ((((1 / x) * y) \ y) \ 1) \ 1 = ((x \ 1) * y) \ y
    ]]></literal>
    <justification jstring="[hyper(188,a,2750,a)].">
      <j1 rule="hyper" parents="188 2750"/>
    </justification>
  </clause>

  <clause id="2752">
    <literal><![CDATA[
      (((x * y) \ y) \ 1) \ 1 = (((x \ 1) \ 1) * y) \ y
    ]]></literal>
    <justification jstring="[para(72(a,1),2751(a,1,1,1,1,1))].">
      <j1 rule="para" parents="72 2751"/>
    </justification>
  </clause>

  <clause id="2753">
    <literal><![CDATA[
      T((x * y) \ y,x) = (((x \ 1) \ 1) * y) \ y
    ]]></literal>
    <justification jstring="[hyper(58,a,2236,a,b,2752,a)].">
      <j1 rule="hyper" parents="58 2236 2752"/>
    </justification>
  </clause>

  <clause id="2754">
    <literal><![CDATA[
      (T(x,x \ 1) * y) \ y = T((x * y) \ y,x)
    ]]></literal>
    <justification jstring="[para(106(a,2),2753(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="106 2753"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2755">
    <literal><![CDATA[
      R((x \ 1) \ (T(x,y) \ 1),x \ 1,x) = T(T(x,y) \ x,x \ 1)
    ]]></literal>
    <justification jstring="[para(2231(a,1),2671(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2231 2671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2756">
    <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,645,a,b,2731,a)].">
      <j1 rule="hyper" parents="58 645 2731"/>
    </justification>
  </clause>

  <clause id="2757">
    <literal><![CDATA[
      (x * y) * K(T(x,y),1 / x) = y * ((T(x,y) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(2179(a,1),2681(a,1,2))].">
      <j1 rule="para" parents="2179 2681"/>
    </justification>
  </clause>

  <clause id="2758">
    <literal><![CDATA[
      (x * y) * K(T(x,y),1 / x) = ((x \ 1) \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(320,a,2167,a(flip),b,2757,a),flip(a)].">
      <j1 rule="hyper" parents="320 2167 2757"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2759">
    <literal><![CDATA[
      ((1 / x) * (y * x)) \ (y * (y * x)) = (1 / x) \ y
    ]]></literal>
    <justification jstring="[para(2609(a,1),2615(a,1,2,2))].">
      <j1 rule="para" parents="2609 2615"/>
    </justification>
  </clause>

  <clause id="2760">
    <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(2686(a,1),2669(a,1,2,1))].">
      <j1 rule="para" parents="2686 2669"/>
    </justification>
  </clause>

  <clause id="2761">
    <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(1826(a,1),2734(a,1,1))].">
      <j1 rule="para" parents="1826 2734"/>
    </justification>
  </clause>

  <clause id="2762">
    <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(1152(a,1),2598(a,2,1))].">
      <j1 rule="para" parents="1152 2598"/>
    </justification>
  </clause>

  <clause id="2763">
    <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,2420,a(flip),b,2762,a),flip(a)].">
      <j1 rule="hyper" parents="320 2420 2762"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2764">
    <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(1147(a,1),2016(a,2,2,1))].">
      <j1 rule="para" parents="1147 2016"/>
    </justification>
  </clause>

  <clause id="2765">
    <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(1742(a,1),2764(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1742 2764"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2766">
    <literal><![CDATA[
      K(T(x,y),1 / T(x,z)) = T(K(T(x,y),1 / x),z)
    ]]></literal>
    <justification jstring="[hyper(58,a,2028,a(flip),b,2765,a)].">
      <j1 rule="hyper" parents="58 2028 2765"/>
    </justification>
  </clause>

  <clause id="2767">
    <literal><![CDATA[
      K(T(x,y),T(x,y) \ 1) = K(T(x,y),1 / T(x,z))
    ]]></literal>
    <justification jstring="[hyper(2747,a,2766,a(flip))].">
      <j1 rule="hyper" parents="2747 2766"/>
    </justification>
  </clause>

  <clause id="2768">
    <literal><![CDATA[
      K(T(x,y),T(x,y) \ 1) = K(T(x,y),x \ 1)
    ]]></literal>
    <justification jstring="[para(265(a,1),2767(a,2,2))].">
      <j1 rule="para" parents="265 2767"/>
    </justification>
  </clause>

  <clause id="2769">
    <literal><![CDATA[
      K(T(x,y),1 / x) = K(T(x,y),x \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,2179,a(flip),b,2768,a)].">
      <j1 rule="hyper" parents="58 2179 2768"/>
    </justification>
  </clause>

  <clause id="2770">
    <literal><![CDATA[
      (x * y) * K(T(x,y),x \ 1) = ((x \ 1) \ 1) * y
    ]]></literal>
    <justification jstring="[para(2769(a,1),2758(a,1,2))].">
      <j1 rule="para" parents="2769 2758"/>
    </justification>
  </clause>

  <clause id="2771">
    <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),2128(a,2,1))].">
      <j1 rule="para" parents="262 2128"/>
    </justification>
  </clause>

  <clause id="2772">
    <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(1902(a,1),2771(a,2,1))].">
      <j1 rule="para" parents="1902 2771"/>
    </justification>
  </clause>

  <clause id="2773">
    <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(2127,a,2772,a)].">
      <j1 rule="hyper" parents="2127 2772"/>
    </justification>
  </clause>

  <clause id="2774">
    <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),2251(a,1,1))].">
      <j1 rule="para" parents="5 2251"/>
    </justification>
  </clause>

  <clause id="2775">
    <literal><![CDATA[
      K(x \ (((y * x) / y) \ x),x) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(2221,a,2774,a),flip(a)].">
      <j1 rule="hyper" parents="2221 2774"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2778">
    <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(2691(a,1),2727(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2691 2727"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2779">
    <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,2778,a),flip(a)].">
      <j1 rule="hyper" parents="320 15 2778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2780">
    <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(2778(a,2),518(a,1))].">
      <j1 rule="para" parents="2778 518"/>
    </justification>
  </clause>

  <clause id="2781">
    <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),2779(a,1,2,2))].">
      <j1 rule="para" parents="106 2779"/>
    </justification>
  </clause>

  <clause id="2783">
    <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(1798(a,1),2781(a,1,3))].">
      <j1 rule="para" parents="1798 2781"/>
    </justification>
  </clause>

  <clause id="2784">
    <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),2783(a,2,3))].">
      <j1 rule="para" parents="72 2783"/>
    </justification>
  </clause>

  <clause id="2786">
    <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(2454(a,1),1852(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="2454 1852"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2787">
    <literal><![CDATA[
      x * ((y \ 1) * (y * T(y \ 1,x))) = (1 / y) * (x * K(y \ 1,y))
    ]]></literal>
    <justification jstring="[para(2725(a,1),2786(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2725 2786"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2789">
    <literal><![CDATA[
      L(L(x,L(y,z,u) \ 1,y),L(y,z,u) \ y,L(y,z,u)) = y \ (y * (L(y,z,u) * ((L(y,z,u) \ 1) * x)))
    ]]></literal>
    <justification jstring="[para(1404(a,1),1964(a,2,2))].">
      <j1 rule="para" parents="1404 1964"/>
    </justification>
  </clause>

  <clause id="2790">
    <literal><![CDATA[
      L(L(x,L(y,z,u) \ 1,y),L(y,z,u) \ y,L(y,z,u)) = y \ (y * L(x,L(y,z,u) \ 1,L(y,z,u)))
    ]]></literal>
    <justification jstring="[para(257(a,1),2789(a,2,2,2))].">
      <j1 rule="para" parents="257 2789"/>
    </justification>
  </clause>

  <clause id="2791">
    <literal><![CDATA[
      L(L(x,L(y,z,u) \ 1,y),L(y,z,u) \ y,L(y,z,u)) = L(x,L(y,z,u) \ 1,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,4,a(flip),b,2790,a),flip(a)].">
      <j1 rule="hyper" parents="320 4 2790"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2792">
    <literal><![CDATA[
      L(L(x,L(y,z,u) \ y,L(y,z,u)),L(y,z,u) \ 1,y) = L(x,L(y,z,u) \ 1,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(978,a,2791,a)].">
      <j1 rule="hyper" parents="978 2791"/>
    </justification>
  </clause>

  <clause id="2794">
    <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(1969(a,1),2456(a,1,2))].">
      <j1 rule="para" parents="1969 2456"/>
    </justification>
  </clause>

  <clause id="2795">
    <literal><![CDATA[
      K(T(x,R(x \ 1,x,y)),R(x \ 1,x,y)) = K(x,y / (x * y))
    ]]></literal>
    <justification jstring="[hyper(790,a,2794,a),flip(a)].">
      <j1 rule="hyper" parents="790 2794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2796">
    <literal><![CDATA[
      x \ T(x,y / (x * y)) = K(x,y / (x * y))
    ]]></literal>
    <justification jstring="[hyper(58,a,2513,a(flip),b,2795,a)].">
      <j1 rule="hyper" parents="58 2513 2795"/>
    </justification>
  </clause>

  <clause id="2797">
    <literal><![CDATA[
      K(x,y / (x * y)) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(2070,a,2796,a),flip(a)].">
      <j1 rule="hyper" parents="2070 2796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2798">
    <literal><![CDATA[
      K((x / (y * x)) \ 1,x / (y * x)) = K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,2738,a,b,2797,a)].">
      <j1 rule="hyper" parents="58 2738 2797"/>
    </justification>
  </clause>

  <clause id="2799">
    <literal><![CDATA[
      K(x / y,(x / y) \ 1) = K(x / y,y / x)
    ]]></literal>
    <justification jstring="[para(7(a,1),2797(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7 2797"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2801">
    <literal><![CDATA[
      K(x,x \ 1) * (x * y) = T(x,x \ 1) * y
    ]]></literal>
    <justification jstring="[para(2798(a,1),2068(a,1,1))].">
      <j1 rule="para" parents="2798 2068"/>
    </justification>
  </clause>

  <clause id="2802">
    <literal><![CDATA[
      (x * y) * K(x,x \ 1) = T(x,x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(2189,a,2801,a)].">
      <j1 rule="hyper" parents="2189 2801"/>
    </justification>
  </clause>

  <clause id="2803">
    <literal><![CDATA[
      K(x,x \ 1) * (x * y) = ((x \ 1) \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(320,a,314,a(flip),b,2801,a),flip(a)].">
      <j1 rule="hyper" parents="320 314 2801"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2804">
    <literal><![CDATA[
      x * (((x \ 1) \ 1) \ y) = K(x,x \ 1) \ y
    ]]></literal>
    <justification jstring="[hyper(116,a,309,a(flip),b,2801,a),flip(a)].">
      <j1 rule="hyper" parents="116 309 2801"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2805">
    <literal><![CDATA[
      x * (K(x,x \ 1) * y) = T(x,x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(58,a,1860,a(flip),b,2801,a)].">
      <j1 rule="hyper" parents="58 1860 2801"/>
    </justification>
  </clause>

  <clause id="2806">
    <literal><![CDATA[
      L(x,y,K(y,y \ 1)) = x
    ]]></literal>
    <justification jstring="[hyper(1818,a,2801,a(flip))].">
      <j1 rule="hyper" parents="1818 2801"/>
    </justification>
  </clause>

  <clause id="2808">
    <literal><![CDATA[
      K(x,x \ 1) * (((x \ 1) \ 1) \ y) = x \ y
    ]]></literal>
    <justification jstring="[hyper(58,a,2564,a(flip),b,2806,a)].">
      <j1 rule="hyper" parents="58 2564 2806"/>
    </justification>
  </clause>

  <clause id="2809">
    <literal><![CDATA[
      L(x,K(y,y \ 1),1 / (1 / y)) = x
    ]]></literal>
    <justification jstring="[hyper(58,a,1920,a(flip),b,2806,a)].">
      <j1 rule="hyper" parents="58 1920 2806"/>
    </justification>
  </clause>

  <clause id="2810">
    <literal><![CDATA[
      L(x,K(y \ 1,y),1 / y) = x
    ]]></literal>
    <justification jstring="[hyper(58,a,1868,a(flip),b,2806,a)].">
      <j1 rule="hyper" parents="58 1868 2806"/>
    </justification>
  </clause>

  <clause id="2811">
    <literal><![CDATA[
      L(x,1 / y,K(y \ 1,y)) = x
    ]]></literal>
    <justification jstring="[para(1826(a,1),2806(a,1,3))].">
      <j1 rule="para" parents="1826 2806"/>
    </justification>
  </clause>

  <clause id="2813">
    <literal><![CDATA[
      (1 / x) * (K(x \ 1,x) * y) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(119,a,2810,a(flip),b,781,a),flip(a)].">
      <j1 rule="hyper" parents="119 2810 781"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2814">
    <literal><![CDATA[
      K(x \ 1,x) * ((1 / x) * y) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[para(2811(a,1),1809(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2811 1809"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2815">
    <literal><![CDATA[
      L(x \ y,x,x \ 1) = (1 / x) * y
    ]]></literal>
    <justification jstring="[para(2811(a,1),1948(a,1,1,2))].">
      <j1 rule="para" parents="2811 1948"/>
    </justification>
  </clause>

  <clause id="2817">
    <literal><![CDATA[
      (1 / (1 / x)) * (K(x,x \ 1) * y) = x * y
    ]]></literal>
    <justification jstring="[para(2809(a,1),1822(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2809 1822"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2818">
    <literal><![CDATA[
      L((x \ 1) \ y,x \ 1,(x \ 1) \ 1) = x * y
    ]]></literal>
    <justification jstring="[hyper(320,a,183,a(flip),b,2815,a),flip(a)].">
      <j1 rule="hyper" parents="320 183 2815"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2819">
    <literal><![CDATA[
      K(x,x \ 1) * ((x \ 1) * y) = (1 / x) * y
    ]]></literal>
    <justification jstring="[hyper(58,a,2713,a,b,2815,a)].">
      <j1 rule="hyper" parents="58 2713 2815"/>
    </justification>
  </clause>

  <clause id="2820">
    <literal><![CDATA[
      (1 / x) * (x * y) = L(y,x,x \ 1)
    ]]></literal>
    <justification jstring="[para(4(a,1),2815(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4 2815"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2821">
    <literal><![CDATA[
      L(T(x,y),y,y \ 1) = (1 / y) * (x * y)
    ]]></literal>
    <justification jstring="[para(17(a,2),2815(a,1,1))].">
      <j1 rule="para" parents="17 2815"/>
    </justification>
  </clause>

  <clause id="2822">
    <literal><![CDATA[
      L(T(x \ y,z),x,x \ 1) = T((1 / x) * y,z)
    ]]></literal>
    <justification jstring="[para(2815(a,1),20(a,2,1))].">
      <j1 rule="para" parents="2815 20"/>
    </justification>
  </clause>

  <clause id="2823">
    <literal><![CDATA[
      L(L(x \ y,z,u),x,x \ 1) = L((1 / x) * y,z,u)
    ]]></literal>
    <justification jstring="[para(2815(a,1),25(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2815 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2824">
    <literal><![CDATA[
      x * ((1 / x) * (y * x)) = L(y,x,x \ 1) * x
    ]]></literal>
    <justification jstring="[para(2815(a,1),634(a,1,2))].">
      <j1 rule="para" parents="2815 634"/>
    </justification>
  </clause>

  <clause id="2825">
    <literal><![CDATA[
      L(x,y,y \ 1) / (y * x) = 1 / y
    ]]></literal>
    <justification jstring="[hyper(131,a,2820,a)].">
      <j1 rule="hyper" parents="131 2820"/>
    </justification>
  </clause>

  <clause id="2826">
    <literal><![CDATA[
      (1 / x) \ L(y,x,x \ 1) = x * y
    ]]></literal>
    <justification jstring="[hyper(123,a,2820,a)].">
      <j1 rule="hyper" parents="123 2820"/>
    </justification>
  </clause>

  <clause id="2827">
    <literal><![CDATA[
      L(x,y,y \ 1) \ x = a(1 / y,y,x)
    ]]></literal>
    <justification jstring="[para(2820(a,1),218(a,1,1))].">
      <j1 rule="para" parents="2820 218"/>
    </justification>
  </clause>

  <clause id="2828">
    <literal><![CDATA[
      L(x,y,y \ 1) \ ((1 / y) * (x * y)) = L(K(x,y),y * x,1 / y)
    ]]></literal>
    <justification jstring="[para(2820(a,1),304(a,1,1))].">
      <j1 rule="para" parents="2820 304"/>
    </justification>
  </clause>

  <clause id="2829">
    <literal><![CDATA[
      ((L(x,y,y \ 1) \ (y * x)) \ 1) \ 1 = ((y \ 1) * (y * x)) \ (y * x)
    ]]></literal>
    <justification jstring="[para(2820(a,1),2751(a,1,1,1,1))].">
      <j1 rule="para" parents="2820 2751"/>
    </justification>
  </clause>

  <clause id="2830">
    <literal><![CDATA[
      (1 / x) * (x * y) != z
    ]]></literal>
    <literal><![CDATA[
      L(y,x,x \ 1) = z
    ]]></literal>
    <justification jstring="[para(2825(a,1),251(a,1,1)),flip(b)].">
      <j1 rule="para" parents="2825 251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2831">
    <literal><![CDATA[
      (1 / (1 / x)) \ L(y,1 / x,x) = (1 / x) * y
    ]]></literal>
    <justification jstring="[para(75(a,1),2826(a,1,2,3))].">
      <j1 rule="para" parents="75 2826"/>
    </justification>
  </clause>

  <clause id="2832">
    <literal><![CDATA[
      (x * y) * K(x,x \ 1) = ((x \ 1) \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(320,a,314,a(flip),b,2802,a),flip(a)].">
      <j1 rule="hyper" parents="320 314 2802"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2833">
    <literal><![CDATA[
      K(x \ 1,x) * (((x \ 1) \ 1) * y) = x * y
    ]]></literal>
    <justification jstring="[hyper(2700,a,2803,a)].">
      <j1 rule="hyper" parents="2700 2803"/>
    </justification>
  </clause>

  <clause id="2834">
    <literal><![CDATA[
      x * (((x \ 1) \ 1) \ y) = y * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,2707,a(flip),b,2804,a),flip(a)].">
      <j1 rule="hyper" parents="320 2707 2804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2835">
    <literal><![CDATA[
      (T(x,x \ 1) * y) \ ((K(x,x \ 1) * y) * x) = K(K(x,x \ 1) * y,x)
    ]]></literal>
    <justification jstring="[para(2805(a,1),11(a,2,1)),flip(a)].">
      <j1 rule="para" parents="2805 11"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2836">
    <literal><![CDATA[
      T(x,x \ 1) * (K(x \ 1,x) * y) = x * y
    ]]></literal>
    <justification jstring="[para(2696(a,1),2805(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2696 2805"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2837">
    <literal><![CDATA[
      (x \ y) * K(x \ 1,x) = ((x \ 1) \ 1) \ y
    ]]></literal>
    <justification jstring="[hyper(2708,a,2808,a)].">
      <j1 rule="hyper" parents="2708 2808"/>
    </justification>
  </clause>

  <clause id="2838">
    <literal><![CDATA[
      K(x \ 1,x) * (x \ y) = ((x \ 1) \ 1) \ y
    ]]></literal>
    <justification jstring="[hyper(2700,a,2808,a)].">
      <j1 rule="hyper" parents="2700 2808"/>
    </justification>
  </clause>

  <clause id="2839">
    <literal><![CDATA[
      (((x \ 1) \ 1) \ y) * K(x,x \ 1) = x \ y
    ]]></literal>
    <justification jstring="[hyper(2189,a,2808,a)].">
      <j1 rule="hyper" parents="2189 2808"/>
    </justification>
  </clause>

  <clause id="2841">
    <literal><![CDATA[
      (((x \ 1) \ 1) \ y) * ((x \ 1) \ 1) = (x \ y) * x
    ]]></literal>
    <justification jstring="[para(2808(a,1),2688(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2808 2688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2842">
    <literal><![CDATA[
      K(x \ 1,x) * ((x \ 1) \ y) = (1 / x) \ y
    ]]></literal>
    <justification jstring="[hyper(116,a,5,a(flip),b,2813,a),flip(a)].">
      <j1 rule="hyper" parents="116 5 2813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2843">
    <literal><![CDATA[
      (1 / x) * (y * K(x \ 1,x)) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(58,a,2215,a(flip),b,2813,a)].">
      <j1 rule="hyper" parents="58 2215 2813"/>
    </justification>
  </clause>

  <clause id="2844">
    <literal><![CDATA[
      (1 / x) * (y / (1 / x)) = (x \ 1) * (y / (x \ 1))
    ]]></literal>
    <justification jstring="[para(2626(a,1),2813(a,1,2))].">
      <j1 rule="para" parents="2626 2813"/>
    </justification>
  </clause>

  <clause id="2845">
    <literal><![CDATA[
      (x \ 1) * (K(x,x \ 1) * y) = (1 / x) * y
    ]]></literal>
    <justification jstring="[para(2697(a,1),2813(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2697 2813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2846">
    <literal><![CDATA[
      ((x \ 1) * y) * K(x,x \ 1) = (1 / x) * y
    ]]></literal>
    <justification jstring="[hyper(2709,a,2814,a)].">
      <j1 rule="hyper" parents="2709 2814"/>
    </justification>
  </clause>

  <clause id="2847">
    <literal><![CDATA[
      ((1 / x) * y) * K(x \ 1,x) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(2196,a,2814,a)].">
      <j1 rule="hyper" parents="2196 2814"/>
    </justification>
  </clause>

  <clause id="2848">
    <literal><![CDATA[
      (x \ 1) * ((1 / x) \ y) = K(x \ 1,x) * y
    ]]></literal>
    <justification jstring="[hyper(342,a,2814,a),flip(a)].">
      <j1 rule="hyper" parents="342 2814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2849">
    <literal><![CDATA[
      K(x \ 1,x) * y != (x \ 1) * z
    ]]></literal>
    <literal><![CDATA[
      (1 / x) * z = y
    ]]></literal>
    <justification jstring="[para(2814(a,1),38(a,1)),flip(a)].">
      <j1 rule="para" parents="2814 38"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2850">
    <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(2814(a,1),92(a,2,1))].">
      <j1 rule="para" parents="2814 92"/>
    </justification>
  </clause>

  <clause id="2851">
    <literal><![CDATA[
      ((x \ 1) * y) / L(T(1 / x,y),y,K(x \ 1,x)) = K(x \ 1,x) * y
    ]]></literal>
    <justification jstring="[para(2814(a,1),545(a,1,1))].">
      <j1 rule="para" parents="2814 545"/>
    </justification>
  </clause>

  <clause id="2852">
    <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(2814(a,1),477(a,1,1))].">
      <j1 rule="para" parents="2814 477"/>
    </justification>
  </clause>

  <clause id="2853">
    <literal><![CDATA[
      T(x,(1 / x) * y) = T(x,(x \ 1) * y)
    ]]></literal>
    <justification jstring="[para(2814(a,1),2468(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2814 2468"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2854">
    <literal><![CDATA[
      ((x \ 1) * y) * ((x \ 1) \ 1) = ((1 / x) * y) * x
    ]]></literal>
    <justification jstring="[para(2814(a,1),2661(a,1,1))].">
      <j1 rule="para" parents="2814 2661"/>
    </justification>
  </clause>

  <clause id="2855">
    <literal><![CDATA[
      K(x,x \ 1) * ((1 / (1 / x)) * y) = x * y
    ]]></literal>
    <justification jstring="[hyper(1463,a,2817,a),flip(a)].">
      <j1 rule="hyper" parents="1463 2817"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2856">
    <literal><![CDATA[
      K(x,x \ 1) * (x \ y) = (1 / (1 / x)) \ y
    ]]></literal>
    <justification jstring="[hyper(116,a,5,a(flip),b,2817,a),flip(a)].">
      <j1 rule="hyper" parents="116 5 2817"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2857">
    <literal><![CDATA[
      (1 / (1 / x)) * (y / (1 / (1 / x))) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(2630(a,1),2817(a,1,2))].">
      <j1 rule="para" parents="2630 2817"/>
    </justification>
  </clause>

  <clause id="2858">
    <literal><![CDATA[
      x * (K(x \ 1,x) * y) = (1 / (1 / x)) * y
    ]]></literal>
    <justification jstring="[para(2696(a,1),2817(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2696 2817"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2859">
    <literal><![CDATA[
      x \ L(y,1 / x,x) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(1864,a,2819,a)].">
      <j1 rule="hyper" parents="1864 2819"/>
    </justification>
  </clause>

  <clause id="2860">
    <literal><![CDATA[
      L(x,1 / y,y) = L(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(843,a,2859,a)].">
      <j1 rule="hyper" parents="843 2859"/>
    </justification>
  </clause>

  <clause id="2861">
    <literal><![CDATA[
      (x \ 1) \ L(y,x,x \ 1) = ((x \ 1) \ 1) * y
    ]]></literal>
    <justification jstring="[para(72(a,1),2859(a,1,2,2))].">
      <j1 rule="para" parents="72 2859"/>
    </justification>
  </clause>

  <clause id="2862">
    <literal><![CDATA[
      L(x,(y \ 1) \ 1,y \ 1) = L(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[para(72(a,1),2860(a,1,2)),flip(a)].">
      <j1 rule="para" parents="72 2860"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2863">
    <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),2860(a,1,2)),flip(a)].">
      <j1 rule="para" parents="312 2860"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2864">
    <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(2860(a,1),2113(a,1))].">
      <j1 rule="para" parents="2860 2113"/>
    </justification>
  </clause>

  <clause id="2865">
    <literal><![CDATA[
      x * (y * K(x,x \ 1)) = ((x \ 1) \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(58,a,2448,a(flip),b,2832,a)].">
      <j1 rule="hyper" parents="58 2448 2832"/>
    </justification>
  </clause>

  <clause id="2866">
    <literal><![CDATA[
      K(T(x,y),x \ 1) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(29,a,2770,a,b,2832,a)].">
      <j1 rule="hyper" parents="29 2770 2832"/>
    </justification>
  </clause>

  <clause id="2869">
    <literal><![CDATA[
      K(T(x,y),T(x,y) \ 1) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,2768,a,b,2866,a)].">
      <j1 rule="hyper" parents="58 2768 2866"/>
    </justification>
  </clause>

  <clause id="2873">
    <literal><![CDATA[
      T(x,y) \ K(x,x \ 1) = 1 / T(x,y)
    ]]></literal>
    <justification jstring="[hyper(116,a,2869,a(flip),b,1794,a(flip))].">
      <j1 rule="hyper" parents="116 2869 1794"/>
    </justification>
  </clause>

  <clause id="2876">
    <literal><![CDATA[
      x * (T(x,y) \ (1 / x)) = 1 / T(x,y)
    ]]></literal>
    <justification jstring="[hyper(1805,a,2873,a)].">
      <j1 rule="hyper" parents="1805 2873"/>
    </justification>
  </clause>

  <clause id="2877">
    <literal><![CDATA[
      (T(x,y) \ x) / x = 1 / T(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,2182,a(flip),b,2873,a)].">
      <j1 rule="hyper" parents="58 2182 2873"/>
    </justification>
  </clause>

  <clause id="2878">
    <literal><![CDATA[
      (1 / T(x,y)) * x = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(133,a,2877,a)].">
      <j1 rule="hyper" parents="133 2877"/>
    </justification>
  </clause>

  <clause id="2879">
    <literal><![CDATA[
      x / T(x,y) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(32,a,1477,a,b,2877,a)].">
      <j1 rule="hyper" parents="32 1477 2877"/>
    </justification>
  </clause>

  <clause id="2880">
    <literal><![CDATA[
      T(1 / T(x,y),x) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[para(2877(a,1),1123(a,1,1))].">
      <j1 rule="para" parents="2877 1123"/>
    </justification>
  </clause>

  <clause id="2881">
    <literal><![CDATA[
      (T(x,y) \ x) \ x = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(188,a,2879,a)].">
      <j1 rule="hyper" parents="188 2879"/>
    </justification>
  </clause>

  <clause id="2882">
    <literal><![CDATA[
      (T(x,y) \ x) * T(x,y) = x
    ]]></literal>
    <justification jstring="[hyper(133,a,2879,a)].">
      <j1 rule="hyper" parents="133 2879"/>
    </justification>
  </clause>

  <clause id="2883">
    <literal><![CDATA[
      K(x \ (x / ((y \ x) / T(x,y))),x) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(58,a,1975,a,b,2879,a)].">
      <j1 rule="hyper" parents="58 1975 2879"/>
    </justification>
  </clause>

  <clause id="2884">
    <literal><![CDATA[
      L(x,T(x,y) \ x,x) = x
    ]]></literal>
    <justification jstring="[hyper(58,a,2326,a,b,2882,a)].">
      <j1 rule="hyper" parents="58 2326 2882"/>
    </justification>
  </clause>

  <clause id="2886">
    <literal><![CDATA[
      (x * y) * T(K(y,x),x) = y * x
    ]]></literal>
    <justification jstring="[para(2884(a,1),2325(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2884 2325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2887">
    <literal><![CDATA[
      K(x \ 1,x) / T(x,y) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(58,a,2202,a,b,2880,a)].">
      <j1 rule="hyper" parents="58 2202 2880"/>
    </justification>
  </clause>

  <clause id="2888">
    <literal><![CDATA[
      T(K(x,y),y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(306,a,2886,a),flip(a)].">
      <j1 rule="hyper" parents="306 2886"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2889">
    <literal><![CDATA[
      (x * K(y,x)) / x = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(271,a,2888,a)].">
      <j1 rule="hyper" parents="271 2888"/>
    </justification>
  </clause>

  <clause id="2890">
    <literal><![CDATA[
      T(x,K(y,x)) = x
    ]]></literal>
    <justification jstring="[hyper(49,a,2888,a)].">
      <j1 rule="hyper" parents="49 2888"/>
    </justification>
  </clause>

  <clause id="2891">
    <literal><![CDATA[
      K(x,y) * y = y * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,2888,a(flip),b,17,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 2888 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2892">
    <literal><![CDATA[
      T(L(K(x,y),z,u),y) = L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(2888(a,1),20(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2888 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2893">
    <literal><![CDATA[
      (x * K(y,x)) / x != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(2888(a,1),331(a,1,1,2)),flip(b)].">
      <j1 rule="para" parents="2888 331"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2894">
    <literal><![CDATA[
      T(x,K(y,R(x,z,u))) = x
    ]]></literal>
    <justification jstring="[hyper(143,a,2890,a)].">
      <j1 rule="hyper" parents="143 2890"/>
    </justification>
  </clause>

  <clause id="2895">
    <literal><![CDATA[
      T(x,K(y,T(x,z))) = x
    ]]></literal>
    <justification jstring="[hyper(138,a,2890,a)].">
      <j1 rule="hyper" parents="138 2890"/>
    </justification>
  </clause>

  <clause id="2896">
    <literal><![CDATA[
      T(T(x,y),K(z,x)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(2890(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2890 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2897">
    <literal><![CDATA[
      T(x,y) * K(z,x) = K(z,x) * T(x,y)
    ]]></literal>
    <justification jstring="[para(2890(a,1),236(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2890 236"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2898">
    <literal><![CDATA[
      L(x,y,z) * K(u,x) = K(u,x) * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(2890(a,1),237(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2890 237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2899">
    <literal><![CDATA[
      R(x,y,z) * K(u,x) = K(u,x) * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(2890(a,1),238(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2890 238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2900">
    <literal><![CDATA[
      K(x,y) * T(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,z) * K(x,y) = u
    ]]></literal>
    <justification jstring="[para(2890(a,1),417(a,1,2,1))].">
      <j1 rule="para" parents="2890 417"/>
    </justification>
  </clause>

  <clause id="2901">
    <literal><![CDATA[
      L(x \ y,x,K(z,y)) = (K(z,y) * x) \ (y * K(z,y))
    ]]></literal>
    <justification jstring="[para(2890(a,1),450(a,1,1,2))].">
      <j1 rule="para" parents="2890 450"/>
    </justification>
  </clause>

  <clause id="2902">
    <literal><![CDATA[
      T(T(x,y),z) * K(u,x) = K(u,x) * T(T(x,y),z)
    ]]></literal>
    <justification jstring="[para(2890(a,1),452(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="2890 452"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2903">
    <literal><![CDATA[
      T(x,y * T(y \ 1,x)) = x
    ]]></literal>
    <justification jstring="[para(1025(a,1),2890(a,1,2))].">
      <j1 rule="para" parents="1025 2890"/>
    </justification>
  </clause>

  <clause id="2904">
    <literal><![CDATA[
      T(x,y \ T(y,x)) = x
    ]]></literal>
    <justification jstring="[para(1028(a,1),2890(a,1,2))].">
      <j1 rule="para" parents="1028 2890"/>
    </justification>
  </clause>

  <clause id="2905">
    <literal><![CDATA[
      T(x,x \ ((y * x) / y)) = x
    ]]></literal>
    <justification jstring="[para(1507(a,1),2890(a,1,2))].">
      <j1 rule="para" parents="1507 2890"/>
    </justification>
  </clause>

  <clause id="2906">
    <literal><![CDATA[
      x * ((K(x,y) \ y) * K(x,y)) = (y * x) * K(x,y)
    ]]></literal>
    <justification jstring="[para(2890(a,1),2484(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="2890 2484"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2907">
    <literal><![CDATA[
      K(x,T(y,z)) * y = y * K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(119,a,2895,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 2895 17"/>
    </justification>
  </clause>

  <clause id="2908">
    <literal><![CDATA[
      T(x / y,K(z,y \ x)) = x / y
    ]]></literal>
    <justification jstring="[para(107(a,1),2895(a,1,2,2))].">
      <j1 rule="para" parents="107 2895"/>
    </justification>
  </clause>

  <clause id="2909">
    <literal><![CDATA[
      T(x \ T(x,y),y) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(49,a,2904,a)].">
      <j1 rule="hyper" parents="49 2904"/>
    </justification>
  </clause>

  <clause id="2910">
    <literal><![CDATA[
      T(T(x,y),K(z,R(x,u,w))) = T(x,y)
    ]]></literal>
    <justification jstring="[para(2894(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2894 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2911">
    <literal><![CDATA[
      L(K(x,y),y,1 / y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,2360,a,b,2889,a)].">
      <j1 rule="hyper" parents="58 2360 2889"/>
    </justification>
  </clause>

  <clause id="2912">
    <literal><![CDATA[
      L((T(x,y) * (x \ y)) / y,y,x) = K(T(x,y),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,1356,a,b,2889,a)].">
      <j1 rule="hyper" parents="58 1356 2889"/>
    </justification>
  </clause>

  <clause id="2913">
    <literal><![CDATA[
      T(K(x,y),y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(2889(a,1),292(a,1,1)),flip(b)].">
      <j1 rule="para" parents="2889 292"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2914">
    <literal><![CDATA[
      R(K(x,y),y,(y * K(x,y)) \ z) \ z = y * ((y * K(x,y)) \ z)
    ]]></literal>
    <justification jstring="[para(2889(a,1),504(a,1,1,1))].">
      <j1 rule="para" parents="2889 504"/>
    </justification>
  </clause>

  <clause id="2915">
    <literal><![CDATA[
      R(x,K(y,z),z) * (z * K(y,z)) = (x * K(y,z)) * z
    ]]></literal>
    <justification jstring="[hyper(119,a,2891,a(flip),b,184,a)].">
      <j1 rule="hyper" parents="119 2891 184"/>
    </justification>
  </clause>

  <clause id="2916">
    <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(2891(a,1),515(a,2,2))].">
      <j1 rule="para" parents="2891 515"/>
    </justification>
  </clause>

  <clause id="2917">
    <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(2891(a,1),518(a,1,2))].">
      <j1 rule="para" parents="2891 518"/>
    </justification>
  </clause>

  <clause id="2918">
    <literal><![CDATA[
      T(K(x,y),T(y,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(49,a,2896,a)].">
      <j1 rule="hyper" parents="49 2896"/>
    </justification>
  </clause>

  <clause id="2919">
    <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(2896(a,1),417(a,1,2,1))].">
      <j1 rule="para" parents="2896 417"/>
    </justification>
  </clause>

  <clause id="2920">
    <literal><![CDATA[
      T(x * T(x \ 1,y),y) = x * T(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(49,a,2903,a)].">
      <j1 rule="hyper" parents="49 2903"/>
    </justification>
  </clause>

  <clause id="2921">
    <literal><![CDATA[
      ((x * y) / x) / y = y \ ((x * y) / x)
    ]]></literal>
    <justification jstring="[para(2905(a,1),265(a,1,2))].">
      <j1 rule="para" parents="2905 265"/>
    </justification>
  </clause>

  <clause id="2922">
    <literal><![CDATA[
      K(K(x,y),T(y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(50,a,2918,a)].">
      <j1 rule="hyper" parents="50 2918"/>
    </justification>
  </clause>

  <clause id="2923">
    <literal><![CDATA[
      T(x,y) * K(z,x) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,x) * T(x,y) = u
    ]]></literal>
    <justification jstring="[para(2918(a,1),284(a,1,2))].">
      <j1 rule="para" parents="2918 284"/>
    </justification>
  </clause>

  <clause id="2924">
    <literal><![CDATA[
      K(x \ T(x,y),T(y,z)) = 1
    ]]></literal>
    <justification jstring="[para(1028(a,1),2922(a,1,1))].">
      <j1 rule="para" parents="1028 2922"/>
    </justification>
  </clause>

  <clause id="2925">
    <literal><![CDATA[
      T(x \ T(x,y),T(y,z)) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(51,a,2924,a)].">
      <j1 rule="hyper" parents="51 2924"/>
    </justification>
  </clause>

  <clause id="2926">
    <literal><![CDATA[
      (1 / x) * (x * K(y,x)) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(387,a,2911,a)].">
      <j1 rule="hyper" parents="387 2911"/>
    </justification>
  </clause>

  <clause id="2927">
    <literal><![CDATA[
      K(x,y) / (y * K(x,y)) = 1 / y
    ]]></literal>
    <justification jstring="[hyper(117,a,2911,a(flip),b,259,a)].">
      <j1 rule="hyper" parents="117 2911 259"/>
    </justification>
  </clause>

  <clause id="2928">
    <literal><![CDATA[
      (1 / x) \ K(y,x) = x * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,2911,a(flip),b,259,a)].">
      <j1 rule="hyper" parents="116 2911 259"/>
    </justification>
  </clause>

  <clause id="2929">
    <literal><![CDATA[
      x * (y \ T(y,x)) != z
    ]]></literal>
    <literal><![CDATA[
      (y \ T(y,x)) * x = z
    ]]></literal>
    <justification jstring="[para(2909(a,1),284(a,1,2))].">
      <j1 rule="para" parents="2909 284"/>
    </justification>
  </clause>

  <clause id="2930">
    <literal><![CDATA[
      (x \ 1) * K(y,x \ 1) = x \ K(y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(116,a,2926,a(flip),b,183,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="116 2926 183"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2931">
    <literal><![CDATA[
      (T(x,y) \ 1) * T(x,y) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(133,a,2887,a)].">
      <j1 rule="hyper" parents="133 2887"/>
    </justification>
  </clause>

  <clause id="2932">
    <literal><![CDATA[
      K(T(x,y) \ 1,T(x,y)) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(32,a,359,a,b,2887,a)].">
      <j1 rule="hyper" parents="32 359 2887"/>
    </justification>
  </clause>

  <clause id="2933">
    <literal><![CDATA[
      T(x,L(K(y,x),z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(49,a,2892,a)].">
      <j1 rule="hyper" parents="49 2892"/>
    </justification>
  </clause>

  <clause id="2934">
    <literal><![CDATA[
      x * (((y * x) / y) / x) = (y * x) / y
    ]]></literal>
    <justification jstring="[hyper(119,a,2921,a,b,xx)].">
      <j1 rule="hyper" parents="119 2921"/>
    </justification>
  </clause>

  <clause id="2935">
    <literal><![CDATA[
      (x \ 1) * (x * ((y * (x \ 1)) / y)) = (y * (x \ 1)) / y
    ]]></literal>
    <justification jstring="[hyper(1475,a,2921,a(flip))].">
      <j1 rule="hyper" parents="1475 2921"/>
    </justification>
  </clause>

  <clause id="2936">
    <literal><![CDATA[
      (1 / T(x,y)) * K(x \ 1,x) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[para(2931(a,1),774(a,1,2))].">
      <j1 rule="para" parents="2931 774"/>
    </justification>
  </clause>

  <clause id="2938">
    <literal><![CDATA[
      K((x * y) \ y,y \ (x * y)) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,2597,a,b,2932,a)].">
      <j1 rule="hyper" parents="58 2597 2932"/>
    </justification>
  </clause>

  <clause id="2939">
    <literal><![CDATA[
      K((x / y) \ 1,x / y) = K(x \ y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,2763,a(flip),b,2932,a),flip(a)].">
      <j1 rule="hyper" parents="58 2763 2932"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2940">
    <literal><![CDATA[
      T(x,y) * K(x \ 1,x) = T(1 / (1 / x),y)
    ]]></literal>
    <justification jstring="[para(2932(a,1),2169(a,1,2))].">
      <j1 rule="para" parents="2932 2169"/>
    </justification>
  </clause>

  <clause id="2941">
    <literal><![CDATA[
      (x * T(y,z)) / T(T(y,y \ 1),z) = x * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[para(2932(a,1),2657(a,2,2))].">
      <j1 rule="para" parents="2932 2657"/>
    </justification>
  </clause>

  <clause id="2942">
    <literal><![CDATA[
      K(x \ 1,x) * (y / T(1 / (1 / x),z)) = y / ((1 / T(x,z)) \ 1)
    ]]></literal>
    <justification jstring="[para(2932(a,1),2761(a,1,1))].">
      <j1 rule="para" parents="2932 2761"/>
    </justification>
  </clause>

  <clause id="2943">
    <literal><![CDATA[
      x * K(y \ 1,y) != y * z
    ]]></literal>
    <literal><![CDATA[
      ((y \ 1) \ 1) * z = x
    ]]></literal>
    <justification jstring="[para(2833(a,1),2195(a,1)),flip(a)].">
      <j1 rule="para" parents="2833 2195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2944">
    <literal><![CDATA[
      ((x \ 1) \ 1) \ (x * y) = y * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(29,a,2474,a(flip),b,2834,a),flip(a)].">
      <j1 rule="hyper" parents="29 2474 2834"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2945">
    <literal><![CDATA[
      ((x \ 1) \ 1) \ (x * y) = K(x \ 1,x) * y
    ]]></literal>
    <justification jstring="[hyper(656,a,2836,a)].">
      <j1 rule="hyper" parents="656 2836"/>
    </justification>
  </clause>

  <clause id="2946">
    <literal><![CDATA[
      K(x \ 1,x) * (x \ y) = T(x,x \ 1) \ y
    ]]></literal>
    <justification jstring="[hyper(116,a,5,a(flip),b,2836,a),flip(a)].">
      <j1 rule="hyper" parents="116 5 2836"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2947">
    <literal><![CDATA[
      x * T(x \ (y \ x),y) = ((y \ 1) \ 1) \ x
    ]]></literal>
    <justification jstring="[hyper(1225,a,2838,a)].">
      <j1 rule="hyper" parents="1225 2838"/>
    </justification>
  </clause>

  <clause id="2948">
    <literal><![CDATA[
      ((1 / x) \ y) * K(x,x \ 1) = (x \ 1) \ y
    ]]></literal>
    <justification jstring="[hyper(2709,a,2842,a)].">
      <j1 rule="hyper" parents="2709 2842"/>
    </justification>
  </clause>

  <clause id="2949">
    <literal><![CDATA[
      ((x \ 1) \ y) * K(x \ 1,x) = (1 / x) \ y
    ]]></literal>
    <justification jstring="[hyper(2196,a,2842,a)].">
      <j1 rule="hyper" parents="2196 2842"/>
    </justification>
  </clause>

  <clause id="2950">
    <literal><![CDATA[
      T((x \ 1) * y,K(z \ 1,z)) = (1 / x) * (y * K(x \ 1,x))
    ]]></literal>
    <justification jstring="[hyper(320,a,2190,a,b,2843,a)].">
      <j1 rule="hyper" parents="320 2190 2843"/>
    </justification>
  </clause>

  <clause id="2952">
    <literal><![CDATA[
      (x \ 1) \ ((1 / x) * y) = K(x,x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(123,a,2845,a)].">
      <j1 rule="hyper" parents="123 2845"/>
    </justification>
  </clause>

  <clause id="2953">
    <literal><![CDATA[
      L(K(x,x \ 1) * y,x \ 1,x) = x * ((1 / x) * y)
    ]]></literal>
    <justification jstring="[hyper(119,a,2845,a(flip),b,437,a),flip(a)].">
      <j1 rule="hyper" parents="119 2845 437"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2954">
    <literal><![CDATA[
      (1 / x) \ (y * (1 / x)) = T(y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(239,a,2619,a(flip),b,2848,a),flip(a)].">
      <j1 rule="hyper" parents="239 2619 2848"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2955">
    <literal><![CDATA[
      K(x \ 1,x) * ((1 / x) * y) != z
    ]]></literal>
    <literal><![CDATA[
      (x \ 1) * y = z
    ]]></literal>
    <justification jstring="[para(2848(a,1),585(a,1))].">
      <j1 rule="para" parents="2848 585"/>
    </justification>
  </clause>

  <clause id="2956">
    <literal><![CDATA[
      T(x,1 / y) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(288,a,2954,a)].">
      <j1 rule="hyper" parents="288 2954"/>
    </justification>
  </clause>

  <clause id="2957">
    <literal><![CDATA[
      T(x,y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,1 / y) = z
    ]]></literal>
    <justification jstring="[para(2954(a,1),288(a,1))].">
      <j1 rule="para" parents="2954 288"/>
    </justification>
  </clause>

  <clause id="2959">
    <literal><![CDATA[
      T(x,(y \ 1) \ 1) = T(x,y)
    ]]></literal>
    <justification jstring="[para(72(a,1),2956(a,1,2)),flip(a)].">
      <j1 rule="para" parents="72 2956"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2960">
    <literal><![CDATA[
      T(x,1 / (1 / y)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(75(a,1),2956(a,2,2))].">
      <j1 rule="para" parents="75 2956"/>
    </justification>
  </clause>

  <clause id="2961">
    <literal><![CDATA[
      T(T(x,y),K(z,z \ 1)) = T(x,(y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,2180,a,b,2959,a)].">
      <j1 rule="hyper" parents="320 2180 2959"/>
    </justification>
  </clause>

  <clause id="2962">
    <literal><![CDATA[
      ((x \ 1) \ 1) * T(y,x) = y * ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(119,a,2959,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 2959 17"/>
    </justification>
  </clause>

  <clause id="2963">
    <literal><![CDATA[
      T(x,T(y,y \ 1)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(106(a,2),2959(a,1,2))].">
      <j1 rule="para" parents="106 2959"/>
    </justification>
  </clause>

  <clause id="2965">
    <literal><![CDATA[
      T(x,R(1 / y,y,z)) = T(x,R(y \ 1,y,z))
    ]]></literal>
    <justification jstring="[para(2074(a,1),2959(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2074 2959"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2966">
    <literal><![CDATA[
      T(x,x \ 1) * T(y,x) = y * T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(119,a,2963,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 2963 17"/>
    </justification>
  </clause>

  <clause id="2967">
    <literal><![CDATA[
      (x * y) * K(x \ 1,x) = (1 / (1 / x)) * y
    ]]></literal>
    <justification jstring="[hyper(2708,a,2855,a)].">
      <j1 rule="hyper" parents="2708 2855"/>
    </justification>
  </clause>

  <clause id="2968">
    <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),2855(a,1,2))].">
      <j1 rule="para" parents="302 2855"/>
    </justification>
  </clause>

  <clause id="2969">
    <literal><![CDATA[
      K(x \ 1,x) * ((1 / (1 / x)) \ y) = x \ y
    ]]></literal>
    <justification jstring="[hyper(2700,a,2856,a)].">
      <j1 rule="hyper" parents="2700 2856"/>
    </justification>
  </clause>

  <clause id="2970">
    <literal><![CDATA[
      (x \ y) * K(x,x \ 1) = (1 / (1 / x)) \ y
    ]]></literal>
    <justification jstring="[hyper(2189,a,2856,a)].">
      <j1 rule="hyper" parents="2189 2856"/>
    </justification>
  </clause>

  <clause id="2971">
    <literal><![CDATA[
      K(x,1 / x) * (x \ y) = (1 / (1 / x)) \ y
    ]]></literal>
    <justification jstring="[para(1791(a,2),2856(a,1,1))].">
      <j1 rule="para" parents="1791 2856"/>
    </justification>
  </clause>

  <clause id="2972">
    <literal><![CDATA[
      ((1 / (1 / x)) \ y) * x = (x \ y) * ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(2856(a,1),2688(a,1,1))].">
      <j1 rule="para" parents="2856 2688"/>
    </justification>
  </clause>

  <clause id="2973">
    <literal><![CDATA[
      T(x,y) * (K(x \ 1,x) * z) = (1 / (1 / T(x,y))) * z
    ]]></literal>
    <justification jstring="[para(2932(a,1),2858(a,1,2,1))].">
      <j1 rule="para" parents="2932 2858"/>
    </justification>
  </clause>

  <clause id="2974">
    <literal><![CDATA[
      L(((x \ 1) \ 1) \ y,x,x \ 1) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(499,a,2862,a),flip(a)].">
      <j1 rule="hyper" parents="499 2862"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2975">
    <literal><![CDATA[
      T(K(x,y),L(y,z,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(240,a,2898,a)].">
      <j1 rule="hyper" parents="240 2898"/>
    </justification>
  </clause>

  <clause id="2976">
    <literal><![CDATA[
      x * ((y \ (x \ y)) * y) = y * (x * T(x \ 1,y))
    ]]></literal>
    <justification jstring="[para(2920(a,1),1401(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2920 1401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2977">
    <literal><![CDATA[
      x * ((x \ R(x,y,z)) / R(x,y,z)) = K(R(x,y,z),x \ 1)
    ]]></literal>
    <justification jstring="[hyper(2576,a,2930,a(flip))].">
      <j1 rule="hyper" parents="2576 2930"/>
    </justification>
  </clause>

  <clause id="2978">
    <literal><![CDATA[
      x * ((1 / T(x,y)) * K(x \ 1,x)) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(119,a,2936,a,b,1125,a)].">
      <j1 rule="hyper" parents="119 2936 1125"/>
    </justification>
  </clause>

  <clause id="2980">
    <literal><![CDATA[
      (x * y) * ((((x * y) \ y) \ 1) \ 1) = y * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(2938(a,1),2586(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2938 2586"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2982">
    <literal><![CDATA[
      K(x / y,y / x) = K(y \ x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,2736,a(flip),b,2939,a)].">
      <j1 rule="hyper" parents="58 2736 2939"/>
    </justification>
  </clause>

  <clause id="2983">
    <literal><![CDATA[
      K(1 / (x \ y),x \ y) = K(x / y,y / x)
    ]]></literal>
    <justification jstring="[hyper(320,a,2585,a,b,2982,a)].">
      <j1 rule="hyper" parents="320 2585 2982"/>
    </justification>
  </clause>

  <clause id="2984">
    <literal><![CDATA[
      K(x / y,(x / y) \ 1) = K(y \ x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,2799,a,b,2982,a)].">
      <j1 rule="hyper" parents="58 2799 2982"/>
    </justification>
  </clause>

  <clause id="2985">
    <literal><![CDATA[
      x * (T(x,y) / x) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(30,a,2264,a,b,2940,a)].">
      <j1 rule="hyper" parents="30 2264 2940"/>
    </justification>
  </clause>

  <clause id="2987">
    <literal><![CDATA[
      T(x,y) / x = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(123,a,2985,a),flip(a)].">
      <j1 rule="hyper" parents="123 2985"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2988">
    <literal><![CDATA[
      K(x,T(x,y) / x) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,2985,a(flip),b,303,a),flip(a)].">
      <j1 rule="hyper" parents="115 2985 303"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2989">
    <literal><![CDATA[
      (x \ T(x,y)) * x = T(x,y)
    ]]></literal>
    <justification jstring="[para(2985(a,1),76(a,1,1,2))].">
      <j1 rule="para" parents="2985 76"/>
    </justification>
  </clause>

  <clause id="2990">
    <literal><![CDATA[
      T(1 / x,T(x,y)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(116,a,2988,a(flip),b,1182,a),flip(a)].">
      <j1 rule="hyper" parents="116 2988 1182"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2991">
    <literal><![CDATA[
      x \ T(x,R(y,y \ 1,x)) = y \ ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(1675,a,2987,a),flip(a)].">
      <j1 rule="hyper" parents="1675 2987"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2992">
    <literal><![CDATA[
      (1 / x) * T(x,y) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(1352,a,2987,a)].">
      <j1 rule="hyper" parents="1352 2987"/>
    </justification>
  </clause>

  <clause id="2993">
    <literal><![CDATA[
      (x \ 1) \ T(x \ 1,y) = x * T(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(1015,a,2987,a),flip(a)].">
      <j1 rule="hyper" parents="1015 2987"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2994">
    <literal><![CDATA[
      (1 / x) * T((1 / x) \ 1,y) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(1011,a,2987,a)].">
      <j1 rule="hyper" parents="1011 2987"/>
    </justification>
  </clause>

  <clause id="2995">
    <literal><![CDATA[
      T(x,x \ T(x,y)) = x
    ]]></literal>
    <justification jstring="[hyper(31,a,265,a,b,2987,a)].">
      <j1 rule="hyper" parents="31 265 2987"/>
    </justification>
  </clause>

  <clause id="2996">
    <literal><![CDATA[
      (x \ T(x,y)) * x != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(2987(a,1),251(a,1,1)),flip(b)].">
      <j1 rule="para" parents="2987 251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2997">
    <literal><![CDATA[
      R(x \ T(x,y),x,z) = (T(x,y) * z) / (x * z)
    ]]></literal>
    <justification jstring="[para(2987(a,1),102(a,1,1))].">
      <j1 rule="para" parents="2987 102"/>
    </justification>
  </clause>

  <clause id="2998">
    <literal><![CDATA[
      R((x / y) \ T(x / y,z),x / y,y) = (T(x / y,z) * y) / x
    ]]></literal>
    <justification jstring="[para(2987(a,1),525(a,1,1))].">
      <j1 rule="para" parents="2987 525"/>
    </justification>
  </clause>

  <clause id="2999">
    <literal><![CDATA[
      (x \ T(x,y)) * (1 / T(x,y)) = 1 / x
    ]]></literal>
    <justification jstring="[para(2987(a,1),2158(a,1,1))].">
      <j1 rule="para" parents="2987 2158"/>
    </justification>
  </clause>

  <clause id="3000">
    <literal><![CDATA[
      (x * (y \ T(y,x))) \ (x * z) = x * ((x * (T(y,x) / y)) \ z)
    ]]></literal>
    <justification jstring="[para(2987(a,1),2434(a,1,1,2))].">
      <j1 rule="para" parents="2987 2434"/>
    </justification>
  </clause>

  <clause id="3001">
    <literal><![CDATA[
      T(x,K(y \ (y / (x \ 1)),y)) = x
    ]]></literal>
    <justification jstring="[para(1028(a,2),2995(a,1,2))].">
      <j1 rule="para" parents="1028 2995"/>
    </justification>
  </clause>

  <clause id="3002">
    <literal><![CDATA[
      T(x,R(1 / y,y,x)) = T(x,x / (x * y))
    ]]></literal>
    <justification jstring="[hyper(58,a,1681,a,b,2989,a)].">
      <j1 rule="hyper" parents="58 1681 2989"/>
    </justification>
  </clause>

  <clause id="3003">
    <literal><![CDATA[
      T(x,y) \ ((x \ T(x,y)) * (x * z)) = L(z,x,x \ T(x,y))
    ]]></literal>
    <justification jstring="[para(2989(a,1),13(a,2,1)),flip(a)].">
      <j1 rule="para" parents="2989 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3004">
    <literal><![CDATA[
      T(x,y) * L(z,x,x \ T(x,y)) = (x \ T(x,y)) * (x * z)
    ]]></literal>
    <justification jstring="[para(2989(a,1),90(a,1,1))].">
      <j1 rule="para" parents="2989 90"/>
    </justification>
  </clause>

  <clause id="3005">
    <literal><![CDATA[
      (T(x,y) * z) / (x * z) != u
    ]]></literal>
    <literal><![CDATA[
      R(x \ T(x,y),x,z) = u
    ]]></literal>
    <justification jstring="[para(2989(a,1),518(a,1,1,1))].">
      <j1 rule="para" parents="2989 518"/>
    </justification>
  </clause>

  <clause id="3006">
    <literal><![CDATA[
      L(x,x \ T(x,y),x) = T(x,y) / (x \ T(x,y))
    ]]></literal>
    <justification jstring="[para(2989(a,1),960(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2989 960"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3007">
    <literal><![CDATA[
      T(1 / (1 / x),T(1 / x,y)) = x
    ]]></literal>
    <justification jstring="[hyper(320,a,75,a(flip),b,2990,a),flip(a)].">
      <j1 rule="hyper" parents="320 75 2990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3008">
    <literal><![CDATA[
      L(x \ 1,x,y \ ((x * y) / x)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(58,a,1677,a(flip),b,2990,a)].">
      <j1 rule="hyper" parents="58 1677 2990"/>
    </justification>
  </clause>

  <clause id="3009">
    <literal><![CDATA[
      T(x,y) * (x \ 1) = (1 / x) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,2990,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 2990 17"/>
    </justification>
  </clause>

  <clause id="3010">
    <literal><![CDATA[
      T(x \ 1,T(x,y)) = T(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(2990(a,1),246(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2990 246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3011">
    <literal><![CDATA[
      T(x / (y * x),T(y,z)) = R(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(2990(a,1),409(a,2,1))].">
      <j1 rule="para" parents="2990 409"/>
    </justification>
  </clause>

  <clause id="3012">
    <literal><![CDATA[
      x * T(x \ 1,T(x,y)) = K(x \ 1,T(x,y))
    ]]></literal>
    <justification jstring="[para(2990(a,1),1031(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2990 1031"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3013">
    <literal><![CDATA[
      (((x * y) / x) \ y) \ y = (x * y) / x
    ]]></literal>
    <justification jstring="[hyper(1191,a,3001,a)].">
      <j1 rule="hyper" parents="1191 3001"/>
    </justification>
  </clause>

  <clause id="3014">
    <literal><![CDATA[
      (((x * y) / x) \ y) * ((x * y) / x) = y
    ]]></literal>
    <justification jstring="[hyper(119,a,3001,a(flip),b,1190,a(flip))].">
      <j1 rule="hyper" parents="119 3001 1190"/>
    </justification>
  </clause>

  <clause id="3015">
    <literal><![CDATA[
      T(x,T(1 / x,y)) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(3007(a,1),1784(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3007 1784"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3017">
    <literal><![CDATA[
      T(x,x \ 1) * T(x \ 1,y) = x * T(1 / x,y)
    ]]></literal>
    <justification jstring="[para(3015(a,1),1716(a,1,1))].">
      <j1 rule="para" parents="3015 1716"/>
    </justification>
  </clause>

  <clause id="3018">
    <literal><![CDATA[
      (1 / x) * T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      x \ T(x,y) = z
    ]]></literal>
    <justification jstring="[para(3009(a,1),996(a,1))].">
      <j1 rule="para" parents="3009 996"/>
    </justification>
  </clause>

  <clause id="3020">
    <literal><![CDATA[
      x / ((y * x) / y) = ((y * x) / y) \ x
    ]]></literal>
    <justification jstring="[hyper(197,a,3013,a)].">
      <j1 rule="hyper" parents="197 3013"/>
    </justification>
  </clause>

  <clause id="3021">
    <literal><![CDATA[
      (((x * y) / x) \ y) / y = 1 / ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(117,a,3020,a(flip),b,1556,a)].">
      <j1 rule="hyper" parents="117 3020 1556"/>
    </justification>
  </clause>

  <clause id="3022">
    <literal><![CDATA[
      T(x,x / (y * x)) = T(x,x / (x * y))
    ]]></literal>
    <justification jstring="[para(219(a,1),3002(a,1,2))].">
      <j1 rule="para" parents="219 3002"/>
    </justification>
  </clause>

  <clause id="3024">
    <literal><![CDATA[
      L(x \ 1,x,T(y,x) \ y) = x \ 1
    ]]></literal>
    <justification jstring="[para(225(a,1),3008(a,1,3,2))].">
      <j1 rule="para" parents="225 3008"/>
    </justification>
  </clause>

  <clause id="3025">
    <literal><![CDATA[
      K(x \ 1,x) * (x \ y) != z
    ]]></literal>
    <literal><![CDATA[
      ((x \ 1) \ 1) \ y = z
    ]]></literal>
    <justification jstring="[para(2946(a,2),657(a,1))].">
      <j1 rule="para" parents="2946 657"/>
    </justification>
  </clause>

  <clause id="3026">
    <literal><![CDATA[
      x * (((x \ (y \ x)) \ 1) \ 1) = ((y \ 1) \ 1) \ x
    ]]></literal>
    <justification jstring="[para(2237(a,1),2947(a,1,2))].">
      <j1 rule="para" parents="2237 2947"/>
    </justification>
  </clause>

  <clause id="3027">
    <literal><![CDATA[
      ((x \ 1) \ y) * K(x \ 1,x) != z
    ]]></literal>
    <literal><![CDATA[
      (1 / x) \ y = z
    ]]></literal>
    <justification jstring="[para(2948(a,1),2719(a,1,1)),flip(b)].">
      <j1 rule="para" parents="2948 2719"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3028">
    <literal><![CDATA[
      ((x \ 1) \ K(y,x)) * K(x \ 1,x) = x * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,2928,a(flip),b,2949,a),flip(a)].">
      <j1 rule="hyper" parents="320 2928 2949"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3029">
    <literal><![CDATA[
      T(x,(y \ 1) \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(2961(a,1),2186(a,1)),flip(b)].">
      <j1 rule="para" parents="2961 2186"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3030">
    <literal><![CDATA[
      T(x,T(y,y \ 1)) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(106(a,2),3029(a,1,2))].">
      <j1 rule="para" parents="106 3029"/>
    </justification>
  </clause>

  <clause id="3031">
    <literal><![CDATA[
      (x * ((y * (x \ 1)) / y)) * y = T(y,R(x \ 1,x,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,1679,a,b,2965,a)].">
      <j1 rule="hyper" parents="58 1679 2965"/>
    </justification>
  </clause>

  <clause id="3032">
    <literal><![CDATA[
      ((x \ y) * z) * K(y \ x,x \ y) = (1 / (1 / (x \ y))) * z
    ]]></literal>
    <justification jstring="[para(2583(a,1),2967(a,1,2))].">
      <j1 rule="para" parents="2583 2967"/>
    </justification>
  </clause>

  <clause id="3033">
    <literal><![CDATA[
      ((1 / (1 / x)) * y) * (1 / x) = (x * y) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(2967(a,1),2624(a,1,1))].">
      <j1 rule="para" parents="2967 2624"/>
    </justification>
  </clause>

  <clause id="3034">
    <literal><![CDATA[
      K(x \ 1,x) * (K(1 / x,y) * (1 / x)) = x \ K(1 / x,y)
    ]]></literal>
    <justification jstring="[para(2560(a,1),2969(a,1,2))].">
      <j1 rule="para" parents="2560 2969"/>
    </justification>
  </clause>

  <clause id="3035">
    <literal><![CDATA[
      ((1 / (1 / x)) \ y) / (1 / x) = (x \ y) / (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(117,a,2970,a(flip),b,2718,a)].">
      <j1 rule="hyper" parents="117 2970 2718"/>
    </justification>
  </clause>

  <clause id="3036">
    <literal><![CDATA[
      (x \ y) * K(x,1 / x) = (1 / (1 / x)) \ y
    ]]></literal>
    <justification jstring="[para(1791(a,2),2970(a,1,2))].">
      <j1 rule="para" parents="1791 2970"/>
    </justification>
  </clause>

  <clause id="3037">
    <literal><![CDATA[
      K((x * y) / x,x / (x * y)) = K(y,1 / y)
    ]]></literal>
    <justification jstring="[hyper(2675,a,2983,a),flip(a)].">
      <j1 rule="hyper" parents="2675 2983"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3038">
    <literal><![CDATA[
      x * K(x / y,(x / y) \ 1) = y * (((y \ x) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(2984(a,2),2586(a,1,2))].">
      <j1 rule="para" parents="2984 2586"/>
    </justification>
  </clause>

  <clause id="3039">
    <literal><![CDATA[
      L(x * T(x \ 1,y),x \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x \ 1,y) = z
    ]]></literal>
    <justification jstring="[para(2993(a,1),751(a,1,1))].">
      <j1 rule="para" parents="2993 751"/>
    </justification>
  </clause>

  <clause id="3040">
    <literal><![CDATA[
      (x * T(x \ 1,y)) \ 1 = T(x \ 1,y) \ (x \ 1)
    ]]></literal>
    <justification jstring="[para(2993(a,1),2529(a,1,1))].">
      <j1 rule="para" parents="2993 2529"/>
    </justification>
  </clause>

  <clause id="3042">
    <literal><![CDATA[
      K(x \ 1,T(x,y)) = x * T(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(3010(a,1),3012(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3010 3012"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3043">
    <literal><![CDATA[
      K(x \ 1,T(x,y)) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,358,a(flip),b,3042,a),flip(a)].">
      <j1 rule="hyper" parents="320 358 3042"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3046">
    <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(2824(a,1),3014(a,1,1,1,1))].">
      <j1 rule="para" parents="2824 3014"/>
    </justification>
  </clause>

  <clause id="3047">
    <literal><![CDATA[
      L(x * K(y \ 1,y),y,y \ 1) = (y \ 1) * (y * x)
    ]]></literal>
    <justification jstring="[para(2944(a,1),2974(a,1,1))].">
      <j1 rule="para" parents="2944 2974"/>
    </justification>
  </clause>

  <clause id="3048">
    <literal><![CDATA[
      x \ ((y * x) / y) != y \ z
    ]]></literal>
    <literal><![CDATA[
      T(y,R(x,x \ 1,y)) = z
    ]]></literal>
    <justification jstring="[para(2991(a,1),42(a,1))].">
      <j1 rule="para" parents="2991 42"/>
    </justification>
  </clause>

  <clause id="3049">
    <literal><![CDATA[
      T(x,R(y,y \ 1,x)) \ x = 1 / (y \ ((x * y) / x))
    ]]></literal>
    <justification jstring="[para(2991(a,1),2530(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2991 2530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3050">
    <literal><![CDATA[
      T(x,y \ ((x * y) / x)) = x
    ]]></literal>
    <justification jstring="[para(2991(a,1),2995(a,1,2))].">
      <j1 rule="para" parents="2991 2995"/>
    </justification>
  </clause>

  <clause id="3051">
    <literal><![CDATA[
      T(x,T(y,x) \ y) = x
    ]]></literal>
    <justification jstring="[para(225(a,1),3050(a,1,2,2))].">
      <j1 rule="para" parents="225 3050"/>
    </justification>
  </clause>

  <clause id="3052">
    <literal><![CDATA[
      (T(x,y) \ x) * y = y * (T(x,y) \ x)
    ]]></literal>
    <justification jstring="[hyper(119,a,3051,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 3051 17"/>
    </justification>
  </clause>

  <clause id="3053">
    <literal><![CDATA[
      T(x,R(T(y,x),T(y,x) \ 1,x)) = x * (T(y,x) \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,1674,a,b,3052,a)].">
      <j1 rule="hyper" parents="58 1674 3052"/>
    </justification>
  </clause>

  <clause id="3054">
    <literal><![CDATA[
      (x * ((x * (T(y,x) \ y)) \ x)) \ (x * x) = (T(y,x) \ y) * x
    ]]></literal>
    <justification jstring="[para(3052(a,1),2112(a,1,1,2,1))].">
      <j1 rule="para" parents="3052 2112"/>
    </justification>
  </clause>

  <clause id="3056">
    <literal><![CDATA[
      L(x,x \ T(x,y),x) = x
    ]]></literal>
    <justification jstring="[hyper(320,a,72,a(flip),b,3006,a),flip(a)].">
      <j1 rule="hyper" parents="320 72 3006"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3057">
    <literal><![CDATA[
      (((x \ 1) \ 1) \ y) * ((x \ 1) \ 1) != y * z
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,x) = z
    ]]></literal>
    <justification jstring="[para(2841(a,2),464(a,1))].">
      <j1 rule="para" parents="2841 464"/>
    </justification>
  </clause>

  <clause id="3058">
    <literal><![CDATA[
      T((x \ 1) * (y / (x \ 1)),K(z \ 1,z)) = (1 / x) * (y / (1 / x))
    ]]></literal>
    <justification jstring="[hyper(320,a,2190,a,b,2844,a)].">
      <j1 rule="hyper" parents="320 2190 2844"/>
    </justification>
  </clause>

  <clause id="3059">
    <literal><![CDATA[
      (1 / x) * K(y,x \ 1) = K(y,x \ 1) / x
    ]]></literal>
    <justification jstring="[hyper(117,a,2355,a(flip),b,2854,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="117 2355 2854"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3060">
    <literal><![CDATA[
      T(x \ 1,T(x,y) \ x) = x \ 1
    ]]></literal>
    <justification jstring="[para(2883(a,1),2288(a,1,2))].">
      <j1 rule="para" parents="2883 2288"/>
    </justification>
  </clause>

  <clause id="3061">
    <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(2883(a,1),2614(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="2883 2614"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3062">
    <literal><![CDATA[
      T(T(x,y) \ x,x \ 1) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(49,a,3060,a)].">
      <j1 rule="hyper" parents="49 3060"/>
    </justification>
  </clause>

  <clause id="3063">
    <literal><![CDATA[
      R((x \ 1) \ (T(x,y) \ 1),x \ 1,x) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(58,a,2755,a,b,3062,a)].">
      <j1 rule="hyper" parents="58 2755 3062"/>
    </justification>
  </clause>

  <clause id="3064">
    <literal><![CDATA[
      (K(x,y) \ y) * K(x,y) = y
    ]]></literal>
    <justification jstring="[hyper(29,a,84,a(flip),b,2906,a),flip(a)].">
      <j1 rule="hyper" parents="29 84 2906"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3065">
    <literal><![CDATA[
      x / K(y,x) = K(y,x) \ x
    ]]></literal>
    <justification jstring="[hyper(131,a,3064,a)].">
      <j1 rule="hyper" parents="131 3064"/>
    </justification>
  </clause>

  <clause id="3066">
    <literal><![CDATA[
      (K(x,y) \ y) \ y = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(123,a,3064,a)].">
      <j1 rule="hyper" parents="123 3064"/>
    </justification>
  </clause>

  <clause id="3067">
    <literal><![CDATA[
      K(x,y) != z \ y
    ]]></literal>
    <literal><![CDATA[
      K(x,y) \ y = z
    ]]></literal>
    <justification jstring="[para(3066(a,1),43(a,1))].">
      <j1 rule="para" parents="3066 43"/>
    </justification>
  </clause>

  <clause id="3068">
    <literal><![CDATA[
      (x * (1 / T(x,y))) * K(x \ 1,x) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(2478,a,2978,a)].">
      <j1 rule="hyper" parents="2478 2978"/>
    </justification>
  </clause>

  <clause id="3069">
    <literal><![CDATA[
      K(x,x \ 1) * T(x \ 1,y) = T(1 / x,y)
    ]]></literal>
    <justification jstring="[hyper(29,a,2805,a,b,3017,a(flip))].">
      <j1 rule="hyper" parents="29 2805 3017"/>
    </justification>
  </clause>

  <clause id="3071">
    <literal><![CDATA[
      (((x \ 1) \ 1) \ y) / y = (((x \ y) / y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(117,a,3026,a(flip),b,2173,a)].">
      <j1 rule="hyper" parents="117 3026 2173"/>
    </justification>
  </clause>

  <clause id="3072">
    <literal><![CDATA[
      (((x / y) \ 1) \ 1) \ x = x * (((x \ y) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(75(a,1),3026(a,1,2,1,1,2)),flip(a)].">
      <j1 rule="para" parents="75 3026"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3073">
    <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),3026(a,1,2,1,1,2))].">
      <j1 rule="para" parents="184 3026"/>
    </justification>
  </clause>

  <clause id="3074">
    <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),3033(a,1,1)),flip(a)].">
      <j1 rule="para" parents="302 3033"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3075">
    <literal><![CDATA[
      T(x / (1 / (1 / y)),1 / (1 / y)) / (1 / y) = (y \ x) / (y \ 1)
    ]]></literal>
    <justification jstring="[para(107(a,2),3035(a,1,1))].">
      <j1 rule="para" parents="107 3035"/>
    </justification>
  </clause>

  <clause id="3076">
    <literal><![CDATA[
      T(L(x \ 1,x,y) \ 1,y) \ (L(x \ 1,x,y) \ 1) = K(x,y) \ 1
    ]]></literal>
    <justification jstring="[para(1102(a,2),3040(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1102 3040"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3077">
    <literal><![CDATA[
      T((x \ y) \ 1,z) \ ((x \ y) \ 1) = (x \ (y * T(y \ x,z))) \ 1
    ]]></literal>
    <justification jstring="[para(1427(a,1),3040(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1427 3040"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3078">
    <literal><![CDATA[
      (x \ 1) * (x * (1 / T(x,y))) = (1 / x) * (T(x,y) \ x)
    ]]></literal>
    <justification jstring="[para(3068(a,1),2843(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3068 2843"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3079">
    <literal><![CDATA[
      ((((1 / x) \ y) / y) \ 1) \ 1 = ((x \ 1) \ y) / y
    ]]></literal>
    <justification jstring="[para(75(a,1),3071(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="75 3071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3080">
    <literal><![CDATA[
      x / (x * (((x \ y) \ 1) \ 1)) = ((x / y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(197,a,3072,a)].">
      <j1 rule="hyper" parents="197 3072"/>
    </justification>
  </clause>

  <clause id="3081">
    <literal><![CDATA[
      x / (x * ((y \ 1) \ 1)) = ((x / (x * y)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(4(a,1),3080(a,1,2,2,1,1))].">
      <j1 rule="para" parents="4 3080"/>
    </justification>
  </clause>

  <clause id="3082">
    <literal><![CDATA[
      x / ((((y / x) \ 1) \ 1) * x) = ((x / y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(2173(a,2),3080(a,1,2))].">
      <j1 rule="para" parents="2173 3080"/>
    </justification>
  </clause>

  <clause id="3083">
    <literal><![CDATA[
      T(x / (x * y),y) = x / (x * ((y \ 1) \ 1))
    ]]></literal>
    <justification jstring="[hyper(320,a,2404,a,b,3081,a)].">
      <j1 rule="hyper" parents="320 2404 3081"/>
    </justification>
  </clause>

  <clause id="3084">
    <literal><![CDATA[
      x / (x * T(y,y \ 1)) = T(x / (x * y),y)
    ]]></literal>
    <justification jstring="[para(106(a,2),3083(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="106 3083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3085">
    <literal><![CDATA[
      T(x / (x * y),y) \ x = x * T(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(188,a,3084,a)].">
      <j1 rule="hyper" parents="188 3084"/>
    </justification>
  </clause>

  <clause id="3086">
    <literal><![CDATA[
      x / (((y \ 1) \ 1) * x) = ((x / (y * x)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(6(a,1),3082(a,1,2,1,1,1))].">
      <j1 rule="para" parents="6 3082"/>
    </justification>
  </clause>

  <clause id="3087">
    <literal><![CDATA[
      R(x \ 1,x,y) = y / (((x \ 1) \ 1) * y)
    ]]></literal>
    <justification jstring="[hyper(320,a,2073,a,b,3086,a)].">
      <j1 rule="hyper" parents="320 2073 3086"/>
    </justification>
  </clause>

  <clause id="3088">
    <literal><![CDATA[
      R(x \ 1,(x \ 1) \ 1,y) = R(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,215,a,b,3087,a)].">
      <j1 rule="hyper" parents="320 215 3087"/>
    </justification>
  </clause>

  <clause id="3089">
    <literal><![CDATA[
      R(x \ 1,x,y) \ y = ((x \ 1) \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(188,a,3087,a(flip))].">
      <j1 rule="hyper" parents="188 3087"/>
    </justification>
  </clause>

  <clause id="3090">
    <literal><![CDATA[
      x / (T(y,y \ 1) * x) = R(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(106(a,2),3087(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="106 3087"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3091">
    <literal><![CDATA[
      R(x,1 / x,y) \ y = (((1 / x) \ 1) \ 1) * y
    ]]></literal>
    <justification jstring="[para(75(a,1),3089(a,1,1,1))].">
      <j1 rule="para" parents="75 3089"/>
    </justification>
  </clause>

  <clause id="3092">
    <literal><![CDATA[
      R(x,1 / x,y) \ y = (x \ 1) * y
    ]]></literal>
    <justification jstring="[para(75(a,1),3091(a,2,1,1))].">
      <j1 rule="para" parents="75 3091"/>
    </justification>
  </clause>

  <clause id="3093">
    <literal><![CDATA[
      R(x,1 / x,y) = R(x,x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(600,a,3092,a),flip(a)].">
      <j1 rule="hyper" parents="600 3092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3094">
    <literal><![CDATA[
      L(R(x,x \ 1,y),x \ 1,x) = R(1 / (1 / x),1 / x,y)
    ]]></literal>
    <justification jstring="[para(3093(a,1),1813(a,1,1))].">
      <j1 rule="para" parents="3093 1813"/>
    </justification>
  </clause>

  <clause id="3095">
    <literal><![CDATA[
      ((x \ 1) \ 1) * K(y,x) = (x \ 1) \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(2943,a,3028,a)].">
      <j1 rule="hyper" parents="2943 3028"/>
    </justification>
  </clause>

  <clause id="3096">
    <literal><![CDATA[
      x * (K(y,x) * K(x,x \ 1)) = (x \ 1) \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,2865,a,b,3095,a)].">
      <j1 rule="hyper" parents="58 2865 3095"/>
    </justification>
  </clause>

  <clause id="3097">
    <literal><![CDATA[
      K(x \ 1,x) * K(y,x) != z
    ]]></literal>
    <literal><![CDATA[
      (x \ 1) * (x * K(y,x)) = z
    ]]></literal>
    <justification jstring="[para(2926(a,1),2955(a,1,2))].">
      <j1 rule="para" parents="2926 2955"/>
    </justification>
  </clause>

  <clause id="3098">
    <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,2294,a(flip),b,3031,a)].">
      <j1 rule="hyper" parents="58 2294 3031"/>
    </justification>
  </clause>

  <clause id="3099">
    <literal><![CDATA[
      T(x,R(y,y \ 1,x)) \ x = ((x * y) / x) \ y
    ]]></literal>
    <justification jstring="[hyper(320,a,2536,a(flip),b,3049,a),flip(a)].">
      <j1 rule="hyper" parents="320 2536 3049"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3100">
    <literal><![CDATA[
      T(x,R(y,y \ 1,x)) \ 1 = x \ (((x * y) / x) \ y)
    ]]></literal>
    <justification jstring="[hyper(116,a,3099,a(flip),b,1118,a),flip(a)].">
      <j1 rule="hyper" parents="116 3099 1118"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3101">
    <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),3099(a,2,1))].">
      <j1 rule="para" parents="225 3099"/>
    </justification>
  </clause>

  <clause id="3102">
    <literal><![CDATA[
      R(T(x,y) \ x,x \ 1,x) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[para(2528(a,1),3063(a,1,1))].">
      <j1 rule="para" parents="2528 3063"/>
    </justification>
  </clause>

  <clause id="3103">
    <literal><![CDATA[
      T(x,x \ (((x * y) / x) \ y)) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(3100(a,1),2177(a,1,2))].">
      <j1 rule="para" parents="3100 2177"/>
    </justification>
  </clause>

  <clause id="3104">
    <literal><![CDATA[
      T(x,x \ (y \ T(y,x))) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(225(a,1),3103(a,1,2,2,1))].">
      <j1 rule="para" parents="225 3103"/>
    </justification>
  </clause>

  <clause id="3105">
    <literal><![CDATA[
      T(x,x \ ((((x * y) \ x) \ 1) \ (((x * y) \ x) \ K(y,x)))) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(1024(a,1),3104(a,1,2,2,2))].">
      <j1 rule="para" parents="1024 3104"/>
    </justification>
  </clause>

  <clause id="3106">
    <literal><![CDATA[
      (x * (T(y,x) \ y)) \ x = y \ T(y,x)
    ]]></literal>
    <justification jstring="[para(3053(a,1),3101(a,1,1))].">
      <j1 rule="para" parents="3053 3101"/>
    </justification>
  </clause>

  <clause id="3107">
    <literal><![CDATA[
      x / (y \ T(y,x)) = x * (T(y,x) \ y)
    ]]></literal>
    <justification jstring="[hyper(197,a,3106,a)].">
      <j1 rule="hyper" parents="197 3106"/>
    </justification>
  </clause>

  <clause id="3108">
    <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(1024(a,1),3107(a,1,2,2))].">
      <j1 rule="para" parents="1024 3107"/>
    </justification>
  </clause>

  <clause id="3109">
    <literal><![CDATA[
      (x * T(y,z)) / T((y \ 1) \ 1,z) = x * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[para(106(a,1),2941(a,1,2,1))].">
      <j1 rule="para" parents="106 2941"/>
    </justification>
  </clause>

  <clause id="3111">
    <literal><![CDATA[
      T(x,y) * (K(x \ 1,x) * z) = T(1 / (1 / x),y) * z
    ]]></literal>
    <justification jstring="[para(2166(a,1),2973(a,2,1))].">
      <j1 rule="para" parents="2166 2973"/>
    </justification>
  </clause>

  <clause id="3112">
    <literal><![CDATA[
      L((1 / T(x,y)) * x,x \ 1,x) = ((1 / x) * (T(x,y) \ x)) * x
    ]]></literal>
    <justification jstring="[para(3078(a,1),1987(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3078 1987"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3113">
    <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(3109(a,1),251(a,1,1)),flip(b)].">
      <j1 rule="para" parents="3109 251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3114">
    <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,3111,a),flip(a)].">
      <j1 rule="hyper" parents="116 5 3111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3115">
    <literal><![CDATA[
      ((x \ 1) \ 1) * (T(x,y) \ z) = x * (T(1 / (1 / x),y) \ z)
    ]]></literal>
    <justification jstring="[hyper(119,a,3114,a(flip),b,2945,a)].">
      <j1 rule="hyper" parents="119 3114 2945"/>
    </justification>
  </clause>

  <clause id="3116">
    <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(2977(a,1),1668(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2977 1668"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3117">
    <literal><![CDATA[
      L(x * y,x \ T(x,z),x) = x * L(y,x,x \ T(x,z))
    ]]></literal>
    <justification jstring="[para(3003(a,1),1137(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3003 1137"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3118">
    <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),3117(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5 3117"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3119">
    <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,2137,a,b,3004,a)].">
      <j1 rule="hyper" parents="58 2137 3004"/>
    </justification>
  </clause>

  <clause id="3120">
    <literal><![CDATA[
      R(1 / (1 / x),1 / x,y) = R(1 / (1 / x),x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,1813,a(flip),b,3094,a),flip(a)].">
      <j1 rule="hyper" parents="58 1813 3094"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3121">
    <literal><![CDATA[
      R(1 / (1 / x),x \ 1,(1 / x) \ y) = ((1 / x) \ y) / y
    ]]></literal>
    <justification jstring="[hyper(944,a,3120,a),flip(a)].">
      <j1 rule="hyper" parents="944 3120"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3122">
    <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(3121(a,2),87(a,1,2,2))].">
      <j1 rule="para" parents="3121 87"/>
    </justification>
  </clause>

  <clause id="3123">
    <literal><![CDATA[
      T((x \ 1) * y,K(z \ 1,z)) = y * ((x \ 1) * (x * T(x \ 1,y)))
    ]]></literal>
    <justification jstring="[hyper(320,a,2787,a,b,2950,a),flip(a)].">
      <j1 rule="hyper" parents="320 2787 2950"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3124">
    <literal><![CDATA[
      (x * (y \ T(y,x))) \ (x * z) = x * ((x * (y \ T(y,x))) \ z)
    ]]></literal>
    <justification jstring="[para(2987(a,1),3000(a,2,2,1,2))].">
      <j1 rule="para" parents="2987 3000"/>
    </justification>
  </clause>

  <clause id="3125">
    <literal><![CDATA[
      ((x \ (x / y)) * z) * K(y,y \ 1) = (1 / (1 / (x \ (x / y)))) * z
    ]]></literal>
    <justification jstring="[para(2386(a,1),3032(a,1,2))].">
      <j1 rule="para" parents="2386 3032"/>
    </justification>
  </clause>

  <clause id="3126">
    <literal><![CDATA[
      (x * ((x * (T(y,x) \ y)) \ x)) \ (x * x) = x * (T(y,x) \ y)
    ]]></literal>
    <justification jstring="[hyper(320,a,3052,a(flip),b,3054,a),flip(a)].">
      <j1 rule="hyper" parents="320 3052 3054"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3127">
    <literal><![CDATA[
      (x * (y \ T(y,x))) \ (x * x) = x * (T(y,x) \ y)
    ]]></literal>
    <justification jstring="[para(3106(a,1),3126(a,1,1,2))].">
      <j1 rule="para" parents="3106 3126"/>
    </justification>
  </clause>

  <clause id="3128">
    <literal><![CDATA[
      (x * (y \ T(y,x))) \ x = T(y,x) \ y
    ]]></literal>
    <justification jstring="[hyper(29,a,3124,a(flip),b,3127,a(flip))].">
      <j1 rule="hyper" parents="29 3124 3127"/>
    </justification>
  </clause>

  <clause id="3129">
    <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(2914(a,2),990(a,1,1,2))].">
      <j1 rule="para" parents="2914 990"/>
    </justification>
  </clause>

  <clause id="3130">
    <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),2998(a,2,1))].">
      <j1 rule="para" parents="453 2998"/>
    </justification>
  </clause>

  <clause id="3131">
    <literal><![CDATA[
      K(((x \ 1) \ 1) \ y,(x \ 1) \ 1) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(3057,a,302,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="3057 302"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3132">
    <literal><![CDATA[
      ((1 / x) * (T(x,y) \ x)) * x = L(T(x,y) \ x,x \ 1,x)
    ]]></literal>
    <justification jstring="[para(2878(a,1),3112(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2878 3112"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3133">
    <literal><![CDATA[
      K(x \ 1,x) * (y / T(1 / (1 / x),z)) = y / T(x,z)
    ]]></literal>
    <justification jstring="[para(75(a,1),2942(a,2,2))].">
      <j1 rule="para" parents="75 2942"/>
    </justification>
  </clause>

  <clause id="3135">
    <literal><![CDATA[
      ((x \ 1) \ 1) * (y / T(x,z)) = x * (y / T(1 / (1 / x),z))
    ]]></literal>
    <justification jstring="[hyper(119,a,3133,a(flip),b,2945,a)].">
      <j1 rule="hyper" parents="119 3133 2945"/>
    </justification>
  </clause>

  <clause id="3137">
    <literal><![CDATA[
      L(x \ 1,x,K(y,x) \ 1) = x \ 1
    ]]></literal>
    <justification jstring="[para(3076(a,1),3024(a,1,3))].">
      <j1 rule="para" parents="3076 3024"/>
    </justification>
  </clause>

  <clause id="3138">
    <literal><![CDATA[
      T(x,K(y,x) \ 1) = x
    ]]></literal>
    <justification jstring="[para(3076(a,1),3051(a,1,2))].">
      <j1 rule="para" parents="3076 3051"/>
    </justification>
  </clause>

  <clause id="3139">
    <literal><![CDATA[
      (K(x,y) \ 1) * y = y * (K(x,y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(119,a,3138,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 3138 17"/>
    </justification>
  </clause>

  <clause id="3140">
    <literal><![CDATA[
      (x * (K(y,x) \ 1)) \ (K(y,x) \ 1) = L(x \ 1,x,K(y,x) \ 1)
    ]]></literal>
    <justification jstring="[para(3139(a,1),217(a,2,1)),flip(a)].">
      <j1 rule="para" parents="3139 217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3141">
    <literal><![CDATA[
      (x * (K(y,x) \ 1)) \ (K(y,x) \ 1) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(320,a,3137,a(flip),b,3140,a),flip(a)].">
      <j1 rule="hyper" parents="320 3137 3140"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3143">
    <literal><![CDATA[
      ((x \ (x / (y \ 1))) * z) * K(y \ 1,y) = (1 / (1 / (x \ (x / (y \ 1))))) * z
    ]]></literal>
    <justification jstring="[para(1798(a,1),3125(a,1,2))].">
      <j1 rule="para" parents="1798 3125"/>
    </justification>
  </clause>

  <clause id="3144">
    <literal><![CDATA[
      ((x \ 1) * y) / T(1 / x,y) = K(x \ 1,x) * y
    ]]></literal>
    <justification jstring="[para(2461(a,1),2851(a,1,2))].">
      <j1 rule="para" parents="2461 2851"/>
    </justification>
  </clause>

  <clause id="3145">
    <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(3144(a,1),1528(a,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="3144 1528"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3147">
    <literal><![CDATA[
      (T(x,x \ 1) * y) \ (y * T(x,x \ 1)) = K(K(x,x \ 1) * y,x)
    ]]></literal>
    <justification jstring="[para(2723(a,1),2835(a,1,2))].">
      <j1 rule="para" parents="2723 2835"/>
    </justification>
  </clause>

  <clause id="3148">
    <literal><![CDATA[
      K(K(x,x \ 1) * y,x) = K(y,T(x,x \ 1))
    ]]></literal>
    <justification jstring="[hyper(307,a,3147,a),flip(a)].">
      <j1 rule="hyper" parents="307 3147"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3149">
    <literal><![CDATA[
      K(K(x,x \ 1) * y,x) = K(y,(x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,1369,a(flip),b,3148,a),flip(a)].">
      <j1 rule="hyper" parents="320 1369 3148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3150">
    <literal><![CDATA[
      K(K(x \ 1,x) * y,(x \ 1) \ 1) = K(y,x)
    ]]></literal>
    <justification jstring="[para(2696(a,1),3149(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2696 3149"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3151">
    <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,440,a,b,3074,a)].">
      <j1 rule="hyper" parents="320 440 3074"/>
    </justification>
  </clause>

  <clause id="3152">
    <literal><![CDATA[
      ((x \ (x / (y \ 1))) * z) * K(y \ 1,y) = (x \ (x / (1 / y))) * z
    ]]></literal>
    <justification jstring="[para(2638(a,1),3143(a,2,1))].">
      <j1 rule="para" parents="2638 3143"/>
    </justification>
  </clause>

  <clause id="3153">
    <literal><![CDATA[
      R((x \ (x / (1 / y))) * x,y \ 1,y) = (x * ((y \ 1) * T((y \ 1) \ 1,x))) * y
    ]]></literal>
    <justification jstring="[para(3152(a,1),2674(a,1,1))].">
      <j1 rule="para" parents="3152 2674"/>
    </justification>
  </clause>

  <clause id="3154">
    <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,3132,a(flip),b,3061,a),flip(a)].">
      <j1 rule="hyper" parents="320 3132 3061"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3155">
    <literal><![CDATA[
      R(T(x,y) \ x,x \ 1,x) = L(T(x,y) \ x,x \ 1,x)
    ]]></literal>
    <justification jstring="[para(2883(a,1),3154(a,1,1))].">
      <j1 rule="para" parents="2883 3154"/>
    </justification>
  </clause>

  <clause id="3156">
    <literal><![CDATA[
      L(T(x,y) \ x,x \ 1,x) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(58,a,3102,a(flip),b,3155,a),flip(a)].">
      <j1 rule="hyper" parents="58 3102 3155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3157">
    <literal><![CDATA[
      L(T(x,y) \ x,T(x,y),y) = L((x * y) \ (y * x),x \ 1,x)
    ]]></literal>
    <justification jstring="[para(3156(a,1),931(a,1,1))].">
      <j1 rule="para" parents="3156 931"/>
    </justification>
  </clause>

  <clause id="3158">
    <literal><![CDATA[
      L((x * y) \ (y * x),x \ 1,x) = (x * y) \ (y * x)
    ]]></literal>
    <justification jstring="[hyper(58,a,496,a(flip),b,3157,a),flip(a)].">
      <j1 rule="hyper" parents="58 496 3157"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3159">
    <literal><![CDATA[
      K(x,y) = L((y * x) \ (x * y),y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,11,a,b,3158,a)].">
      <j1 rule="hyper" parents="320 11 3158"/>
    </justification>
  </clause>

  <clause id="3160">
    <literal><![CDATA[
      L(K(x,y),y \ 1,y) = K(x,y)
    ]]></literal>
    <justification jstring="[para(11(a,2),3159(a,2,1)),flip(a)].">
      <j1 rule="para" parents="11 3159"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3161">
    <literal><![CDATA[
      (x \ 1) * K(y,x) = x \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,3160,a(flip),b,257,a),flip(a)].">
      <j1 rule="hyper" parents="116 3160 257"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3162">
    <literal><![CDATA[
      T(x * y,R(x \ 1,x,x * y)) = x * ((x * y) * (y / (x * y)))
    ]]></literal>
    <justification jstring="[para(1905(a,1),3098(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1905 3098"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3163">
    <literal><![CDATA[
      R((x \ (x / (1 / y))) * x,y \ 1,y) = (x * (y \ T(y,x))) * y
    ]]></literal>
    <justification jstring="[para(991(a,1),3153(a,2,1,2))].">
      <j1 rule="para" parents="991 3153"/>
    </justification>
  </clause>

  <clause id="3164">
    <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,1746,a(flip),b,3116,a),flip(a)].">
      <j1 rule="hyper" parents="320 1746 3116"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3165">
    <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,3022,a,b,3164,a)].">
      <j1 rule="hyper" parents="58 3022 3164"/>
    </justification>
  </clause>

  <clause id="3166">
    <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,3165,a)].">
      <j1 rule="hyper" parents="58 22 3165"/>
    </justification>
  </clause>

  <clause id="3167">
    <literal><![CDATA[
      R(x,y,z) * K(R(x,y,z),x \ 1) = R((x \ 1) \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(2067(a,1),3166(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2067 3166"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3168">
    <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,828,a,b,3167,a)].">
      <j1 rule="hyper" parents="116 828 3167"/>
    </justification>
  </clause>

  <clause id="3170">
    <literal><![CDATA[
      a(R(x,y,z),1 / x,x) = K(R(x,y,z),x \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,1282,a(flip),b,3168,a)].">
      <j1 rule="hyper" parents="58 1282 3168"/>
    </justification>
  </clause>

  <clause id="3171">
    <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,2977,a,b,3170,a)].">
      <j1 rule="hyper" parents="320 2977 3170"/>
    </justification>
  </clause>

  <clause id="3172">
    <literal><![CDATA[
      x * L(x \ 1,R(x,y,z),1 / x) = a(R(x,y,z),1 / x,x)
    ]]></literal>
    <justification jstring="[para(1955(a,2),3171(a,1,2))].">
      <j1 rule="para" parents="1955 3171"/>
    </justification>
  </clause>

  <clause id="3173">
    <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(3118(a,1),3119(a,1,1))].">
      <j1 rule="para" parents="3118 3119"/>
    </justification>
  </clause>

  <clause id="3174">
    <literal><![CDATA[
      L(x \ (x * y),z \ T(z,x),z) = (z \ T(z,x)) * (z * (T(z,x) \ y))
    ]]></literal>
    <justification jstring="[hyper(860,a,3173,a)].">
      <j1 rule="hyper" parents="860 3173"/>
    </justification>
  </clause>

  <clause id="3175">
    <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),3174(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4 3174"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3176">
    <literal><![CDATA[
      (x \ T(x,y)) \ x = x * (T(x,y) \ x)
    ]]></literal>
    <justification jstring="[hyper(116,a,3056,a(flip),b,3175,a)].">
      <j1 rule="hyper" parents="116 3056 3175"/>
    </justification>
  </clause>

  <clause id="3177">
    <literal><![CDATA[
      L(1 / x,x \ T(x,y),x) = (x \ T(x,y)) * (1 / T(x,y))
    ]]></literal>
    <justification jstring="[para(2876(a,1),3175(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2876 3175"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3178">
    <literal><![CDATA[
      x * (T(x,R(y,x,(y * x) \ x)) \ x) = (x \ (x * K(x,y))) \ x
    ]]></literal>
    <justification jstring="[para(1740(a,1),3176(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1740 3176"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3179">
    <literal><![CDATA[
      x * (T(x,R(y,y \ 1,x)) \ x) = (y \ ((x * y) / x)) \ x
    ]]></literal>
    <justification jstring="[para(2991(a,1),3176(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2991 3176"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3180">
    <literal><![CDATA[
      L(1 / x,x \ T(x,y),x) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(320,a,2999,a(flip),b,3177,a),flip(a)].">
      <j1 rule="hyper" parents="320 2999 3177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3182">
    <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(3180(a,1),632(a,2,1))].">
      <j1 rule="para" parents="3180 632"/>
    </justification>
  </clause>

  <clause id="3183">
    <literal><![CDATA[
      (x \ ((y * x) / y)) \ y = y * (((y * x) / y) \ x)
    ]]></literal>
    <justification jstring="[para(3099(a,1),3179(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3099 3179"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3184">
    <literal><![CDATA[
      x * (((x * T(y,x)) / x) \ T(y,x)) = (T(y,x) \ y) \ x
    ]]></literal>
    <justification jstring="[para(225(a,1),3183(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="225 3183"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3185">
    <literal><![CDATA[
      (T(x,y) \ x) \ y = y * (x \ T(x,y))
    ]]></literal>
    <justification jstring="[para(225(a,1),3184(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="225 3184"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3186">
    <literal><![CDATA[
      x * (T(x,R(y,x,(y * x) \ x)) \ x) = K(x,y) \ x
    ]]></literal>
    <justification jstring="[para(4(a,1),3178(a,2,1))].">
      <j1 rule="para" parents="4 3178"/>
    </justification>
  </clause>

  <clause id="3188">
    <literal><![CDATA[
      x * (K(x,y) \ 1) = K(x,y) \ x
    ]]></literal>
    <justification jstring="[para(2537(a,1),3186(a,1,2))].">
      <j1 rule="para" parents="2537 3186"/>
    </justification>
  </clause>

  <clause id="3189">
    <literal><![CDATA[
      x \ (K(x,y) \ x) = K(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(123,a,3188,a)].">
      <j1 rule="hyper" parents="123 3188"/>
    </justification>
  </clause>

  <clause id="3190">
    <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),3182(a,1,2,2,2))].">
      <j1 rule="para" parents="5 3182"/>
    </justification>
  </clause>

  <clause id="3192">
    <literal><![CDATA[
      (1 / x) * (x * (x \ T(x,y))) = x * ((x \ T(x,y)) * (x \ 1))
    ]]></literal>
    <justification jstring="[para(2990(a,1),3190(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2990 3190"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3193">
    <literal><![CDATA[
      (1 / x) * (x * (x \ T(x,y))) = x * ((x \ 1) * (x \ T(x,y)))
    ]]></literal>
    <justification jstring="[para(1254(a,1),3192(a,2,2))].">
      <j1 rule="para" parents="1254 3192"/>
    </justification>
  </clause>

  <clause id="3195">
    <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,3193,a),flip(a)].">
      <j1 rule="hyper" parents="320 257 3193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3196">
    <literal><![CDATA[
      L(x \ T(x,y),x \ 1,x) = (1 / x) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(342,a,3195,a),flip(a)].">
      <j1 rule="hyper" parents="342 3195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3198">
    <literal><![CDATA[
      L(x \ T(x,y),x \ 1,x) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,2992,a(flip),b,3196,a),flip(a)].">
      <j1 rule="hyper" parents="320 2992 3196"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3199">
    <literal><![CDATA[
      L(x \ (x * K(x,y)),x \ 1,x) = x \ T(x,R(y,x,(y * x) \ x))
    ]]></literal>
    <justification jstring="[para(1740(a,1),3198(a,1,1,2))].">
      <j1 rule="para" parents="1740 3198"/>
    </justification>
  </clause>

  <clause id="3200">
    <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),3199(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4 3199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3202">
    <literal><![CDATA[
      L(K(x,y),x \ 1,x) = x \ (x * K(x,y))
    ]]></literal>
    <justification jstring="[para(1740(a,1),3200(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1740 3200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3203">
    <literal><![CDATA[
      L(K(x,y),x \ 1,x) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,4,a(flip),b,3202,a),flip(a)].">
      <j1 rule="hyper" parents="320 4 3202"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3205">
    <literal><![CDATA[
      (x \ 1) * K(x,y) = x \ K(x,y)
    ]]></literal>
    <justification jstring="[hyper(116,a,3203,a(flip),b,257,a),flip(a)].">
      <j1 rule="hyper" parents="116 3203 257"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3206">
    <literal><![CDATA[
      K(x,y) * (x \ 1) = x \ K(x,y)
    ]]></literal>
    <justification jstring="[hyper(1291,a,3205,a)].">
      <j1 rule="hyper" parents="1291 3205"/>
    </justification>
  </clause>

  <clause id="3207">
    <literal><![CDATA[
      K(x,y) \ (x \ K(x,y)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(116,a,3205,a(flip),b,1290,a)].">
      <j1 rule="hyper" parents="116 3205 1290"/>
    </justification>
  </clause>

  <clause id="3208">
    <literal><![CDATA[
      x \ K(x,y) != z * K(x,y)
    ]]></literal>
    <literal><![CDATA[
      x \ 1 = z
    ]]></literal>
    <justification jstring="[para(3205(a,1),39(a,1))].">
      <j1 rule="para" parents="3205 39"/>
    </justification>
  </clause>

  <clause id="3209">
    <literal><![CDATA[
      K(x,y) \ (x \ K(x,y)) != z * u
    ]]></literal>
    <literal><![CDATA[
      (x \ 1) / u = z
    ]]></literal>
    <justification jstring="[para(3206(a,1),575(a,1,2))].">
      <j1 rule="para" parents="3206 575"/>
    </justification>
  </clause>

  <clause id="3210">
    <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(3206(a,1),479(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3206 479"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3211">
    <literal><![CDATA[
      x \ y != K(z,u) * (z \ 1)
    ]]></literal>
    <literal><![CDATA[
      x * (z \ K(z,u)) = y
    ]]></literal>
    <justification jstring="[para(3207(a,1),340(a,2,2))].">
      <j1 rule="para" parents="3207 340"/>
    </justification>
  </clause>

  <clause id="3212">
    <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(2814(a,1),2852(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2814 2852"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3213">
    <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(3212(a,2),482(a,1))].">
      <j1 rule="para" parents="3212 482"/>
    </justification>
  </clause>

  <clause id="3214">
    <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),3046(a,1,1,1))].">
      <j1 rule="para" parents="6 3046"/>
    </justification>
  </clause>

  <clause id="3216">
    <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(3214(a,1),39(a,1)),flip(a)].">
      <j1 rule="para" parents="3214 39"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3217">
    <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(2994(a,1),3145(a,2,1))].">
      <j1 rule="para" parents="2994 3145"/>
    </justification>
  </clause>

  <clause id="3218">
    <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),1373(a,1,2,1,1))].">
      <j1 rule="para" parents="90 1373"/>
    </justification>
  </clause>

  <clause id="3219">
    <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(1371,a,3218,a),flip(a)].">
      <j1 rule="hyper" parents="1371 3218"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3220">
    <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(916(a,1),3219(a,2,2))].">
      <j1 rule="para" parents="916 3219"/>
    </justification>
  </clause>

  <clause id="3221">
    <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,3220,a),flip(a)].">
      <j1 rule="hyper" parents="479 3220"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3222">
    <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,1196,a(flip),b,3221,a),flip(a)].">
      <j1 rule="hyper" parents="58 1196 3221"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3223">
    <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(3221(a,1),2756(a,1,1))].">
      <j1 rule="para" parents="3221 2756"/>
    </justification>
  </clause>

  <clause id="3224">
    <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(2730(a,1),3223(a,1,1,1,2))].">
      <j1 rule="para" parents="2730 3223"/>
    </justification>
  </clause>

  <clause id="3225">
    <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),3224(a,1,1,1,2,1))].">
      <j1 rule="para" parents="2 3224"/>
    </justification>
  </clause>

  <clause id="3226">
    <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(1763(a,1),3222(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1763 3222"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3227">
    <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,2494,a(flip),b,3226,a),flip(a)].">
      <j1 rule="hyper" parents="320 2494 3226"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3228">
    <literal><![CDATA[
      (x \ 1) / (x \ L(x,y,z)) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(30,a,258,a(flip),b,3227,a),flip(a)].">
      <j1 rule="hyper" parents="30 258 3227"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3229">
    <literal><![CDATA[
      x / ((1 / x) \ L(1 / x,y,z)) = L(1 / x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(75(a,1),3228(a,1,1))].">
      <j1 rule="para" parents="75 3228"/>
    </justification>
  </clause>

  <clause id="3230">
    <literal><![CDATA[
      x / (x * L(x \ 1,y,z)) = L(1 / x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(1070(a,1),3229(a,1,2))].">
      <j1 rule="para" parents="1070 3229"/>
    </justification>
  </clause>

  <clause id="3231">
    <literal><![CDATA[
      (L(1 / x,y,z) \ 1) * (x * L(x \ 1,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(133,a,3230,a)].">
      <j1 rule="hyper" parents="133 3230"/>
    </justification>
  </clause>

  <clause id="3232">
    <literal><![CDATA[
      (x * L(x \ 1,y,z)) \ x = L(1 / x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(2572,a,3231,a)].">
      <j1 rule="hyper" parents="2572 3231"/>
    </justification>
  </clause>

  <clause id="3233">
    <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(423,a,3232,a)].">
      <j1 rule="hyper" parents="423 3232"/>
    </justification>
  </clause>

  <clause id="3234">
    <literal><![CDATA[
      L(1 / (1 / x),y,z) \ 1 = (L(x,y,z) / x) \ (1 / x)
    ]]></literal>
    <justification jstring="[para(1693(a,1),3232(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1693 3232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3235">
    <literal><![CDATA[
      (x * L(x \ 1,y,z)) \ 1 = x \ (L(1 / x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(116,a,3233,a(flip),b,2042,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="116 3233 2042"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3236">
    <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,2302,a(flip),b,2304,a),flip(a)].">
      <j1 rule="hyper" parents="320 2302 2304"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3237">
    <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),3151(a,1,1,3))].">
      <j1 rule="para" parents="75 3151"/>
    </justification>
  </clause>

  <clause id="3238">
    <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(2607(a,1),3237(a,1,1))].">
      <j1 rule="para" parents="2607 3237"/>
    </justification>
  </clause>

  <clause id="3239">
    <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),1938(a,1,2,2,2))].">
      <j1 rule="para" parents="13 1938"/>
    </justification>
  </clause>

  <clause id="3240">
    <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),3239(a,2,2))].">
      <j1 rule="para" parents="13 3239"/>
    </justification>
  </clause>

  <clause id="3241">
    <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(1257(a,1),2503(a,1,1,2,1))].">
      <j1 rule="para" parents="1257 2503"/>
    </justification>
  </clause>

  <clause id="3242">
    <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(1572(a,1),3241(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1572 3241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3244">
    <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(2966(a,1),3242(a,2,1))].">
      <j1 rule="para" parents="2966 3242"/>
    </justification>
  </clause>

  <clause id="3245">
    <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),3244(a,2,1))].">
      <j1 rule="para" parents="223 3244"/>
    </justification>
  </clause>

  <clause id="3246">
    <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,3245,a),flip(a)].">
      <j1 rule="hyper" parents="320 376 3245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3249">
    <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,3246,a(flip))].">
      <j1 rule="hyper" parents="167 85 3246"/>
    </justification>
  </clause>

  <clause id="3250">
    <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(3249(a,1),327(a,1,1)),flip(b)].">
      <j1 rule="para" parents="3249 327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3251">
    <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),1664(a,1,2,1,2,1))].">
      <j1 rule="para" parents="90 1664"/>
    </justification>
  </clause>

  <clause id="3252">
    <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(1341,a,3251,a),flip(a)].">
      <j1 rule="hyper" parents="1341 3251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3253">
    <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(1097(a,1),3252(a,2,2))].">
      <j1 rule="para" parents="1097 3252"/>
    </justification>
  </clause>

  <clause id="3254">
    <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,3253,a),flip(a)].">
      <j1 rule="hyper" parents="479 3253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3255">
    <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),3254(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 3254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3256">
    <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,1794,a,b,3255,a),flip(a)].">
      <j1 rule="hyper" parents="320 1794 3255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3257">
    <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(1733(a,1),3256(a,1,1))].">
      <j1 rule="para" parents="1733 3256"/>
    </justification>
  </clause>

  <clause id="3258">
    <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),1670(a,1,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="101 1670"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3259">
    <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,869,a(flip),b,3258,a),flip(a)].">
      <j1 rule="hyper" parents="320 869 3258"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3260">
    <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,2298,a(flip),b,3259,a),flip(a)].">
      <j1 rule="hyper" parents="320 2298 3259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3261">
    <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,2296,a(flip),b,3259,a)].">
      <j1 rule="hyper" parents="117 2296 3259"/>
    </justification>
  </clause>

  <clause id="3262">
    <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(869(a,1),3260(a,1,1))].">
      <j1 rule="para" parents="869 3260"/>
    </justification>
  </clause>

  <clause id="3263">
    <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(1098(a,1),3261(a,1,1,1))].">
      <j1 rule="para" parents="1098 3261"/>
    </justification>
  </clause>

  <clause id="3264">
    <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,3263,a),flip(a)].">
      <j1 rule="hyper" parents="518 3263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3265">
    <literal><![CDATA[
      R(((x * (1 / x)) / x) * x,y,z) = T(x,1 / R(x,y,z)) / x
    ]]></literal>
    <justification jstring="[hyper(58,a,2773,a(flip),b,3264,a),flip(a)].">
      <j1 rule="hyper" parents="58 2773 3264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3266">
    <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),3265(a,1,1,1,1))].">
      <j1 rule="para" parents="260 3265"/>
    </justification>
  </clause>

  <clause id="3267">
    <literal><![CDATA[
      T(x,1 / R(x,y,z)) / x = R(K(x,1 / x),y,z)
    ]]></literal>
    <justification jstring="[para(7(a,1),3266(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7 3266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3269">
    <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(1721(a,1),3262(a,2,1))].">
      <j1 rule="para" parents="1721 3262"/>
    </justification>
  </clause>

  <clause id="3270">
    <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,3269,a),flip(a)].">
      <j1 rule="hyper" parents="30 101 3269"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3271">
    <literal><![CDATA[
      R(x * ((y * (x \ 1)) / y),z,u) = K(y,(y / R(x,z,u)) / y)
    ]]></literal>
    <justification jstring="[hyper(1727,a,3270,a),flip(a)].">
      <j1 rule="hyper" parents="1727 3270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3272">
    <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),3270(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 3270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3273">
    <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,1794,a,b,3272,a),flip(a)].">
      <j1 rule="hyper" parents="320 1794 3272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3274">
    <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(1209(a,1),3273(a,1,1,2,1))].">
      <j1 rule="para" parents="1209 3273"/>
    </justification>
  </clause>

  <clause id="3275">
    <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(2977(a,1),3274(a,1,1))].">
      <j1 rule="para" parents="2977 3274"/>
    </justification>
  </clause>

  <clause id="3276">
    <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),1700(a,2,2,1,1))].">
      <j1 rule="para" parents="13 1700"/>
    </justification>
  </clause>

  <clause id="3277">
    <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(1060(a,1),3276(a,1,2))].">
      <j1 rule="para" parents="1060 3276"/>
    </justification>
  </clause>

  <clause id="3278">
    <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),3277(a,1,2,2,2,1,2))].">
      <j1 rule="para" parents="4 3277"/>
    </justification>
  </clause>

  <clause id="3279">
    <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(918(a,1),3278(a,1,2,2))].">
      <j1 rule="para" parents="918 3278"/>
    </justification>
  </clause>

  <clause id="3280">
    <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(578,a,3279,a)].">
      <j1 rule="hyper" parents="578 3279"/>
    </justification>
  </clause>

  <clause id="3281">
    <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,3279,a),flip(a)].">
      <j1 rule="hyper" parents="482 3279"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3282">
    <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,3280,a),flip(a)].">
      <j1 rule="hyper" parents="119 217 3280"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3283">
    <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(752(a,1),3281(a,2,1,2))].">
      <j1 rule="para" parents="752 3281"/>
    </justification>
  </clause>

  <clause id="3284">
    <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(1416(a,1),3283(a,1,2))].">
      <j1 rule="para" parents="1416 3283"/>
    </justification>
  </clause>

  <clause id="3285">
    <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),3284(a,2,1,2))].">
      <j1 rule="para" parents="198 3284"/>
    </justification>
  </clause>

  <clause id="3286">
    <literal><![CDATA[
      L(x,y,z) * ((1 / x) * (L(x,y,z) \ x)) = L(K(x,x \ 1),y,z)
    ]]></literal>
    <justification jstring="[para(1794(a,2),3285(a,2,1))].">
      <j1 rule="para" parents="1794 3285"/>
    </justification>
  </clause>

  <clause id="3287">
    <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(1085(a,1),3282(a,2,2,1))].">
      <j1 rule="para" parents="1085 3282"/>
    </justification>
  </clause>

  <clause id="3288">
    <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(2489(a,1),3287(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2489 3287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3289">
    <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,3257,a(flip),b,3288,a),flip(a)].">
      <j1 rule="hyper" parents="320 3257 3288"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3290">
    <literal><![CDATA[
      (L(x,y,z) / x) \ (1 / x) = 1 / L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(29,a,1794,a(flip),b,3289,a),flip(a)].">
      <j1 rule="hyper" parents="29 1794 3289"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3291">
    <literal><![CDATA[
      L(1 / (1 / x),y,z) \ 1 = 1 / L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,3234,a,b,3290,a)].">
      <j1 rule="hyper" parents="58 3234 3290"/>
    </justification>
  </clause>

  <clause id="3292">
    <literal><![CDATA[
      L(1 / (1 / x),y,z) = 1 / (1 / L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(197,a,3291,a),flip(a)].">
      <j1 rule="hyper" parents="197 3291"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3293">
    <literal><![CDATA[
      1 / L(x \ 1,y,z) = L(1 / x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(72(a,1),3291(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="72 3291"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3294">
    <literal><![CDATA[
      1 / (1 / L(x \ 1,y,z)) = L(1 / x,y,z)
    ]]></literal>
    <justification jstring="[para(72(a,1),3292(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="72 3292"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3295">
    <literal><![CDATA[
      L(1 / (1 / x),y,z) \ 1 != u
    ]]></literal>
    <literal><![CDATA[
      1 / L(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(3292(a,2),267(a,1,1)),flip(b)].">
      <j1 rule="para" parents="3292 267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3296">
    <literal><![CDATA[
      T(1 / (1 / L(x,y,z)),1 / x) = L((1 / x) \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(3292(a,1),247(a,1,1))].">
      <j1 rule="para" parents="3292 247"/>
    </justification>
  </clause>

  <clause id="3297">
    <literal><![CDATA[
      L(1 / x,x,y) \ 1 = 1 / ((y * x) \ y)
    ]]></literal>
    <justification jstring="[hyper(744,a,3293,a),flip(a)].">
      <j1 rule="hyper" parents="744 3293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3298">
    <literal><![CDATA[
      (L(1 / x,y,z) \ 1) \ 1 = L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(188,a,3293,a)].">
      <j1 rule="hyper" parents="188 3293"/>
    </justification>
  </clause>

  <clause id="3299">
    <literal><![CDATA[
      L(1 / x,x,y) = 1 / (1 / ((y * x) \ y))
    ]]></literal>
    <justification jstring="[hyper(197,a,3297,a),flip(a)].">
      <j1 rule="hyper" parents="197 3297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3300">
    <literal><![CDATA[
      L(x,x \ 1,y) = 1 / (1 / ((y * (x \ 1)) \ y))
    ]]></literal>
    <justification jstring="[para(72(a,1),3299(a,1,1))].">
      <j1 rule="para" parents="72 3299"/>
    </justification>
  </clause>

  <clause id="3301">
    <literal><![CDATA[
      1 / (1 / L(L(x \ 1,y,z),u,w)) = L(L(1 / x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(3294(a,1),3292(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3294 3292"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3302">
    <literal><![CDATA[
      L((x \ 1) \ 1,y,z) = (L(x,y,z) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(72(a,1),3298(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="72 3298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3303">
    <literal><![CDATA[
      (L(x,y,z) \ 1) * L((x \ 1) \ 1,y,z) = 1
    ]]></literal>
    <justification jstring="[hyper(119,a,3302,a,b,xx)].">
      <j1 rule="hyper" parents="119 3302"/>
    </justification>
  </clause>

  <clause id="3304">
    <literal><![CDATA[
      L(((x \ y) \ 1) \ 1,x,1 / x) = (((1 / x) * y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(488(a,1),3302(a,2,1,1))].">
      <j1 rule="para" parents="488 3302"/>
    </justification>
  </clause>

  <clause id="3305">
    <literal><![CDATA[
      L((((x \ y) \ z) \ 1) \ 1,x \ y,x) = ((y \ (x * z)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(490(a,1),3302(a,2,1,1))].">
      <j1 rule="para" parents="490 3302"/>
    </justification>
  </clause>

  <clause id="3306">
    <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,437,a,b,3303,a(flip))].">
      <j1 rule="hyper" parents="167 437 3303"/>
    </justification>
  </clause>

  <clause id="3307">
    <literal><![CDATA[
      x / L(y,y \ 1,x) = x * (1 / (1 / (y \ 1)))
    ]]></literal>
    <justification jstring="[para(3300(a,2),2640(a,1,2))].">
      <j1 rule="para" parents="3300 2640"/>
    </justification>
  </clause>

  <clause id="3308">
    <literal><![CDATA[
      x / L(y,y \ 1,x) = x * (1 / y)
    ]]></literal>
    <justification jstring="[para(72(a,1),3307(a,2,2,2))].">
      <j1 rule="para" parents="72 3307"/>
    </justification>
  </clause>

  <clause id="3310">
    <literal><![CDATA[
      K(x \ (x / L(y,y \ 1,x)),z) = K(1 / y,z)
    ]]></literal>
    <justification jstring="[para(3308(a,2),673(a,1,1,2))].">
      <j1 rule="para" parents="3308 673"/>
    </justification>
  </clause>

  <clause id="3311">
    <literal><![CDATA[
      L(x * T(x \ 1,y),x \ 1,y) = K(1 / x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,2492,a,b,3310,a)].">
      <j1 rule="hyper" parents="58 2492 3310"/>
    </justification>
  </clause>

  <clause id="3312">
    <literal><![CDATA[
      K(1 / x,y) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(3039,a,3311,a),flip(a)].">
      <j1 rule="hyper" parents="3039 3311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3313">
    <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,3311,a)].">
      <j1 rule="hyper" parents="58 93 3311"/>
    </justification>
  </clause>

  <clause id="3314">
    <literal><![CDATA[
      L((1 / x) * T((1 / x) \ 1,y),x,y) = K(1 / (1 / x),y)
    ]]></literal>
    <justification jstring="[para(75(a,1),3311(a,1,2))].">
      <j1 rule="para" parents="75 3311"/>
    </justification>
  </clause>

  <clause id="3315">
    <literal><![CDATA[
      K(1 / (1 / x),y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,674,a(flip),b,3312,a),flip(a)].">
      <j1 rule="hyper" parents="320 674 3312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3316">
    <literal><![CDATA[
      K(x \ 1,(1 / x) \ (y / x)) = (T(y,1 / x) / x) \ (y / x)
    ]]></literal>
    <justification jstring="[hyper(58,a,1053,a(flip),b,3312,a),flip(a)].">
      <j1 rule="hyper" parents="58 1053 3312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3317">
    <literal><![CDATA[
      K((x \ 1) \ 1,y) = K(x,y)
    ]]></literal>
    <justification jstring="[para(72(a,1),3312(a,1,1)),flip(a)].">
      <j1 rule="para" parents="72 3312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3319">
    <literal><![CDATA[
      K(T(1 / x,y),z) = K(T(x \ 1,y),z)
    ]]></literal>
    <justification jstring="[para(2165(a,1),3317(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2165 3317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3320">
    <literal><![CDATA[
      K(((1 / x) * y) \ y,z) = K(((x \ 1) * y) \ y,z)
    ]]></literal>
    <justification jstring="[para(2751(a,1),3317(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2751 3317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3321">
    <literal><![CDATA[
      T(1 / (1 / L(x,y,z)),1 / x) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(75(a,1),3296(a,2,1))].">
      <j1 rule="para" parents="75 3296"/>
    </justification>
  </clause>

  <clause id="3322">
    <literal><![CDATA[
      T(T(1 / (1 / L(x,y,z)),u),1 / x) = T(L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(3321(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3321 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3323">
    <literal><![CDATA[
      (1 / x) \ ((((1 / x) * y) \ 1) \ 1) = x * (((x \ y) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(116,a,3304,a(flip),b,259,a)].">
      <j1 rule="hyper" parents="116 3304 259"/>
    </justification>
  </clause>

  <clause id="3324">
    <literal><![CDATA[
      L(T(x,y) / x,x,y) = K(1 / (1 / x),y)
    ]]></literal>
    <justification jstring="[para(1007(a,1),3314(a,1,1))].">
      <j1 rule="para" parents="1007 3314"/>
    </justification>
  </clause>

  <clause id="3325">
    <literal><![CDATA[
      K(1 / (1 / x),y) = (x * K(x,y)) / x
    ]]></literal>
    <justification jstring="[hyper(58,a,865,a(flip),b,3324,a),flip(a)].">
      <j1 rule="hyper" parents="58 865 3324"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3326">
    <literal><![CDATA[
      T(K(1 / (1 / x),y),x) = K(x,y)
    ]]></literal>
    <justification jstring="[para(3325(a,2),224(a,1,1))].">
      <j1 rule="para" parents="3325 224"/>
    </justification>
  </clause>

  <clause id="3327">
    <literal><![CDATA[
      T(K(x,y),x) = K(x,y)
    ]]></literal>
    <justification jstring="[para(3315(a,1),3326(a,1,1))].">
      <j1 rule="para" parents="3315 3326"/>
    </justification>
  </clause>

  <clause id="3328">
    <literal><![CDATA[
      T(K(x,y),x) = K((x \ 1) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,3317,a,b,3327,a),flip(a)].">
      <j1 rule="hyper" parents="320 3317 3327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3329">
    <literal><![CDATA[
      (((x * y) \ x) \ 1) \ (((x * y) \ x) \ K(y,x)) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,2509,a,b,3327,a)].">
      <j1 rule="hyper" parents="58 2509 3327"/>
    </justification>
  </clause>

  <clause id="3330">
    <literal><![CDATA[
      T(x,K(x,y)) = x
    ]]></literal>
    <justification jstring="[hyper(49,a,3327,a)].">
      <j1 rule="hyper" parents="49 3327"/>
    </justification>
  </clause>

  <clause id="3331">
    <literal><![CDATA[
      R(K(x,y),z,u) * x = x * R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(3327(a,1),238(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3327 238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3332">
    <literal><![CDATA[
      T(T(x,y),K(x,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(3330(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3330 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3333">
    <literal><![CDATA[
      K(x,y) * x != z
    ]]></literal>
    <literal><![CDATA[
      x * K(x,y) = z
    ]]></literal>
    <justification jstring="[para(3330(a,1),284(a,1,2))].">
      <j1 rule="para" parents="3330 284"/>
    </justification>
  </clause>

  <clause id="3334">
    <literal><![CDATA[
      T(x,y) * K(x,z) = K(x,z) * T(x,y)
    ]]></literal>
    <justification jstring="[para(3330(a,1),236(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3330 236"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3335">
    <literal><![CDATA[
      T(T(T(x,y),z),K(x,u)) = T(T(x,y),z)
    ]]></literal>
    <justification jstring="[para(3330(a,1),109(a,2,1,1))].">
      <j1 rule="para" parents="3330 109"/>
    </justification>
  </clause>

  <clause id="3336">
    <literal><![CDATA[
      L(x,y,z) * K(x,u) = K(x,u) * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(3330(a,1),237(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3330 237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3337">
    <literal><![CDATA[
      R(x,y,z) * K(x,u) = K(x,u) * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(3330(a,1),238(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3330 238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3338">
    <literal><![CDATA[
      T((x \ y) \ y,K(x,z)) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(3330(a,1),316(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3330 316"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3339">
    <literal><![CDATA[
      T((x * y) / x,K(y,z)) = (x * y) / x
    ]]></literal>
    <justification jstring="[para(3330(a,1),460(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="3330 460"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3340">
    <literal><![CDATA[
      T(K(x,y),T(x,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(49,a,3332,a)].">
      <j1 rule="hyper" parents="49 3332"/>
    </justification>
  </clause>

  <clause id="3341">
    <literal><![CDATA[
      T(x,y) * K(x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) * T(x,y) = u
    ]]></literal>
    <justification jstring="[para(3340(a,1),284(a,1,2))].">
      <j1 rule="para" parents="3340 284"/>
    </justification>
  </clause>

  <clause id="3342">
    <literal><![CDATA[
      K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      T(K(x,y),x) = z
    ]]></literal>
    <justification jstring="[para(3340(a,1),3030(a,1))].">
      <j1 rule="para" parents="3340 3030"/>
    </justification>
  </clause>

  <clause id="3343">
    <literal><![CDATA[
      x * K((x \ 1) \ 1,y) = K(x,y) * x
    ]]></literal>
    <justification jstring="[hyper(119,a,3328,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 3328 17"/>
    </justification>
  </clause>

  <clause id="3344">
    <literal><![CDATA[
      T(K(x,y),T(T(x,z),u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(49,a,3335,a)].">
      <j1 rule="hyper" parents="49 3335"/>
    </justification>
  </clause>

  <clause id="3345">
    <literal><![CDATA[
      T(K(x,y),(z * x) / z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(49,a,3339,a)].">
      <j1 rule="hyper" parents="49 3339"/>
    </justification>
  </clause>

  <clause id="3346">
    <literal><![CDATA[
      T(K(x \ y,z),y / x) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[para(5(a,1),3345(a,1,2,1))].">
      <j1 rule="para" parents="5 3345"/>
    </justification>
  </clause>

  <clause id="3347">
    <literal><![CDATA[
      K(1 / x,y) * (1 / x) = (1 / x) * K(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(75(a,1),3343(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="75 3343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3348">
    <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(824,a,3331,a),flip(a)].">
      <j1 rule="hyper" parents="824 3331"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3349">
    <literal><![CDATA[
      T(x,R(K(x,y),z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(240,a,3331,a)].">
      <j1 rule="hyper" parents="240 3331"/>
    </justification>
  </clause>

  <clause id="3350">
    <literal><![CDATA[
      K(x,R(K(x,y),z,u)) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,3331,a,b,84,a),flip(a)].">
      <j1 rule="hyper" parents="115 3331 84"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3351">
    <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(3349(a,1),237(a,1,2,1))].">
      <j1 rule="para" parents="3349 237"/>
    </justification>
  </clause>

  <clause id="3352">
    <literal><![CDATA[
      T(K(x,y),L(x,z,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(240,a,3336,a)].">
      <j1 rule="hyper" parents="240 3336"/>
    </justification>
  </clause>

  <clause id="3353">
    <literal><![CDATA[
      T(K(x,y),R(x,z,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(240,a,3337,a)].">
      <j1 rule="hyper" parents="240 3337"/>
    </justification>
  </clause>

  <clause id="3354">
    <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(3353(a,1),284(a,1,2))].">
      <j1 rule="para" parents="3353 284"/>
    </justification>
  </clause>

  <clause id="3355">
    <literal><![CDATA[
      K(x \ 1,x) * ((1 / x) * K(x \ 1,y)) = x \ K(1 / x,y)
    ]]></literal>
    <justification jstring="[para(3347(a,1),3034(a,1,2))].">
      <j1 rule="para" parents="3347 3034"/>
    </justification>
  </clause>

  <clause id="3356">
    <literal><![CDATA[
      T(x,x \ K(y,x)) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(3329(a,1),3105(a,1,2,2))].">
      <j1 rule="para" parents="3329 3105"/>
    </justification>
  </clause>

  <clause id="3357">
    <literal><![CDATA[
      x * (T(((x * y) \ x) \ 1,x) \ (((x * y) \ x) \ 1)) = x / K(y,x)
    ]]></literal>
    <justification jstring="[para(3329(a,1),3108(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3329 3108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3358">
    <literal><![CDATA[
      K(x,y) / T(y,y \ 1) = y \ K(x,y)
    ]]></literal>
    <justification jstring="[para(3356(a,1),265(a,1,2))].">
      <j1 rule="para" parents="3356 265"/>
    </justification>
  </clause>

  <clause id="3359">
    <literal><![CDATA[
      K(x,y) * K(y \ 1,y) = (y \ K(x,y)) * y
    ]]></literal>
    <justification jstring="[para(3358(a,1),2659(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3358 2659"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3360">
    <literal><![CDATA[
      (x \ K(y,x)) * K(x,x \ 1) = K(y,x) / x
    ]]></literal>
    <justification jstring="[para(3358(a,1),2690(a,1,1))].">
      <j1 rule="para" parents="3358 2690"/>
    </justification>
  </clause>

  <clause id="3361">
    <literal><![CDATA[
      K(x,y) * K(y,y \ 1) = y * (K(x,y) / y)
    ]]></literal>
    <justification jstring="[hyper(119,a,3360,a(flip),b,2444,a),flip(a)].">
      <j1 rule="hyper" parents="119 3360 2444"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3362">
    <literal><![CDATA[
      x * (x * (K(y,x) / x)) = (x \ 1) \ K(y,x)
    ]]></literal>
    <justification jstring="[para(3361(a,1),3096(a,1,2))].">
      <j1 rule="para" parents="3361 3096"/>
    </justification>
  </clause>

  <clause id="3363">
    <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,3362,a(flip),b,1114,a),flip(a)].">
      <j1 rule="hyper" parents="116 3362 1114"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3364">
    <literal><![CDATA[
      K(x \ 1,(1 / x) \ (y / x)) = (T(y,x \ 1) / x) \ (y / x)
    ]]></literal>
    <justification jstring="[para(2956(a,1),3316(a,2,1,1))].">
      <j1 rule="para" parents="2956 3316"/>
    </justification>
  </clause>

  <clause id="3365">
    <literal><![CDATA[
      (1 / x) \ ((((1 / x) * y) \ 1) \ 1) = y * K(x \ y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(320,a,2586,a,b,3323,a),flip(a)].">
      <j1 rule="hyper" parents="320 2586 3323"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3366">
    <literal><![CDATA[
      (x \ 1) * K(x \ 1,y) = x \ K(1 / x,y)
    ]]></literal>
    <justification jstring="[hyper(2955,a,3355,a)].">
      <j1 rule="hyper" parents="2955 3355"/>
    </justification>
  </clause>

  <clause id="3367">
    <literal><![CDATA[
      (x \ K(1 / x,y)) * ((x \ 1) \ 1) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(3366(a,1),1745(a,1,1))].">
      <j1 rule="para" parents="3366 1745"/>
    </justification>
  </clause>

  <clause id="3368">
    <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),3367(a,1,1,2))].">
      <j1 rule="para" parents="87 3367"/>
    </justification>
  </clause>

  <clause id="3369">
    <literal><![CDATA[
      L(T((x \ y) \ z,z \ (x \ y)),x \ y,x) = ((y \ (x * z)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(2375(a,2),3305(a,1,1))].">
      <j1 rule="para" parents="2375 3305"/>
    </justification>
  </clause>

  <clause id="3370">
    <literal><![CDATA[
      L((x \ 1) \ 1,L(x,y,z) \ 1,L(x,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(142,a,3306,a)].">
      <j1 rule="hyper" parents="142 3306"/>
    </justification>
  </clause>

  <clause id="3371">
    <literal><![CDATA[
      (L(x,y,z) \ 1) * ((x \ 1) \ 1) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(116,a,3370,a(flip),b,257,a),flip(a)].">
      <j1 rule="hyper" parents="116 3370 257"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3373">
    <literal><![CDATA[
      T(x,L(x,y,z) \ 1) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(239,a,1413,a,b,3371,a)].">
      <j1 rule="hyper" parents="239 1413 3371"/>
    </justification>
  </clause>

  <clause id="3374">
    <literal><![CDATA[
      (L(x,y,z) \ x) * K(x \ 1,x) = (L(x,y,z) \ 1) * x
    ]]></literal>
    <justification jstring="[para(3371(a,1),2658(a,1,1))].">
      <j1 rule="para" parents="3371 2658"/>
    </justification>
  </clause>

  <clause id="3375">
    <literal><![CDATA[
      T(x,L(x,y,z) \ 1) = K(x,x \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(320,a,1815,a,b,3373,a),flip(a)].">
      <j1 rule="hyper" parents="320 1815 3373"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3376">
    <literal><![CDATA[
      T(x,L(x,y,z) \ 1) != u * x
    ]]></literal>
    <literal><![CDATA[
      K(x,x \ 1) = u
    ]]></literal>
    <justification jstring="[para(3375(a,2),39(a,1))].">
      <j1 rule="para" parents="3375 39"/>
    </justification>
  </clause>

  <clause id="3377">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ ((L(x,y,z) \ 1) * x) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(123,a,3374,a)].">
      <j1 rule="hyper" parents="123 3374"/>
    </justification>
  </clause>

  <clause id="3378">
    <literal><![CDATA[
      K(L(x,y,z) \ 1,x) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(1418,a,3377,a)].">
      <j1 rule="hyper" parents="1418 3377"/>
    </justification>
  </clause>

  <clause id="3379">
    <literal><![CDATA[
      L(K(x \ 1,x),y,z) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,2519,a,b,3378,a)].">
      <j1 rule="hyper" parents="58 2519 3378"/>
    </justification>
  </clause>

  <clause id="3380">
    <literal><![CDATA[
      (x * y) * K(z \ 1,z) = x * (y * K(z \ 1,z))
    ]]></literal>
    <justification jstring="[para(3378(a,1),2520(a,1,2))].">
      <j1 rule="para" parents="3378 2520"/>
    </justification>
  </clause>

  <clause id="3383">
    <literal><![CDATA[
      a(x,y,K(z \ 1,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,3379,a,b,1934,a),flip(a)].">
      <j1 rule="hyper" parents="115 3379 1934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3384">
    <literal><![CDATA[
      (x \ 1) * K(y \ 1,y) = x \ K(y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(116,a,3379,a(flip),b,257,a),flip(a)].">
      <j1 rule="hyper" parents="116 3379 257"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3385">
    <literal><![CDATA[
      x \ (y * K(z \ 1,z)) = (x \ y) * K(z \ 1,z)
    ]]></literal>
    <justification jstring="[para(3379(a,1),474(a,1,2,2))].">
      <j1 rule="para" parents="3379 474"/>
    </justification>
  </clause>

  <clause id="3388">
    <literal><![CDATA[
      a(x,y,K(z,z \ 1)) = 1
    ]]></literal>
    <justification jstring="[para(1795(a,1),3383(a,1,3))].">
      <j1 rule="para" parents="1795 3383"/>
    </justification>
  </clause>

  <clause id="3389">
    <literal><![CDATA[
      a(x,y,K(1 / z,z)) = 1
    ]]></literal>
    <justification jstring="[para(1827(a,2),3383(a,1,3))].">
      <j1 rule="para" parents="1827 3383"/>
    </justification>
  </clause>

  <clause id="3390">
    <literal><![CDATA[
      (x * y) * K(z,z \ 1) = x * (y * K(z,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(977,a,3388,a)].">
      <j1 rule="hyper" parents="977 3388"/>
    </justification>
  </clause>

  <clause id="3391">
    <literal><![CDATA[
      L(K(x,x \ 1),y,z) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(47,a,3388,a)].">
      <j1 rule="hyper" parents="47 3388"/>
    </justification>
  </clause>

  <clause id="3393">
    <literal><![CDATA[
      (x * y) * K(1 / z,z) = x * (y * K(1 / z,z))
    ]]></literal>
    <justification jstring="[hyper(977,a,3389,a)].">
      <j1 rule="hyper" parents="977 3389"/>
    </justification>
  </clause>

  <clause id="3394">
    <literal><![CDATA[
      L(K(1 / x,x),y,z) = K(1 / x,x)
    ]]></literal>
    <justification jstring="[hyper(47,a,3389,a)].">
      <j1 rule="hyper" parents="47 3389"/>
    </justification>
  </clause>

  <clause id="3396">
    <literal><![CDATA[
      L(x,y,z) * ((1 / x) * (L(x,y,z) \ x)) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,3286,a,b,3391,a)].">
      <j1 rule="hyper" parents="58 3286 3391"/>
    </justification>
  </clause>

  <clause id="3397">
    <literal><![CDATA[
      (x \ 1) * K(y,y \ 1) = x \ K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(116,a,3391,a(flip),b,257,a),flip(a)].">
      <j1 rule="hyper" parents="116 3391 257"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3398">
    <literal><![CDATA[
      x \ (y * K(z,z \ 1)) = (x \ y) * K(z,z \ 1)
    ]]></literal>
    <justification jstring="[para(3391(a,1),474(a,1,2,2))].">
      <j1 rule="para" parents="3391 474"/>
    </justification>
  </clause>

  <clause id="3399">
    <literal><![CDATA[
      K(x \ 1,x) * (y \ 1) = y \ K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(2201,a,3384,a)].">
      <j1 rule="hyper" parents="2201 3384"/>
    </justification>
  </clause>

  <clause id="3400">
    <literal><![CDATA[
      (x \ K(y,y \ 1)) * y = (x \ 1) * ((y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(3397(a,1),2683(a,1,1))].">
      <j1 rule="para" parents="3397 2683"/>
    </justification>
  </clause>

  <clause id="3401">
    <literal><![CDATA[
      K(x \ 1,x) * L((y \ 1) \ 1,z,u) = (L(y,z,u) \ 1) \ K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(3302(a,2),3399(a,1,2))].">
      <j1 rule="para" parents="3302 3399"/>
    </justification>
  </clause>

  <clause id="3402">
    <literal><![CDATA[
      K(x \ 1,x) * (y * z) = y * (z * K(x \ 1,x))
    ]]></literal>
    <justification jstring="[hyper(2201,a,3380,a)].">
      <j1 rule="hyper" parents="2201 3380"/>
    </justification>
  </clause>

  <clause id="3403">
    <literal><![CDATA[
      R(x,y,K(z \ 1,z)) = x
    ]]></literal>
    <justification jstring="[hyper(515,a,3380,a)].">
      <j1 rule="hyper" parents="515 3380"/>
    </justification>
  </clause>

  <clause id="3404">
    <literal><![CDATA[
      (x * y) * K(z \ 1,z) = x * (K(z \ 1,z) * y)
    ]]></literal>
    <justification jstring="[hyper(320,a,2215,a,b,3380,a),flip(a)].">
      <j1 rule="hyper" parents="320 2215 3380"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3409">
    <literal><![CDATA[
      (x * K(y,y \ 1)) / z = x / (z * K(y \ 1,y))
    ]]></literal>
    <justification jstring="[hyper(2721,a,3403,a),flip(a)].">
      <j1 rule="hyper" parents="2721 3403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3410">
    <literal><![CDATA[
      R(x,y,(z \ 1) \ 1) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,2784,a(flip),b,3403,a),flip(a)].">
      <j1 rule="hyper" parents="58 2784 3403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3411">
    <literal><![CDATA[
      R(x,y,K(z,1 / z)) = x
    ]]></literal>
    <justification jstring="[para(75(a,1),3403(a,1,3,1))].">
      <j1 rule="para" parents="75 3403"/>
    </justification>
  </clause>

  <clause id="3413">
    <literal><![CDATA[
      R(x,y,K(z,z \ 1)) = x
    ]]></literal>
    <justification jstring="[para(1795(a,1),3403(a,1,3))].">
      <j1 rule="para" parents="1795 3403"/>
    </justification>
  </clause>

  <clause id="3414">
    <literal><![CDATA[
      R(x,y,K(1 / z,z)) = x
    ]]></literal>
    <justification jstring="[para(1827(a,2),3403(a,1,3))].">
      <j1 rule="para" parents="1827 3403"/>
    </justification>
  </clause>

  <clause id="3415">
    <literal><![CDATA[
      x \ (K(y \ 1,y) * z) = (x \ z) * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[para(3403(a,1),2218(a,1,1))].">
      <j1 rule="para" parents="3403 2218"/>
    </justification>
  </clause>

  <clause id="3416">
    <literal><![CDATA[
      (x * K(y,y \ 1)) / z != u
    ]]></literal>
    <literal><![CDATA[
      x / (z * K(y \ 1,y)) = u
    ]]></literal>
    <justification jstring="[para(3403(a,1),2721(a,1))].">
      <j1 rule="para" parents="3403 2721"/>
    </justification>
  </clause>

  <clause id="3417">
    <literal><![CDATA[
      R(x,y,K(z,1 / z)) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(3411(a,1),46(a,2))].">
      <j1 rule="para" parents="3411 46"/>
    </justification>
  </clause>

  <clause id="3418">
    <literal><![CDATA[
      (x * y) * K(z,1 / z) = x * (y * K(z,1 / z))
    ]]></literal>
    <justification jstring="[para(3411(a,1),101(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3411 101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3419">
    <literal><![CDATA[
      R(x,y,1 / z) = R(x,y,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(2780,a,3413,a)].">
      <j1 rule="hyper" parents="2780 3413"/>
    </justification>
  </clause>

  <clause id="3422">
    <literal><![CDATA[
      R(x,y,K(z,z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(3413(a,1),46(a,2))].">
      <j1 rule="para" parents="3413 46"/>
    </justification>
  </clause>

  <clause id="3423">
    <literal><![CDATA[
      x \ (K(y,y \ 1) * z) = (x \ z) * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[para(3413(a,1),2207(a,1,1))].">
      <j1 rule="para" parents="3413 2207"/>
    </justification>
  </clause>

  <clause id="3424">
    <literal><![CDATA[
      (x * y) \ ((x * (y * z)) * K(1 / u,u)) = L(z,y,x) * K(1 / u,u)
    ]]></literal>
    <justification jstring="[para(3414(a,1),543(a,1,1))].">
      <j1 rule="para" parents="3414 543"/>
    </justification>
  </clause>

  <clause id="3426">
    <literal><![CDATA[
      R(x,y,z) * (y * ((z \ 1) \ 1)) = (x * y) * ((z \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(3410(a,1),101(a,1,1))].">
      <j1 rule="para" parents="3410 101"/>
    </justification>
  </clause>

  <clause id="3430">
    <literal><![CDATA[
      x \ (y * K(z \ 1,z)) = K(z \ 1,z) * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(320,a,2192,a,b,3385,a),flip(a)].">
      <j1 rule="hyper" parents="320 2192 3385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3431">
    <literal><![CDATA[
      (x \ (1 / y)) * K(y \ 1,y) = x \ (y \ 1)
    ]]></literal>
    <justification jstring="[para(778(a,1),3385(a,1,2)),flip(a)].">
      <j1 rule="para" parents="778 3385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3432">
    <literal><![CDATA[
      (x \ ((y \ 1) \ 1)) * K(y \ 1,y) = x \ y
    ]]></literal>
    <justification jstring="[para(1258(a,1),3385(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1258 3385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3433">
    <literal><![CDATA[
      (x \ y) * K(y \ 1,y) = x \ (1 / (1 / y))
    ]]></literal>
    <justification jstring="[para(1790(a,1),3385(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1790 3385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3434">
    <literal><![CDATA[
      (x \ (y / (z \ 1))) * K(z \ 1,z) = x \ (y / (1 / z))
    ]]></literal>
    <justification jstring="[para(2618(a,1),3385(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2618 3385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3435">
    <literal><![CDATA[
      (x \ ((y \ 1) \ z)) * K(y \ 1,y) = x \ ((1 / y) \ z)
    ]]></literal>
    <justification jstring="[para(2949(a,1),3385(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2949 3385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3436">
    <literal><![CDATA[
      K(x,x \ 1) * (y \ x) = y \ ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(2717,a,3432,a)].">
      <j1 rule="hyper" parents="2717 3432"/>
    </justification>
  </clause>

  <clause id="3437">
    <literal><![CDATA[
      (x \ y) * K(y,y \ 1) = x \ ((y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(2711,a,3432,a)].">
      <j1 rule="hyper" parents="2711 3432"/>
    </justification>
  </clause>

  <clause id="3438">
    <literal><![CDATA[
      T(x,y) \ ((x \ 1) \ 1) = x * (1 / T(x,y))
    ]]></literal>
    <justification jstring="[hyper(30,a,3068,a,b,3432,a),flip(a)].">
      <j1 rule="hyper" parents="30 3068 3432"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3439">
    <literal><![CDATA[
      K(x \ 1,x) * (y \ x) = y \ (1 / (1 / x))
    ]]></literal>
    <justification jstring="[hyper(2201,a,3433,a)].">
      <j1 rule="hyper" parents="2201 3433"/>
    </justification>
  </clause>

  <clause id="3441">
    <literal><![CDATA[
      K(x,x \ 1) * (y * z) = y * (z * K(x,x \ 1))
    ]]></literal>
    <justification jstring="[hyper(2183,a,3390,a)].">
      <j1 rule="hyper" parents="2183 3390"/>
    </justification>
  </clause>

  <clause id="3442">
    <literal><![CDATA[
      x \ (y * K(z,z \ 1)) = K(z,z \ 1) * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(320,a,2181,a,b,3398,a),flip(a)].">
      <j1 rule="hyper" parents="320 2181 3398"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3444">
    <literal><![CDATA[
      K(x \ 1,x) * (y * z) = y * (K(x \ 1,x) * z)
    ]]></literal>
    <justification jstring="[hyper(320,a,2215,a,b,3402,a),flip(a)].">
      <j1 rule="hyper" parents="320 2215 3402"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3445">
    <literal><![CDATA[
      (x * y) \ (x * (K(z \ 1,z) * (y * u))) = L(u * K(z \ 1,z),y,x)
    ]]></literal>
    <justification jstring="[para(3402(a,2),13(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="3402 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3446">
    <literal><![CDATA[
      K(x,x \ 1) * (y * (K(x \ 1,x) * z)) = y * z
    ]]></literal>
    <justification jstring="[hyper(2717,a,3404,a)].">
      <j1 rule="hyper" parents="2717 3404"/>
    </justification>
  </clause>

  <clause id="3447">
    <literal><![CDATA[
      x \ (y * (K(z \ 1,z) * u)) = (x \ (y * u)) * K(z \ 1,z)
    ]]></literal>
    <justification jstring="[para(3404(a,1),3385(a,1,2))].">
      <j1 rule="para" parents="3404 3385"/>
    </justification>
  </clause>

  <clause id="3448">
    <literal><![CDATA[
      1 / (x * K(y \ 1,y)) = K(y,y \ 1) / x
    ]]></literal>
    <justification jstring="[para(2(a,1),3409(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2 3409"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3449">
    <literal><![CDATA[
      (x * K(y,y \ 1)) / (z * ((y \ 1) \ 1)) = x / (z * y)
    ]]></literal>
    <justification jstring="[para(2658(a,1),3409(a,2,2))].">
      <j1 rule="para" parents="2658 3409"/>
    </justification>
  </clause>

  <clause id="3450">
    <literal><![CDATA[
      x \ (K(y \ 1,y) * z) = K(y \ 1,y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(320,a,2192,a,b,3415,a),flip(a)].">
      <j1 rule="hyper" parents="320 2192 3415"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3452">
    <literal><![CDATA[
      x * (K(y,y \ 1) * (x \ z)) = K(y,y \ 1) * z
    ]]></literal>
    <justification jstring="[hyper(2184,a,3423,a)].">
      <j1 rule="hyper" parents="2184 3423"/>
    </justification>
  </clause>

  <clause id="3454">
    <literal><![CDATA[
      K(x \ 1,x) * (y \ (z * (1 / x))) = y \ (z * (x \ 1))
    ]]></literal>
    <justification jstring="[para(2604(a,1),3430(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2604 3430"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3455">
    <literal><![CDATA[
      K(x,x \ 1) * (y * z) = y * (K(x,x \ 1) * z)
    ]]></literal>
    <justification jstring="[para(2181(a,2),3441(a,2,2))].">
      <j1 rule="para" parents="2181 3441"/>
    </justification>
  </clause>

  <clause id="3456">
    <literal><![CDATA[
      K(x,x \ 1) * (y * (z * x)) = y * (z * ((x \ 1) \ 1))
    ]]></literal>
    <justification jstring="[para(2677(a,1),3441(a,2,2))].">
      <j1 rule="para" parents="2677 3441"/>
    </justification>
  </clause>

  <clause id="3457">
    <literal><![CDATA[
      K(x,x \ 1) * (y * (z * (x \ 1))) = y * (z * (1 / x))
    ]]></literal>
    <justification jstring="[para(2691(a,1),3441(a,2,2))].">
      <j1 rule="para" parents="2691 3441"/>
    </justification>
  </clause>

  <clause id="3458">
    <literal><![CDATA[
      K(x,x \ 1) * (y * (z / (1 / x))) = y * (z / (x \ 1))
    ]]></literal>
    <justification jstring="[para(2701(a,1),3441(a,2,2))].">
      <j1 rule="para" parents="2701 3441"/>
    </justification>
  </clause>

  <clause id="3459">
    <literal><![CDATA[
      K(x,x \ 1) * (y * ((x \ 1) * z)) = y * ((1 / x) * z)
    ]]></literal>
    <justification jstring="[para(2846(a,1),3441(a,2,2))].">
      <j1 rule="para" parents="2846 3441"/>
    </justification>
  </clause>

  <clause id="3460">
    <literal><![CDATA[
      K(x,x \ 1) * (y * ((1 / x) \ z)) = y * ((x \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(2948(a,1),3441(a,2,2))].">
      <j1 rule="para" parents="2948 3441"/>
    </justification>
  </clause>

  <clause id="3461">
    <literal><![CDATA[
      K(x,x \ 1) * (y \ ((x \ 1) * z)) = y \ ((1 / x) * z)
    ]]></literal>
    <justification jstring="[para(2846(a,1),3442(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2846 3442"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3462">
    <literal><![CDATA[
      K(x,x \ 1) * (y \ ((1 / x) \ z)) = y \ ((x \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(2948(a,1),3442(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2948 3442"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3463">
    <literal><![CDATA[
      (x * y) \ (x * (K(z \ 1,z) * (y * u))) = L(K(z \ 1,z) * u,y,x)
    ]]></literal>
    <justification jstring="[para(3444(a,2),13(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="3444 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3470">
    <literal><![CDATA[
      x \ (y * (K(z,z \ 1) * u)) = (x \ (y * u)) * K(z,z \ 1)
    ]]></literal>
    <justification jstring="[para(3455(a,1),3423(a,1,2))].">
      <j1 rule="para" parents="3455 3423"/>
    </justification>
  </clause>

  <clause id="3472">
    <literal><![CDATA[
      (1 / (1 / x)) / (y * x) = x / (y * ((x \ 1) \ 1))
    ]]></literal>
    <justification jstring="[para(1801(a,1),3449(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1801 3449"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3473">
    <literal><![CDATA[
      (1 / x) * (y * ((1 / x) \ z)) = (x \ 1) * (y * ((x \ 1) \ z))
    ]]></literal>
    <justification jstring="[hyper(119,a,3460,a(flip),b,2952,a),flip(a)].">
      <j1 rule="hyper" parents="119 3460 2952"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3474">
    <literal><![CDATA[
      K(x,x \ 1) * (y \ (z * ((1 / x) \ u))) = y \ (z * ((x \ 1) \ u))
    ]]></literal>
    <justification jstring="[hyper(116,a,3460,a(flip),b,3452,a),flip(a)].">
      <j1 rule="hyper" parents="116 3460 3452"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3476">
    <literal><![CDATA[
      (x * y) * ((z \ 1) \ 1) != u * (y * ((z \ 1) \ 1))
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(3426(a,1),39(a,1))].">
      <j1 rule="para" parents="3426 39"/>
    </justification>
  </clause>

  <clause id="3477">
    <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),3447(a,2,1))].">
      <j1 rule="para" parents="13 3447"/>
    </justification>
  </clause>

  <clause id="3478">
    <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,3470,a),flip(a)].">
      <j1 rule="hyper" parents="691 3470"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3479">
    <literal><![CDATA[
      x * (((x * y) \ (x * T(x \ (x * y),x))) \ 1) = x / K(y,x)
    ]]></literal>
    <justification jstring="[para(3077(a,1),3357(a,1,2))].">
      <j1 rule="para" parents="3077 3357"/>
    </justification>
  </clause>

  <clause id="3480">
    <literal><![CDATA[
      x * (((x * y) \ (x * T(y,x))) \ 1) = x / K(y,x)
    ]]></literal>
    <justification jstring="[para(4(a,1),3479(a,1,2,1,2,2,1))].">
      <j1 rule="para" parents="4 3479"/>
    </justification>
  </clause>

  <clause id="3481">
    <literal><![CDATA[
      x * (((x * y) \ (y * x)) \ 1) = x / K(y,x)
    ]]></literal>
    <justification jstring="[para(105(a,1),3480(a,1,2,1,2))].">
      <j1 rule="para" parents="105 3480"/>
    </justification>
  </clause>

  <clause id="3482">
    <literal><![CDATA[
      x * (K(y,x) \ 1) = x / K(y,x)
    ]]></literal>
    <justification jstring="[para(11(a,2),3481(a,1,2,1))].">
      <j1 rule="para" parents="11 3481"/>
    </justification>
  </clause>

  <clause id="3483">
    <literal><![CDATA[
      x * (K(y,x) \ 1) = K(y,x) \ x
    ]]></literal>
    <justification jstring="[hyper(320,a,3065,a(flip),b,3482,a),flip(a)].">
      <j1 rule="hyper" parents="320 3065 3482"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3484">
    <literal><![CDATA[
      (K(x,y) \ 1) \ (K(x,y) \ y) = y
    ]]></literal>
    <justification jstring="[hyper(116,a,3483,a(flip),b,3139,a)].">
      <j1 rule="hyper" parents="116 3483 3139"/>
    </justification>
  </clause>

  <clause id="3485">
    <literal><![CDATA[
      K(x,y) \ y != y * z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) \ 1 = z
    ]]></literal>
    <justification jstring="[para(3483(a,1),38(a,1))].">
      <j1 rule="para" parents="3483 38"/>
    </justification>
  </clause>

  <clause id="3486">
    <literal><![CDATA[
      (K(x,y) \ y) \ (K(x,y) \ 1) = y \ 1
    ]]></literal>
    <justification jstring="[para(3483(a,1),3141(a,1,1))].">
      <j1 rule="para" parents="3483 3141"/>
    </justification>
  </clause>

  <clause id="3487">
    <literal><![CDATA[
      (K(x,y) \ 1) * T(y,z) = K(x,y) \ T(y,z)
    ]]></literal>
    <justification jstring="[para(3484(a,1),992(a,1,2,1))].">
      <j1 rule="para" parents="3484 992"/>
    </justification>
  </clause>

  <clause id="3488">
    <literal><![CDATA[
      (K(x,y) \ y) * (y \ 1) = K(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(134,a,3486,a)].">
      <j1 rule="hyper" parents="134 3486"/>
    </justification>
  </clause>

  <clause id="3489">
    <literal><![CDATA[
      R(K(x,y) \ y,y \ 1,y) = (K(x,y) \ 1) * ((y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(3488(a,1),2663(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3488 2663"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3490">
    <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,3487,a),flip(a)].">
      <j1 rule="hyper" parents="58 313 3487"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3491">
    <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,3490,a),flip(a)].">
      <j1 rule="hyper" parents="58 310 3490"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3492">
    <literal><![CDATA[
      R(K(x,y) \ y,y \ 1,y) = K(x,y) \ ((y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,3491,a(flip),b,3489,a),flip(a)].">
      <j1 rule="hyper" parents="320 3491 3489"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3493">
    <literal><![CDATA[
      x * (K(x,y) * (K(x,y) \ ((y \ 1) \ 1))) = (T(y,y \ 1) * x) * K(x,y)
    ]]></literal>
    <justification jstring="[para(3492(a,1),2545(a,1,2,2))].">
      <j1 rule="para" parents="3492 2545"/>
    </justification>
  </clause>

  <clause id="3494">
    <literal><![CDATA[
      x * (x * (T(x,y) \ (K(z,x) / x))) = T(x,y) \ ((x \ 1) \ K(z,x))
    ]]></literal>
    <justification jstring="[para(1116(a,1),3363(a,1,2))].">
      <j1 rule="para" parents="1116 3363"/>
    </justification>
  </clause>

  <clause id="3495">
    <literal><![CDATA[
      T(x \ (y * z),z \ (y \ x)) = ((x \ (y * z)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(58,a,757,a(flip),b,3369,a)].">
      <j1 rule="hyper" parents="58 757 3369"/>
    </justification>
  </clause>

  <clause id="3496">
    <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),3424(a,1,2))].">
      <j1 rule="para" parents="3393 3424"/>
    </justification>
  </clause>

  <clause id="3497">
    <literal><![CDATA[
      L(K(x \ 1,x) * y,z,u) = L(y,z,u) * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,3463,a(flip),b,3477,a)].">
      <j1 rule="hyper" parents="58 3463 3477"/>
    </justification>
  </clause>

  <clause id="3498">
    <literal><![CDATA[
      L(x * K(y \ 1,y),z,u) = L(x,z,u) * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,3445,a(flip),b,3477,a)].">
      <j1 rule="hyper" parents="58 3445 3477"/>
    </justification>
  </clause>

  <clause id="3499">
    <literal><![CDATA[
      L(K(x \ 1,x) * y,z,u) = K(x \ 1,x) * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(320,a,2192,a,b,3497,a),flip(a)].">
      <j1 rule="hyper" parents="320 2192 3497"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3500">
    <literal><![CDATA[
      L(x,y,z) * K(x \ 1,x) = L(1 / (1 / x),y,z)
    ]]></literal>
    <justification jstring="[para(1811(a,1),3497(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1811 3497"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3502">
    <literal><![CDATA[
      K(x \ 1,x) * L((x \ 1) \ 1,y,z) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(912(a,1),3499(a,1,1)),flip(a)].">
      <j1 rule="para" parents="912 3499"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3503">
    <literal><![CDATA[
      K(x \ 1,x) * L(1 / x,y,z) = L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(1788(a,1),3499(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1788 3499"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3505">
    <literal><![CDATA[
      K(x \ 1,x) * L(y * K(x,x \ 1),z,u) = L(y,z,u)
    ]]></literal>
    <justification jstring="[para(2694(a,1),3499(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2694 3499"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3506">
    <literal><![CDATA[
      K(x,x \ 1) * L(x,y,z) = L((x \ 1) \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(2716,a,3502,a)].">
      <j1 rule="hyper" parents="2716 3502"/>
    </justification>
  </clause>

  <clause id="3507">
    <literal><![CDATA[
      L(x,y,z) * K(x,x \ 1) = L((x \ 1) \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(2709,a,3502,a)].">
      <j1 rule="hyper" parents="2709 3502"/>
    </justification>
  </clause>

  <clause id="3508">
    <literal><![CDATA[
      K(x \ 1,x) * ((y * (x \ 1)) \ y) = L(x,x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,394,a(flip),b,3502,a)].">
      <j1 rule="hyper" parents="58 394 3502"/>
    </justification>
  </clause>

  <clause id="3509">
    <literal><![CDATA[
      L(x \ 1,y,z) * K(x,x \ 1) = L(1 / x,y,z)
    ]]></literal>
    <justification jstring="[hyper(2709,a,3503,a)].">
      <j1 rule="hyper" parents="2709 3503"/>
    </justification>
  </clause>

  <clause id="3511">
    <literal><![CDATA[
      (x \ 1) \ L(x \ 1,y,z) = x * L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(116,a,3503,a(flip),b,1841,a(flip))].">
      <j1 rule="hyper" parents="116 3503 1841"/>
    </justification>
  </clause>

  <clause id="3512">
    <literal><![CDATA[
      K(x,x \ 1) * L(x,y,z) = L(T(x,x \ 1),y,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,827,a,b,3506,a),flip(a)].">
      <j1 rule="hyper" parents="320 827 3506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3513">
    <literal><![CDATA[
      x \ L((x \ 1) \ 1,y,z) = L(x,y,z) * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(116,a,3506,a(flip),b,2203,a(flip))].">
      <j1 rule="hyper" parents="116 3506 2203"/>
    </justification>
  </clause>

  <clause id="3514">
    <literal><![CDATA[
      L(x,y,z) * K(x,1 / x) = L((x \ 1) \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(1791(a,2),3507(a,1,2))].">
      <j1 rule="para" parents="1791 3507"/>
    </justification>
  </clause>

  <clause id="3515">
    <literal><![CDATA[
      ((x * y) \ x) \ L(1 / y,y,x) = K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(731,a,3509,a)].">
      <j1 rule="hyper" parents="731 3509"/>
    </justification>
  </clause>

  <clause id="3516">
    <literal><![CDATA[
      x \ L(T(x,x \ 1),y,z) = L(x,y,z) * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(116,a,3512,a(flip),b,2203,a(flip))].">
      <j1 rule="hyper" parents="116 3512 2203"/>
    </justification>
  </clause>

  <clause id="3517">
    <literal><![CDATA[
      T(L(x,y,z) * (1 / x),x) = L(x,y,z) * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(58,a,1284,a,b,3513,a)].">
      <j1 rule="hyper" parents="58 1284 3513"/>
    </justification>
  </clause>

  <clause id="3518">
    <literal><![CDATA[
      (x \ L(x,y,z)) * x = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(2341,a,3517,a)].">
      <j1 rule="hyper" parents="2341 3517"/>
    </justification>
  </clause>

  <clause id="3519">
    <literal><![CDATA[
      T(x,x \ L(x,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(355,a,3518,a)].">
      <j1 rule="hyper" parents="355 3518"/>
    </justification>
  </clause>

  <clause id="3520">
    <literal><![CDATA[
      L(x,y,z) / x = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(131,a,3518,a)].">
      <j1 rule="hyper" parents="131 3518"/>
    </justification>
  </clause>

  <clause id="3521">
    <literal><![CDATA[
      K(x \ L(x,y,z),x) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,3518,a(flip),b,302,a),flip(a)].">
      <j1 rule="hyper" parents="115 3518 302"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3522">
    <literal><![CDATA[
      L(x,y,z) \ ((x \ L(x,y,z)) * (x * u)) = L(u,x,x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[para(3518(a,1),13(a,2,1)),flip(a)].">
      <j1 rule="para" parents="3518 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3523">
    <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(3518(a,1),423(a,1,1))].">
      <j1 rule="para" parents="3518 423"/>
    </justification>
  </clause>

  <clause id="3524">
    <literal><![CDATA[
      T(x,y) * (x \ L(x,z,u)) = (x \ L(x,z,u)) * T(x,y)
    ]]></literal>
    <justification jstring="[para(3519(a,1),236(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3519 236"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3525">
    <literal><![CDATA[
      L(x * K(y,y \ 1),z,u) = K(y,y \ 1) * L(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(2716,a,3505,a),flip(a)].">
      <j1 rule="hyper" parents="2716 3505"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3526">
    <literal><![CDATA[
      L(x * K(y,y \ 1),z,u) = L(x,z,u) * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(2709,a,3505,a),flip(a)].">
      <j1 rule="hyper" parents="2709 3505"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3527">
    <literal><![CDATA[
      (x \ L(x * (y / x),z,u)) * x = L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,2760,a(flip),b,3505,a)].">
      <j1 rule="hyper" parents="58 2760 3505"/>
    </justification>
  </clause>

  <clause id="3529">
    <literal><![CDATA[
      (x \ L(x * y,z,u)) * x = L(y * x,z,u)
    ]]></literal>
    <justification jstring="[para(6(a,1),3527(a,1,1,2,1,2))].">
      <j1 rule="para" parents="6 3527"/>
    </justification>
  </clause>

  <clause id="3530">
    <literal><![CDATA[
      L(x * (y / x),z,u) = x * (L(y,z,u) / x)
    ]]></literal>
    <justification jstring="[para(3527(a,1),71(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3527 71"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3531">
    <literal><![CDATA[
      L((x \ y) * x,z,u) = (x \ L(y,z,u)) * x
    ]]></literal>
    <justification jstring="[para(71(a,1),3527(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="71 3527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3532">
    <literal><![CDATA[
      (x \ 1) \ L((x \ 1) * y,z,u) = x * L(x \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(30,a,1239,a,b,3529,a),flip(a)].">
      <j1 rule="hyper" parents="30 1239 3529"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3533">
    <literal><![CDATA[
      L(x * ((y \ (z \ u)) / x),y,z) = x * (((z * y) \ u) / x)
    ]]></literal>
    <justification jstring="[para(298(a,1),3530(a,2,2,1))].">
      <j1 rule="para" parents="298 3530"/>
    </justification>
  </clause>

  <clause id="3534">
    <literal><![CDATA[
      L(x * (y / x),y \ 1,y) = x * ((1 / (1 / y)) / x)
    ]]></literal>
    <justification jstring="[para(1812(a,1),3530(a,2,2,1))].">
      <j1 rule="para" parents="1812 3530"/>
    </justification>
  </clause>

  <clause id="3535">
    <literal><![CDATA[
      L((x \ y) * x,z,u) != w * x
    ]]></literal>
    <literal><![CDATA[
      x \ L(y,z,u) = w
    ]]></literal>
    <justification jstring="[para(3531(a,2),39(a,1))].">
      <j1 rule="para" parents="3531 39"/>
    </justification>
  </clause>

  <clause id="3536">
    <literal><![CDATA[
      L((x \ (y \ (z \ u))) * x,y,z) = (x \ ((z * y) \ u)) * x
    ]]></literal>
    <justification jstring="[para(298(a,1),3531(a,2,1,2))].">
      <j1 rule="para" parents="298 3531"/>
    </justification>
  </clause>

  <clause id="3537">
    <literal><![CDATA[
      L((x \ ((y \ 1) \ z)) * x,y \ 1,y) = (x \ (y * z)) * x
    ]]></literal>
    <justification jstring="[para(489(a,1),3531(a,2,1,2))].">
      <j1 rule="para" parents="489 3531"/>
    </justification>
  </clause>

  <clause id="3538">
    <literal><![CDATA[
      L((x \ ((y \ z) \ u)) * x,y \ z,y) = (x \ (z \ (y * u))) * x
    ]]></literal>
    <justification jstring="[para(490(a,1),3531(a,2,1,2))].">
      <j1 rule="para" parents="490 3531"/>
    </justification>
  </clause>

  <clause id="3539">
    <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,3524,a(flip),b,1113,a)].">
      <j1 rule="hyper" parents="116 3524 1113"/>
    </justification>
  </clause>

  <clause id="3540">
    <literal><![CDATA[
      L(K(x,x \ 1) * y,z,u) = K(x,x \ 1) * L(y,z,u)
    ]]></literal>
    <justification jstring="[para(2181(a,2),3525(a,1,1))].">
      <j1 rule="para" parents="2181 3525"/>
    </justification>
  </clause>

  <clause id="3541">
    <literal><![CDATA[
      x \ L(y * K(z,z \ 1),u,w) = (x \ L(y,u,w)) * K(z,z \ 1)
    ]]></literal>
    <justification jstring="[para(3525(a,2),3423(a,1,2))].">
      <j1 rule="para" parents="3525 3423"/>
    </justification>
  </clause>

  <clause id="3542">
    <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(2381(a,1),3526(a,2,2))].">
      <j1 rule="para" parents="2381 3526"/>
    </justification>
  </clause>

  <clause id="3543">
    <literal><![CDATA[
      (x * y) * (z * (((x * y) \ u) / z)) = x * (y * (z * ((y \ (x \ u)) / z)))
    ]]></literal>
    <justification jstring="[hyper(119,a,3533,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="119 3533 13"/>
    </justification>
  </clause>

  <clause id="3544">
    <literal><![CDATA[
      (x * y) * ((z \ ((x * y) \ u)) * z) = x * (y * ((z \ (y \ (x \ u))) * z))
    ]]></literal>
    <justification jstring="[hyper(119,a,3536,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="119 3536 13"/>
    </justification>
  </clause>

  <clause id="3545">
    <literal><![CDATA[
      (x \ 1) * ((y \ ((x \ 1) \ z)) * y) = x \ ((y \ (x * z)) * y)
    ]]></literal>
    <justification jstring="[hyper(116,a,3537,a(flip),b,257,a),flip(a)].">
      <j1 rule="hyper" parents="116 3537 257"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3546">
    <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),3496(a,1,2,2))].">
      <j1 rule="para" parents="3393 3496"/>
    </justification>
  </clause>

  <clause id="3547">
    <literal><![CDATA[
      L(x \ 1,x,x \ L(x,y,z)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(3523,a,1195,a)].">
      <j1 rule="hyper" parents="3523 1195"/>
    </justification>
  </clause>

  <clause id="3548">
    <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(3547(a,1),3280(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="3547 3280"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3549">
    <literal><![CDATA[
      L(x * K(1 / y,y),z,u) = L(x,z,u) * K(1 / y,y)
    ]]></literal>
    <justification jstring="[hyper(482,a,3546,a)].">
      <j1 rule="hyper" parents="482 3546"/>
    </justification>
  </clause>

  <clause id="3550">
    <literal><![CDATA[
      (L(x,y,z) \ 1) \ K(x \ 1,x) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,3502,a(flip),b,3401,a),flip(a)].">
      <j1 rule="hyper" parents="58 3502 3401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3551">
    <literal><![CDATA[
      K(x \ 1,x) / L(x,y,z) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(197,a,3550,a)].">
      <j1 rule="hyper" parents="197 3550"/>
    </justification>
  </clause>

  <clause id="3552">
    <literal><![CDATA[
      K(1 / x,x) / L(x,y,z) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(1827(a,2),3551(a,1,1))].">
      <j1 rule="para" parents="1827 3551"/>
    </justification>
  </clause>

  <clause id="3553">
    <literal><![CDATA[
      K(x,y) = (T(y,y \ 1) * x) \ (x * ((y \ 1) \ 1))
    ]]></literal>
    <justification jstring="[hyper(599,a,3493,a),flip(a)].">
      <j1 rule="hyper" parents="599 3493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3554">
    <literal><![CDATA[
      K(x,(y \ 1) \ 1) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,665,a(flip),b,3553,a)].">
      <j1 rule="hyper" parents="320 665 3553"/>
    </justification>
  </clause>

  <clause id="3556">
    <literal><![CDATA[
      K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,(y \ 1) \ 1) = z
    ]]></literal>
    <justification jstring="[para(3553(a,2),666(a,1))].">
      <j1 rule="para" parents="3553 666"/>
    </justification>
  </clause>

  <clause id="3557">
    <literal><![CDATA[
      K(K(x,x \ 1) * y,x) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,3149,a,b,3554,a)].">
      <j1 rule="hyper" parents="58 3149 3554"/>
    </justification>
  </clause>

  <clause id="3558">
    <literal><![CDATA[
      K(x,1 / y) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(75(a,1),3554(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="75 3554"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3559">
    <literal><![CDATA[
      K(x,1 / (1 / y)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(196(a,1),3554(a,1,2)),flip(a)].">
      <j1 rule="para" parents="196 3554"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3560">
    <literal><![CDATA[
      K(x,T(y,1 / y)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(1267(a,2),3554(a,1,2))].">
      <j1 rule="para" parents="1267 3554"/>
    </justification>
  </clause>

  <clause id="3561">
    <literal><![CDATA[
      K(x,T(y / z,z / y)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(2069(a,2),3554(a,1,2))].">
      <j1 rule="para" parents="2069 3554"/>
    </justification>
  </clause>

  <clause id="3562">
    <literal><![CDATA[
      K(x,T(y / z,y \ z)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(2403(a,2),3554(a,1,2))].">
      <j1 rule="para" parents="2403 3554"/>
    </justification>
  </clause>

  <clause id="3563">
    <literal><![CDATA[
      K(x,((1 / y) \ z) / z) = K(x,((y \ 1) \ z) / z)
    ]]></literal>
    <justification jstring="[para(3079(a,1),3554(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3079 3554"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3567">
    <literal><![CDATA[
      (1 / x) * K(y,1 / x) = K(y,x \ 1) / x
    ]]></literal>
    <justification jstring="[para(3558(a,1),2356(a,2,1))].">
      <j1 rule="para" parents="3558 2356"/>
    </justification>
  </clause>

  <clause id="3568">
    <literal><![CDATA[
      (x \ 1) * K(y,x \ 1) = x \ K(y,1 / x)
    ]]></literal>
    <justification jstring="[para(3558(a,2),2930(a,2,2))].">
      <j1 rule="para" parents="3558 2930"/>
    </justification>
  </clause>

  <clause id="3570">
    <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(3301(a,1),3559(a,1,2))].">
      <j1 rule="para" parents="3301 3559"/>
    </justification>
  </clause>

  <clause id="3571">
    <literal><![CDATA[
      K((1 / x) * y,x) = K((x \ 1) * y,x)
    ]]></literal>
    <justification jstring="[para(2819(a,1),3557(a,1,1))].">
      <j1 rule="para" parents="2819 3557"/>
    </justification>
  </clause>

  <clause id="3572">
    <literal><![CDATA[
      K(x \ ((1 / y) \ z),y) = K(x \ ((y \ 1) \ z),y)
    ]]></literal>
    <justification jstring="[para(3462(a,1),3557(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3462 3557"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3573">
    <literal><![CDATA[
      K((1 / (1 / x)) * y,1 / x) = K(x * y,1 / x)
    ]]></literal>
    <justification jstring="[para(75(a,1),3571(a,2,1,1))].">
      <j1 rule="para" parents="75 3571"/>
    </justification>
  </clause>

  <clause id="3574">
    <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,3122,a,b,3563,a)].">
      <j1 rule="hyper" parents="58 3122 3563"/>
    </justification>
  </clause>

  <clause id="3575">
    <literal><![CDATA[
      ((1 / x) \ y) \ ((1 / x) \ T(y,x)) = K(x \ ((x \ 1) \ y),x)
    ]]></literal>
    <justification jstring="[hyper(58,a,893,a,b,3572,a)].">
      <j1 rule="hyper" parents="58 893 3572"/>
    </justification>
  </clause>

  <clause id="3576">
    <literal><![CDATA[
      L(x * K(y \ z,z \ y),u,w) = L(x,u,w) * K(y \ z,z \ y)
    ]]></literal>
    <justification jstring="[para(2381(a,1),3542(a,1,1,2))].">
      <j1 rule="para" parents="2381 3542"/>
    </justification>
  </clause>

  <clause id="3577">
    <literal><![CDATA[
      (x * y) * (z * (((x * y) \ x) / z)) = x * (y * (z * ((y \ 1) / z)))
    ]]></literal>
    <justification jstring="[para(61(a,1),3543(a,2,2,2,2,1,2))].">
      <j1 rule="para" parents="61 3543"/>
    </justification>
  </clause>

  <clause id="3578">
    <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),3548(a,2,2,1))].">
      <j1 rule="para" parents="5 3548"/>
    </justification>
  </clause>

  <clause id="3580">
    <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),3578(a,2,2))].">
      <j1 rule="para" parents="179 3578"/>
    </justification>
  </clause>

  <clause id="3581">
    <literal><![CDATA[
      (x \ L(x,y,z)) * (x * (L(x,u,w) \ 1)) = L(x,y,z) * (L(x,u,w) \ 1)
    ]]></literal>
    <justification jstring="[hyper(119,a,3580,a(flip),b,3522,a),flip(a)].">
      <j1 rule="hyper" parents="119 3580 3522"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3583">
    <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(1413(a,1),3581(a,1,2))].">
      <j1 rule="para" parents="1413 3581"/>
    </justification>
  </clause>

  <clause id="3584">
    <literal><![CDATA[
      1 / (L(x,y,z) \ x) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(117,a,5,a(flip),b,3583,a)].">
      <j1 rule="hyper" parents="117 5 3583"/>
    </justification>
  </clause>

  <clause id="3585">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ 1 = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(116,a,5,a(flip),b,3583,a)].">
      <j1 rule="hyper" parents="116 5 3583"/>
    </justification>
  </clause>

  <clause id="3586">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ (x \ 1) = (x \ 1) * (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[para(3585(a,1),2346(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3585 2346"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3587">
    <literal><![CDATA[
      (x * L(x \ 1,y,z)) \ 1 = L(x \ 1,y,z) \ (x \ 1)
    ]]></literal>
    <justification jstring="[para(3511(a,1),3585(a,1,1))].">
      <j1 rule="para" parents="3511 3585"/>
    </justification>
  </clause>

  <clause id="3588">
    <literal><![CDATA[
      L(x \ 1,y,z) \ (x \ 1) = x \ (L(1 / x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,3235,a(flip),b,3587,a),flip(a)].">
      <j1 rule="hyper" parents="58 3235 3587"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3589">
    <literal><![CDATA[
      L((x \ 1) \ 1,y,z) \ ((x \ 1) \ 1) = (x \ L(x,y,z)) \ 1
    ]]></literal>
    <justification jstring="[para(1193(a,1),3587(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1193 3587"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3590">
    <literal><![CDATA[
      L((x \ 1) \ 1,y,z) \ ((x \ 1) \ 1) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(320,a,3585,a(flip),b,3589,a),flip(a)].">
      <j1 rule="hyper" parents="320 3585 3589"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3591">
    <literal><![CDATA[
      x \ T((y \ 1) * (x / (y \ 1)),K(z \ 1,z)) = K(1 / y,x / (y \ 1))
    ]]></literal>
    <justification jstring="[para(3123(a,2),3313(a,1,2))].">
      <j1 rule="para" parents="3123 3313"/>
    </justification>
  </clause>

  <clause id="3592">
    <literal><![CDATA[
      x \ ((1 / y) * (x / (1 / y))) = K(1 / y,x / (y \ 1))
    ]]></literal>
    <justification jstring="[para(3058(a,1),3591(a,1,2))].">
      <j1 rule="para" parents="3058 3591"/>
    </justification>
  </clause>

  <clause id="3593">
    <literal><![CDATA[
      (x \ K(1 / x,y / (x \ 1))) * ((x \ 1) \ 1) = K(x \ 1,y / (1 / x))
    ]]></literal>
    <justification jstring="[para(3592(a,1),3368(a,1,1,2))].">
      <j1 rule="para" parents="3592 3368"/>
    </justification>
  </clause>

  <clause id="3594">
    <literal><![CDATA[
      K(x \ 1,y / (1 / x)) = K(x \ 1,y / (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(58,a,3367,a(flip),b,3593,a),flip(a)].">
      <j1 rule="hyper" parents="58 3367 3593"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3595">
    <literal><![CDATA[
      K(x \ 1,(y * (1 / x)) / (x \ 1)) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(6(a,1),3594(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6 3594"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3596">
    <literal><![CDATA[
      K(x \ 1,(y / (x \ 1)) * (1 / x)) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(1521(a,1),3595(a,1,2))].">
      <j1 rule="para" parents="1521 3595"/>
    </justification>
  </clause>

  <clause id="3597">
    <literal><![CDATA[
      K(x \ 1,y * K(x,x \ 1)) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(2718(a,1),3596(a,1,2))].">
      <j1 rule="para" parents="2718 3596"/>
    </justification>
  </clause>

  <clause id="3598">
    <literal><![CDATA[
      K(x \ 1,((x \ 1) \ 1) * y) = K(x \ 1,x * y)
    ]]></literal>
    <justification jstring="[para(2832(a,1),3597(a,1,2))].">
      <j1 rule="para" parents="2832 3597"/>
    </justification>
  </clause>

  <clause id="3599">
    <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(3455(a,2),3478(a,1,1,1,2))].">
      <j1 rule="para" parents="3455 3478"/>
    </justification>
  </clause>

  <clause id="3600">
    <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),1706(a,2,2,1,1))].">
      <j1 rule="para" parents="15 1706"/>
    </justification>
  </clause>

  <clause id="3601">
    <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(1720(a,1),3600(a,1,1))].">
      <j1 rule="para" parents="1720 3600"/>
    </justification>
  </clause>

  <clause id="3602">
    <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(1524(a,1),3601(a,1,1,1))].">
      <j1 rule="para" parents="1524 3601"/>
    </justification>
  </clause>

  <clause id="3603">
    <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,3602,a),flip(a)].">
      <j1 rule="hyper" parents="518 3602"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3604">
    <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,1213,a(flip),b,3603,a),flip(a)].">
      <j1 rule="hyper" parents="58 1213 3603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3605">
    <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(651(a,1),3603(a,2,1,2))].">
      <j1 rule="para" parents="651 3603"/>
    </justification>
  </clause>

  <clause id="3606">
    <literal><![CDATA[
      R(x * T(1 * (x \ 1),x),y,z) = a(1 / R(x,y,z),x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(1219,a,3605,a),flip(a)].">
      <j1 rule="hyper" parents="1219 3605"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3607">
    <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),3606(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2 3606"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3608">
    <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(1574(a,1),3604(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1574 3604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3609">
    <literal><![CDATA[
      (x \ 1) / (x \ R(x,y,z)) = R(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(30,a,2505,a(flip),b,3608,a),flip(a)].">
      <j1 rule="hyper" parents="30 2505 3608"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3610">
    <literal><![CDATA[
      (x \ R(x,y,z)) \ (x \ 1) = R(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(3250,a,3609,a)].">
      <j1 rule="hyper" parents="3250 3609"/>
    </justification>
  </clause>

  <clause id="3611">
    <literal><![CDATA[
      (x \ 1) \ (R(x,y,z) \ 1) = (x \ R(x,y,z)) \ 1
    ]]></literal>
    <justification jstring="[hyper(116,a,3610,a(flip),b,2348,a)].">
      <j1 rule="hyper" parents="116 3610 2348"/>
    </justification>
  </clause>

  <clause id="3612">
    <literal><![CDATA[
      ((1 / x) \ R(1 / x,y,z)) \ x = R(1 / x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(75(a,1),3610(a,1,2))].">
      <j1 rule="para" parents="75 3610"/>
    </justification>
  </clause>

  <clause id="3613">
    <literal><![CDATA[
      (x * R(x \ 1,y,z)) \ x = R(1 / x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(1215(a,1),3612(a,1,1))].">
      <j1 rule="para" parents="1215 3612"/>
    </justification>
  </clause>

  <clause id="3614">
    <literal><![CDATA[
      R(1 / (1 / x),y,z) \ 1 = (R(x,y,z) / x) \ (1 / x)
    ]]></literal>
    <justification jstring="[para(1895(a,1),3613(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1895 3613"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3615">
    <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),1911(a,2,2,1,1))].">
      <j1 rule="para" parents="15 1911"/>
    </justification>
  </clause>

  <clause id="3616">
    <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(1718(a,1),3615(a,1,1))].">
      <j1 rule="para" parents="1718 3615"/>
    </justification>
  </clause>

  <clause id="3617">
    <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(1752(a,1),3616(a,1,1,1))].">
      <j1 rule="para" parents="1752 3616"/>
    </justification>
  </clause>

  <clause id="3618">
    <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,3617,a),flip(a)].">
      <j1 rule="hyper" parents="518 3617"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3619">
    <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(752(a,1),3618(a,2,1,2))].">
      <j1 rule="para" parents="752 3618"/>
    </justification>
  </clause>

  <clause id="3620">
    <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(1886(a,1),3618(a,1,2))].">
      <j1 rule="para" parents="1886 3618"/>
    </justification>
  </clause>

  <clause id="3621">
    <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(1319(a,1),3619(a,1,2))].">
      <j1 rule="para" parents="1319 3619"/>
    </justification>
  </clause>

  <clause id="3622">
    <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),3621(a,2,1,2))].">
      <j1 rule="para" parents="198 3621"/>
    </justification>
  </clause>

  <clause id="3623">
    <literal><![CDATA[
      R(x,y,z) * ((1 / x) * (R(x,y,z) \ x)) = R(K(x,x \ 1),y,z)
    ]]></literal>
    <justification jstring="[para(1794(a,2),3622(a,2,1))].">
      <j1 rule="para" parents="1794 3622"/>
    </justification>
  </clause>

  <clause id="3624">
    <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),3620(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3 3620"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3625">
    <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(3172(a,1),3624(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3172 3624"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3626">
    <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(3170(a,1),3625(a,2,1))].">
      <j1 rule="para" parents="3170 3625"/>
    </justification>
  </clause>

  <clause id="3627">
    <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,3275,a(flip),b,3626,a),flip(a)].">
      <j1 rule="hyper" parents="320 3275 3626"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3628">
    <literal><![CDATA[
      (R(x,y,z) / x) \ (1 / x) = 1 / R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(29,a,1794,a(flip),b,3627,a),flip(a)].">
      <j1 rule="hyper" parents="29 1794 3627"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3629">
    <literal><![CDATA[
      R(1 / (1 / x),y,z) \ 1 = 1 / R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,3614,a,b,3628,a)].">
      <j1 rule="hyper" parents="58 3614 3628"/>
    </justification>
  </clause>

  <clause id="3630">
    <literal><![CDATA[
      R(1 / (1 / x),y,z) = 1 / (1 / R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(197,a,3629,a),flip(a)].">
      <j1 rule="hyper" parents="197 3629"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3631">
    <literal><![CDATA[
      (R(1 / (1 / x),y,z) \ 1) \ 1 = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(188,a,3629,a(flip))].">
      <j1 rule="hyper" parents="188 3629"/>
    </justification>
  </clause>

  <clause id="3632">
    <literal><![CDATA[
      R(T(1 / (1 / x),y),z,u) \ 1 = 1 / R(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(2166(a,1),3629(a,1,1,1))].">
      <j1 rule="para" parents="2166 3629"/>
    </justification>
  </clause>

  <clause id="3633">
    <literal><![CDATA[
      1 / (1 / R(x \ 1,y,z)) = R(1 / x,y,z)
    ]]></literal>
    <justification jstring="[para(72(a,1),3630(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="72 3630"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3634">
    <literal><![CDATA[
      (R(1 / x,y,z) \ 1) \ 1 = R(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(72(a,1),3631(a,1,1,1,1,2))].">
      <j1 rule="para" parents="72 3631"/>
    </justification>
  </clause>

  <clause id="3635">
    <literal><![CDATA[
      R((x \ 1) \ 1,y,z) = (R(x,y,z) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(190(a,1),3631(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="190 3631"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3636">
    <literal><![CDATA[
      T(x,R(1 / y,z,u)) = T(x,R(y \ 1,z,u))
    ]]></literal>
    <justification jstring="[para(3633(a,1),2960(a,1,2))].">
      <j1 rule="para" parents="3633 2960"/>
    </justification>
  </clause>

  <clause id="3637">
    <literal><![CDATA[
      T(x,R(x,y,z) \ 1) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(702,a,3635,a)].">
      <j1 rule="hyper" parents="702 3635"/>
    </justification>
  </clause>

  <clause id="3638">
    <literal><![CDATA[
      R(((x / y) \ 1) \ 1,y,y \ 1) = ((x * (y \ 1)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(523(a,1),3635(a,2,1,1))].">
      <j1 rule="para" parents="523 3635"/>
    </justification>
  </clause>

  <clause id="3639">
    <literal><![CDATA[
      R(((x / y) \ 1) \ 1,y,z) * (y * z) = (y * z) * ((((y * z) \ (x * z)) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(3635(a,2),2174(a,1,1))].">
      <j1 rule="para" parents="3635 2174"/>
    </justification>
  </clause>

  <clause id="3640">
    <literal><![CDATA[
      R(((x / (1 / y)) \ 1) \ 1,y \ 1,y) = ((x * y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(2609(a,1),3635(a,2,1,1))].">
      <j1 rule="para" parents="2609 3635"/>
    </justification>
  </clause>

  <clause id="3641">
    <literal><![CDATA[
      T(x,R((y \ 1) \ 1,z,u)) = T(x,R(y,z,u))
    ]]></literal>
    <justification jstring="[para(3635(a,2),2959(a,1,2))].">
      <j1 rule="para" parents="3635 2959"/>
    </justification>
  </clause>

  <clause id="3642">
    <literal><![CDATA[
      T(x,1 / R(x,y,z)) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(2957,a,3637,a)].">
      <j1 rule="hyper" parents="2957 3637"/>
    </justification>
  </clause>

  <clause id="3643">
    <literal><![CDATA[
      (R(x,y,z) \ 1) * ((x \ 1) \ 1) = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[para(3637(a,1),1318(a,1,2))].">
      <j1 rule="para" parents="3637 1318"/>
    </justification>
  </clause>

  <clause id="3644">
    <literal><![CDATA[
      R(K(x,1 / x),y,z) = ((x \ 1) \ 1) / x
    ]]></literal>
    <justification jstring="[para(3642(a,1),3267(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3642 3267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3645">
    <literal><![CDATA[
      R(K(x,1 / x),y,z) = K(x,1 / x)
    ]]></literal>
    <justification jstring="[hyper(320,a,1269,a(flip),b,3644,a),flip(a)].">
      <j1 rule="hyper" parents="320 1269 3644"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3647">
    <literal><![CDATA[
      K(x,1 / x) * (1 / y) = K(x,1 / x) / y
    ]]></literal>
    <justification jstring="[hyper(117,a,3645,a(flip),b,2605,a),flip(a)].">
      <j1 rule="hyper" parents="117 3645 2605"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3648">
    <literal><![CDATA[
      R(K(x \ 1,x),y,z) = K(x \ 1,1 / (x \ 1))
    ]]></literal>
    <justification jstring="[para(72(a,1),3645(a,1,1,2))].">
      <j1 rule="para" parents="72 3645"/>
    </justification>
  </clause>

  <clause id="3649">
    <literal><![CDATA[
      (K(x,1 / x) * y) * z = K(x,1 / x) * (y * z)
    ]]></literal>
    <justification jstring="[para(3645(a,1),101(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3645 101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3650">
    <literal><![CDATA[
      K(x,1 / x) * (y * z) != u
    ]]></literal>
    <literal><![CDATA[
      (K(x,1 / x) * y) * z = u
    ]]></literal>
    <justification jstring="[para(3645(a,1),283(a,1,1))].">
      <j1 rule="para" parents="3645 283"/>
    </justification>
  </clause>

  <clause id="3651">
    <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(3448(a,1),3636(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3448 3636"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3652">
    <literal><![CDATA[
      R(K(x \ 1,x),y,z) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(72(a,1),3648(a,2,2))].">
      <j1 rule="para" parents="72 3648"/>
    </justification>
  </clause>

  <clause id="3654">
    <literal><![CDATA[
      K(x \ 1,x) * (1 / y) = K(x \ 1,x) / y
    ]]></literal>
    <justification jstring="[hyper(117,a,3652,a(flip),b,2605,a),flip(a)].">
      <j1 rule="hyper" parents="117 3652 2605"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3655">
    <literal><![CDATA[
      R(x,y,z) != K(u \ 1,u)
    ]]></literal>
    <literal><![CDATA[
      K(u \ 1,u) = x
    ]]></literal>
    <justification jstring="[para(3652(a,1),46(a,1)),flip(a)].">
      <j1 rule="para" parents="3652 46"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3656">
    <literal><![CDATA[
      (K(x \ 1,x) * y) * z = K(x \ 1,x) * (y * z)
    ]]></literal>
    <justification jstring="[para(3652(a,1),101(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3652 101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3657">
    <literal><![CDATA[
      (x * K(y \ 1,y)) * z = K(y \ 1,y) * (x * z)
    ]]></literal>
    <justification jstring="[para(3652(a,1),2216(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3652 2216"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3658">
    <literal><![CDATA[
      (1 / x) * K(y \ 1,y) = K(y \ 1,y) / x
    ]]></literal>
    <justification jstring="[hyper(2196,a,3654,a)].">
      <j1 rule="hyper" parents="2196 3654"/>
    </justification>
  </clause>

  <clause id="3659">
    <literal><![CDATA[
      (R(x,y,z) \ 1) \ (R(x,y,z) \ x) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(123,a,3643,a)].">
      <j1 rule="hyper" parents="123 3643"/>
    </justification>
  </clause>

  <clause id="3661">
    <literal><![CDATA[
      L(x,y,K(z,1 / z)) = x
    ]]></literal>
    <justification jstring="[hyper(479,a,3649,a)].">
      <j1 rule="hyper" parents="479 3649"/>
    </justification>
  </clause>

  <clause id="3662">
    <literal><![CDATA[
      K(x,1 / x) * ((x \ y) * z) = ((1 / (1 / x)) \ y) * z
    ]]></literal>
    <justification jstring="[para(2971(a,1),3649(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2971 3649"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3663">
    <literal><![CDATA[
      L(x,y,K(z \ 1,z)) = x
    ]]></literal>
    <justification jstring="[para(72(a,1),3661(a,1,3,2))].">
      <j1 rule="para" parents="72 3661"/>
    </justification>
  </clause>

  <clause id="3664">
    <literal><![CDATA[
      L(x,y,1) = x
    ]]></literal>
    <justification jstring="[para(201(a,1),3661(a,1,3))].">
      <j1 rule="para" parents="201 3661"/>
    </justification>
  </clause>

  <clause id="3665">
    <literal><![CDATA[
      L(x,y,K(z,z \ 1)) = x
    ]]></literal>
    <justification jstring="[para(1791(a,1),3661(a,1,3))].">
      <j1 rule="para" parents="1791 3661"/>
    </justification>
  </clause>

  <clause id="3666">
    <literal><![CDATA[
      L(x,y,1) != z
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(3664(a,1),45(a,2))].">
      <j1 rule="para" parents="3664 45"/>
    </justification>
  </clause>

  <clause id="3667">
    <literal><![CDATA[
      L(x,y,1 / z) = L(x,y,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(3213,a,3663,a),flip(a)].">
      <j1 rule="hyper" parents="3213 3663"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3668">
    <literal><![CDATA[
      ((x \ 1) * y) \ (K(x \ 1,x) * z) = ((1 / x) * y) \ z
    ]]></literal>
    <justification jstring="[hyper(58,a,2850,a(flip),b,3663,a)].">
      <j1 rule="hyper" parents="58 2850 3663"/>
    </justification>
  </clause>

  <clause id="3669">
    <literal><![CDATA[
      (x * K(y,y \ 1)) \ z = x \ (K(y \ 1,y) * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,2710,a(flip),b,3663,a),flip(a)].">
      <j1 rule="hyper" parents="58 2710 3663"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3670">
    <literal><![CDATA[
      x \ R(x,y \ 1,y) = a(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,2295,a(flip),b,3663,a),flip(a)].">
      <j1 rule="hyper" parents="58 2295 3663"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3671">
    <literal><![CDATA[
      (K(x \ 1,x) * y) \ (K(x \ 1,x) * z) = y \ z
    ]]></literal>
    <justification jstring="[hyper(58,a,92,a(flip),b,3663,a)].">
      <j1 rule="hyper" parents="58 92 3663"/>
    </justification>
  </clause>

  <clause id="3672">
    <literal><![CDATA[
      L(x,y,K(z \ 1,z)) != u
    ]]></literal>
    <literal><![CDATA[
      u = x
    ]]></literal>
    <justification jstring="[para(3663(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="3663 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3673">
    <literal><![CDATA[
      L(x,y,K(z \ 1,z)) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(3663(a,1),45(a,2))].">
      <j1 rule="para" parents="3663 45"/>
    </justification>
  </clause>

  <clause id="3674">
    <literal><![CDATA[
      (K(x \ 1,x) * y) / z = K(x \ 1,x) * (y / z)
    ]]></literal>
    <justification jstring="[para(3663(a,1),544(a,1,2))].">
      <j1 rule="para" parents="3663 544"/>
    </justification>
  </clause>

  <clause id="3675">
    <literal><![CDATA[
      L(x,y,K(z \ u,u \ z)) = x
    ]]></literal>
    <justification jstring="[para(2583(a,1),3663(a,1,3))].">
      <j1 rule="para" parents="2583 3663"/>
    </justification>
  </clause>

  <clause id="3677">
    <literal><![CDATA[
      (K(x,x \ 1) * y) * z = K(x,x \ 1) * (y * z)
    ]]></literal>
    <justification jstring="[hyper(1338,a,3665,a),flip(a)].">
      <j1 rule="hyper" parents="1338 3665"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3681">
    <literal><![CDATA[
      R(T(x,y * K(z,z \ 1)),y,K(z,z \ 1)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,2549,a,b,3665,a)].">
      <j1 rule="hyper" parents="58 2549 3665"/>
    </justification>
  </clause>

  <clause id="3682">
    <literal><![CDATA[
      (K(x,x \ 1) * y) \ (K(x,x \ 1) * z) = y \ z
    ]]></literal>
    <justification jstring="[hyper(58,a,92,a(flip),b,3665,a)].">
      <j1 rule="hyper" parents="58 92 3665"/>
    </justification>
  </clause>

  <clause id="3683">
    <literal><![CDATA[
      K(x,x \ 1) * (1 / y) = K(x,x \ 1) / y
    ]]></literal>
    <justification jstring="[para(3665(a,1),422(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3665 422"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3684">
    <literal><![CDATA[
      (K(x,x \ 1) * y) / z = K(x,x \ 1) * (y / z)
    ]]></literal>
    <justification jstring="[para(3665(a,1),544(a,1,2))].">
      <j1 rule="para" parents="3665 544"/>
    </justification>
  </clause>

  <clause id="3685">
    <literal><![CDATA[
      K(x,x \ 1) * ((x \ 1) / y) = (1 / x) / y
    ]]></literal>
    <justification jstring="[para(3665(a,1),1824(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3665 1824"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3686">
    <literal><![CDATA[
      (K(x \ y,y \ x) * z) * u = K(x \ y,y \ x) * (z * u)
    ]]></literal>
    <justification jstring="[hyper(1338,a,3675,a),flip(a)].">
      <j1 rule="hyper" parents="1338 3675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3687">
    <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,2828,a,b,3667,a)].">
      <j1 rule="hyper" parents="58 2828 3667"/>
    </justification>
  </clause>

  <clause id="3688">
    <literal><![CDATA[
      ((1 / x) * y) * L(z,y,x \ 1) = (1 / x) * (y * z)
    ]]></literal>
    <justification jstring="[hyper(119,a,3667,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="119 3667 13"/>
    </justification>
  </clause>

  <clause id="3689">
    <literal><![CDATA[
      L(x,y,(z \ 1) \ 1) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(72(a,1),3667(a,1,3)),flip(a)].">
      <j1 rule="para" parents="72 3667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3690">
    <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(2550(a,2),3672(a,1)),flip(b)].">
      <j1 rule="para" parents="2550 3672"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3691">
    <literal><![CDATA[
      L(x,y,T(T(z,z \ 1),u)) = L(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[para(2162(a,2),3689(a,1,3))].">
      <j1 rule="para" parents="2162 3689"/>
    </justification>
  </clause>

  <clause id="3692">
    <literal><![CDATA[
      ((x \ 1) \ 1) \ L(y,x \ 1,x) = (((x \ 1) \ 1) \ 1) * y
    ]]></literal>
    <justification jstring="[para(3689(a,1),2861(a,1,2))].">
      <j1 rule="para" parents="3689 2861"/>
    </justification>
  </clause>

  <clause id="3693">
    <literal><![CDATA[
      L(x,y,R(1 / z,u,w)) = L(x,y,R(z \ 1,u,w))
    ]]></literal>
    <justification jstring="[para(3634(a,1),3689(a,1,3)),flip(a)].">
      <j1 rule="para" parents="3634 3689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3694">
    <literal><![CDATA[
      a(x,y \ 1,(y \ 1) \ 1) = a(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(2672,a,3670,a)].">
      <j1 rule="hyper" parents="2672 3670"/>
    </justification>
  </clause>

  <clause id="3696">
    <literal><![CDATA[
      K(x,x \ 1) / y != z
    ]]></literal>
    <literal><![CDATA[
      (1 / y) * K(x,x \ 1) = z
    ]]></literal>
    <justification jstring="[para(3683(a,1),2189(a,1))].">
      <j1 rule="para" parents="3683 2189"/>
    </justification>
  </clause>

  <clause id="3698">
    <literal><![CDATA[
      K(x,x \ 1) * ((K(x \ 1,x) * y) * z) = y * z
    ]]></literal>
    <justification jstring="[hyper(2716,a,3656,a(flip))].">
      <j1 rule="hyper" parents="2716 3656"/>
    </justification>
  </clause>

  <clause id="3699">
    <literal><![CDATA[
      ((K(x \ 1,x) * (y * z)) * u) / (z * u) = R(K(x \ 1,x) * y,z,u)
    ]]></literal>
    <justification jstring="[para(3656(a,1),15(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="3656 15"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3700">
    <literal><![CDATA[
      (x * (y * K(z \ 1,z))) * u = K(z \ 1,z) * ((x * y) * u)
    ]]></literal>
    <justification jstring="[para(3402(a,1),3656(a,1,1))].">
      <j1 rule="para" parents="3402 3656"/>
    </justification>
  </clause>

  <clause id="3701">
    <literal><![CDATA[
      K(x \ 1,x) * (y * T((x \ 1) \ 1,z)) = y * T(x,z)
    ]]></literal>
    <justification jstring="[hyper(3113,a,3657,a),flip(a)].">
      <j1 rule="hyper" parents="3113 3657"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3702">
    <literal><![CDATA[
      (x * K(y \ 1,y)) * z = x * (K(y \ 1,y) * z)
    ]]></literal>
    <justification jstring="[hyper(320,a,3444,a(flip),b,3657,a),flip(a)].">
      <j1 rule="hyper" parents="320 3444 3657"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3704">
    <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(3657(a,1),9(a,2,1)),flip(a)].">
      <j1 rule="para" parents="3657 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3705">
    <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(3657(a,1),13(a,2,1)),flip(a)].">
      <j1 rule="para" parents="3657 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3706">
    <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(3657(a,1),13(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="3657 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3707">
    <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(3657(a,1),307(a,1,2))].">
      <j1 rule="para" parents="3657 307"/>
    </justification>
  </clause>

  <clause id="3709">
    <literal><![CDATA[
      (R(x,y,z) \ 1) * ((x \ 1) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) \ x = u
    ]]></literal>
    <justification jstring="[para(3659(a,1),255(a,1,2)),flip(b)].">
      <j1 rule="para" parents="3659 255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3710">
    <literal><![CDATA[
      (x * K(y,y \ 1)) \ z = K(y \ 1,y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(320,a,3450,a(flip),b,3669,a),flip(a)].">
      <j1 rule="hyper" parents="320 3450 3669"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3712">
    <literal><![CDATA[
      (x * K(y,y \ 1)) \ (1 / y) = x \ (y \ 1)
    ]]></literal>
    <justification jstring="[para(1788(a,1),3669(a,2,2))].">
      <j1 rule="para" parents="1788 3669"/>
    </justification>
  </clause>

  <clause id="3713">
    <literal><![CDATA[
      (K(x,x \ 1) * y) \ z = y \ (K(x \ 1,x) * z)
    ]]></literal>
    <justification jstring="[para(2181(a,2),3669(a,1,1))].">
      <j1 rule="para" parents="2181 3669"/>
    </justification>
  </clause>

  <clause id="3714">
    <literal><![CDATA[
      L(1 / x,y,z) \ (1 / x) = L(x \ 1,y,z) \ (x \ 1)
    ]]></literal>
    <justification jstring="[para(3509(a,1),3712(a,1,1))].">
      <j1 rule="para" parents="3509 3712"/>
    </justification>
  </clause>

  <clause id="3715">
    <literal><![CDATA[
      (K(x \ 1,x) * y) \ z = y \ (z * K(x,x \ 1))
    ]]></literal>
    <justification jstring="[para(2694(a,1),3671(a,1,2))].">
      <j1 rule="para" parents="2694 3671"/>
    </justification>
  </clause>

  <clause id="3716">
    <literal><![CDATA[
      (K(x \ 1,x) * y) \ z = y \ (K(x,x \ 1) * z)
    ]]></literal>
    <justification jstring="[para(2697(a,1),3671(a,1,2))].">
      <j1 rule="para" parents="2697 3671"/>
    </justification>
  </clause>

  <clause id="3717">
    <literal><![CDATA[
      (x * (y * K(z \ 1,z))) \ (K(z \ 1,z) * u) = (x * y) \ u
    ]]></literal>
    <justification jstring="[para(3402(a,1),3671(a,1,1))].">
      <j1 rule="para" parents="3402 3671"/>
    </justification>
  </clause>

  <clause id="3718">
    <literal><![CDATA[
      R(K(x,x \ 1),y,z) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(3476,a,3677,a)].">
      <j1 rule="hyper" parents="3476 3677"/>
    </justification>
  </clause>

  <clause id="3719">
    <literal><![CDATA[
      (K(x,x \ 1) * y) * z = y * (K(x,x \ 1) * z)
    ]]></literal>
    <justification jstring="[hyper(320,a,3455,a(flip),b,3677,a),flip(a)].">
      <j1 rule="hyper" parents="320 3455 3677"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3721">
    <literal><![CDATA[
      K(x,x \ 1) * ((y \ x) * z) = (y \ ((x \ 1) \ 1)) * z
    ]]></literal>
    <justification jstring="[para(3436(a,1),3677(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3436 3677"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3722">
    <literal><![CDATA[
      R(x,y,z) * ((1 / x) * (R(x,y,z) \ x)) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,3623,a,b,3718,a)].">
      <j1 rule="hyper" parents="58 3623 3718"/>
    </justification>
  </clause>

  <clause id="3724">
    <literal><![CDATA[
      (x * K(y \ 1,y)) \ z = x \ (K(y,y \ 1) * z)
    ]]></literal>
    <justification jstring="[para(2703(a,1),3682(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2703 3682"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3725">
    <literal><![CDATA[
      (x * K(y,y \ 1)) / z = K(y,y \ 1) * (x / z)
    ]]></literal>
    <justification jstring="[hyper(58,a,2205,a(flip),b,3684,a)].">
      <j1 rule="hyper" parents="58 2205 3684"/>
    </justification>
  </clause>

  <clause id="3726">
    <literal><![CDATA[
      (K(x \ 1,x) * y) \ 1 = y \ K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(415,a,3698,a),flip(a)].">
      <j1 rule="hyper" parents="415 3698"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3727">
    <literal><![CDATA[
      K(x,x \ 1) * ((y \ (1 / (1 / x))) * z) = (y \ x) * z
    ]]></literal>
    <justification jstring="[para(3439(a,1),3698(a,1,2,1))].">
      <j1 rule="para" parents="3439 3698"/>
    </justification>
  </clause>

  <clause id="3728">
    <literal><![CDATA[
      (x * K(y \ 1,y)) \ 1 = x \ K(y,y \ 1)
    ]]></literal>
    <justification jstring="[para(2192(a,1),3726(a,1,1))].">
      <j1 rule="para" parents="2192 3726"/>
    </justification>
  </clause>

  <clause id="3729">
    <literal><![CDATA[
      L(1 / (1 / x),y,z) \ 1 = L(x,y,z) \ K(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(3500(a,1),3728(a,1,1))].">
      <j1 rule="para" parents="3500 3728"/>
    </justification>
  </clause>

  <clause id="3730">
    <literal><![CDATA[
      R(x,K(y \ 1,y),z) = x
    ]]></literal>
    <justification jstring="[hyper(3476,a,3702,a)].">
      <j1 rule="hyper" parents="3476 3702"/>
    </justification>
  </clause>

  <clause id="3732">
    <literal><![CDATA[
      R(x,K(y,y \ 1),z) = x
    ]]></literal>
    <justification jstring="[para(1795(a,1),3730(a,1,2))].">
      <j1 rule="para" parents="1795 3730"/>
    </justification>
  </clause>

  <clause id="3733">
    <literal><![CDATA[
      (x * K(y,y \ 1)) * z = x * (K(y,y \ 1) * z)
    ]]></literal>
    <justification jstring="[para(3732(a,1),101(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3732 101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3734">
    <literal><![CDATA[
      (K(x,x \ 1) * y) \ z = K(x \ 1,x) * (y \ z)
    ]]></literal>
    <justification jstring="[para(2181(a,2),3710(a,1,1))].">
      <j1 rule="para" parents="2181 3710"/>
    </justification>
  </clause>

  <clause id="3735">
    <literal><![CDATA[
      K(x \ 1,x) * ((y * x) \ z) = (y * ((x \ 1) \ 1)) \ z
    ]]></literal>
    <justification jstring="[para(2677(a,1),3710(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2677 3710"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3736">
    <literal><![CDATA[
      K(x \ 1,x) * ((x * y) \ z) = (((x \ 1) \ 1) * y) \ z
    ]]></literal>
    <justification jstring="[para(2832(a,1),3710(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2832 3710"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3737">
    <literal><![CDATA[
      (K(x,x \ 1) * y) \ z = (y \ z) * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,3415,a(flip),b,3713,a),flip(a)].">
      <j1 rule="hyper" parents="320 3415 3713"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3738">
    <literal><![CDATA[
      (K(x \ 1,x) * y) \ z = K(x,x \ 1) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(320,a,3442,a(flip),b,3715,a),flip(a)].">
      <j1 rule="hyper" parents="320 3442 3715"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3739">
    <literal><![CDATA[
      (K(x \ 1,x) * y) \ z = (y \ z) * K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,3398,a(flip),b,3715,a),flip(a)].">
      <j1 rule="hyper" parents="320 3398 3715"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3740">
    <literal><![CDATA[
      (x * (y * K(z \ 1,z))) \ u = (x * y) \ (K(z,z \ 1) * u)
    ]]></literal>
    <justification jstring="[para(3402(a,1),3716(a,1,1))].">
      <j1 rule="para" parents="3402 3716"/>
    </justification>
  </clause>

  <clause id="3741">
    <literal><![CDATA[
      (x * (y * K(z,z \ 1))) * u = (x * y) * (K(z,z \ 1) * u)
    ]]></literal>
    <justification jstring="[para(3441(a,1),3719(a,1,1))].">
      <j1 rule="para" parents="3441 3719"/>
    </justification>
  </clause>

  <clause id="3742">
    <literal><![CDATA[
      (x * K(y \ 1,y)) \ (z * K(y \ 1,y)) = x \ z
    ]]></literal>
    <justification jstring="[para(2703(a,1),3724(a,2,2))].">
      <j1 rule="para" parents="2703 3724"/>
    </justification>
  </clause>

  <clause id="3743">
    <literal><![CDATA[
      x / (y * K(z \ 1,z)) = K(z,z \ 1) * (x / y)
    ]]></literal>
    <justification jstring="[hyper(3416,a,3725,a)].">
      <j1 rule="hyper" parents="3416 3725"/>
    </justification>
  </clause>

  <clause id="3746">
    <literal><![CDATA[
      (((x \ 1) * y) \ z) * K(x \ 1,x) = ((1 / x) * y) \ z
    ]]></literal>
    <justification jstring="[para(2819(a,1),3737(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2819 3737"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3747">
    <literal><![CDATA[
      (x * (K(y,y \ 1) * z)) \ u = ((x * z) \ u) * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[para(3455(a,1),3737(a,1,1))].">
      <j1 rule="para" parents="3455 3737"/>
    </justification>
  </clause>

  <clause id="3748">
    <literal><![CDATA[
      K(x,x \ 1) * ((y * x) \ z) = (y * (1 / (1 / x))) \ z
    ]]></literal>
    <justification jstring="[para(2695(a,1),3738(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2695 3738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3749">
    <literal><![CDATA[
      K(x,x \ 1) * (((x \ 1) \ y) \ z) = ((1 / x) \ y) \ z
    ]]></literal>
    <justification jstring="[para(2842(a,1),3738(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2842 3738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3750">
    <literal><![CDATA[
      (x * (y * K(z \ 1,z))) \ u = K(z,z \ 1) * ((x * y) \ u)
    ]]></literal>
    <justification jstring="[para(3402(a,1),3738(a,1,1))].">
      <j1 rule="para" parents="3402 3738"/>
    </justification>
  </clause>

  <clause id="3751">
    <literal><![CDATA[
      K(x,x \ 1) * (L(1 / x,y,z) \ u) = L(x \ 1,y,z) \ u
    ]]></literal>
    <justification jstring="[para(3503(a,1),3738(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3503 3738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3752">
    <literal><![CDATA[
      (((1 / x) * y) \ z) * K(x,x \ 1) = ((x \ 1) * y) \ z
    ]]></literal>
    <justification jstring="[para(2814(a,1),3739(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2814 3739"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3754">
    <literal><![CDATA[
      x / (K(y \ 1,y) * z) = K(y,y \ 1) * (x / z)
    ]]></literal>
    <justification jstring="[para(2192(a,2),3743(a,1,2))].">
      <j1 rule="para" parents="2192 3743"/>
    </justification>
  </clause>

  <clause id="3755">
    <literal><![CDATA[
      x / (y * (z * K(u \ 1,u))) = K(u,u \ 1) * (x / (y * z))
    ]]></literal>
    <justification jstring="[para(3380(a,1),3743(a,1,2))].">
      <j1 rule="para" parents="3380 3743"/>
    </justification>
  </clause>

  <clause id="3756">
    <literal><![CDATA[
      T(x,y * K(z,z \ 1)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(3422,a,3681,a)].">
      <j1 rule="hyper" parents="3422 3681"/>
    </justification>
  </clause>

  <clause id="3759">
    <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,3636,a(flip),b,3756,a),flip(a)].">
      <j1 rule="hyper" parents="320 3636 3756"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3761">
    <literal><![CDATA[
      T(x,y * K(z \ 1,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(1798(a,1),3756(a,1,2,2))].">
      <j1 rule="para" parents="1798 3756"/>
    </justification>
  </clause>

  <clause id="3762">
    <literal><![CDATA[
      T(x,K(y,y \ 1) * z) = T(x,z)
    ]]></literal>
    <justification jstring="[para(2181(a,2),3756(a,1,2))].">
      <j1 rule="para" parents="2181 3756"/>
    </justification>
  </clause>

  <clause id="3763">
    <literal><![CDATA[
      T(x,L(y,z,u) * (1 / y)) = T(x,y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[para(2254(a,1),3756(a,1,2))].">
      <j1 rule="para" parents="2254 3756"/>
    </justification>
  </clause>

  <clause id="3764">
    <literal><![CDATA[
      T(x,K(y \ 1,y) * z) = T(x,z)
    ]]></literal>
    <justification jstring="[para(2692(a,1),3756(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2692 3756"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3765">
    <literal><![CDATA[
      T(x,y * (1 / z)) = T(x,y * (z \ 1))
    ]]></literal>
    <justification jstring="[para(2691(a,1),3756(a,1,2))].">
      <j1 rule="para" parents="2691 3756"/>
    </justification>
  </clause>

  <clause id="3766">
    <literal><![CDATA[
      T(x,y / (1 / z)) = T(x,y / (z \ 1))
    ]]></literal>
    <justification jstring="[para(2701(a,1),3756(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2701 3756"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3767">
    <literal><![CDATA[
      T(x,T(y,y \ 1) * z) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(2802(a,1),3756(a,1,2))].">
      <j1 rule="para" parents="2802 3756"/>
    </justification>
  </clause>

  <clause id="3768">
    <literal><![CDATA[
      T(x,((y \ 1) \ 1) \ z) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[para(2839(a,1),3756(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2839 3756"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3769">
    <literal><![CDATA[
      T(x,(1 / y) * z) = T(x,(y \ 1) * z)
    ]]></literal>
    <justification jstring="[para(2846(a,1),3756(a,1,2))].">
      <j1 rule="para" parents="2846 3756"/>
    </justification>
  </clause>

  <clause id="3770">
    <literal><![CDATA[
      T(x,(1 / y) \ z) = T(x,(y \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(2948(a,1),3756(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2948 3756"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3771">
    <literal><![CDATA[
      T(x,y * (((y \ z) \ 1) \ 1)) = T(x,z)
    ]]></literal>
    <justification jstring="[para(3038(a,1),3756(a,1,2))].">
      <j1 rule="para" parents="3038 3756"/>
    </justification>
  </clause>

  <clause id="3772">
    <literal><![CDATA[
      T(x,y \ ((z \ 1) \ 1)) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[para(3437(a,1),3756(a,1,2))].">
      <j1 rule="para" parents="3437 3756"/>
    </justification>
  </clause>

  <clause id="3774">
    <literal><![CDATA[
      T(x,(y \ 1) \ K(z,y)) = T(x,y * K(z,y))
    ]]></literal>
    <justification jstring="[para(3028(a,1),3761(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3028 3761"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3775">
    <literal><![CDATA[
      T(x,y \ (1 / z)) = T(x,y \ (z \ 1))
    ]]></literal>
    <justification jstring="[para(3431(a,1),3761(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3431 3761"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3776">
    <literal><![CDATA[
      T(x,(K(y,y \ 1) * z) \ u) = T(x,z \ u)
    ]]></literal>
    <justification jstring="[para(3737(a,2),3761(a,1,2))].">
      <j1 rule="para" parents="3737 3761"/>
    </justification>
  </clause>

  <clause id="3777">
    <literal><![CDATA[
      T(x,y * ((1 / z) * u)) = T(x,y * ((z \ 1) * u))
    ]]></literal>
    <justification jstring="[para(3459(a,1),3762(a,1,2))].">
      <j1 rule="para" parents="3459 3762"/>
    </justification>
  </clause>

  <clause id="3778">
    <literal><![CDATA[
      T(x,L(K(y,y \ 1) * z,u,w)) = T(x,L(z,u,w))
    ]]></literal>
    <justification jstring="[para(3540(a,2),3762(a,1,2))].">
      <j1 rule="para" parents="3540 3762"/>
    </justification>
  </clause>

  <clause id="3779">
    <literal><![CDATA[
      T(x,y \ (z * (1 / u))) = T(x,y \ (z * (u \ 1)))
    ]]></literal>
    <justification jstring="[para(3454(a,1),3764(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3454 3764"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3780">
    <literal><![CDATA[
      T((x \ 1) * y,x \ y) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(58,a,683,a(flip),b,3768,a),flip(a)].">
      <j1 rule="hyper" parents="58 683 3768"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3781">
    <literal><![CDATA[
      T(x,R(y \ 1,y,z) \ u) = T(x,(z / (y * z)) \ u)
    ]]></literal>
    <justification jstring="[para(2073(a,2),3768(a,1,2,1))].">
      <j1 rule="para" parents="2073 3768"/>
    </justification>
  </clause>

  <clause id="3782">
    <literal><![CDATA[
      T(x,(1 / y) * K(z,y \ 1)) = T(x,y \ K(z,y \ 1))
    ]]></literal>
    <justification jstring="[para(2930(a,1),3769(a,2,2))].">
      <j1 rule="para" parents="2930 3769"/>
    </justification>
  </clause>

  <clause id="3783">
    <literal><![CDATA[
      T(x,y \ (L(1 / z,u,w) \ 1)) = T(x,y \ (L(z \ 1,u,w) \ 1))
    ]]></literal>
    <justification jstring="[para(3298(a,1),3772(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="3298 3772"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3784">
    <literal><![CDATA[
      (1 / x) / T(y,y \ (x \ 1)) = y \ (1 / x)
    ]]></literal>
    <justification jstring="[para(3775(a,1),265(a,1,2))].">
      <j1 rule="para" parents="3775 265"/>
    </justification>
  </clause>

  <clause id="3785">
    <literal><![CDATA[
      K((x \ 1) * y,x \ y) = 1
    ]]></literal>
    <justification jstring="[hyper(50,a,3780,a)].">
      <j1 rule="hyper" parents="50 3780"/>
    </justification>
  </clause>

  <clause id="3786">
    <literal><![CDATA[
      T(x,(((y \ 1) \ 1) \ z) \ u) = T(x,(y \ z) \ u)
    ]]></literal>
    <justification jstring="[para(2808(a,1),3776(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2808 3776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3787">
    <literal><![CDATA[
      T(x,L(y * (z * (1 / u)),w,v5)) = T(x,L(y * (z * (u \ 1)),w,v5))
    ]]></literal>
    <justification jstring="[para(3457(a,1),3778(a,1,2,1))].">
      <j1 rule="para" parents="3457 3778"/>
    </justification>
  </clause>

  <clause id="3788">
    <literal><![CDATA[
      1 / R(T(x,(1 / x) * y),1 / x,y) = (((1 / x) * y) \ y) \ 1
    ]]></literal>
    <justification jstring="[para(738(a,1),3632(a,1,1)),flip(a)].">
      <j1 rule="para" parents="738 3632"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3790">
    <literal><![CDATA[
      (x \ T(x,(x \ 1) * y)) * y = y * K(((1 / x) * y) \ y,(x \ 1) * y)
    ]]></literal>
    <justification jstring="[para(3668(a,1),3217(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3668 3217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3791">
    <literal><![CDATA[
      L(1 / x,y,z) \ (1 / x) = x \ (L(1 / x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,3588,a(flip),b,3714,a),flip(a)].">
      <j1 rule="hyper" parents="320 3588 3714"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3792">
    <literal><![CDATA[
      K(x,x \ 1) * ((y \ x) * z) = (y \ T(x,x \ 1)) * z
    ]]></literal>
    <justification jstring="[para(106(a,2),3721(a,2,1,2))].">
      <j1 rule="para" parents="106 3721"/>
    </justification>
  </clause>

  <clause id="3793">
    <literal><![CDATA[
      L((x \ ((y \ 1) \ 1)) * z,y \ 1,y) = y * ((1 / y) * ((x \ y) * z))
    ]]></literal>
    <justification jstring="[para(3721(a,1),2953(a,1,1))].">
      <j1 rule="para" parents="3721 2953"/>
    </justification>
  </clause>

  <clause id="3795">
    <literal><![CDATA[
      x * K(y \ (1 / (1 / x)),y) = (y \ x) * y
    ]]></literal>
    <justification jstring="[hyper(58,a,2968,a(flip),b,3727,a)].">
      <j1 rule="hyper" parents="58 2968 3727"/>
    </justification>
  </clause>

  <clause id="3796">
    <literal><![CDATA[
      L(x,y,z) \ K(x,x \ 1) = 1 / L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(3295,a,3729,a),flip(a)].">
      <j1 rule="hyper" parents="3295 3729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3797">
    <literal><![CDATA[
      K(x,x \ 1) * ((y * x) \ y) = 1 / (1 / ((y * x) \ y))
    ]]></literal>
    <justification jstring="[hyper(320,a,2644,a,b,3748,a),flip(a)].">
      <j1 rule="hyper" parents="320 2644 3748"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3798">
    <literal><![CDATA[
      T(x,K(y,z \ 1) / z) = T(x,z \ K(y,z \ 1))
    ]]></literal>
    <justification jstring="[para(3059(a,1),3782(a,1,2))].">
      <j1 rule="para" parents="3059 3782"/>
    </justification>
  </clause>

  <clause id="3799">
    <literal><![CDATA[
      (x \ 1) * ((y \ T(x,x \ 1)) * z) = (1 / x) * ((y \ x) * z)
    ]]></literal>
    <justification jstring="[hyper(119,a,3792,a(flip),b,2952,a)].">
      <j1 rule="hyper" parents="119 3792 2952"/>
    </justification>
  </clause>

  <clause id="3800">
    <literal><![CDATA[
      (x * y) * (1 / (1 / ((x * y) \ x))) = x * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(119,a,3797,a(flip),b,3442,a)].">
      <j1 rule="hyper" parents="119 3797 3442"/>
    </justification>
  </clause>

  <clause id="3801">
    <literal><![CDATA[
      x * L(x \ 1,((y * x) \ y) \ 1,L(x \ 1,x,y)) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(2565,a,3800,a)].">
      <j1 rule="hyper" parents="2565 3800"/>
    </justification>
  </clause>

  <clause id="3802">
    <literal><![CDATA[
      T(x * y,x \ (1 / y)) = ((x * y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(58,a,2634,a,b,3640,a)].">
      <j1 rule="hyper" parents="58 2634 3640"/>
    </justification>
  </clause>

  <clause id="3803">
    <literal><![CDATA[
      T(x * y,x \ (y \ 1)) = ((x * y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(58,a,3775,a(flip),b,3802,a)].">
      <j1 rule="hyper" parents="58 3775 3802"/>
    </justification>
  </clause>

  <clause id="3804">
    <literal><![CDATA[
      (x * K(y \ z,z \ y)) * u = K(y \ z,z \ y) * (x * u)
    ]]></literal>
    <justification jstring="[para(2401(a,1),3686(a,1,1))].">
      <j1 rule="para" parents="2401 3686"/>
    </justification>
  </clause>

  <clause id="3805">
    <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(2618(a,1),3690(a,1,1,2))].">
      <j1 rule="para" parents="2618 3690"/>
    </justification>
  </clause>

  <clause id="3806">
    <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,3700,a(flip),b,101,a)].">
      <j1 rule="hyper" parents="117 3700 101"/>
    </justification>
  </clause>

  <clause id="3807">
    <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,3741,a(flip),b,80,a)].">
      <j1 rule="hyper" parents="116 3741 80"/>
    </justification>
  </clause>

  <clause id="3808">
    <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(3747(a,1),3599(a,1,1))].">
      <j1 rule="para" parents="3747 3599"/>
    </justification>
  </clause>

  <clause id="3809">
    <literal><![CDATA[
      K(x,x \ 1) * ((y * (z / (x \ 1))) \ u) = (y * (z / (1 / x))) \ u
    ]]></literal>
    <justification jstring="[para(2618(a,1),3750(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="2618 3750"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3810">
    <literal><![CDATA[
      K(x \ 1,x) * (y / (z * (u * K(x \ 1,x)))) = y / (z * u)
    ]]></literal>
    <justification jstring="[hyper(119,a,3755,a,b,2712,a)].">
      <j1 rule="hyper" parents="119 3755 2712"/>
    </justification>
  </clause>

  <clause id="3811">
    <literal><![CDATA[
      (x * K(y \ z,z \ y)) * (x \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ z,z \ y) = u
    ]]></literal>
    <justification jstring="[para(3804(a,2),206(a,1)),flip(b)].">
      <j1 rule="para" parents="3804 206"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3812">
    <literal><![CDATA[
      x / (K(y,y \ 1) * z) = K(y \ 1,y) * (x / z)
    ]]></literal>
    <justification jstring="[para(2703(a,1),3810(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2703 3810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3813">
    <literal><![CDATA[
      x / (K(y,y \ 1) * z) = (x / z) * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,2192,a(flip),b,3812,a),flip(a)].">
      <j1 rule="hyper" parents="320 2192 3812"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3814">
    <literal><![CDATA[
      (x / T(y \ 1,z)) * K(y \ 1,y) = x / T(1 / y,z)
    ]]></literal>
    <justification jstring="[para(3069(a,1),3813(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3069 3813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3815">
    <literal><![CDATA[
      (x / T(y \ 1,z)) \ K(y,y \ 1) = (x / T(1 / y,z)) \ 1
    ]]></literal>
    <justification jstring="[para(3814(a,1),3728(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3814 3728"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3816">
    <literal><![CDATA[
      T(x,y / T(1 / z,u)) = T(x,y / T(z \ 1,u))
    ]]></literal>
    <justification jstring="[para(3814(a,1),3761(a,1,2))].">
      <j1 rule="para" parents="3814 3761"/>
    </justification>
  </clause>

  <clause id="3817">
    <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(3783(a,1),265(a,1,2))].">
      <j1 rule="para" parents="3783 265"/>
    </justification>
  </clause>

  <clause id="3818">
    <literal><![CDATA[
      L(x \ 1,((y * x) \ y) \ 1,L(x \ 1,x,y)) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(29,a,1794,a(flip),b,3801,a),flip(a)].">
      <j1 rule="hyper" parents="29 1794 3801"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3820">
    <literal><![CDATA[
      L(x \ 1,((y * x) \ y) \ 1,(y * x) \ y) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(58,a,2332,a(flip),b,3818,a)].">
      <j1 rule="hyper" parents="58 2332 3818"/>
    </justification>
  </clause>

  <clause id="3821">
    <literal><![CDATA[
      (((x * y) \ x) \ 1) * L(y \ 1,z,u) = ((x * y) \ x) \ L(1 / y,z,u)
    ]]></literal>
    <justification jstring="[para(3820(a,1),548(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3820 548"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3822">
    <literal><![CDATA[
      (K(x \ 1,x) * ((y * z) * u)) / (z * u) = R(K(x \ 1,x) * y,z,u)
    ]]></literal>
    <justification jstring="[para(3656(a,1),3699(a,1,1))].">
      <j1 rule="para" parents="3656 3699"/>
    </justification>
  </clause>

  <clause id="3823">
    <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,3674,a(flip),b,3822,a)].">
      <j1 rule="hyper" parents="58 3674 3822"/>
    </justification>
  </clause>

  <clause id="3824">
    <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),3823(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15 3823"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3825">
    <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,2668,a(flip),b,3824,a),flip(a)].">
      <j1 rule="hyper" parents="320 2668 3824"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3826">
    <literal><![CDATA[
      K(x,x \ 1) * R(K(x \ 1,x) * y,z,u) = R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(2716,a,3824,a(flip))].">
      <j1 rule="hyper" parents="2716 3824"/>
    </justification>
  </clause>

  <clause id="3827">
    <literal><![CDATA[
      R(x * K(y \ 1,y),z,u) = K(y \ 1,y) * R(x,z,u)
    ]]></literal>
    <justification jstring="[para(2192(a,1),3824(a,1,1))].">
      <j1 rule="para" parents="2192 3824"/>
    </justification>
  </clause>

  <clause id="3828">
    <literal><![CDATA[
      K(x,x \ 1) * R(x \ 1,y,z) = R(1 / x,y,z)
    ]]></literal>
    <justification jstring="[para(1788(a,1),3826(a,1,2,1))].">
      <j1 rule="para" parents="1788 3826"/>
    </justification>
  </clause>

  <clause id="3829">
    <literal><![CDATA[
      R(K(x,x \ 1) * y,z,u) = K(x,x \ 1) * R(y,z,u)
    ]]></literal>
    <justification jstring="[para(2697(a,1),3826(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2697 3826"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3830">
    <literal><![CDATA[
      K(x \ 1,x) * (R(x \ 1,y,z) \ u) = R(1 / x,y,z) \ u
    ]]></literal>
    <justification jstring="[para(3828(a,1),3734(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3828 3734"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3831">
    <literal><![CDATA[
      R(x * K(y \ 1,y),z,u) = R(x,z,u) * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,2197,a,b,3827,a),flip(a)].">
      <j1 rule="hyper" parents="320 2197 3827"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3832">
    <literal><![CDATA[
      R(K(x,x \ 1) * y,z,u) = R(y,z,u) * K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,2181,a(flip),b,3829,a),flip(a)].">
      <j1 rule="hyper" parents="320 2181 3829"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3833">
    <literal><![CDATA[
      T(x,R(K(y,y \ 1) * (1 / z),u,w)) = T(x,R(z \ 1,u,w))
    ]]></literal>
    <justification jstring="[para(3832(a,2),3759(a,1,2))].">
      <j1 rule="para" parents="3832 3759"/>
    </justification>
  </clause>

  <clause id="3834">
    <literal><![CDATA[
      T(x,R(K(y,y \ 1) / z,u,w)) = T(x,R(z \ 1,u,w))
    ]]></literal>
    <justification jstring="[para(3683(a,1),3833(a,1,2,1))].">
      <j1 rule="para" parents="3683 3833"/>
    </justification>
  </clause>

  <clause id="3835">
    <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(3728(a,1),3651(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3728 3651"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3836">
    <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,3834,a(flip),b,3835,a),flip(a)].">
      <j1 rule="hyper" parents="58 3834 3835"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3838">
    <literal><![CDATA[
      (x \ T(x,(x \ 1) * y)) * y = y * K(((x \ 1) * y) \ y,(x \ 1) * y)
    ]]></literal>
    <justification jstring="[para(3320(a,1),3790(a,2,2))].">
      <j1 rule="para" parents="3320 3790"/>
    </justification>
  </clause>

  <clause id="3839">
    <literal><![CDATA[
      (((x * y) \ x) \ 1) * L(y \ 1,y,x) = K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,3515,a(flip),b,3821,a),flip(a)].">
      <j1 rule="hyper" parents="320 3515 3821"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3840">
    <literal><![CDATA[
      K(x,x \ 1) / ((y * x) \ y) = ((y * x) \ y) \ 1
    ]]></literal>
    <justification jstring="[hyper(735,a,3839,a)].">
      <j1 rule="hyper" parents="735 3839"/>
    </justification>
  </clause>

  <clause id="3841">
    <literal><![CDATA[
      (1 / ((x * y) \ x)) * K(y,y \ 1) = ((x * y) \ x) \ 1
    ]]></literal>
    <justification jstring="[hyper(3696,a,3840,a)].">
      <j1 rule="hyper" parents="3696 3840"/>
    </justification>
  </clause>

  <clause id="3842">
    <literal><![CDATA[
      (((x * y) \ x) \ 1) / ((y \ 1) \ 1) = (1 / ((x * y) \ x)) / y
    ]]></literal>
    <justification jstring="[hyper(117,a,3841,a(flip),b,2682,a)].">
      <j1 rule="hyper" parents="117 3841 2682"/>
    </justification>
  </clause>

  <clause id="3843">
    <literal><![CDATA[
      (x \ R(x * y,z,u)) * x = R(y * x,z,u)
    ]]></literal>
    <justification jstring="[para(2664(a,1),3825(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2664 3825"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3844">
    <literal><![CDATA[
      (x \ 1) \ R((x \ 1) * y,z,u) = x * R(x \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(30,a,1220,a,b,3843,a),flip(a)].">
      <j1 rule="hyper" parents="30 1220 3843"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3845">
    <literal><![CDATA[
      R((x \ y) * x,z,u) = (x \ R(y,z,u)) * x
    ]]></literal>
    <justification jstring="[para(5(a,1),3843(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 3843"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3846">
    <literal><![CDATA[
      x * (R(y * x,z,u) / x) = R(x * y,z,u)
    ]]></literal>
    <justification jstring="[para(3843(a,1),71(a,1,2,1))].">
      <j1 rule="para" parents="3843 71"/>
    </justification>
  </clause>

  <clause id="3847">
    <literal><![CDATA[
      R((x \ (y / z)) * x,z,z \ 1) = (x \ (y * (z \ 1))) * x
    ]]></literal>
    <justification jstring="[para(523(a,1),3845(a,2,1,2))].">
      <j1 rule="para" parents="523 3845"/>
    </justification>
  </clause>

  <clause id="3848">
    <literal><![CDATA[
      R((x \ (y / (1 / z))) * x,z \ 1,z) = (x \ (y * z)) * x
    ]]></literal>
    <justification jstring="[para(2609(a,1),3845(a,2,1,2))].">
      <j1 rule="para" parents="2609 3845"/>
    </justification>
  </clause>

  <clause id="3849">
    <literal><![CDATA[
      R(x * (y / x),z,u) = x * (R(y,z,u) / x)
    ]]></literal>
    <justification jstring="[para(7(a,1),3846(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="7 3846"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3850">
    <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(3849(a,2),3236(a,1,1))].">
      <j1 rule="para" parents="3849 3236"/>
    </justification>
  </clause>

  <clause id="3851">
    <literal><![CDATA[
      (x \ 1) \ R(x \ 1,y,z) = x * R(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(3(a,1),3844(a,1,2,1))].">
      <j1 rule="para" parents="3 3844"/>
    </justification>
  </clause>

  <clause id="3852">
    <literal><![CDATA[
      (x \ 1) * (x * R(x \ 1,y,z)) = R(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(134,a,3851,a)].">
      <j1 rule="hyper" parents="134 3851"/>
    </justification>
  </clause>

  <clause id="3853">
    <literal><![CDATA[
      ((x \ (y * (z \ 1))) * x) / (z \ 1) = ((x \ (y / z)) * x) * z
    ]]></literal>
    <justification jstring="[hyper(117,a,3847,a(flip),b,261,a)].">
      <j1 rule="hyper" parents="117 3847 261"/>
    </justification>
  </clause>

  <clause id="3854">
    <literal><![CDATA[
      (x \ (x * y)) * x = (x * (y \ T(y,x))) * y
    ]]></literal>
    <justification jstring="[hyper(58,a,3163,a(flip),b,3848,a),flip(a)].">
      <j1 rule="hyper" parents="58 3163 3848"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3855">
    <literal><![CDATA[
      ((x \ (y / (1 / z))) * x) * (1 / z) = ((x \ (y * z)) * x) / z
    ]]></literal>
    <justification jstring="[hyper(117,a,3848,a(flip),b,2605,a),flip(a)].">
      <j1 rule="hyper" parents="117 3848 2605"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3856">
    <literal><![CDATA[
      (x * K(y \ (1 / (1 / x)),y)) * (x \ 1) = ((y \ (1 * x)) * y) / ((1 / x) \ 1)
    ]]></literal>
    <justification jstring="[para(3848(a,1),3238(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3848 3238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3857">
    <literal><![CDATA[
      (x * (y \ T(y,x))) * y = y * x
    ]]></literal>
    <justification jstring="[para(4(a,1),3854(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4 3854"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3858">
    <literal><![CDATA[
      x * (y \ T(y,x)) = (y * x) / y
    ]]></literal>
    <justification jstring="[hyper(131,a,3857,a),flip(a)].">
      <j1 rule="hyper" parents="131 3857"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3859">
    <literal><![CDATA[
      (x \ y) * (x \ T(x,x \ y)) = y / x
    ]]></literal>
    <justification jstring="[hyper(117,a,5,a(flip),b,3857,a),flip(a)].">
      <j1 rule="hyper" parents="117 5 3857"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3860">
    <literal><![CDATA[
      (x \ T(x,y)) * y = (x * y) / x
    ]]></literal>
    <justification jstring="[hyper(2929,a,3858,a)].">
      <j1 rule="hyper" parents="2929 3858"/>
    </justification>
  </clause>

  <clause id="3861">
    <literal><![CDATA[
      x \ ((y * x) / y) = y \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(123,a,3858,a)].">
      <j1 rule="hyper" parents="123 3858"/>
    </justification>
  </clause>

  <clause id="3862">
    <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,822,a(flip),b,3858,a)].">
      <j1 rule="hyper" parents="116 822 3858"/>
    </justification>
  </clause>

  <clause id="3863">
    <literal><![CDATA[
      T(x,y) \ x = y \ T(y,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(116,a,225,a(flip),b,3858,a)].">
      <j1 rule="hyper" parents="116 225 3858"/>
    </justification>
  </clause>

  <clause id="3864">
    <literal><![CDATA[
      (x / y) \ T(x / y,y) = y \ (x / (x / y))
    ]]></literal>
    <justification jstring="[hyper(116,a,153,a(flip),b,3858,a),flip(a)].">
      <j1 rule="hyper" parents="116 153 3858"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3865">
    <literal><![CDATA[
      x * ((y * (x \ 1)) / y) = y \ T(y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(29,a,2935,a,b,3858,a)].">
      <j1 rule="hyper" parents="29 2935 3858"/>
    </justification>
  </clause>

  <clause id="3866">
    <literal><![CDATA[
      ((x * y) / x) / y = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(29,a,2934,a,b,3858,a)].">
      <j1 rule="hyper" parents="29 2934 3858"/>
    </justification>
  </clause>

  <clause id="3867">
    <literal><![CDATA[
      (T(x,y) \ x) * ((x * y) / x) = y
    ]]></literal>
    <justification jstring="[hyper(119,a,3858,a(flip),b,3185,a)].">
      <j1 rule="hyper" parents="119 3858 3185"/>
    </justification>
  </clause>

  <clause id="3868">
    <literal><![CDATA[
      (x * y) \ ((x * y) / x) = L(x \ 1,T(x,y),y)
    ]]></literal>
    <justification jstring="[para(3858(a,1),995(a,1,2))].">
      <j1 rule="para" parents="3858 995"/>
    </justification>
  </clause>

  <clause id="3869">
    <literal><![CDATA[
      ((x * y) / x) * (y \ 1) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[para(3858(a,1),2354(a,1,1))].">
      <j1 rule="para" parents="3858 2354"/>
    </justification>
  </clause>

  <clause id="3870">
    <literal><![CDATA[
      ((x * y) / x) \ y = T(x,y) \ x
    ]]></literal>
    <justification jstring="[para(3858(a,1),3128(a,1,1))].">
      <j1 rule="para" parents="3858 3128"/>
    </justification>
  </clause>

  <clause id="3871">
    <literal><![CDATA[
      R(x \ T(x,y),y,z) \ (((x * y) / x) * z) = y * z
    ]]></literal>
    <justification jstring="[para(3860(a,1),184(a,1,2,1))].">
      <j1 rule="para" parents="3860 184"/>
    </justification>
  </clause>

  <clause id="3872">
    <literal><![CDATA[
      T(x,R(y,y \ 1,x)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(3048,a,3861,a)].">
      <j1 rule="hyper" parents="3048 3861"/>
    </justification>
  </clause>

  <clause id="3873">
    <literal><![CDATA[
      L(x \ T(x,y),y,x) = K(x,(x * y) / x)
    ]]></literal>
    <justification jstring="[para(3861(a,1),491(a,1,1))].">
      <j1 rule="para" parents="3861 491"/>
    </justification>
  </clause>

  <clause id="3874">
    <literal><![CDATA[
      T(x,R(y \ 1,y,x)) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(3088(a,1),3872(a,1,2))].">
      <j1 rule="para" parents="3088 3872"/>
    </justification>
  </clause>

  <clause id="3875">
    <literal><![CDATA[
      T(x,T(y,x)) \ x = y \ T(y,x)
    ]]></literal>
    <justification jstring="[para(3872(a,1),3101(a,1,1))].">
      <j1 rule="para" parents="3872 3101"/>
    </justification>
  </clause>

  <clause id="3876">
    <literal><![CDATA[
      R(T(x,y) \ x,y,z) = (T(y,T(x,y)) * z) / (y * z)
    ]]></literal>
    <justification jstring="[para(3863(a,2),2997(a,1,1))].">
      <j1 rule="para" parents="3863 2997"/>
    </justification>
  </clause>

  <clause id="3877">
    <literal><![CDATA[
      x \ y != (z \ T(z,u)) * u
    ]]></literal>
    <literal><![CDATA[
      x * ((z * u) / z) = y
    ]]></literal>
    <justification jstring="[para(3866(a,1),581(a,2,1))].">
      <j1 rule="para" parents="3866 581"/>
    </justification>
  </clause>

  <clause id="3878">
    <literal><![CDATA[
      R(x \ T(x,y),y,((x * y) / x) \ z) \ z = y * (((x * y) / x) \ z)
    ]]></literal>
    <justification jstring="[para(3866(a,1),504(a,1,1,1))].">
      <j1 rule="para" parents="3866 504"/>
    </justification>
  </clause>

  <clause id="3879">
    <literal><![CDATA[
      L(x,y,y \ 1) \ ((1 / y) * (x * y)) = T(y,(1 / y) * (x * y)) \ y
    ]]></literal>
    <justification jstring="[hyper(3216,a,3867,a)].">
      <j1 rule="hyper" parents="3216 3867"/>
    </justification>
  </clause>

  <clause id="3880">
    <literal><![CDATA[
      T(x,x \ y) \ x = (y / x) \ (x \ y)
    ]]></literal>
    <justification jstring="[para(5(a,1),3870(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5 3870"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3881">
    <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(3870(a,1),1188(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3870 1188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3882">
    <literal><![CDATA[
      ((x * y) / x) * (y \ ((T(x,y) \ x) * z)) = L(z,((x * y) / x) \ y,(x * y) / x)
    ]]></literal>
    <justification jstring="[para(3870(a,1),1458(a,1,2,2,1))].">
      <j1 rule="para" parents="3870 1458"/>
    </justification>
  </clause>

  <clause id="3883">
    <literal><![CDATA[
      (x \ T(x,y)) \ y = T(y,T(x,y))
    ]]></literal>
    <justification jstring="[para(3875(a,1),2881(a,1,1))].">
      <j1 rule="para" parents="3875 2881"/>
    </justification>
  </clause>

  <clause id="3884">
    <literal><![CDATA[
      (x * T(x \ 1,y)) \ y = T(y,T(x \ 1,y))
    ]]></literal>
    <justification jstring="[para(2993(a,1),3883(a,1,1))].">
      <j1 rule="para" parents="2993 3883"/>
    </justification>
  </clause>

  <clause id="3885">
    <literal><![CDATA[
      x * ((x * y) * (y / (x * y))) = T(x * y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,3162,a(flip),b,3874,a)].">
      <j1 rule="hyper" parents="58 3162 3874"/>
    </justification>
  </clause>

  <clause id="3887">
    <literal><![CDATA[
      (x \ y) \ (y / x) = x \ ((x \ y) \ y)
    ]]></literal>
    <justification jstring="[hyper(116,a,3859,a(flip),b,655,a(flip))].">
      <j1 rule="hyper" parents="116 3859 655"/>
    </justification>
  </clause>

  <clause id="3888">
    <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(3869(a,1),482(a,1,1))].">
      <j1 rule="para" parents="3869 482"/>
    </justification>
  </clause>

  <clause id="3889">
    <literal><![CDATA[
      K(x,y) = L(x \ T(x,T(y,x)),T(y,x),x)
    ]]></literal>
    <justification jstring="[para(225(a,1),3873(a,2,2)),flip(a)].">
      <j1 rule="para" parents="225 3873"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3890">
    <literal><![CDATA[
      (x / y) \ (y \ x) = y \ (x / (x / y))
    ]]></literal>
    <justification jstring="[para(107(a,1),3864(a,1,2))].">
      <j1 rule="para" parents="107 3864"/>
    </justification>
  </clause>

  <clause id="3891">
    <literal><![CDATA[
      T(x,x \ y) \ x = x \ (y / (y / x))
    ]]></literal>
    <justification jstring="[hyper(58,a,3880,a,b,3890,a)].">
      <j1 rule="hyper" parents="58 3880 3890"/>
    </justification>
  </clause>

  <clause id="3892">
    <literal><![CDATA[
      x / (x / y) = y * (T(y,y \ x) \ y)
    ]]></literal>
    <justification jstring="[hyper(119,a,3880,a,b,3890,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 3880 3890"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3893">
    <literal><![CDATA[
      (x * y) / ((x * y) / x) = x * (T(x,y) \ x)
    ]]></literal>
    <justification jstring="[para(4(a,1),3892(a,2,2,1,2))].">
      <j1 rule="para" parents="4 3892"/>
    </justification>
  </clause>

  <clause id="3894">
    <literal><![CDATA[
      K(x,(x / y) / x) = x \ T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(1727,a,3865,a)].">
      <j1 rule="hyper" parents="1727 3865"/>
    </justification>
  </clause>

  <clause id="3895">
    <literal><![CDATA[
      (x * ((y \ x) / x)) / (y \ x) = x \ T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,1221,a,b,3865,a)].">
      <j1 rule="hyper" parents="58 1221 3865"/>
    </justification>
  </clause>

  <clause id="3896">
    <literal><![CDATA[
      L(x * ((y * (x \ 1)) / y),z,u) = y \ T(y,L(x,z,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,3254,a(flip),b,3865,a)].">
      <j1 rule="hyper" parents="58 3254 3865"/>
    </justification>
  </clause>

  <clause id="3897">
    <literal><![CDATA[
      x \ (y * ((z * (y \ x)) / z)) = z \ T(z,(x \ y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,1989,a(flip),b,3865,a)].">
      <j1 rule="hyper" parents="58 1989 3865"/>
    </justification>
  </clause>

  <clause id="3898">
    <literal><![CDATA[
      x * K(x,(x / y) / x) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(1912,a,3865,a(flip))].">
      <j1 rule="hyper" parents="1912 3865"/>
    </justification>
  </clause>

  <clause id="3899">
    <literal><![CDATA[
      T(x,x / (x * y)) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(1667,a,3865,a(flip))].">
      <j1 rule="hyper" parents="1667 3865"/>
    </justification>
  </clause>

  <clause id="3900">
    <literal><![CDATA[
      T(x,(y \ x) \ 1) = x * K(x,y / x)
    ]]></literal>
    <justification jstring="[hyper(119,a,1731,a(flip),b,3865,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 1731 3865"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3901">
    <literal><![CDATA[
      x \ T(x,y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,(x / y) / x) = z
    ]]></literal>
    <justification jstring="[para(3865(a,1),1727(a,1))].">
      <j1 rule="para" parents="3865 1727"/>
    </justification>
  </clause>

  <clause id="3902">
    <literal><![CDATA[
      T(x \ T(x,y \ 1),z) = K(x,(x / T(y,z)) / x)
    ]]></literal>
    <justification jstring="[para(3865(a,1),1992(a,1,1))].">
      <j1 rule="para" parents="3865 1992"/>
    </justification>
  </clause>

  <clause id="3903">
    <literal><![CDATA[
      (x * ((y / (z * (x \ y))) / x)) * (z * (x \ y)) = x * ((x \ T(x,z \ 1)) * (x \ y))
    ]]></literal>
    <justification jstring="[para(3865(a,1),2305(a,2,2,1))].">
      <j1 rule="para" parents="3865 2305"/>
    </justification>
  </clause>

  <clause id="3904">
    <literal><![CDATA[
      R(x \ T(x,y \ 1),z,u) = K(x,(x / R(y,z,u)) / x)
    ]]></literal>
    <justification jstring="[para(3865(a,1),3271(a,1,1))].">
      <j1 rule="para" parents="3865 3271"/>
    </justification>
  </clause>

  <clause id="3905">
    <literal><![CDATA[
      (x * ((x / y) / x)) * y = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(2306,a,3899,a)].">
      <j1 rule="hyper" parents="2306 3899"/>
    </justification>
  </clause>

  <clause id="3906">
    <literal><![CDATA[
      T(x * ((x / y) / x),y) = y \ T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(2303,a,3899,a)].">
      <j1 rule="hyper" parents="2303 3899"/>
    </justification>
  </clause>

  <clause id="3909">
    <literal><![CDATA[
      T(x,x / (y * x)) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,3022,a,b,3899,a)].">
      <j1 rule="hyper" parents="58 3022 3899"/>
    </justification>
  </clause>

  <clause id="3910">
    <literal><![CDATA[
      T(x,y \ 1) / y = x * ((x / y) / x)
    ]]></literal>
    <justification jstring="[hyper(117,a,3899,a(flip),b,2301,a)].">
      <j1 rule="hyper" parents="117 3899 2301"/>
    </justification>
  </clause>

  <clause id="3911">
    <literal><![CDATA[
      (x * ((x / y) / x)) \ T(x,y \ 1) = y
    ]]></literal>
    <justification jstring="[hyper(116,a,3899,a(flip),b,2301,a)].">
      <j1 rule="hyper" parents="116 3899 2301"/>
    </justification>
  </clause>

  <clause id="3912">
    <literal><![CDATA[
      x * (y * ((x \ y) / y)) = T(y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(1184,a,3909,a)].">
      <j1 rule="hyper" parents="1184 3909"/>
    </justification>
  </clause>

  <clause id="3913">
    <literal><![CDATA[
      x \ T(y,x \ 1) = y * ((x \ y) / y)
    ]]></literal>
    <justification jstring="[hyper(116,a,3909,a(flip),b,1183,a)].">
      <j1 rule="hyper" parents="116 3909 1183"/>
    </justification>
  </clause>

  <clause id="3914">
    <literal><![CDATA[
      T(x,T(y,y \ x) \ 1) = x * K(x,(y \ x) / x)
    ]]></literal>
    <justification jstring="[para(265(a,1),3898(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="265 3898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3915">
    <literal><![CDATA[
      T(x,y) / (y \ 1) = x * ((x / (y \ 1)) / x)
    ]]></literal>
    <justification jstring="[hyper(117,a,2959,a(flip),b,3905,a)].">
      <j1 rule="hyper" parents="117 2959 3905"/>
    </justification>
  </clause>

  <clause id="3916">
    <literal><![CDATA[
      T(x,(y \ x) \ 1) / (y \ x) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(72(a,1),3910(a,2,2,1))].">
      <j1 rule="para" parents="72 3910"/>
    </justification>
  </clause>

  <clause id="3917">
    <literal><![CDATA[
      T(x,y) / (1 / y) = x * ((x / (1 / y)) / x)
    ]]></literal>
    <justification jstring="[para(75(a,1),3910(a,1,1,2))].">
      <j1 rule="para" parents="75 3910"/>
    </justification>
  </clause>

  <clause id="3918">
    <literal><![CDATA[
      L(((x / y) / x) \ 1,(x / y) / x,x) = (T(x,y \ 1) / y) \ x
    ]]></literal>
    <justification jstring="[para(3910(a,2),217(a,2,1))].">
      <j1 rule="para" parents="3910 217"/>
    </justification>
  </clause>

  <clause id="3919">
    <literal><![CDATA[
      (x \ 1) \ T(y,x) = y * (((x \ 1) \ y) / y)
    ]]></literal>
    <justification jstring="[hyper(116,a,2959,a(flip),b,3912,a)].">
      <j1 rule="hyper" parents="116 2959 3912"/>
    </justification>
  </clause>

  <clause id="3920">
    <literal><![CDATA[
      x * R(1 / y,y,y \ x) = y \ T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,591,a,b,3913,a)].">
      <j1 rule="hyper" parents="320 591 3913"/>
    </justification>
  </clause>

  <clause id="3921">
    <literal><![CDATA[
      (x / y) \ T(x,(x / y) \ 1) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(75(a,1),3913(a,2,2,1))].">
      <j1 rule="para" parents="75 3913"/>
    </justification>
  </clause>

  <clause id="3922">
    <literal><![CDATA[
      R(x,(y \ x) / x,x) = ((y \ T(x,y \ 1)) * x) / (y \ x)
    ]]></literal>
    <justification jstring="[para(3913(a,2),103(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="3913 103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3923">
    <literal><![CDATA[
      x / (y \ ((y * x) / y)) = y * (T(y,x) \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,1177,a(flip),b,3893,a)].">
      <j1 rule="hyper" parents="58 1177 3893"/>
    </justification>
  </clause>

  <clause id="3924">
    <literal><![CDATA[
      x \ (T(x,y) / (1 / y)) = (x / (1 / y)) / x
    ]]></literal>
    <justification jstring="[hyper(116,a,3917,a,b,xx)].">
      <j1 rule="hyper" parents="116 3917"/>
    </justification>
  </clause>

  <clause id="3925">
    <literal><![CDATA[
      (((x / y) \ 1) \ y) * ((x / y) \ 1) = x * (y / x)
    ]]></literal>
    <justification jstring="[hyper(58,a,1021,a(flip),b,3921,a)].">
      <j1 rule="hyper" parents="58 1021 3921"/>
    </justification>
  </clause>

  <clause id="3926">
    <literal><![CDATA[
      (x * (T(x,y) \ x)) \ y = x \ ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(188,a,3923,a)].">
      <j1 rule="hyper" parents="188 3923"/>
    </justification>
  </clause>

  <clause id="3927">
    <literal><![CDATA[
      x * R(1 / (1 / y),1 / y,(1 / y) \ x) = (1 / y) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(75(a,1),3920(a,2,2,2))].">
      <j1 rule="para" parents="75 3920"/>
    </justification>
  </clause>

  <clause id="3928">
    <literal><![CDATA[
      ((x \ 1) \ y) * (x \ 1) = (x * y) * (y / (x * y))
    ]]></literal>
    <justification jstring="[hyper(29,a,948,a,b,3885,a)].">
      <j1 rule="hyper" parents="29 948 3885"/>
    </justification>
  </clause>

  <clause id="3929">
    <literal><![CDATA[
      x \ y != (x * ((z \ x) / x)) / (z \ x)
    ]]></literal>
    <literal><![CDATA[
      T(x,z \ 1) = y
    ]]></literal>
    <justification jstring="[para(3895(a,2),42(a,1)),flip(a)].">
      <j1 rule="para" parents="3895 42"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3930">
    <literal><![CDATA[
      T(x \ T(x,y \ 1),z) = x \ T(x,T(y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,3894,a(flip),b,3902,a),flip(a)].">
      <j1 rule="hyper" parents="320 3894 3902"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3931">
    <literal><![CDATA[
      T(x,T(y,y \ x) \ 1) != x * z
    ]]></literal>
    <literal><![CDATA[
      K(x,(y \ x) / x) = z
    ]]></literal>
    <justification jstring="[para(3914(a,2),38(a,1))].">
      <j1 rule="para" parents="3914 38"/>
    </justification>
  </clause>

  <clause id="3932">
    <literal><![CDATA[
      x \ (y * (x / y)) != z
    ]]></literal>
    <literal><![CDATA[
      K(((y / x) \ 1) \ x,(y / x) \ 1) = z
    ]]></literal>
    <justification jstring="[para(3925(a,1),465(a,1,2))].">
      <j1 rule="para" parents="3925 465"/>
    </justification>
  </clause>

  <clause id="3933">
    <literal><![CDATA[
      ((x \ 1) * y) * (y / ((x \ 1) * y)) = (x \ y) * x
    ]]></literal>
    <justification jstring="[hyper(58,a,2841,a(flip),b,3928,a),flip(a)].">
      <j1 rule="hyper" parents="58 2841 3928"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3934">
    <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(3011(a,1),3930(a,2,2,2,1))].">
      <j1 rule="para" parents="3011 3930"/>
    </justification>
  </clause>

  <clause id="3935">
    <literal><![CDATA[
      ((x \ 1) * y) * R(x,x \ 1,y) = (x \ y) * x
    ]]></literal>
    <justification jstring="[para(215(a,2),3933(a,1,2))].">
      <j1 rule="para" parents="215 3933"/>
    </justification>
  </clause>

  <clause id="3936">
    <literal><![CDATA[
      ((((x \ 1) * y) * x) / ((x \ 1) * y)) * (x \ 1) = ((x \ y) * x) / y
    ]]></literal>
    <justification jstring="[hyper(117,a,3935,a(flip),b,853,a),flip(a)].">
      <j1 rule="hyper" parents="117 3935 853"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3937">
    <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(3876(a,1),930(a,1,1))].">
      <j1 rule="para" parents="3876 930"/>
    </justification>
  </clause>

  <clause id="3938">
    <literal><![CDATA[
      R(x \ T(x,y \ 1),z,u) = x \ T(x,R(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,3894,a(flip),b,3904,a),flip(a)].">
      <j1 rule="hyper" parents="320 3894 3904"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3939">
    <literal><![CDATA[
      x * (T((x \ y) * z,x) / z) = ((x \ (y * z)) * x) / z
    ]]></literal>
    <justification jstring="[hyper(58,a,1391,a(flip),b,3855,a)].">
      <j1 rule="hyper" parents="58 1391 3855"/>
    </justification>
  </clause>

  <clause id="3940">
    <literal><![CDATA[
      L(x \ T(x,y \ 1),z,u) = x \ T(x,L(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(3865(a,1),3896(a,1,1))].">
      <j1 rule="para" parents="3865 3896"/>
    </justification>
  </clause>

  <clause id="3941">
    <literal><![CDATA[
      x * R(1 / (1 / y),y \ 1,(1 / y) \ x) = (1 / y) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(3120(a,1),3927(a,1,2))].">
      <j1 rule="para" parents="3120 3927"/>
    </justification>
  </clause>

  <clause id="3942">
    <literal><![CDATA[
      K(x,((y \ 1) \ x) / x) = ((1 / y) \ x) \ ((1 / y) \ T(x,y))
    ]]></literal>
    <justification jstring="[para(3941(a,1),3574(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3941 3574"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3943">
    <literal><![CDATA[
      K(x \ ((x \ 1) \ y),x) = K(y,((x \ 1) \ y) / y)
    ]]></literal>
    <justification jstring="[hyper(320,a,3575,a(flip),b,3942,a)].">
      <j1 rule="hyper" parents="320 3575 3942"/>
    </justification>
  </clause>

  <clause id="3944">
    <literal><![CDATA[
      ((x \ 1) * y) \ T((x \ 1) * y,x) = ((x \ y) * x) / y
    ]]></literal>
    <justification jstring="[hyper(58,a,3869,a(flip),b,3936,a)].">
      <j1 rule="hyper" parents="58 3869 3936"/>
    </justification>
  </clause>

  <clause id="3945">
    <literal><![CDATA[
      L(K(x \ y,x),y,x \ 1) = ((x \ y) * x) / y
    ]]></literal>
    <justification jstring="[hyper(58,a,1983,a(flip),b,3944,a)].">
      <j1 rule="hyper" parents="58 1983 3944"/>
    </justification>
  </clause>

  <clause id="3946">
    <literal><![CDATA[
      ((x \ (x * y)) * x) / (x * y) = L(K(y,x),x * y,x \ 1)
    ]]></literal>
    <justification jstring="[para(4(a,1),3945(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4 3945"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3947">
    <literal><![CDATA[
      L(K(x,y),y * x,y \ 1) = (x * y) / (y * x)
    ]]></literal>
    <justification jstring="[para(4(a,1),3946(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4 3946"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3948">
    <literal><![CDATA[
      L(K(x,y),y * x,y \ 1) = T(y,(1 / y) * (x * y)) \ y
    ]]></literal>
    <justification jstring="[hyper(58,a,3687,a(flip),b,3879,a)].">
      <j1 rule="hyper" parents="58 3687 3879"/>
    </justification>
  </clause>

  <clause id="3949">
    <literal><![CDATA[
      L(K(x,y),y * x,y \ 1) = T(y,(y \ 1) * (x * y)) \ y
    ]]></literal>
    <justification jstring="[para(2853(a,1),3948(a,2,1))].">
      <j1 rule="para" parents="2853 3948"/>
    </justification>
  </clause>

  <clause id="3950">
    <literal><![CDATA[
      T(x,(x \ 1) * (y * x)) \ x = (y * x) / (x * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,3947,a(flip),b,3949,a),flip(a)].">
      <j1 rule="hyper" parents="58 3947 3949"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3951">
    <literal><![CDATA[
      x \ y != (z * y) / (y * z)
    ]]></literal>
    <literal><![CDATA[
      T(y,(y \ 1) * (z * y)) = x
    ]]></literal>
    <justification jstring="[para(3950(a,1),43(a,1)),flip(a)].">
      <j1 rule="para" parents="3950 43"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3952">
    <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,3838,a)].">
      <j1 rule="hyper" parents="320 302 3838"/>
    </justification>
  </clause>

  <clause id="3953">
    <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),3937(a,2,1))].">
      <j1 rule="para" parents="11 3937"/>
    </justification>
  </clause>

  <clause id="3954">
    <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,3938,a,b,3934,a),flip(a)].">
      <j1 rule="hyper" parents="320 3938 3934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3955">
    <literal><![CDATA[
      T(x \ T(x,(y / (z * y)) \ 1),T(z,u)) = R(x \ T(x,z),z,y)
    ]]></literal>
    <justification jstring="[para(2959(a,1),3954(a,2,1,2))].">
      <j1 rule="para" parents="2959 3954"/>
    </justification>
  </clause>

  <clause id="3956">
    <literal><![CDATA[
      T(x,y / (1 / z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y / (z \ 1)) = u
    ]]></literal>
    <justification jstring="[para(3403(a,1),3805(a,1))].">
      <j1 rule="para" parents="3403 3805"/>
    </justification>
  </clause>

  <clause id="3958">
    <literal><![CDATA[
      (x * K(y \ (1 / (1 / x)),y)) * (x \ 1) = ((y \ x) * y) / ((1 / x) \ 1)
    ]]></literal>
    <justification jstring="[para(2(a,1),3856(a,2,1,1,2))].">
      <j1 rule="para" parents="2 3856"/>
    </justification>
  </clause>

  <clause id="3959">
    <literal><![CDATA[
      (x * K(y \ (1 / (1 / x)),y)) * (x \ 1) = ((y \ x) * y) / x
    ]]></literal>
    <justification jstring="[para(75(a,1),3958(a,2,2))].">
      <j1 rule="para" parents="75 3958"/>
    </justification>
  </clause>

  <clause id="3960">
    <literal><![CDATA[
      ((x \ y) * x) * (y \ 1) = ((x \ y) * x) / y
    ]]></literal>
    <justification jstring="[para(3795(a,1),3959(a,1,1))].">
      <j1 rule="para" parents="3795 3959"/>
    </justification>
  </clause>

  <clause id="3961">
    <literal><![CDATA[
      ((x \ y) * x) / y != ((x \ y) * x) * z
    ]]></literal>
    <literal><![CDATA[
      y \ 1 = z
    ]]></literal>
    <justification jstring="[para(3960(a,1),38(a,1))].">
      <j1 rule="para" parents="3960 38"/>
    </justification>
  </clause>

  <clause id="3962">
    <literal><![CDATA[
      (x * y) * ((((x * y) \ (z * y)) \ 1) \ 1) = ((((z / x) \ 1) \ 1) * x) * y
    ]]></literal>
    <justification jstring="[hyper(283,a,3639,a),flip(a)].">
      <j1 rule="hyper" parents="283 3639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3963">
    <literal><![CDATA[
      (x * y) * ((((x * y) \ (z * y)) \ 1) \ 1) = (x * (((x \ z) \ 1) \ 1)) * y
    ]]></literal>
    <justification jstring="[para(2173(a,1),3962(a,2,1))].">
      <j1 rule="para" parents="2173 3962"/>
    </justification>
  </clause>

  <clause id="3964">
    <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,3073,a(flip),b,3963,a)].">
      <j1 rule="hyper" parents="58 3073 3963"/>
    </justification>
  </clause>

  <clause id="3965">
    <literal><![CDATA[
      ((x * y) / x) * (y \ ((T(x,y) \ x) * z)) = L(z,T(x,y) \ x,(x * y) / x)
    ]]></literal>
    <justification jstring="[para(3870(a,1),3882(a,2,2))].">
      <j1 rule="para" parents="3870 3882"/>
    </justification>
  </clause>

  <clause id="3966">
    <literal><![CDATA[
      R((x \ 1) \ 1,y,z) \ ((x * y) * z) = ((x * y) * ((((x * y) \ y) \ 1) \ 1)) * z
    ]]></literal>
    <justification jstring="[para(3635(a,2),3964(a,1,1))].">
      <j1 rule="para" parents="3635 3964"/>
    </justification>
  </clause>

  <clause id="3967">
    <literal><![CDATA[
      R((x \ 1) \ 1,y,z) \ ((x * y) * z) = (y * K(x \ 1,x)) * z
    ]]></literal>
    <justification jstring="[para(2980(a,1),3966(a,2,1))].">
      <j1 rule="para" parents="2980 3966"/>
    </justification>
  </clause>

  <clause id="3968">
    <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(3638(a,1),3967(a,1,1))].">
      <j1 rule="para" parents="3638 3967"/>
    </justification>
  </clause>

  <clause id="3969">
    <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(3657(a,1),3705(a,1,2))].">
      <j1 rule="para" parents="3657 3705"/>
    </justification>
  </clause>

  <clause id="3970">
    <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,3740,a(flip),b,3706,a)].">
      <j1 rule="hyper" parents="58 3740 3706"/>
    </justification>
  </clause>

  <clause id="3971">
    <literal><![CDATA[
      K(x * K(y \ 1,y),z) = (z * x) \ (x * z)
    ]]></literal>
    <justification jstring="[hyper(3707,a,3717,a)].">
      <j1 rule="hyper" parents="3707 3717"/>
    </justification>
  </clause>

  <clause id="3972">
    <literal><![CDATA[
      K(x * K(y \ 1,y),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,11,a,b,3971,a),flip(a)].">
      <j1 rule="hyper" parents="320 11 3971"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3973">
    <literal><![CDATA[
      K(x * K(y,y \ 1),z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(1795(a,1),3972(a,1,1,2))].">
      <j1 rule="para" parents="1795 3972"/>
    </justification>
  </clause>

  <clause id="3974">
    <literal><![CDATA[
      K(K(x \ 1,x) * y,z) = K(y,z)
    ]]></literal>
    <justification jstring="[para(2192(a,2),3972(a,1,1))].">
      <j1 rule="para" parents="2192 3972"/>
    </justification>
  </clause>

  <clause id="3975">
    <literal><![CDATA[
      K(x * (1 / y),z) = K(x * (y \ 1),z)
    ]]></literal>
    <justification jstring="[para(2604(a,1),3972(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2604 3972"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3976">
    <literal><![CDATA[
      K(x / (1 / y),z) = K(x / (y \ 1),z)
    ]]></literal>
    <justification jstring="[para(2618(a,1),3972(a,1,1))].">
      <j1 rule="para" parents="2618 3972"/>
    </justification>
  </clause>

  <clause id="3977">
    <literal><![CDATA[
      K(x * ((y \ 1) \ 1),z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(2658(a,1),3972(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2658 3972"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3978">
    <literal><![CDATA[
      K(K(x,x \ 1) * y,z) = K(y,z)
    ]]></literal>
    <justification jstring="[para(2706(a,1),3972(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2706 3972"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3979">
    <literal><![CDATA[
      K(x * (1 / (1 / y)),z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(2702(a,1),3972(a,1,1))].">
      <j1 rule="para" parents="2702 3972"/>
    </justification>
  </clause>

  <clause id="3980">
    <literal><![CDATA[
      K(((x \ 1) \ 1) \ y,z) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[para(2837(a,1),3972(a,1,1))].">
      <j1 rule="para" parents="2837 3972"/>
    </justification>
  </clause>

  <clause id="3981">
    <literal><![CDATA[
      K((1 / x) * y,z) = K((x \ 1) * y,z)
    ]]></literal>
    <justification jstring="[para(2847(a,1),3972(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2847 3972"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3982">
    <literal><![CDATA[
      K((1 / x) \ y,z) = K((x \ 1) \ y,z)
    ]]></literal>
    <justification jstring="[para(2949(a,1),3972(a,1,1))].">
      <j1 rule="para" parents="2949 3972"/>
    </justification>
  </clause>

  <clause id="3984">
    <literal><![CDATA[
      K(x \ K(y \ 1,y),z) = K(x \ 1,z)
    ]]></literal>
    <justification jstring="[para(3384(a,1),3972(a,1,1))].">
      <j1 rule="para" parents="3384 3972"/>
    </justification>
  </clause>

  <clause id="3985">
    <literal><![CDATA[
      K(x \ (1 / y),z) = K(x \ (y \ 1),z)
    ]]></literal>
    <justification jstring="[para(3431(a,1),3972(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3431 3972"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3986">
    <literal><![CDATA[
      K(x \ ((y \ 1) \ 1),z) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[para(3432(a,1),3972(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3432 3972"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3987">
    <literal><![CDATA[
      K(x \ ((1 / y) \ z),u) = K(x \ ((y \ 1) \ z),u)
    ]]></literal>
    <justification jstring="[para(3435(a,1),3972(a,1,1))].">
      <j1 rule="para" parents="3435 3972"/>
    </justification>
  </clause>

  <clause id="3988">
    <literal><![CDATA[
      K((K(x,x \ 1) * y) \ z,u) = K(y \ z,u)
    ]]></literal>
    <justification jstring="[para(3737(a,2),3972(a,1,1))].">
      <j1 rule="para" parents="3737 3972"/>
    </justification>
  </clause>

  <clause id="3989">
    <literal><![CDATA[
      K(((1 / x) * y) \ z,u) = K(((x \ 1) * y) \ z,u)
    ]]></literal>
    <justification jstring="[para(3746(a,1),3972(a,1,1))].">
      <j1 rule="para" parents="3746 3972"/>
    </justification>
  </clause>

  <clause id="3990">
    <literal><![CDATA[
      K((x * (K(y,y \ 1) * z)) \ u,w) = K((x * z) \ u,w)
    ]]></literal>
    <justification jstring="[para(3747(a,2),3972(a,1,1))].">
      <j1 rule="para" parents="3747 3972"/>
    </justification>
  </clause>

  <clause id="3991">
    <literal><![CDATA[
      K(x \ (y * K(z,z \ 1)),u) = K(x \ y,u)
    ]]></literal>
    <justification jstring="[para(3398(a,2),3973(a,1,1))].">
      <j1 rule="para" parents="3398 3973"/>
    </justification>
  </clause>

  <clause id="3993">
    <literal><![CDATA[
      K(x \ (y * (1 / z)),u) = K(x \ (y * (z \ 1)),u)
    ]]></literal>
    <justification jstring="[para(3454(a,1),3974(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3454 3974"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3994">
    <literal><![CDATA[
      K((x * ((y \ 1) \ 1)) \ z,u) = K((x * y) \ z,u)
    ]]></literal>
    <justification jstring="[para(3735(a,1),3974(a,1,1))].">
      <j1 rule="para" parents="3735 3974"/>
    </justification>
  </clause>

  <clause id="3996">
    <literal><![CDATA[
      K(T(K(x,x \ 1) * y,x),z) = K(T(y,x),z)
    ]]></literal>
    <justification jstring="[para(2441(a,2),3978(a,1,1))].">
      <j1 rule="para" parents="2441 3978"/>
    </justification>
  </clause>

  <clause id="3997">
    <literal><![CDATA[
      K(L(1 / x,y,z) \ u,w) = K(L(x \ 1,y,z) \ u,w)
    ]]></literal>
    <justification jstring="[para(3751(a,1),3978(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3751 3978"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3998">
    <literal><![CDATA[
      K(x * T((y * z) \ z,y),u) = K(x * ((y * z) \ z),u)
    ]]></literal>
    <justification jstring="[para(2236(a,2),3977(a,1,1,2))].">
      <j1 rule="para" parents="2236 3977"/>
    </justification>
  </clause>

  <clause id="3999">
    <literal><![CDATA[
      K(x * R(1 / y,z,u),w) = K(x * R(y \ 1,z,u),w)
    ]]></literal>
    <justification jstring="[para(3634(a,1),3977(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="3634 3977"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4001">
    <literal><![CDATA[
      K(x \ ((y \ 1) * y),z) = K(x \ 1,z)
    ]]></literal>
    <justification jstring="[para(258(a,1),3984(a,1,1,2))].">
      <j1 rule="para" parents="258 3984"/>
    </justification>
  </clause>

  <clause id="4002">
    <literal><![CDATA[
      K(x \ R(1 / y,z,u),w) = K(x \ R(y \ 1,z,u),w)
    ]]></literal>
    <justification jstring="[para(3634(a,1),3986(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="3634 3986"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4003">
    <literal><![CDATA[
      K((((x \ 1) \ 1) \ y) \ z,u) = K((x \ y) \ z,u)
    ]]></literal>
    <justification jstring="[para(2808(a,1),3988(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="2808 3988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4004">
    <literal><![CDATA[
      K(((1 / x) / y) \ z,u) = K(((x \ 1) / y) \ z,u)
    ]]></literal>
    <justification jstring="[para(3685(a,1),3988(a,1,1,1))].">
      <j1 rule="para" parents="3685 3988"/>
    </justification>
  </clause>

  <clause id="4005">
    <literal><![CDATA[
      K((((1 / x) \ y) \ z) \ u,w) = K((((x \ 1) \ y) \ z) \ u,w)
    ]]></literal>
    <justification jstring="[para(3749(a,1),3988(a,1,1,1))].">
      <j1 rule="para" parents="3749 3988"/>
    </justification>
  </clause>

  <clause id="4006">
    <literal><![CDATA[
      K(x \ (y * (((y \ z) \ 1) \ 1)),u) = K(x \ z,u)
    ]]></literal>
    <justification jstring="[para(3038(a,1),3991(a,1,1,2))].">
      <j1 rule="para" parents="3038 3991"/>
    </justification>
  </clause>

  <clause id="4007">
    <literal><![CDATA[
      K(T((1 / x) * y,x),z) = K(T((x \ 1) * y,x),z)
    ]]></literal>
    <justification jstring="[para(2819(a,1),3996(a,1,1,1))].">
      <j1 rule="para" parents="2819 3996"/>
    </justification>
  </clause>

  <clause id="4008">
    <literal><![CDATA[
      K(((x \ 1) * (x * y)) \ z,u) = K(L(y,x,x \ 1) \ z,u)
    ]]></literal>
    <justification jstring="[para(2820(a,1),3989(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="2820 3989"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4009">
    <literal><![CDATA[
      K((x * ((1 / y) / z)) \ u,w) = K((x * ((y \ 1) / z)) \ u,w)
    ]]></literal>
    <justification jstring="[para(3685(a,1),3990(a,1,1,1,2))].">
      <j1 rule="para" parents="3685 3990"/>
    </justification>
  </clause>

  <clause id="4010">
    <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(3657(a,1),3806(a,1,2))].">
      <j1 rule="para" parents="3657 3806"/>
    </justification>
  </clause>

  <clause id="4011">
    <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(833,a,3969,a)].">
      <j1 rule="hyper" parents="833 3969"/>
    </justification>
  </clause>

  <clause id="4012">
    <literal><![CDATA[
      L(x,y,z * K(u \ 1,u)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(3673,a,4011,a),flip(a)].">
      <j1 rule="hyper" parents="3673 4011"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4014">
    <literal><![CDATA[
      L(x,y,z * K(u,u \ 1)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(1795(a,1),4012(a,1,3,2))].">
      <j1 rule="para" parents="1795 4012"/>
    </justification>
  </clause>

  <clause id="4015">
    <literal><![CDATA[
      L(x,y,((z \ 1) \ 1) * u) = L(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(2832(a,1),4014(a,1,3))].">
      <j1 rule="para" parents="2832 4014"/>
    </justification>
  </clause>

  <clause id="4016">
    <literal><![CDATA[
      L(x,y * K(z \ 1,z),u) = (u * y) \ (u * (y * x))
    ]]></literal>
    <justification jstring="[para(3446(a,1),3970(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3446 3970"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4017">
    <literal><![CDATA[
      L(x,y * K(z \ 1,z),u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(320,a,13,a,b,4016,a),flip(a)].">
      <j1 rule="hyper" parents="320 13 4016"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4019">
    <literal><![CDATA[
      L(x,1 / y,z) = L(x,y \ 1,z)
    ]]></literal>
    <justification jstring="[para(778(a,1),4017(a,1,2)),flip(a)].">
      <j1 rule="para" parents="778 4017"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4020">
    <literal><![CDATA[
      L(x,(y \ 1) \ 1,z) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(1258(a,1),4017(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1258 4017"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4021">
    <literal><![CDATA[
      L(x,1 / (1 / y),z) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(1790(a,1),4017(a,1,2))].">
      <j1 rule="para" parents="1790 4017"/>
    </justification>
  </clause>

  <clause id="4022">
    <literal><![CDATA[
      L(x,K(y \ 1,y) * z,u) = L(x,z,u)
    ]]></literal>
    <justification jstring="[para(2192(a,2),4017(a,1,2))].">
      <j1 rule="para" parents="2192 4017"/>
    </justification>
  </clause>

  <clause id="4023">
    <literal><![CDATA[
      L(x,y * (1 / z),u) = L(x,y * (z \ 1),u)
    ]]></literal>
    <justification jstring="[para(2604(a,1),4017(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2604 4017"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4024">
    <literal><![CDATA[
      L(x,y / T(1 / z,u),w) = L(x,y / T(z \ 1,u),w)
    ]]></literal>
    <justification jstring="[para(3814(a,1),4017(a,1,2))].">
      <j1 rule="para" parents="3814 4017"/>
    </justification>
  </clause>

  <clause id="4027">
    <literal><![CDATA[
      (x * (1 / (1 / y))) * L(z,y,x) = x * ((1 / (1 / y)) * z)
    ]]></literal>
    <justification jstring="[hyper(119,a,4021,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="119 4021 13"/>
    </justification>
  </clause>

  <clause id="4028">
    <literal><![CDATA[
      (x * (1 / (1 / y))) * z != x * ((1 / (1 / y)) * u)
    ]]></literal>
    <literal><![CDATA[
      L(u,y,x) = z
    ]]></literal>
    <justification jstring="[para(4027(a,1),38(a,1)),flip(a)].">
      <j1 rule="para" parents="4027 38"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4029">
    <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,3754,a(flip),b,4010,a)].">
      <j1 rule="hyper" parents="58 3754 4010"/>
    </justification>
  </clause>

  <clause id="4030">
    <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(3822(a,1),4029(a,1,2))].">
      <j1 rule="para" parents="3822 4029"/>
    </justification>
  </clause>

  <clause id="4031">
    <literal><![CDATA[
      R(x,y * K(z \ 1,z),u) = R(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,3826,a(flip),b,4030,a),flip(a)].">
      <j1 rule="hyper" parents="58 3826 4030"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4033">
    <literal><![CDATA[
      R(x,1 / y,z) = R(x,y \ 1,z)
    ]]></literal>
    <justification jstring="[para(778(a,1),4031(a,1,2)),flip(a)].">
      <j1 rule="para" parents="778 4031"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4034">
    <literal><![CDATA[
      R(x,(y \ 1) \ 1,z) = R(x,y,z)
    ]]></literal>
    <justification jstring="[para(1258(a,1),4031(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1258 4031"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4036">
    <literal><![CDATA[
      1 / R(T(x,(1 / x) * y),x \ 1,y) = (((1 / x) * y) \ y) \ 1
    ]]></literal>
    <justification jstring="[para(4033(a,1),3788(a,1,2))].">
      <j1 rule="para" parents="4033 3788"/>
    </justification>
  </clause>

  <clause id="4037">
    <literal><![CDATA[
      R(x,y,z) * (((y \ 1) \ 1) * z) = (x * ((y \ 1) \ 1)) * z
    ]]></literal>
    <justification jstring="[para(4034(a,1),101(a,1,1))].">
      <j1 rule="para" parents="4034 101"/>
    </justification>
  </clause>

  <clause id="4038">
    <literal><![CDATA[
      (x * ((y \ 1) \ 1)) * z != u * (((y \ 1) \ 1) * z)
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(4037(a,1),39(a,1))].">
      <j1 rule="para" parents="4037 39"/>
    </justification>
  </clause>

  <clause id="4039">
    <literal><![CDATA[
      1 / R(T(x,(x \ 1) * y),x \ 1,y) = (((1 / x) * y) \ y) \ 1
    ]]></literal>
    <justification jstring="[para(2853(a,1),4036(a,1,2,1))].">
      <j1 rule="para" parents="2853 4036"/>
    </justification>
  </clause>

  <clause id="4040">
    <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(3657(a,1),3704(a,1,2,1))].">
      <j1 rule="para" parents="3657 3704"/>
    </justification>
  </clause>

  <clause id="4041">
    <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(3733(a,1),3807(a,1,1,2))].">
      <j1 rule="para" parents="3733 3807"/>
    </justification>
  </clause>

  <clause id="4042">
    <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),3808(a,1,1,1))].">
      <j1 rule="para" parents="9 3808"/>
    </justification>
  </clause>

  <clause id="4043">
    <literal><![CDATA[
      a(x,y,K(z,z \ 1) * u) = a(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(2720,a,4042,a),flip(a)].">
      <j1 rule="hyper" parents="2720 4042"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4044">
    <literal><![CDATA[
      a(x,y,K(z,z \ 1) * u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,u) = w
    ]]></literal>
    <justification jstring="[para(4042(a,1),2720(a,1))].">
      <j1 rule="para" parents="4042 2720"/>
    </justification>
  </clause>

  <clause id="4046">
    <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,3478,a,b,4043,a)].">
      <j1 rule="hyper" parents="58 3478 4043"/>
    </justification>
  </clause>

  <clause id="4048">
    <literal><![CDATA[
      a(x,y,1 / z) = a(x,y,z \ 1)
    ]]></literal>
    <justification jstring="[para(1820(a,1),4043(a,1,3))].">
      <j1 rule="para" parents="1820 4043"/>
    </justification>
  </clause>

  <clause id="4049">
    <literal><![CDATA[
      a(x,y,K(z \ 1,z) * u) = a(x,y,u)
    ]]></literal>
    <justification jstring="[para(1798(a,1),4043(a,1,3,1))].">
      <j1 rule="para" parents="1798 4043"/>
    </justification>
  </clause>

  <clause id="4050">
    <literal><![CDATA[
      a(x,y,L(z,z \ 1,u)) = a(x,y,(u * (z \ 1)) \ u)
    ]]></literal>
    <justification jstring="[para(3508(a,1),4049(a,1,3))].">
      <j1 rule="para" parents="3508 4049"/>
    </justification>
  </clause>

  <clause id="4052">
    <literal><![CDATA[
      ((x * (y * (z * K(u,u \ 1)))) \ ((x * y) * z)) * K(u,u \ 1) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(2181(a,1),4046(a,1,1,1,2,2))].">
      <j1 rule="para" parents="2181 4046"/>
    </justification>
  </clause>

  <clause id="4053">
    <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(3656(a,1),4040(a,1,2))].">
      <j1 rule="para" parents="3656 4040"/>
    </justification>
  </clause>

  <clause id="4054">
    <literal><![CDATA[
      a(x,y * K(z,z \ 1),u) = a(x,y,K(z,z \ 1) * u)
    ]]></literal>
    <justification jstring="[hyper(691,a,4041,a),flip(a)].">
      <j1 rule="hyper" parents="691 4041"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4055">
    <literal><![CDATA[
      a(x,y * K(z,z \ 1),u) = a(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(320,a,4043,a(flip),b,4054,a),flip(a)].">
      <j1 rule="hyper" parents="320 4043 4054"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4056">
    <literal><![CDATA[
      a(x,y * K(z,z \ 1),u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,u) = w
    ]]></literal>
    <justification jstring="[para(4054(a,2),4044(a,1))].">
      <j1 rule="para" parents="4054 4044"/>
    </justification>
  </clause>

  <clause id="4058">
    <literal><![CDATA[
      a(x,1 / y,z) = a(x,y \ 1,z)
    ]]></literal>
    <justification jstring="[para(1796(a,1),4055(a,1,2))].">
      <j1 rule="para" parents="1796 4055"/>
    </justification>
  </clause>

  <clause id="4059">
    <literal><![CDATA[
      a(x,(y \ 1) \ 1,z) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(1833(a,1),4056(a,1,2))].">
      <j1 rule="para" parents="1833 4056"/>
    </justification>
  </clause>

  <clause id="4060">
    <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(835,a,4053,a)].">
      <j1 rule="hyper" parents="835 4053"/>
    </justification>
  </clause>

  <clause id="4061">
    <literal><![CDATA[
      a(x * K(y \ 1,y),z,u) = a(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(3673,a,4060,a),flip(a)].">
      <j1 rule="hyper" parents="3673 4060"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4063">
    <literal><![CDATA[
      a(1 / x,y,z) = a(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(778(a,1),4061(a,1,1)),flip(a)].">
      <j1 rule="para" parents="778 4061"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4064">
    <literal><![CDATA[
      a((x \ 1) \ 1,y,z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(1258(a,1),4061(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1258 4061"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4065">
    <literal><![CDATA[
      a((1 / x) \ y,z,u) = a((x \ 1) \ y,z,u)
    ]]></literal>
    <justification jstring="[para(2949(a,1),4061(a,1,1))].">
      <j1 rule="para" parents="2949 4061"/>
    </justification>
  </clause>

  <clause id="4066">
    <literal><![CDATA[
      L(x,y,y \ 1) \ x = a(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,2827,a,b,4063,a)].">
      <j1 rule="hyper" parents="58 2827 4063"/>
    </justification>
  </clause>

  <clause id="4067">
    <literal><![CDATA[
      L(x,y,y \ 1) * a(y \ 1,y,x) = x
    ]]></literal>
    <justification jstring="[hyper(119,a,4063,a(flip),b,2827,a)].">
      <j1 rule="hyper" parents="119 4063 2827"/>
    </justification>
  </clause>

  <clause id="4068">
    <literal><![CDATA[
      L(x,y,y \ 1) \ 1 = x \ a(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,4066,a(flip),b,1413,a),flip(a)].">
      <j1 rule="hyper" parents="116 4066 1413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4069">
    <literal><![CDATA[
      L(x,y,y \ 1) \ x != z
    ]]></literal>
    <literal><![CDATA[
      a(y \ 1,y,x) = z
    ]]></literal>
    <justification jstring="[para(4067(a,1),287(a,1,2)),flip(b)].">
      <j1 rule="para" parents="4067 287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4070">
    <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(4067(a,1),90(a,1,1))].">
      <j1 rule="para" parents="4067 90"/>
    </justification>
  </clause>

  <clause id="4071">
    <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,1408,a,b,4070,a)].">
      <j1 rule="hyper" parents="29 1408 4070"/>
    </justification>
  </clause>

  <clause id="4072">
    <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),4071(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5 4071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4073">
    <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(2336(a,1),3881(a,1,1))].">
      <j1 rule="para" parents="2336 3881"/>
    </justification>
  </clause>

  <clause id="4074">
    <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),4073(a,1,1,1,2))].">
      <j1 rule="para" parents="105 4073"/>
    </justification>
  </clause>

  <clause id="4075">
    <literal><![CDATA[
      ((x * ((y \ T(z,x)) * y)) / x) * (T(x,y) \ x) = (y \ (z * (T(x,y) \ x))) * y
    ]]></literal>
    <justification jstring="[para(3870(a,1),4074(a,1,2))].">
      <j1 rule="para" parents="3870 4074"/>
    </justification>
  </clause>

  <clause id="4076">
    <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),3968(a,1,2,1))].">
      <j1 rule="para" parents="7 3968"/>
    </justification>
  </clause>

  <clause id="4077">
    <literal><![CDATA[
      (x * K((y / x) \ 1,y / x)) * (x \ 1) = K((y * (x \ 1)) \ 1,y * (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(1259,a,4076,a),flip(a)].">
      <j1 rule="hyper" parents="1259 4076"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4079">
    <literal><![CDATA[
      (x * ((y / (z * (u \ y))) / x)) * (z * (u \ y)) = ((x * ((u / z) / x)) * z) * (u \ y)
    ]]></literal>
    <justification jstring="[hyper(283,a,3850,a),flip(a)].">
      <j1 rule="hyper" parents="283 3850"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4080">
    <literal><![CDATA[
      ((x * ((x / y) / x)) * y) * (x \ z) = x * ((x \ T(x,y \ 1)) * (x \ z))
    ]]></literal>
    <justification jstring="[hyper(58,a,3903,a(flip),b,4079,a),flip(a)].">
      <j1 rule="hyper" parents="58 3903 4079"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4081">
    <literal><![CDATA[
      x * ((x \ T(x,y \ 1)) * (x \ z)) = T(x,y \ 1) * (x \ z)
    ]]></literal>
    <justification jstring="[para(3905(a,1),4080(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3905 4080"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4082">
    <literal><![CDATA[
      T(x,(y \ 1) \ 1) * (x \ z) = x * ((x \ T(x,y)) * (x \ z))
    ]]></literal>
    <justification jstring="[para(2959(a,1),4081(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="2959 4081"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4083">
    <literal><![CDATA[
      x * ((x \ T(x,y)) * (x \ z)) = T(x,y) * (x \ z)
    ]]></literal>
    <justification jstring="[para(2959(a,1),4082(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2959 4082"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4084">
    <literal><![CDATA[
      T(x,y) * (x \ (x * z)) = x * ((x \ T(x,y)) * z)
    ]]></literal>
    <justification jstring="[para(4(a,1),4083(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 4083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4085">
    <literal><![CDATA[
      (T(x,y) * z) / ((x \ T(x,y)) * z) = x
    ]]></literal>
    <justification jstring="[hyper(617,a,4084,a)].">
      <j1 rule="hyper" parents="617 4084"/>
    </justification>
  </clause>

  <clause id="4086">
    <literal><![CDATA[
      x \ (T(x,y) * z) = (x \ T(x,y)) * z
    ]]></literal>
    <justification jstring="[hyper(615,a,4084,a)].">
      <j1 rule="hyper" parents="615 4084"/>
    </justification>
  </clause>

  <clause id="4087">
    <literal><![CDATA[
      x * ((x \ T(x,y)) * z) = T(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(585,a,4084,a),flip(a)].">
      <j1 rule="hyper" parents="585 4084"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4088">
    <literal><![CDATA[
      (x \ T(x,y)) * z = T(x,y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(1133,a,4085,a),flip(a)].">
      <j1 rule="hyper" parents="1133 4085"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4089">
    <literal><![CDATA[
      R(x,x \ T(x,y),z) = x
    ]]></literal>
    <justification jstring="[hyper(763,a,4085,a)].">
      <j1 rule="hyper" parents="763 4085"/>
    </justification>
  </clause>

  <clause id="4090">
    <literal><![CDATA[
      R(x,T(y,x) \ y,z) = x
    ]]></literal>
    <justification jstring="[para(3863(a,2),4089(a,1,2))].">
      <j1 rule="para" parents="3863 4089"/>
    </justification>
  </clause>

  <clause id="4091">
    <literal><![CDATA[
      R(x,K(y,x) \ 1,z) = x
    ]]></literal>
    <justification jstring="[para(3076(a,1),4090(a,1,2))].">
      <j1 rule="para" parents="3076 4090"/>
    </justification>
  </clause>

  <clause id="4092">
    <literal><![CDATA[
      T(x,y) * y = x * ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(3877,a,4086,a),flip(a)].">
      <j1 rule="hyper" parents="3877 4086"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4094">
    <literal><![CDATA[
      L(x,y \ T(y,z),y) = x
    ]]></literal>
    <justification jstring="[hyper(755,a,4086,a),flip(a)].">
      <j1 rule="hyper" parents="755 4086"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4095">
    <literal><![CDATA[
      (x \ T(x,y)) * z != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) * (x \ z) = u
    ]]></literal>
    <justification jstring="[para(4086(a,1),1135(a,1))].">
      <j1 rule="para" parents="4086 1135"/>
    </justification>
  </clause>

  <clause id="4098">
    <literal><![CDATA[
      (x \ T(x,y)) \ z = x * (T(x,y) \ z)
    ]]></literal>
    <justification jstring="[hyper(116,a,4094,a(flip),b,3175,a)].">
      <j1 rule="hyper" parents="116 4094 3175"/>
    </justification>
  </clause>

  <clause id="4100">
    <literal><![CDATA[
      L(x,T(y,T(z,y)) \ y,z) = x
    ]]></literal>
    <justification jstring="[para(3875(a,2),4094(a,1,2))].">
      <j1 rule="para" parents="3875 4094"/>
    </justification>
  </clause>

  <clause id="4101">
    <literal><![CDATA[
      L(x,T(y,z) \ y,(y * z) / y) = x
    ]]></literal>
    <justification jstring="[para(224(a,1),4100(a,1,2,1,2))].">
      <j1 rule="para" parents="224 4100"/>
    </justification>
  </clause>

  <clause id="4102">
    <literal><![CDATA[
      T(x,y) * (x \ y) = (x * y) / x
    ]]></literal>
    <justification jstring="[hyper(1134,a,4092,a)].">
      <j1 rule="hyper" parents="1134 4092"/>
    </justification>
  </clause>

  <clause id="4103">
    <literal><![CDATA[
      (x * (x * y)) / x = T(x,x * y) * y
    ]]></literal>
    <justification jstring="[hyper(1120,a,4092,a),flip(a)].">
      <j1 rule="hyper" parents="1120 4092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4104">
    <literal><![CDATA[
      T(x,x / (x / y)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(30,a,1559,a,b,4092,a)].">
      <j1 rule="hyper" parents="30 1559 4092"/>
    </justification>
  </clause>

  <clause id="4105">
    <literal><![CDATA[
      T(x,x \ y) * (x \ y) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(5(a,1),4092(a,2,2,1))].">
      <j1 rule="para" parents="5 4092"/>
    </justification>
  </clause>

  <clause id="4106">
    <literal><![CDATA[
      ((T(x,y) * y) / x) \ ((x * (x * y)) / x) = L(x,(x * y) / x,x)
    ]]></literal>
    <justification jstring="[para(4092(a,2),1658(a,1,1,1))].">
      <j1 rule="para" parents="4092 1658"/>
    </justification>
  </clause>

  <clause id="4107">
    <literal><![CDATA[
      T(x,y) = ((x * y) / x) / (x \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,1562,a,b,4104,a),flip(a)].">
      <j1 rule="hyper" parents="58 1562 4104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4108">
    <literal><![CDATA[
      T(x,x / (1 / y)) = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,1564,a(flip),b,4104,a)].">
      <j1 rule="hyper" parents="58 1564 4104"/>
    </justification>
  </clause>

  <clause id="4109">
    <literal><![CDATA[
      (x / T(y,x)) * y = T(x,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(58,a,1178,a(flip),b,4104,a)].">
      <j1 rule="hyper" parents="58 1178 4104"/>
    </justification>
  </clause>

  <clause id="4110">
    <literal><![CDATA[
      T(x,y) / ((x * y) / x) = x / y
    ]]></literal>
    <justification jstring="[hyper(117,a,4104,a(flip),b,1168,a)].">
      <j1 rule="hyper" parents="117 4104 1168"/>
    </justification>
  </clause>

  <clause id="4111">
    <literal><![CDATA[
      (x / y) \ T(x,y) = (x * y) / x
    ]]></literal>
    <justification jstring="[hyper(116,a,4104,a(flip),b,1168,a)].">
      <j1 rule="hyper" parents="116 4104 1168"/>
    </justification>
  </clause>

  <clause id="4112">
    <literal><![CDATA[
      T(x * y,(x * y) / x) = T(x * y,y)
    ]]></literal>
    <justification jstring="[para(6(a,1),4104(a,1,2,2))].">
      <j1 rule="para" parents="6 4104"/>
    </justification>
  </clause>

  <clause id="4113">
    <literal><![CDATA[
      T(x,x / y) = T(x,y \ x)
    ]]></literal>
    <justification jstring="[para(72(a,1),4104(a,1,2,2))].">
      <j1 rule="para" parents="72 4104"/>
    </justification>
  </clause>

  <clause id="4114">
    <literal><![CDATA[
      T(x,(y \ x) \ x) = T(x,y)
    ]]></literal>
    <justification jstring="[para(190(a,1),4104(a,1,2)),flip(a)].">
      <j1 rule="para" parents="190 4104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4115">
    <literal><![CDATA[
      T(x,T(y,x)) * (y * x) = x * (x * y)
    ]]></literal>
    <justification jstring="[para(4104(a,1),1512(a,1,1))].">
      <j1 rule="para" parents="4104 1512"/>
    </justification>
  </clause>

  <clause id="4116">
    <literal><![CDATA[
      T(x,T(y,y \ x)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(106(a,2),4114(a,1,2))].">
      <j1 rule="para" parents="106 4114"/>
    </justification>
  </clause>

  <clause id="4117">
    <literal><![CDATA[
      T(x * y,T(x,y)) = T(x * y,x)
    ]]></literal>
    <justification jstring="[para(4(a,1),4116(a,1,2,2))].">
      <j1 rule="para" parents="4 4116"/>
    </justification>
  </clause>

  <clause id="4118">
    <literal><![CDATA[
      T(x / y,T(y,x)) = y \ x
    ]]></literal>
    <justification jstring="[hyper(239,a,1500,a,b,4102,a)].">
      <j1 rule="hyper" parents="239 1500 4102"/>
    </justification>
  </clause>

  <clause id="4119">
    <literal><![CDATA[
      T(x,T(y,x * y)) = y \ (x * y)
    ]]></literal>
    <justification jstring="[hyper(239,a,821,a(flip),b,4102,a)].">
      <j1 rule="hyper" parents="239 821 4102"/>
    </justification>
  </clause>

  <clause id="4120">
    <literal><![CDATA[
      T(x,y) \ ((x * y) / x) = x \ y
    ]]></literal>
    <justification jstring="[hyper(123,a,4102,a)].">
      <j1 rule="hyper" parents="123 4102"/>
    </justification>
  </clause>

  <clause id="4121">
    <literal><![CDATA[
      ((x * y) / x) \ (T(x,y) * ((x \ y) * z)) = L(z,x \ y,T(x,y))
    ]]></literal>
    <justification jstring="[para(4102(a,1),13(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4102 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4122">
    <literal><![CDATA[
      L((x \ y) \ z,x \ y,T(x,y)) = ((x * y) / x) \ (T(x,y) * z)
    ]]></literal>
    <justification jstring="[para(4102(a,1),92(a,2,1))].">
      <j1 rule="para" parents="4102 92"/>
    </justification>
  </clause>

  <clause id="4123">
    <literal><![CDATA[
      L(((x * y) / x) / y,y,x) = K(T(x,y),y)
    ]]></literal>
    <justification jstring="[para(4102(a,1),2912(a,1,1,1))].">
      <j1 rule="para" parents="4102 2912"/>
    </justification>
  </clause>

  <clause id="4124">
    <literal><![CDATA[
      T(x \ y,T(x,y)) = T(x \ y,x)
    ]]></literal>
    <justification jstring="[para(4118(a,1),246(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4118 246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4125">
    <literal><![CDATA[
      x \ (y * T(y \ x,T(y,x))) = K(y \ x,T(y,x))
    ]]></literal>
    <justification jstring="[para(4118(a,1),1952(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4118 1952"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4126">
    <literal><![CDATA[
      T(x,y) * (x \ y) != z
    ]]></literal>
    <literal><![CDATA[
      (x * y) / x = z
    ]]></literal>
    <justification jstring="[para(4107(a,2),251(a,1,1)),flip(b)].">
      <j1 rule="para" parents="4107 251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4127">
    <literal><![CDATA[
      R(T(x,x * y),y,x) = (x / T(y,x)) * y
    ]]></literal>
    <justification jstring="[para(4108(a,1),1517(a,1,1))].">
      <j1 rule="para" parents="4108 1517"/>
    </justification>
  </clause>

  <clause id="4128">
    <literal><![CDATA[
      T(x / T(y,x),y) = T(y,x) \ x
    ]]></literal>
    <justification jstring="[hyper(239,a,4109,a,b,1136,a)].">
      <j1 rule="hyper" parents="239 4109 1136"/>
    </justification>
  </clause>

  <clause id="4129">
    <literal><![CDATA[
      ((x * y) * y) / (x * y) = x \ T(x * y,y)
    ]]></literal>
    <justification jstring="[hyper(31,a,181,a(flip),b,4110,a),flip(a)].">
      <j1 rule="hyper" parents="31 181 4110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4130">
    <literal><![CDATA[
      T(x,T(y,x * y)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,17,a,b,4119,a),flip(a)].">
      <j1 rule="hyper" parents="320 17 4119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4131">
    <literal><![CDATA[
      T(x,x \ y) \ (y / x) = x \ (x \ y)
    ]]></literal>
    <justification jstring="[para(5(a,1),4120(a,1,2,1))].">
      <j1 rule="para" parents="5 4120"/>
    </justification>
  </clause>

  <clause id="4132">
    <literal><![CDATA[
      T(x,y) * T(x \ y,x) = (x \ y) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,4124,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 4124 17"/>
    </justification>
  </clause>

  <clause id="4133">
    <literal><![CDATA[
      x \ (y * T(y \ x,T(y,x))) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[para(4124(a,2),431(a,1,2,2))].">
      <j1 rule="para" parents="4124 431"/>
    </justification>
  </clause>

  <clause id="4134">
    <literal><![CDATA[
      T(x / T(y,x),z) * y = y * T(T(y,x) \ x,z)
    ]]></literal>
    <justification jstring="[para(4128(a,1),236(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4128 236"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4135">
    <literal><![CDATA[
      x \ ((T(y,x) \ y) * z) = ((y * x) / y) \ z
    ]]></literal>
    <justification jstring="[hyper(116,a,4101,a(flip),b,3965,a),flip(a)].">
      <j1 rule="hyper" parents="116 4101 3965"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4137">
    <literal><![CDATA[
      (x \ T(x,y)) * (x * z) = T(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(29,a,1108,a(flip),b,4087,a),flip(a)].">
      <j1 rule="hyper" parents="29 1108 4087"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4140">
    <literal><![CDATA[
      (T(x,y) * z) / (x * z) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(117,a,152,a(flip),b,4088,a)].">
      <j1 rule="hyper" parents="117 152 4088"/>
    </justification>
  </clause>

  <clause id="4141">
    <literal><![CDATA[
      (x \ T(x,y)) \ (T(x,y) * z) = x * z
    ]]></literal>
    <justification jstring="[hyper(116,a,152,a(flip),b,4088,a)].">
      <j1 rule="hyper" parents="116 152 4088"/>
    </justification>
  </clause>

  <clause id="4142">
    <literal><![CDATA[
      (x \ T(x,y)) \ (T(x,y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      x * z = u
    ]]></literal>
    <justification jstring="[para(4098(a,2),585(a,1))].">
      <j1 rule="para" parents="4098 585"/>
    </justification>
  </clause>

  <clause id="4143">
    <literal><![CDATA[
      (x \ T(x,y)) \ (x \ z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) \ z = u
    ]]></literal>
    <justification jstring="[para(4098(a,2),1143(a,1))].">
      <j1 rule="para" parents="4098 1143"/>
    </justification>
  </clause>

  <clause id="4146">
    <literal><![CDATA[
      (T(x,x * y) * y) * x = x * (x * y)
    ]]></literal>
    <justification jstring="[hyper(133,a,4103,a)].">
      <j1 rule="hyper" parents="133 4103"/>
    </justification>
  </clause>

  <clause id="4147">
    <literal><![CDATA[
      T(T(x,x * y) * y,x) = x * y
    ]]></literal>
    <justification jstring="[para(4103(a,1),224(a,1,1))].">
      <j1 rule="para" parents="4103 224"/>
    </justification>
  </clause>

  <clause id="4148">
    <literal><![CDATA[
      ((x \ y) \ y) * (x \ y) = x * (y / x)
    ]]></literal>
    <justification jstring="[hyper(667,a,4105,a)].">
      <j1 rule="hyper" parents="667 4105"/>
    </justification>
  </clause>

  <clause id="4149">
    <literal><![CDATA[
      T(x,x \ (y \ x)) \ (y \ T(x,y \ 1)) = x \ (y \ x)
    ]]></literal>
    <justification jstring="[hyper(116,a,3913,a,b,4105,a)].">
      <j1 rule="hyper" parents="116 3913 4105"/>
    </justification>
  </clause>

  <clause id="4150">
    <literal><![CDATA[
      (x \ T(x,x \ y)) * y = x * (y / x)
    ]]></literal>
    <justification jstring="[hyper(58,a,4088,a,b,4105,a)].">
      <j1 rule="hyper" parents="58 4088 4105"/>
    </justification>
  </clause>

  <clause id="4151">
    <literal><![CDATA[
      (x * (y / x)) \ (T(x,x \ y) * ((x \ y) * z)) = L(z,x \ y,T(x,x \ y))
    ]]></literal>
    <justification jstring="[para(4105(a,1),13(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4105 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4152">
    <literal><![CDATA[
      x * (x * T(T(x,x \ (y * x)) \ ((y * x) / x),z)) = (x * T(x \ y,z)) * x
    ]]></literal>
    <justification jstring="[para(4131(a,2),1542(a,1,2,2,1))].">
      <j1 rule="para" parents="4131 1542"/>
    </justification>
  </clause>

  <clause id="4153">
    <literal><![CDATA[
      R(x \ T(x,y),x,z) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(3005,a,4140,a)].">
      <j1 rule="hyper" parents="3005 4140"/>
    </justification>
  </clause>

  <clause id="4154">
    <literal><![CDATA[
      R(K(x,y),x,z) = L(x \ T(x,T(y,x)),T(y,x),x)
    ]]></literal>
    <justification jstring="[para(4140(a,1),3953(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4140 3953"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4156">
    <literal><![CDATA[
      (x * T(x \ y,z)) / y = (y / x) \ T(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,3130,a(flip),b,4153,a)].">
      <j1 rule="hyper" parents="58 3130 4153"/>
    </justification>
  </clause>

  <clause id="4157">
    <literal><![CDATA[
      L(x \ T(x,y),y,x) = K(T(x,y),y)
    ]]></literal>
    <justification jstring="[para(3866(a,1),4123(a,1,1))].">
      <j1 rule="para" parents="3866 4123"/>
    </justification>
  </clause>

  <clause id="4158">
    <literal><![CDATA[
      K(T(x,T(y,x)),T(y,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,3889,a,b,4157,a),flip(a)].">
      <j1 rule="hyper" parents="58 3889 4157"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4159">
    <literal><![CDATA[
      R(T(x,x * y),y,x) = T(x,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(320,a,4109,a(flip),b,4127,a),flip(a)].">
      <j1 rule="hyper" parents="320 4109 4127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4160">
    <literal><![CDATA[
      L(R(x,y,x),y,x) * y = y * T(x,T(y,x))
    ]]></literal>
    <justification jstring="[para(4159(a,1),973(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4159 973"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4161">
    <literal><![CDATA[
      T(x \ T(x * y,y),x) = R(y,x,y)
    ]]></literal>
    <justification jstring="[para(4129(a,1),785(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4129 785"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4162">
    <literal><![CDATA[
      (x \ T(x * y,y)) * x = x * R(y,x,y)
    ]]></literal>
    <justification jstring="[para(4129(a,1),802(a,1,1))].">
      <j1 rule="para" parents="4129 802"/>
    </justification>
  </clause>

  <clause id="4163">
    <literal><![CDATA[
      x * R(y,x,y) != z
    ]]></literal>
    <literal><![CDATA[
      (x \ T(x * y,y)) * x = z
    ]]></literal>
    <justification jstring="[para(4161(a,1),284(a,1,2))].">
      <j1 rule="para" parents="4161 284"/>
    </justification>
  </clause>

  <clause id="4164">
    <literal><![CDATA[
      (x * R(y,x,y)) \ T(x * y,y) = K(x,x \ T(x * y,y))
    ]]></literal>
    <justification jstring="[para(4162(a,1),86(a,1,1))].">
      <j1 rule="para" parents="4162 86"/>
    </justification>
  </clause>

  <clause id="4165">
    <literal><![CDATA[
      x * (((y * x) / y) \ z) = (T(y,x) \ y) * z
    ]]></literal>
    <justification jstring="[hyper(134,a,4135,a)].">
      <j1 rule="hyper" parents="134 4135"/>
    </justification>
  </clause>

  <clause id="4166">
    <literal><![CDATA[
      (T(x,y) \ x) * (x * y) = y * x
    ]]></literal>
    <justification jstring="[hyper(119,a,75,a(flip),b,4135,a),flip(a)].">
      <j1 rule="hyper" parents="119 75 4135"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4167">
    <literal><![CDATA[
      K(x,y) = T(T(y,x) \ y,y * x)
    ]]></literal>
    <justification jstring="[hyper(239,a,4166,a,b,84,a),flip(a)].">
      <j1 rule="hyper" parents="239 4166 84"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4168">
    <literal><![CDATA[
      (x * y) / (y * x) = T(y,x) \ y
    ]]></literal>
    <justification jstring="[hyper(131,a,4166,a)].">
      <j1 rule="hyper" parents="131 4166"/>
    </justification>
  </clause>

  <clause id="4169">
    <literal><![CDATA[
      T(x,y * z) != K(z,y)
    ]]></literal>
    <literal><![CDATA[
      T(y,z) \ y = x
    ]]></literal>
    <justification jstring="[para(4167(a,2),44(a,1)),flip(a)].">
      <j1 rule="para" parents="4167 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4170">
    <literal><![CDATA[
      T(x,(x \ 1) * (y * x)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(3951,a,4168,a(flip))].">
      <j1 rule="hyper" parents="3951 4168"/>
    </justification>
  </clause>

  <clause id="4171">
    <literal><![CDATA[
      T(x / y,y) \ (x / y) = (y * (x / y)) / x
    ]]></literal>
    <justification jstring="[para(7(a,1),4168(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7 4168"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4172">
    <literal><![CDATA[
      T(x,y / x) \ x != z
    ]]></literal>
    <literal><![CDATA[
      y / (x * (y / x)) = z
    ]]></literal>
    <justification jstring="[para(4168(a,1),576(a,1))].">
      <j1 rule="para" parents="4168 576"/>
    </justification>
  </clause>

  <clause id="4173">
    <literal><![CDATA[
      T(x,T((x \ 1) * y,x)) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(1981(a,1),4170(a,1,2))].">
      <j1 rule="para" parents="1981 4170"/>
    </justification>
  </clause>

  <clause id="4174">
    <literal><![CDATA[
      (((1 / x) * (y * x)) \ (y * x)) \ 1 = 1 / R(T(x,y),x \ 1,y * x)
    ]]></literal>
    <justification jstring="[para(4170(a,1),4039(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4170 4039"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4175">
    <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,4160,a)].">
      <j1 rule="hyper" parents="30 454 4160"/>
    </justification>
  </clause>

  <clause id="4176">
    <literal><![CDATA[
      R(x \ T(x,y),y,((x * y) / x) \ z) \ z = (T(x,y) \ x) * z
    ]]></literal>
    <justification jstring="[hyper(58,a,3878,a,b,4165,a)].">
      <j1 rule="hyper" parents="58 3878 4165"/>
    </justification>
  </clause>

  <clause id="4177">
    <literal><![CDATA[
      (x * (y / x)) / y = (x \ y) \ (y / x)
    ]]></literal>
    <justification jstring="[para(107(a,1),4171(a,1,1)),flip(a)].">
      <j1 rule="para" parents="107 4171"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4178">
    <literal><![CDATA[
      (x * (y / x)) / y = x \ ((x \ y) \ y)
    ]]></literal>
    <justification jstring="[hyper(320,a,3887,a(flip),b,4177,a),flip(a)].">
      <j1 rule="hyper" parents="320 3887 4177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4179">
    <literal><![CDATA[
      (x \ (y \ x)) \ (y \ x) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(3929,a,4178,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="3929 4178"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4180">
    <literal><![CDATA[
      T(x,x \ (y \ x)) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(356,a,4179,a)].">
      <j1 rule="hyper" parents="356 4179"/>
    </justification>
  </clause>

  <clause id="4181">
    <literal><![CDATA[
      (x \ y) / T(y,x \ 1) = y \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(197,a,4179,a)].">
      <j1 rule="hyper" parents="197 4179"/>
    </justification>
  </clause>

  <clause id="4182">
    <literal><![CDATA[
      (x \ (y \ x)) * T(x,y \ 1) = y \ x
    ]]></literal>
    <justification jstring="[hyper(134,a,4179,a)].">
      <j1 rule="hyper" parents="134 4179"/>
    </justification>
  </clause>

  <clause id="4183">
    <literal><![CDATA[
      T(x * y,(x * y) \ y) = T(x * y,x \ 1)
    ]]></literal>
    <justification jstring="[para(4(a,1),4180(a,1,2,2))].">
      <j1 rule="para" parents="4 4180"/>
    </justification>
  </clause>

  <clause id="4184">
    <literal><![CDATA[
      T(x,(x / y) \ 1) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(75(a,1),4180(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="75 4180"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4185">
    <literal><![CDATA[
      x \ ((y \ x) / ((y \ x) / x)) = T(x,y \ 1) \ x
    ]]></literal>
    <justification jstring="[para(4180(a,1),3891(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4180 3891"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4186">
    <literal><![CDATA[
      (x / y) \ T(x,x \ y) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(4184(a,1),3921(a,1,2))].">
      <j1 rule="para" parents="4184 3921"/>
    </justification>
  </clause>

  <clause id="4187">
    <literal><![CDATA[
      ((x \ 1) \ y) / T(y,x) = y \ ((x \ 1) \ y)
    ]]></literal>
    <justification jstring="[para(2959(a,1),4181(a,1,2))].">
      <j1 rule="para" parents="2959 4181"/>
    </justification>
  </clause>

  <clause id="4188">
    <literal><![CDATA[
      ((x * y) \ (y \ (x * y))) * T(x * y,y \ 1) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,17,a,b,4182,a),flip(a)].">
      <j1 rule="hyper" parents="320 17 4182"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4189">
    <literal><![CDATA[
      (x \ ((1 / y) \ x)) * T(x,y) = (1 / y) \ x
    ]]></literal>
    <justification jstring="[para(75(a,1),4182(a,1,2,2))].">
      <j1 rule="para" parents="75 4182"/>
    </justification>
  </clause>

  <clause id="4190">
    <literal><![CDATA[
      (x / (y * x)) \ T(x,x \ (y * x)) = x * y
    ]]></literal>
    <justification jstring="[para(6(a,1),4186(a,2,2))].">
      <j1 rule="para" parents="6 4186"/>
    </justification>
  </clause>

  <clause id="4191">
    <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(4129(a,1),4175(a,1,1))].">
      <j1 rule="para" parents="4129 4175"/>
    </justification>
  </clause>

  <clause id="4192">
    <literal><![CDATA[
      T(x * y,x \ 1) = ((x * y) \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(427,a,4183,a),flip(a)].">
      <j1 rule="hyper" parents="427 4183"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4193">
    <literal><![CDATA[
      x / T(y * x,y \ 1) = (y * x) \ x
    ]]></literal>
    <justification jstring="[para(4183(a,1),265(a,1,2))].">
      <j1 rule="para" parents="4183 265"/>
    </justification>
  </clause>

  <clause id="4194">
    <literal><![CDATA[
      T((x \ 1) * y,x) = (((x \ 1) * y) \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(3029,a,4192,a)].">
      <j1 rule="hyper" parents="3029 4192"/>
    </justification>
  </clause>

  <clause id="4195">
    <literal><![CDATA[
      x * ((x * y) * (y / (x * y))) = ((x * y) \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(58,a,3885,a,b,4192,a)].">
      <j1 rule="hyper" parents="58 3885 4192"/>
    </justification>
  </clause>

  <clause id="4196">
    <literal><![CDATA[
      (x \ 1) * (((x * y) \ y) \ y) = (x * y) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(119,a,4192,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 4192 17"/>
    </justification>
  </clause>

  <clause id="4197">
    <literal><![CDATA[
      T((1 / x) * y,x) = (((1 / x) * y) \ y) \ y
    ]]></literal>
    <justification jstring="[para(75(a,1),4192(a,1,2))].">
      <j1 rule="para" parents="75 4192"/>
    </justification>
  </clause>

  <clause id="4198">
    <literal><![CDATA[
      (x / (y * x)) \ T(x,T(y,x)) = x * y
    ]]></literal>
    <justification jstring="[para(17(a,2),4190(a,1,2,2))].">
      <j1 rule="para" parents="17 4190"/>
    </justification>
  </clause>

  <clause id="4199">
    <literal><![CDATA[
      (x \ T(x,y)) \ z != u
    ]]></literal>
    <literal><![CDATA[
      x * (T(x,y) \ z) = u
    ]]></literal>
    <justification jstring="[para(5(a,1),4142(a,1,2))].">
      <j1 rule="para" parents="5 4142"/>
    </justification>
  </clause>

  <clause id="4200">
    <literal><![CDATA[
      K(x \ y,T(x,y)) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,4133,a(flip),b,4125,a),flip(a)].">
      <j1 rule="hyper" parents="58 4133 4125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4201">
    <literal><![CDATA[
      K(x \ (x * y),x) = K(y,T(x,x * y))
    ]]></literal>
    <justification jstring="[hyper(58,a,673,a(flip),b,4200,a),flip(a)].">
      <j1 rule="hyper" parents="58 673 4200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4202">
    <literal><![CDATA[
      K(x,T(y,y * x)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(1359,a,4201,a),flip(a)].">
      <j1 rule="hyper" parents="1359 4201"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4204">
    <literal><![CDATA[
      R(K(x,y),x,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,3889,a,b,4154,a),flip(a)].">
      <j1 rule="hyper" parents="320 3889 4154"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4205">
    <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(4154(a,1),384(a,1)),flip(b)].">
      <j1 rule="para" parents="4154 384"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4207">
    <literal><![CDATA[
      (K(x,y) * x) * z = K(x,y) * (x * z)
    ]]></literal>
    <justification jstring="[para(4204(a,1),101(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4204 101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4208">
    <literal><![CDATA[
      L(x,y,K(y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(479,a,4207,a)].">
      <j1 rule="hyper" parents="479 4207"/>
    </justification>
  </clause>

  <clause id="4213">
    <literal><![CDATA[
      L(x,y,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      u = x
    ]]></literal>
    <justification jstring="[para(4208(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="4208 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4214">
    <literal><![CDATA[
      L(x,y,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(4208(a,1),45(a,2))].">
      <j1 rule="para" parents="4208 45"/>
    </justification>
  </clause>

  <clause id="4216">
    <literal><![CDATA[
      ((x \ y) / y) \ T((x \ y) / y,z) = x * T(x \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(1303,a,4156,a),flip(a)].">
      <j1 rule="hyper" parents="1303 4156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4218">
    <literal><![CDATA[
      K(T(x,T(y,x)),T(y,x)) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(4157(a,1),4205(a,1))].">
      <j1 rule="para" parents="4157 4205"/>
    </justification>
  </clause>

  <clause id="4219">
    <literal><![CDATA[
      R(K(x,y),x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(4154(a,2),4205(a,1))].">
      <j1 rule="para" parents="4154 4205"/>
    </justification>
  </clause>

  <clause id="4220">
    <literal><![CDATA[
      T(x,y \ 1) \ (y \ T(x,y \ 1)) = x \ (y \ x)
    ]]></literal>
    <justification jstring="[para(4180(a,1),4149(a,1,1))].">
      <j1 rule="para" parents="4180 4149"/>
    </justification>
  </clause>

  <clause id="4221">
    <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(2826(a,1),4220(a,2,2))].">
      <j1 rule="para" parents="2826 4220"/>
    </justification>
  </clause>

  <clause id="4222">
    <literal><![CDATA[
      ((x * y) \ T(x,y)) * T(x * y,y \ 1) = T(x,y)
    ]]></literal>
    <justification jstring="[para(17(a,2),4188(a,1,1,2))].">
      <j1 rule="para" parents="17 4188"/>
    </justification>
  </clause>

  <clause id="4223">
    <literal><![CDATA[
      x \ ((y \ x) / ((y \ x) / x)) = y * T(y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,3864,a(flip),b,4216,a)].">
      <j1 rule="hyper" parents="58 3864 4216"/>
    </justification>
  </clause>

  <clause id="4224">
    <literal><![CDATA[
      T(x,T((y \ z) / z,x)) = (y * T(y \ 1,x)) \ x
    ]]></literal>
    <justification jstring="[para(4216(a,1),3883(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4216 3883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4225">
    <literal><![CDATA[
      T(x,y \ 1) \ x = y * T(y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,4185,a(flip),b,4223,a)].">
      <j1 rule="hyper" parents="58 4185 4223"/>
    </justification>
  </clause>

  <clause id="4226">
    <literal><![CDATA[
      K(x \ (x / y),x) = T(x,y \ 1) \ x
    ]]></literal>
    <justification jstring="[hyper(320,a,1025,a,b,4225,a)].">
      <j1 rule="hyper" parents="320 1025 4225"/>
    </justification>
  </clause>

  <clause id="4227">
    <literal><![CDATA[
      T(x,(y \ 1) \ 1) \ x = y \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,991,a(flip),b,4225,a),flip(a)].">
      <j1 rule="hyper" parents="320 991 4225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4228">
    <literal><![CDATA[
      K(x \ (x / y),x) \ x = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(3067,a,4226,a)].">
      <j1 rule="hyper" parents="3067 4226"/>
    </justification>
  </clause>

  <clause id="4229">
    <literal><![CDATA[
      K(x \ (x / y),x) != z \ x
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ 1) = z
    ]]></literal>
    <justification jstring="[para(4226(a,2),43(a,1))].">
      <j1 rule="para" parents="4226 43"/>
    </justification>
  </clause>

  <clause id="4230">
    <literal><![CDATA[
      T(x,y) \ x = y \ T(y,x)
    ]]></literal>
    <justification jstring="[para(2959(a,1),4227(a,1,1))].">
      <j1 rule="para" parents="2959 4227"/>
    </justification>
  </clause>

  <clause id="4231">
    <literal><![CDATA[
      T(x,y / x) \ x = x \ (y / (y / x))
    ]]></literal>
    <justification jstring="[hyper(320,a,3864,a(flip),b,4230,a),flip(a)].">
      <j1 rule="hyper" parents="320 3864 4230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4232">
    <literal><![CDATA[
      (x * y) / x = y * (T(y,x) \ y)
    ]]></literal>
    <justification jstring="[hyper(119,a,4230,a,b,3861,a),flip(a)].">
      <j1 rule="hyper" parents="119 4230 3861"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4233">
    <literal><![CDATA[
      T(x,T(y,x)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(34,a,3875,a,b,4230,a)].">
      <j1 rule="hyper" parents="34 3875 4230"/>
    </justification>
  </clause>

  <clause id="4234">
    <literal><![CDATA[
      x * ((T(y,x) \ y) * z) = T(x,y) * z
    ]]></literal>
    <justification jstring="[para(4230(a,2),4087(a,1,2,1))].">
      <j1 rule="para" parents="4230 4087"/>
    </justification>
  </clause>

  <clause id="4235">
    <literal><![CDATA[
      T(x,y) * (x \ z) = (T(y,x) \ y) * z
    ]]></literal>
    <justification jstring="[para(4230(a,2),4088(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4230 4088"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4236">
    <literal><![CDATA[
      K(x,y) = T(x \ T(x,y),y * x)
    ]]></literal>
    <justification jstring="[para(4230(a,1),4167(a,2,1))].">
      <j1 rule="para" parents="4230 4167"/>
    </justification>
  </clause>

  <clause id="4237">
    <literal><![CDATA[
      (T(x,y) \ x) * z != u
    ]]></literal>
    <literal><![CDATA[
      T(y,x) * (y \ z) = u
    ]]></literal>
    <justification jstring="[para(4230(a,2),4095(a,1,1))].">
      <j1 rule="para" parents="4230 4095"/>
    </justification>
  </clause>

  <clause id="4238">
    <literal><![CDATA[
      x * (T(x,y) \ y) = T(y,x)
    ]]></literal>
    <justification jstring="[hyper(1179,a,4233,a)].">
      <j1 rule="hyper" parents="1179 4233"/>
    </justification>
  </clause>

  <clause id="4239">
    <literal><![CDATA[
      T(x \ y,x) = ((x \ y) \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(602,a,4233,a),flip(a)].">
      <j1 rule="hyper" parents="602 4233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4240">
    <literal><![CDATA[
      T(x,y) \ (x * y) = T(y,x)
    ]]></literal>
    <justification jstring="[hyper(428,a,4233,a)].">
      <j1 rule="hyper" parents="428 4233"/>
    </justification>
  </clause>

  <clause id="4241">
    <literal><![CDATA[
      R(T(x,x * y),y,x) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,4159,a,b,4233,a)].">
      <j1 rule="hyper" parents="58 4159 4233"/>
    </justification>
  </clause>

  <clause id="4242">
    <literal><![CDATA[
      (x / T(y,x)) * y = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,4109,a,b,4233,a)].">
      <j1 rule="hyper" parents="58 4109 4233"/>
    </justification>
  </clause>

  <clause id="4243">
    <literal><![CDATA[
      T(x,(x \ 1) * y) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,4173,a(flip),b,4233,a),flip(a)].">
      <j1 rule="hyper" parents="58 4173 4233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4244">
    <literal><![CDATA[
      T(x / T(y,x),y) = y \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(439,a,4233,a(flip),b,4109,a)].">
      <j1 rule="hyper" parents="439 4233 4109"/>
    </justification>
  </clause>

  <clause id="4245">
    <literal><![CDATA[
      T(x,y) * T(y,x) = x * y
    ]]></literal>
    <justification jstring="[hyper(119,a,4233,a(flip),b,235,a)].">
      <j1 rule="hyper" parents="119 4233 235"/>
    </justification>
  </clause>

  <clause id="4246">
    <literal><![CDATA[
      T(x,y) / y = x / T(y,x)
    ]]></literal>
    <justification jstring="[hyper(117,a,4233,a(flip),b,4109,a)].">
      <j1 rule="hyper" parents="117 4233 4109"/>
    </justification>
  </clause>

  <clause id="4247">
    <literal><![CDATA[
      T(x,y) / (T(y,x) \ x) = y
    ]]></literal>
    <justification jstring="[hyper(117,a,4233,a(flip),b,1136,a)].">
      <j1 rule="hyper" parents="117 4233 1136"/>
    </justification>
  </clause>

  <clause id="4248">
    <literal><![CDATA[
      T(x,y) \ y = x \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,4233,a(flip),b,1136,a),flip(a)].">
      <j1 rule="hyper" parents="116 4233 1136"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4249">
    <literal><![CDATA[
      T(T(x,y),T(z,x)) = T(T(x,z),y)
    ]]></literal>
    <justification jstring="[para(4233(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4233 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4250">
    <literal><![CDATA[
      T(x,T(T(y,x),z)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(18(a,1),4233(a,1,2))].">
      <j1 rule="para" parents="18 4233"/>
    </justification>
  </clause>

  <clause id="4251">
    <literal><![CDATA[
      T(L(x,y,z),T(u,x)) = L(T(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(4233(a,1),20(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4233 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4252">
    <literal><![CDATA[
      T(x,L(T(y,x),z,u)) = T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(20(a,2),4233(a,1,2))].">
      <j1 rule="para" parents="20 4233"/>
    </justification>
  </clause>

  <clause id="4253">
    <literal><![CDATA[
      T(x,y / x) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(107(a,1),4233(a,1,2)),flip(a)].">
      <j1 rule="para" parents="107 4233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4255">
    <literal><![CDATA[
      T(x,y) * T(T(y,x),z) = T(y,z) * T(x,y)
    ]]></literal>
    <justification jstring="[para(4233(a,1),236(a,1,2,1))].">
      <j1 rule="para" parents="4233 236"/>
    </justification>
  </clause>

  <clause id="4256">
    <literal><![CDATA[
      T(x,y) * L(T(y,x),z,u) = L(y,z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[para(4233(a,1),237(a,1,2,1))].">
      <j1 rule="para" parents="4233 237"/>
    </justification>
  </clause>

  <clause id="4257">
    <literal><![CDATA[
      T(x,y) * R(T(y,x),z,u) = R(y,z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[para(4233(a,1),238(a,1,2,1))].">
      <j1 rule="para" parents="4233 238"/>
    </justification>
  </clause>

  <clause id="4258">
    <literal><![CDATA[
      T(x,T(y,y * x)) = T(x,L(y,x,y))
    ]]></literal>
    <justification jstring="[para(712(a,1),4233(a,1,2))].">
      <j1 rule="para" parents="712 4233"/>
    </justification>
  </clause>

  <clause id="4259">
    <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(4233(a,1),417(a,1,2,1))].">
      <j1 rule="para" parents="4233 417"/>
    </justification>
  </clause>

  <clause id="4260">
    <literal><![CDATA[
      T(x,y) * (y * x) = x * (x * y)
    ]]></literal>
    <justification jstring="[para(4233(a,1),4115(a,1,1))].">
      <j1 rule="para" parents="4233 4115"/>
    </justification>
  </clause>

  <clause id="4261">
    <literal><![CDATA[
      K(T(x,y),T(y,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(4233(a,1),4158(a,1,1))].">
      <j1 rule="para" parents="4233 4158"/>
    </justification>
  </clause>

  <clause id="4262">
    <literal><![CDATA[
      (x / (y * x)) \ T(x,y) = x * y
    ]]></literal>
    <justification jstring="[para(4233(a,1),4198(a,1,2))].">
      <j1 rule="para" parents="4233 4198"/>
    </justification>
  </clause>

  <clause id="4264">
    <literal><![CDATA[
      T(x,y) * (x \ T(y,x)) = y
    ]]></literal>
    <justification jstring="[para(4238(a,1),67(a,1,2,2))].">
      <j1 rule="para" parents="4238 67"/>
    </justification>
  </clause>

  <clause id="4266">
    <literal><![CDATA[
      (x * y) / T(y,x) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(197,a,4240,a)].">
      <j1 rule="hyper" parents="197 4240"/>
    </justification>
  </clause>

  <clause id="4268">
    <literal><![CDATA[
      T(x,y) = (x \ (y * x)) \ (y * x)
    ]]></literal>
    <justification jstring="[para(17(a,1),4240(a,1,1)),flip(a)].">
      <j1 rule="para" parents="17 4240"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4269">
    <literal><![CDATA[
      T(x,y) / T(y,x) = x / T(T(y,x),x)
    ]]></literal>
    <justification jstring="[hyper(117,a,4233,a(flip),b,4242,a)].">
      <j1 rule="hyper" parents="117 4233 4242"/>
    </justification>
  </clause>

  <clause id="4270">
    <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(4242(a,1),605(a,1,2))].">
      <j1 rule="para" parents="4242 605"/>
    </justification>
  </clause>

  <clause id="4271">
    <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,4245,a(flip),b,184,a)].">
      <j1 rule="hyper" parents="119 4245 184"/>
    </justification>
  </clause>

  <clause id="4272">
    <literal><![CDATA[
      (T(x,y) * (T(y,x) * z)) \ ((x * y) * z) = a(T(x,y),T(y,x),z)
    ]]></literal>
    <justification jstring="[para(4245(a,1),9(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="4245 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4273">
    <literal><![CDATA[
      (x * y) \ (T(x,y) * (T(y,x) * z)) = L(z,T(y,x),T(x,y))
    ]]></literal>
    <justification jstring="[para(4245(a,1),13(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4245 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4274">
    <literal><![CDATA[
      (x * (y * z)) * a(x,T(y,z),T(z,y)) = (x * T(y,z)) * T(z,y)
    ]]></literal>
    <justification jstring="[para(4245(a,1),80(a,1,1,2))].">
      <j1 rule="para" parents="4245 80"/>
    </justification>
  </clause>

  <clause id="4275">
    <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(4245(a,1),518(a,1,1,1))].">
      <j1 rule="para" parents="4245 518"/>
    </justification>
  </clause>

  <clause id="4276">
    <literal><![CDATA[
      (T(x,y) / y) * z = (x / T(y,x)) * z
    ]]></literal>
    <justification jstring="[hyper(52,a,4246,a)].">
      <j1 rule="hyper" parents="52 4246"/>
    </justification>
  </clause>

  <clause id="4277">
    <literal><![CDATA[
      (T(x,y) / y) \ x = T(y,x)
    ]]></literal>
    <justification jstring="[hyper(188,a,4246,a(flip))].">
      <j1 rule="hyper" parents="188 4246"/>
    </justification>
  </clause>

  <clause id="4278">
    <literal><![CDATA[
      T(x * (y / x),x) = x * (y / T(x,y))
    ]]></literal>
    <justification jstring="[hyper(119,a,4246,a(flip),b,1385,a),flip(a)].">
      <j1 rule="hyper" parents="119 4246 1385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4279">
    <literal><![CDATA[
      (x / T(y,x)) * y != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(4246(a,1),251(a,1,1)),flip(b)].">
      <j1 rule="para" parents="4246 251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4280">
    <literal><![CDATA[
      T(x,T(y,z)) / (T(T(y,x),z) \ x) = T(y,z)
    ]]></literal>
    <justification jstring="[para(18(a,1),4247(a,1,2,1))].">
      <j1 rule="para" parents="18 4247"/>
    </justification>
  </clause>

  <clause id="4281">
    <literal><![CDATA[
      (T(x,y) \ y) * z = (x \ T(y,x)) * z
    ]]></literal>
    <justification jstring="[para(4247(a,1),194(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4247 194"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4282">
    <literal><![CDATA[
      (x \ T(y,x)) * z != u
    ]]></literal>
    <literal><![CDATA[
      (T(x,y) \ y) * z = u
    ]]></literal>
    <justification jstring="[para(4247(a,1),620(a,1,1,1))].">
      <j1 rule="para" parents="4247 620"/>
    </justification>
  </clause>

  <clause id="4283">
    <literal><![CDATA[
      (T(x,y) \ y) \ z = (x \ T(y,x)) \ z
    ]]></literal>
    <justification jstring="[hyper(56,a,4248,a)].">
      <j1 rule="hyper" parents="56 4248"/>
    </justification>
  </clause>

  <clause id="4284">
    <literal><![CDATA[
      T(x,y) \ ((T(y,x) \ x) * y) = K(y \ T(x,y),y)
    ]]></literal>
    <justification jstring="[para(4248(a,2),85(a,1,2,1))].">
      <j1 rule="para" parents="4248 85"/>
    </justification>
  </clause>

  <clause id="4285">
    <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(4248(a,1),81(a,1,1,2,1))].">
      <j1 rule="para" parents="4248 81"/>
    </justification>
  </clause>

  <clause id="4286">
    <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(4248(a,1),2046(a,1,2,1))].">
      <j1 rule="para" parents="4248 2046"/>
    </justification>
  </clause>

  <clause id="4287">
    <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(4248(a,1),2139(a,1,2,1))].">
      <j1 rule="para" parents="4248 2139"/>
    </justification>
  </clause>

  <clause id="4288">
    <literal><![CDATA[
      T(x,y / x) = (x \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(320,a,106,a(flip),b,4253,a),flip(a)].">
      <j1 rule="hyper" parents="320 106 4253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4289">
    <literal><![CDATA[
      (x / y) * T(y,y \ x) = y * (x / y)
    ]]></literal>
    <justification jstring="[hyper(119,a,4253,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 4253 17"/>
    </justification>
  </clause>

  <clause id="4290">
    <literal><![CDATA[
      x / T(y,x / y) = y \ x
    ]]></literal>
    <justification jstring="[para(4253(a,2),265(a,1,2))].">
      <j1 rule="para" parents="4253 265"/>
    </justification>
  </clause>

  <clause id="4291">
    <literal><![CDATA[
      T(x,y / x) != z
    ]]></literal>
    <literal><![CDATA[
      (x \ y) \ y = z
    ]]></literal>
    <justification jstring="[para(4253(a,2),427(a,1))].">
      <j1 rule="para" parents="4253 427"/>
    </justification>
  </clause>

  <clause id="4293">
    <literal><![CDATA[
      (x * (y / x)) * x = y * T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(4253(a,1),907(a,2,2))].">
      <j1 rule="para" parents="4253 907"/>
    </justification>
  </clause>

  <clause id="4294">
    <literal><![CDATA[
      (x * y) \ (y * T(x,x \ y)) = a(x,y / x,x)
    ]]></literal>
    <justification jstring="[para(4253(a,1),913(a,1,2,2))].">
      <j1 rule="para" parents="4253 913"/>
    </justification>
  </clause>

  <clause id="4295">
    <literal><![CDATA[
      x \ (T(x,y / x) / (1 / (x \ y))) = (x / (1 / (x \ y))) / x
    ]]></literal>
    <justification jstring="[para(4253(a,2),3924(a,1,2,1))].">
      <j1 rule="para" parents="4253 3924"/>
    </justification>
  </clause>

  <clause id="4296">
    <literal><![CDATA[
      T(x,T(y,x / y)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(4253(a,2),4116(a,1,2))].">
      <j1 rule="para" parents="4253 4116"/>
    </justification>
  </clause>

  <clause id="4299">
    <literal><![CDATA[
      T(x,y) * z != y
    ]]></literal>
    <literal><![CDATA[
      x \ T(y,x) = z
    ]]></literal>
    <justification jstring="[para(4264(a,1),38(a,1)),flip(a)].">
      <j1 rule="para" parents="4264 38"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4300">
    <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),4266(a,1,2))].">
      <j1 rule="para" parents="22 4266"/>
    </justification>
  </clause>

  <clause id="4301">
    <literal><![CDATA[
      (T(x,y) * (y * x)) / T(x,y) = T(y,x) * T(T(x,y),y * x)
    ]]></literal>
    <justification jstring="[para(4266(a,1),1500(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4266 1500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4302">
    <literal><![CDATA[
      (x / T(y,x)) * z != u
    ]]></literal>
    <literal><![CDATA[
      (T(x,y) / y) * z = u
    ]]></literal>
    <justification jstring="[para(4277(a,1),348(a,1,1,2))].">
      <j1 rule="para" parents="4277 348"/>
    </justification>
  </clause>

  <clause id="4303">
    <literal><![CDATA[
      T(T(x,y),z / x) = T((x \ z) \ z,y)
    ]]></literal>
    <justification jstring="[para(4288(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4288 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4304">
    <literal><![CDATA[
      (x * (y / x)) * x = y * ((x \ y) \ y)
    ]]></literal>
    <justification jstring="[para(4288(a,1),907(a,2,2))].">
      <j1 rule="para" parents="4288 907"/>
    </justification>
  </clause>

  <clause id="4305">
    <literal><![CDATA[
      x / T(y \ x,y) = (y \ x) \ x
    ]]></literal>
    <justification jstring="[para(72(a,1),4290(a,1,2,2))].">
      <j1 rule="para" parents="72 4290"/>
    </justification>
  </clause>

  <clause id="4306">
    <literal><![CDATA[
      T(x,x * (y / x)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(814,a,4241,a),flip(a)].">
      <j1 rule="hyper" parents="814 4241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4307">
    <literal><![CDATA[
      T(x,y * x) = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(810,a,4241,a)].">
      <j1 rule="hyper" parents="810 4241"/>
    </justification>
  </clause>

  <clause id="4308">
    <literal><![CDATA[
      T(R(x,y,x),x * y) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(630,a,4241,a)].">
      <j1 rule="hyper" parents="630 4241"/>
    </justification>
  </clause>

  <clause id="4309">
    <literal><![CDATA[
      R(T(x,y),x \ y,x) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(5(a,1),4241(a,1,1,2))].">
      <j1 rule="para" parents="5 4241"/>
    </justification>
  </clause>

  <clause id="4310">
    <literal><![CDATA[
      T(x,y * z) != T(y,z)
    ]]></literal>
    <literal><![CDATA[
      R(y,z,y) = x
    ]]></literal>
    <justification jstring="[para(4241(a,1),140(a,2))].">
      <j1 rule="para" parents="4241 140"/>
    </justification>
  </clause>

  <clause id="4311">
    <literal><![CDATA[
      T(x,(x \ y) * x) = T(x,y)
    ]]></literal>
    <justification jstring="[para(71(a,1),4306(a,1,2)),flip(a)].">
      <j1 rule="para" parents="71 4306"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4312">
    <literal><![CDATA[
      T(x,x * T(y / x,z)) = T(x,x * T(x \ y,z))
    ]]></literal>
    <justification jstring="[para(457(a,1),4306(a,1,2,2))].">
      <j1 rule="para" parents="457 4306"/>
    </justification>
  </clause>

  <clause id="4313">
    <literal><![CDATA[
      T(x,y) * (x \ T(x * (y / x),x)) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(4306(a,1),4264(a,1,1))].">
      <j1 rule="para" parents="4306 4264"/>
    </justification>
  </clause>

  <clause id="4314">
    <literal><![CDATA[
      T(L(x,y,x),y) = T(x,y * x)
    ]]></literal>
    <justification jstring="[hyper(320,a,712,a,b,4307,a)].">
      <j1 rule="hyper" parents="320 712 4307"/>
    </justification>
  </clause>

  <clause id="4315">
    <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,4307,a)].">
      <j1 rule="hyper" parents="58 22 4307"/>
    </justification>
  </clause>

  <clause id="4316">
    <literal><![CDATA[
      T(T(x,x * y),z) = T(T(x,z),y * x)
    ]]></literal>
    <justification jstring="[para(4307(a,1),18(a,1,1))].">
      <j1 rule="para" parents="4307 18"/>
    </justification>
  </clause>

  <clause id="4317">
    <literal><![CDATA[
      T(T(x,y * x),z) = T(T(x,z),x * y)
    ]]></literal>
    <justification jstring="[para(4307(a,2),18(a,1,1))].">
      <j1 rule="para" parents="4307 18"/>
    </justification>
  </clause>

  <clause id="4318">
    <literal><![CDATA[
      T(x,y * z) != T(y,z * y)
    ]]></literal>
    <literal><![CDATA[
      y = x
    ]]></literal>
    <justification jstring="[para(4307(a,2),44(a,1)),flip(a)].">
      <j1 rule="para" parents="4307 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4319">
    <literal><![CDATA[
      x * T(y,x * y) = L(y,x,y) * x
    ]]></literal>
    <justification jstring="[para(4307(a,2),715(a,1,2))].">
      <j1 rule="para" parents="4307 715"/>
    </justification>
  </clause>

  <clause id="4320">
    <literal><![CDATA[
      x * L(T(y,x * y),z,u) = L(L(y,x,y),z,u) * x
    ]]></literal>
    <justification jstring="[para(4307(a,2),720(a,1,2,1))].">
      <j1 rule="para" parents="4307 720"/>
    </justification>
  </clause>

  <clause id="4321">
    <literal><![CDATA[
      T(x,T(y,y * x)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(4307(a,1),4130(a,1,2))].">
      <j1 rule="para" parents="4307 4130"/>
    </justification>
  </clause>

  <clause id="4322">
    <literal><![CDATA[
      (T(x,y * x) * y) * x = x * (x * y)
    ]]></literal>
    <justification jstring="[para(4307(a,2),4146(a,1,1,1))].">
      <j1 rule="para" parents="4307 4146"/>
    </justification>
  </clause>

  <clause id="4323">
    <literal><![CDATA[
      K(x,T(y,x * y)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(4307(a,2),4202(a,1,2))].">
      <j1 rule="para" parents="4307 4202"/>
    </justification>
  </clause>

  <clause id="4324">
    <literal><![CDATA[
      ((x \ y) * x) * T(x,y) = x * ((x \ y) * x)
    ]]></literal>
    <justification jstring="[hyper(119,a,4311,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 4311 17"/>
    </justification>
  </clause>

  <clause id="4325">
    <literal><![CDATA[
      (((x \ y) * x) / T(x,y)) * x = T((x \ y) * x,x)
    ]]></literal>
    <justification jstring="[para(4311(a,1),4242(a,1,1,2))].">
      <j1 rule="para" parents="4311 4242"/>
    </justification>
  </clause>

  <clause id="4326">
    <literal><![CDATA[
      T(x,x * y) * L(T(y,x),z,u) = L(y,z,u) * T(x,x * y)
    ]]></literal>
    <justification jstring="[para(4321(a,1),237(a,1,2,1))].">
      <j1 rule="para" parents="4321 237"/>
    </justification>
  </clause>

  <clause id="4327">
    <literal><![CDATA[
      T(x,x * y) * R(T(y,x),z,u) = R(y,z,u) * T(x,x * y)
    ]]></literal>
    <justification jstring="[para(4321(a,1),238(a,1,2,1))].">
      <j1 rule="para" parents="4321 238"/>
    </justification>
  </clause>

  <clause id="4328">
    <literal><![CDATA[
      K(x,T(x \ y,y)) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[para(5(a,1),4323(a,1,2,2))].">
      <j1 rule="para" parents="5 4323"/>
    </justification>
  </clause>

  <clause id="4329">
    <literal><![CDATA[
      R(x,y,T(x,y)) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(905,a,4308,a)].">
      <j1 rule="hyper" parents="905 4308"/>
    </justification>
  </clause>

  <clause id="4330">
    <literal><![CDATA[
      x \ T(y * x,y) = R(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(1175,a,4329,a)].">
      <j1 rule="hyper" parents="1175 4329"/>
    </justification>
  </clause>

  <clause id="4331">
    <literal><![CDATA[
      x * R(y,x,y) = T(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,4329,a(flip),b,1174,a)].">
      <j1 rule="hyper" parents="119 4329 1174"/>
    </justification>
  </clause>

  <clause id="4332">
    <literal><![CDATA[
      L(R(x,y,x),y,x) = x
    ]]></literal>
    <justification jstring="[para(4329(a,1),1176(a,1,1))].">
      <j1 rule="para" parents="4329 1176"/>
    </justification>
  </clause>

  <clause id="4333">
    <literal><![CDATA[
      R(x,T(y,x),T(x,y)) = R(x,T(y,x),x)
    ]]></literal>
    <justification jstring="[para(4233(a,1),4329(a,1,3))].">
      <j1 rule="para" parents="4233 4329"/>
    </justification>
  </clause>

  <clause id="4334">
    <literal><![CDATA[
      T((x * y) / x,x * y) = L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(461,a,4314,a)].">
      <j1 rule="hyper" parents="461 4314"/>
    </justification>
  </clause>

  <clause id="4335">
    <literal><![CDATA[
      R(x,x \ y,x) = (x \ y) \ T(y,x)
    ]]></literal>
    <justification jstring="[para(5(a,1),4330(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 4330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4336">
    <literal><![CDATA[
      R(x / y,y,x / y) = y \ T(x,x / y)
    ]]></literal>
    <justification jstring="[para(7(a,1),4330(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7 4330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4337">
    <literal><![CDATA[
      (x * y) \ (x * T(z * y,z)) = L(R(z,y,z),y,x)
    ]]></literal>
    <justification jstring="[para(4330(a,1),92(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4330 92"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4338">
    <literal><![CDATA[
      (x \ T(x * y,y)) * x = T(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(4163,a,4331,a)].">
      <j1 rule="hyper" parents="4163 4331"/>
    </justification>
  </clause>

  <clause id="4339">
    <literal><![CDATA[
      T(x * y,x) != y * z
    ]]></literal>
    <literal><![CDATA[
      R(x,y,x) = z
    ]]></literal>
    <justification jstring="[para(4331(a,1),38(a,1))].">
      <j1 rule="para" parents="4331 38"/>
    </justification>
  </clause>

  <clause id="4340">
    <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(4331(a,1),482(a,1,2,2))].">
      <j1 rule="para" parents="4331 482"/>
    </justification>
  </clause>

  <clause id="4341">
    <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(4331(a,1),1060(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4331 1060"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4342">
    <literal><![CDATA[
      T(x * y,x) * T(x,y) = (x * y) * R(x,y,x)
    ]]></literal>
    <justification jstring="[para(4331(a,1),1893(a,1,1))].">
      <j1 rule="para" parents="4331 1893"/>
    </justification>
  </clause>

  <clause id="4343">
    <literal><![CDATA[
      ((x \ y) * x) / (x \ y) = y / (y / x)
    ]]></literal>
    <justification jstring="[hyper(320,a,3892,a,b,4232,a),flip(a)].">
      <j1 rule="hyper" parents="320 3892 4232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4344">
    <literal><![CDATA[
      T(x * (T(x,y) \ x),y) = x
    ]]></literal>
    <justification jstring="[para(4232(a,1),224(a,1,1))].">
      <j1 rule="para" parents="4232 224"/>
    </justification>
  </clause>

  <clause id="4345">
    <literal><![CDATA[
      ((x * y) / x) \ x = y \ ((y * x) / y)
    ]]></literal>
    <justification jstring="[para(4232(a,2),3926(a,1,1))].">
      <j1 rule="para" parents="4232 3926"/>
    </justification>
  </clause>

  <clause id="4346">
    <literal><![CDATA[
      T(x / (x / y),y \ x) = y
    ]]></literal>
    <justification jstring="[para(3892(a,2),4344(a,1,1))].">
      <j1 rule="para" parents="3892 4344"/>
    </justification>
  </clause>

  <clause id="4348">
    <literal><![CDATA[
      T(x / (x / (x / y)),y) = x / y
    ]]></literal>
    <justification jstring="[para(75(a,1),4346(a,1,2))].">
      <j1 rule="para" parents="75 4346"/>
    </justification>
  </clause>

  <clause id="4350">
    <literal><![CDATA[
      x \ T(x,T(y,(y \ 1) * x) \ 1) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,3930,a(flip),b,4236,a)].">
      <j1 rule="hyper" parents="320 3930 4236"/>
    </justification>
  </clause>

  <clause id="4351">
    <literal><![CDATA[
      T(x,y * z) != K(z,y)
    ]]></literal>
    <literal><![CDATA[
      z \ T(z,y) = x
    ]]></literal>
    <justification jstring="[para(4236(a,2),44(a,1)),flip(a)].">
      <j1 rule="para" parents="4236 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4352">
    <literal><![CDATA[
      T(T(x \ y,z),x) = T(((x \ y) \ y) \ y,z)
    ]]></literal>
    <justification jstring="[para(4239(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4239 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4354">
    <literal><![CDATA[
      L((((x \ y) \ z) \ z) \ z,x \ y,x) = T(y \ (x * z),x \ y)
    ]]></literal>
    <justification jstring="[para(4239(a,1),757(a,1,1))].">
      <j1 rule="para" parents="4239 757"/>
    </justification>
  </clause>

  <clause id="4355">
    <literal><![CDATA[
      T(x \ (y \ x),x) = T(x,y \ 1) \ (y \ x)
    ]]></literal>
    <justification jstring="[para(4179(a,1),4239(a,2,1))].">
      <j1 rule="para" parents="4179 4239"/>
    </justification>
  </clause>

  <clause id="4357">
    <literal><![CDATA[
      T(x,(1 / x) * y) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,3769,a,b,4243,a)].">
      <j1 rule="hyper" parents="58 3769 4243"/>
    </justification>
  </clause>

  <clause id="4358">
    <literal><![CDATA[
      (((x \ 1) * y) \ y) * ((x \ 1) * y) = (x \ T(x,x \ y)) * y
    ]]></literal>
    <justification jstring="[para(4243(a,1),3952(a,2,1,2))].">
      <j1 rule="para" parents="4243 3952"/>
    </justification>
  </clause>

  <clause id="4359">
    <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),4249(a,1,2))].">
      <j1 rule="para" parents="20 4249"/>
    </justification>
  </clause>

  <clause id="4360">
    <literal><![CDATA[
      T(x,T(y,T(z,T(y,x)))) = T(x,T(T(y,x),z))
    ]]></literal>
    <justification jstring="[para(4233(a,1),4250(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4233 4250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4361">
    <literal><![CDATA[
      (x * (x * y)) \ ((x * y) * x) = K(y * x,T(x,y))
    ]]></literal>
    <justification jstring="[para(4260(a,1),910(a,1,1))].">
      <j1 rule="para" parents="4260 910"/>
    </justification>
  </clause>

  <clause id="4362">
    <literal><![CDATA[
      ((T(x,y) * y) / x) \ ((x * (x * y)) / x) = L(x,y,T(x,y))
    ]]></literal>
    <justification jstring="[para(4260(a,1),1655(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="4260 1655"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4363">
    <literal><![CDATA[
      T(x,x \ y) / y = x / ((x \ y) * x)
    ]]></literal>
    <justification jstring="[hyper(351,a,4262,a)].">
      <j1 rule="hyper" parents="351 4262"/>
    </justification>
  </clause>

  <clause id="4364">
    <literal><![CDATA[
      T(x,y) / (x * y) = x / (y * x)
    ]]></literal>
    <justification jstring="[hyper(197,a,4262,a)].">
      <j1 rule="hyper" parents="197 4262"/>
    </justification>
  </clause>

  <clause id="4365">
    <literal><![CDATA[
      (x * (y / x)) / x = y / (y / (y / x))
    ]]></literal>
    <justification jstring="[hyper(271,a,4348,a)].">
      <j1 rule="hyper" parents="271 4348"/>
    </justification>
  </clause>

  <clause id="4366">
    <literal><![CDATA[
      x / T(y,(1 / y) * x) = y \ x
    ]]></literal>
    <justification jstring="[para(4357(a,2),265(a,1,2))].">
      <j1 rule="para" parents="4357 265"/>
    </justification>
  </clause>

  <clause id="4367">
    <literal><![CDATA[
      T(x,y) / (x * y) = R(1 / y,y,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,219,a,b,4364,a),flip(a)].">
      <j1 rule="hyper" parents="320 219 4364"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4368">
    <literal><![CDATA[
      x / T(y \ 1,y * x) = (y \ 1) \ x
    ]]></literal>
    <justification jstring="[para(72(a,1),4366(a,1,2,2,1))].">
      <j1 rule="para" parents="72 4366"/>
    </justification>
  </clause>

  <clause id="4369">
    <literal><![CDATA[
      T(x,L(y,x,y)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,4321,a(flip),b,4258,a),flip(a)].">
      <j1 rule="hyper" parents="58 4321 4258"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4370">
    <literal><![CDATA[
      T((x * y) / x,L(x,y,x)) = y
    ]]></literal>
    <justification jstring="[hyper(461,a,4369,a(flip))].">
      <j1 rule="hyper" parents="461 4369"/>
    </justification>
  </clause>

  <clause id="4371">
    <literal><![CDATA[
      L(x,y,x) * T(y,x) = y * L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,4369,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 4369 17"/>
    </justification>
  </clause>

  <clause id="4372">
    <literal><![CDATA[
      L(x,y,x) \ ((x * (y * x)) / x) = y
    ]]></literal>
    <justification jstring="[hyper(1657,a,4370,a)].">
      <j1 rule="hyper" parents="1657 4370"/>
    </justification>
  </clause>

  <clause id="4373">
    <literal><![CDATA[
      (x * (y * x)) / x = L(x,y,x) * y
    ]]></literal>
    <justification jstring="[hyper(119,a,4370,a(flip),b,1654,a),flip(a)].">
      <j1 rule="hyper" parents="119 4370 1654"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4374">
    <literal><![CDATA[
      T(x,T(y,x)) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(4109(a,1),4279(a,1))].">
      <j1 rule="para" parents="4109 4279"/>
    </justification>
  </clause>

  <clause id="4375">
    <literal><![CDATA[
      R(T(x,y),x \ y,x) = (x \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(320,a,106,a(flip),b,4309,a),flip(a)].">
      <j1 rule="hyper" parents="320 106 4309"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4376">
    <literal><![CDATA[
      T(L(x,y,x) * y,x) = y * x
    ]]></literal>
    <justification jstring="[para(4319(a,1),820(a,1,1))].">
      <j1 rule="para" parents="4319 820"/>
    </justification>
  </clause>

  <clause id="4377">
    <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(4134(a,1),4319(a,1,2,2))].">
      <j1 rule="para" parents="4134 4319"/>
    </justification>
  </clause>

  <clause id="4378">
    <literal><![CDATA[
      T(x,L(x,y,x) * y) = T(x,y * x)
    ]]></literal>
    <justification jstring="[para(4376(a,1),4233(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4376 4233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4379">
    <literal><![CDATA[
      R(1 / x,x,T(y,x)) = R(1 / x,x,y)
    ]]></literal>
    <justification jstring="[hyper(670,a,4367,a)].">
      <j1 rule="hyper" parents="670 4367"/>
    </justification>
  </clause>

  <clause id="4380">
    <literal><![CDATA[
      (x * ((x \ y) * x)) / x != z
    ]]></literal>
    <literal><![CDATA[
      (x \ y) * T(x,y) = z
    ]]></literal>
    <justification jstring="[para(4373(a,2),961(a,1))].">
      <j1 rule="para" parents="4373 961"/>
    </justification>
  </clause>

  <clause id="4381">
    <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(4134(a,1),4373(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4134 4373"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4382">
    <literal><![CDATA[
      R(x,x \ y,x) * y = y * ((x \ y) \ y)
    ]]></literal>
    <justification jstring="[hyper(119,a,4375,a(flip),b,110,a),flip(a)].">
      <j1 rule="hyper" parents="119 4375 110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4383">
    <literal><![CDATA[
      T(x,L(x,y,x) * y) = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(320,a,4307,a(flip),b,4378,a),flip(a)].">
      <j1 rule="hyper" parents="320 4307 4378"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4384">
    <literal><![CDATA[
      T(x,(x \ y) * T(x,y)) = T(x,(x \ y) * x)
    ]]></literal>
    <justification jstring="[para(721(a,1),4378(a,1,2))].">
      <j1 rule="para" parents="721 4378"/>
    </justification>
  </clause>

  <clause id="4385">
    <literal><![CDATA[
      R(T(x,x * y),y,T(x,x * y)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(4383(a,1),1511(a,1,1))].">
      <j1 rule="para" parents="4383 1511"/>
    </justification>
  </clause>

  <clause id="4386">
    <literal><![CDATA[
      T(x,(y \ x) \ 1) = K(x \ y,x) \ x
    ]]></literal>
    <justification jstring="[para(72(a,1),4228(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="72 4228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4387">
    <literal><![CDATA[
      x / (y * (x / y)) = y \ (x / (x / y))
    ]]></literal>
    <justification jstring="[hyper(4172,a,4231,a)].">
      <j1 rule="hyper" parents="4172 4231"/>
    </justification>
  </clause>

  <clause id="4388">
    <literal><![CDATA[
      x \ (y / (y / x)) != z
    ]]></literal>
    <literal><![CDATA[
      y / (x * (y / x)) = z
    ]]></literal>
    <justification jstring="[para(4231(a,1),4172(a,1))].">
      <j1 rule="para" parents="4231 4172"/>
    </justification>
  </clause>

  <clause id="4389">
    <literal><![CDATA[
      (T(x,y / z) \ x) * y = z * T(z \ y,x)
    ]]></literal>
    <justification jstring="[hyper(29,a,1181,a,b,4234,a),flip(a)].">
      <j1 rule="hyper" parents="29 1181 4234"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4390">
    <literal><![CDATA[
      x * (((y * x) / y) \ z) = T(x,y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(320,a,4165,a,b,4235,a)].">
      <j1 rule="hyper" parents="320 4165 4235"/>
    </justification>
  </clause>

  <clause id="4391">
    <literal><![CDATA[
      T(T(x,y) / y,z) = T(x / T(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(239,a,4276,a,b,105,a)].">
      <j1 rule="hyper" parents="239 4276 105"/>
    </justification>
  </clause>

  <clause id="4392">
    <literal><![CDATA[
      T(T(x,y) \ y,z) = T(x \ T(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(239,a,4281,a,b,105,a)].">
      <j1 rule="hyper" parents="239 4281 105"/>
    </justification>
  </clause>

  <clause id="4393">
    <literal><![CDATA[
      x \ ((T(y,z) \ z) \ u) = x \ ((y \ T(z,y)) \ u)
    ]]></literal>
    <justification jstring="[hyper(116,a,4283,a,b,5,a)].">
      <j1 rule="hyper" parents="116 4283 5"/>
    </justification>
  </clause>

  <clause id="4394">
    <literal><![CDATA[
      (x / (x / y)) * (y \ x) = (x / y) * (x / (x / y))
    ]]></literal>
    <justification jstring="[para(643(a,1),4289(a,1,2))].">
      <j1 rule="para" parents="643 4289"/>
    </justification>
  </clause>

  <clause id="4395">
    <literal><![CDATA[
      T(x * (y / x),x) = x \ (y * ((x \ y) \ y))
    ]]></literal>
    <justification jstring="[hyper(439,a,313,a(flip),b,4293,a)].">
      <j1 rule="hyper" parents="439 313 4293"/>
    </justification>
  </clause>

  <clause id="4396">
    <literal><![CDATA[
      (x \ y) * T(y,y \ (x \ y)) = (x \ T(y,x \ 1)) * y
    ]]></literal>
    <justification jstring="[para(3913(a,2),4293(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3913 4293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4397">
    <literal><![CDATA[
      T(T(x,y),z / x) = T(T(x,y),x \ z)
    ]]></literal>
    <justification jstring="[hyper(320,a,316,a,b,4303,a),flip(a)].">
      <j1 rule="hyper" parents="320 316 4303"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4398">
    <literal><![CDATA[
      T(T(x,y),z * x) = T(T(x,y),x * z)
    ]]></literal>
    <justification jstring="[hyper(434,a,4316,a),flip(a)].">
      <j1 rule="hyper" parents="434 4316"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4399">
    <literal><![CDATA[
      T(T(x,y),x * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(T(x,y),z * x) = u
    ]]></literal>
    <justification jstring="[para(4317(a,1),434(a,1))].">
      <j1 rule="para" parents="4317 434"/>
    </justification>
  </clause>

  <clause id="4400">
    <literal><![CDATA[
      (x / (x / y)) * (y \ x) != z
    ]]></literal>
    <literal><![CDATA[
      (y \ x) * y = z
    ]]></literal>
    <justification jstring="[para(4343(a,1),251(a,1,1)),flip(b)].">
      <j1 rule="para" parents="4343 251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4401">
    <literal><![CDATA[
      T(x / (x / y),x) = L(y,y \ x,y)
    ]]></literal>
    <justification jstring="[para(4343(a,1),723(a,1,1))].">
      <j1 rule="para" parents="4343 723"/>
    </justification>
  </clause>

  <clause id="4402">
    <literal><![CDATA[
      x * T(x / (x / y),x) = y * ((y \ x) * y)
    ]]></literal>
    <justification jstring="[hyper(119,a,4401,a,b,91,a)].">
      <j1 rule="hyper" parents="119 4401 91"/>
    </justification>
  </clause>

  <clause id="4403">
    <literal><![CDATA[
      T(T(x / (x / y),x),z) = L(T(y,z),y \ x,y)
    ]]></literal>
    <justification jstring="[para(4401(a,2),20(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4401 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4404">
    <literal><![CDATA[
      L(x \ y,(x \ y) \ y,x \ y) = T(y / x,y)
    ]]></literal>
    <justification jstring="[para(72(a,1),4401(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="72 4401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4405">
    <literal><![CDATA[
      (T(x,x \ y) / y) \ x = (x \ y) * x
    ]]></literal>
    <justification jstring="[hyper(188,a,4363,a(flip))].">
      <j1 rule="hyper" parents="188 4363"/>
    </justification>
  </clause>

  <clause id="4406">
    <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(4363(a,2),687(a,1,2,1))].">
      <j1 rule="para" parents="4363 687"/>
    </justification>
  </clause>

  <clause id="4407">
    <literal><![CDATA[
      T(x,y \ 1) / (y \ x) = x / ((x \ (y \ x)) * x)
    ]]></literal>
    <justification jstring="[para(4180(a,1),4363(a,1,1))].">
      <j1 rule="para" parents="4180 4363"/>
    </justification>
  </clause>

  <clause id="4408">
    <literal><![CDATA[
      R(1 / (1 / (1 / x)),x,y) = (x * (y / (x * y))) / x
    ]]></literal>
    <justification jstring="[para(4365(a,1),855(a,1,1))].">
      <j1 rule="para" parents="4365 855"/>
    </justification>
  </clause>

  <clause id="4409">
    <literal><![CDATA[
      T(x \ 1,x * y) = ((x \ 1) \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(188,a,4368,a),flip(a)].">
      <j1 rule="hyper" parents="188 4368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4410">
    <literal><![CDATA[
      R(1 / x,x,y / x) = R(1 / x,x,x \ y)
    ]]></literal>
    <justification jstring="[para(107(a,1),4379(a,1,3)),flip(a)].">
      <j1 rule="para" parents="107 4379"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4411">
    <literal><![CDATA[
      K(x \ y,x) \ x = x * K(x,y / x)
    ]]></literal>
    <justification jstring="[hyper(58,a,3900,a(flip),b,4386,a),flip(a)].">
      <j1 rule="hyper" parents="58 3900 4386"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4412">
    <literal><![CDATA[
      T(T(x,y),z * x) != u
    ]]></literal>
    <literal><![CDATA[
      T(T(x,x * z),y) = u
    ]]></literal>
    <justification jstring="[para(4398(a,2),434(a,1))].">
      <j1 rule="para" parents="4398 434"/>
    </justification>
  </clause>

  <clause id="4413">
    <literal><![CDATA[
      (T(x,y \ 1) / (y \ x)) \ x = (x \ (y \ x)) * x
    ]]></literal>
    <justification jstring="[para(4180(a,1),4405(a,1,1,1))].">
      <j1 rule="para" parents="4180 4405"/>
    </justification>
  </clause>

  <clause id="4414">
    <literal><![CDATA[
      T((x / y) \ 1,x) = (((x / y) \ 1) \ y) \ y
    ]]></literal>
    <justification jstring="[para(7(a,1),4409(a,1,2))].">
      <j1 rule="para" parents="7 4409"/>
    </justification>
  </clause>

  <clause id="4415">
    <literal><![CDATA[
      K(x \ y,x) \ 1 = K(x,y / x)
    ]]></literal>
    <justification jstring="[hyper(3485,a,4411,a)].">
      <j1 rule="hyper" parents="3485 4411"/>
    </justification>
  </clause>

  <clause id="4416">
    <literal><![CDATA[
      K(x,(x * y) / x) = K(y,x) \ 1
    ]]></literal>
    <justification jstring="[para(4(a,1),4415(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4 4415"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4417">
    <literal><![CDATA[
      K(T(x,y),y) \ 1 = K(y,x)
    ]]></literal>
    <justification jstring="[para(225(a,1),4416(a,1,2)),flip(a)].">
      <j1 rule="para" parents="225 4416"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4419">
    <literal><![CDATA[
      R(x,K(x,y),z) = x
    ]]></literal>
    <justification jstring="[para(4417(a,1),4091(a,1,2))].">
      <j1 rule="para" parents="4417 4091"/>
    </justification>
  </clause>

  <clause id="4420">
    <literal><![CDATA[
      R(T(x,y),K(x,z),u) = T(x,y)
    ]]></literal>
    <justification jstring="[para(4419(a,1),22(a,2,1))].">
      <j1 rule="para" parents="4419 22"/>
    </justification>
  </clause>

  <clause id="4421">
    <literal><![CDATA[
      (L(x,y,z) * K(x,u)) * w = L(x,y,z) * (K(x,u) * w)
    ]]></literal>
    <justification jstring="[para(4419(a,1),513(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4419 513"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4422">
    <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(4420(a,1),514(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4420 514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4423">
    <literal><![CDATA[
      R(x / y,y,x / y) = y \ T(x,y \ x)
    ]]></literal>
    <justification jstring="[para(4113(a,1),4336(a,2,2))].">
      <j1 rule="para" parents="4113 4336"/>
    </justification>
  </clause>

  <clause id="4424">
    <literal><![CDATA[
      R(x,x \ y,x) * y = (x * (y / x)) * x
    ]]></literal>
    <justification jstring="[hyper(320,a,4304,a,b,4382,a),flip(a)].">
      <j1 rule="hyper" parents="320 4304 4382"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4425">
    <literal><![CDATA[
      R(x,y / x,x) = R(x,x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(30,a,508,a,b,4424,a)].">
      <j1 rule="hyper" parents="30 508 4424"/>
    </justification>
  </clause>

  <clause id="4426">
    <literal><![CDATA[
      R(x,y / x,x) = (x \ y) \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,4335,a(flip),b,4425,a),flip(a)].">
      <j1 rule="hyper" parents="320 4335 4425"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4427">
    <literal><![CDATA[
      R(x,x \ (y \ x),x) = ((y \ T(x,y \ 1)) * x) / (y \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,3922,a(flip),b,4425,a),flip(a)].">
      <j1 rule="hyper" parents="58 3922 4425"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4428">
    <literal><![CDATA[
      R(x,(x * y) / x,x) = R(x,y,x)
    ]]></literal>
    <justification jstring="[para(4(a,1),4425(a,2,2))].">
      <j1 rule="para" parents="4 4425"/>
    </justification>
  </clause>

  <clause id="4429">
    <literal><![CDATA[
      R(x,T(y,x),x) = R(x,y,x)
    ]]></literal>
    <justification jstring="[para(225(a,1),4428(a,1,2)),flip(a)].">
      <j1 rule="para" parents="225 4428"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4430">
    <literal><![CDATA[
      R(x,T(y,x),T(x,y)) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,4333,a,b,4429,a)].">
      <j1 rule="hyper" parents="58 4333 4429"/>
    </justification>
  </clause>

  <clause id="4431">
    <literal><![CDATA[
      R(R(x,y,z),T(u,x),T(x,u)) = R(R(x,u,x),y,z)
    ]]></literal>
    <justification jstring="[para(4430(a,1),26(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4430 26"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4432">
    <literal><![CDATA[
      (x \ (y * x)) \ T(y * x,x) = R(x,y,x)
    ]]></literal>
    <justification jstring="[para(6(a,1),4426(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6 4426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4433">
    <literal><![CDATA[
      (x * y) / T(T(x,y),y) = T(y,x)
    ]]></literal>
    <justification jstring="[hyper(117,a,4245,a(flip),b,4255,a)].">
      <j1 rule="hyper" parents="117 4245 4255"/>
    </justification>
  </clause>

  <clause id="4434">
    <literal><![CDATA[
      T(x,y) \ (y * x) = T(T(y,x),x)
    ]]></literal>
    <justification jstring="[hyper(116,a,4245,a(flip),b,4255,a)].">
      <j1 rule="hyper" parents="116 4245 4255"/>
    </justification>
  </clause>

  <clause id="4435">
    <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,4255,a)].">
      <j1 rule="hyper" parents="58 150 4255"/>
    </justification>
  </clause>

  <clause id="4436">
    <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),4434(a,1,1))].">
      <j1 rule="para" parents="20 4434"/>
    </justification>
  </clause>

  <clause id="4437">
    <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(4233(a,1),4280(a,1,2,1))].">
      <j1 rule="para" parents="4233 4280"/>
    </justification>
  </clause>

  <clause id="4438">
    <literal><![CDATA[
      T(x,T(y,T(z,T(y,x)))) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,4250,a(flip),b,4360,a),flip(a)].">
      <j1 rule="hyper" parents="320 4250 4360"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4439">
    <literal><![CDATA[
      T(x,(x \ y) * T(x,y)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,4311,a(flip),b,4384,a),flip(a)].">
      <j1 rule="hyper" parents="320 4311 4384"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4440">
    <literal><![CDATA[
      R(T(x,y),x \ y,T(x,y)) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(4439(a,1),1508(a,1,1))].">
      <j1 rule="para" parents="4439 1508"/>
    </justification>
  </clause>

  <clause id="4441">
    <literal><![CDATA[
      x * K(y \ (y / (x \ z)),y) = (T(y,x / z) \ y) * x
    ]]></literal>
    <justification jstring="[hyper(320,a,1429,a(flip),b,4389,a)].">
      <j1 rule="hyper" parents="320 1429 4389"/>
    </justification>
  </clause>

  <clause id="4442">
    <literal><![CDATA[
      ((x * y) / x) \ (y * z) = T(y,x) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,1457,a,b,4390,a)].">
      <j1 rule="hyper" parents="58 1457 4390"/>
    </justification>
  </clause>

  <clause id="4443">
    <literal><![CDATA[
      T(x,y) * z != x * (((y * x) / y) \ u)
    ]]></literal>
    <literal><![CDATA[
      x \ u = z
    ]]></literal>
    <justification jstring="[para(4390(a,2),38(a,1)),flip(a)].">
      <j1 rule="para" parents="4390 38"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4444">
    <literal><![CDATA[
      ((x / y) \ T((x / y) * y,y)) * (x / y) = y \ (x * ((y \ x) \ x))
    ]]></literal>
    <justification jstring="[hyper(58,a,4338,a,b,4395,a)].">
      <j1 rule="hyper" parents="58 4338 4395"/>
    </justification>
  </clause>

  <clause id="4445">
    <literal><![CDATA[
      x \ (y * ((x \ y) \ y)) = x * (y / T(x,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,4278,a(flip),b,4395,a),flip(a)].">
      <j1 rule="hyper" parents="58 4278 4395"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4446">
    <literal><![CDATA[
      (x / (x / y)) * x = y * ((y \ x) * y)
    ]]></literal>
    <justification jstring="[hyper(284,a,4402,a)].">
      <j1 rule="hyper" parents="284 4402"/>
    </justification>
  </clause>

  <clause id="4447">
    <literal><![CDATA[
      R(1 / x,x,y / x) = (x \ y) / y
    ]]></literal>
    <justification jstring="[hyper(320,a,407,a(flip),b,4410,a),flip(a)].">
      <j1 rule="hyper" parents="320 407 4410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4448">
    <literal><![CDATA[
      (x / y) / (y * (x / y)) = (y \ x) / x
    ]]></literal>
    <justification jstring="[hyper(737,a,4447,a)].">
      <j1 rule="hyper" parents="737 4447"/>
    </justification>
  </clause>

  <clause id="4449">
    <literal><![CDATA[
      ((x \ y) / y) * (x * (y / x)) = y / x
    ]]></literal>
    <justification jstring="[hyper(133,a,4448,a)].">
      <j1 rule="hyper" parents="133 4448"/>
    </justification>
  </clause>

  <clause id="4450">
    <literal><![CDATA[
      T(x,y) * (T(y,z) * x) = x * (T(y,z) * T(x,y))
    ]]></literal>
    <justification jstring="[para(4435(a,1),1121(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4435 1121"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4451">
    <literal><![CDATA[
      T(x,T((y \ z) / z,x)) = T(x,T(y \ 1,x))
    ]]></literal>
    <justification jstring="[hyper(320,a,3884,a(flip),b,4224,a),flip(a)].">
      <j1 rule="hyper" parents="320 3884 4224"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4452">
    <literal><![CDATA[
      T(x,T(y \ 1,x)) = T(x,(y \ z) / z)
    ]]></literal>
    <justification jstring="[hyper(4374,a,4451,a),flip(a)].">
      <j1 rule="hyper" parents="4374 4451"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4453">
    <literal><![CDATA[
      T(x,(y \ z) / z) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(4374,a,4452,a),flip(a)].">
      <j1 rule="hyper" parents="4374 4452"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4454">
    <literal><![CDATA[
      T(x,(y \ z) / z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ 1) = u
    ]]></literal>
    <justification jstring="[para(4452(a,1),4374(a,1))].">
      <j1 rule="para" parents="4452 4374"/>
    </justification>
  </clause>

  <clause id="4455">
    <literal><![CDATA[
      T(x,y / (z * y)) = T(x,z \ 1)
    ]]></literal>
    <justification jstring="[para(4(a,1),4453(a,1,2,1))].">
      <j1 rule="para" parents="4 4453"/>
    </justification>
  </clause>

  <clause id="4456">
    <literal><![CDATA[
      T(x,(y / z) \ 1) = T(x,z / y)
    ]]></literal>
    <justification jstring="[para(75(a,1),4453(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="75 4453"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4457">
    <literal><![CDATA[
      T(x / (y * x),y \ 1) = x / (y * x)
    ]]></literal>
    <justification jstring="[hyper(344,a,4455,a),flip(a)].">
      <j1 rule="hyper" parents="344 4455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4461">
    <literal><![CDATA[
      T(x \ T(x,(y * z) / z),T(y,u)) = R(x \ T(x,y),y,z)
    ]]></literal>
    <justification jstring="[para(4456(a,1),3955(a,1,1,2))].">
      <j1 rule="para" parents="4456 3955"/>
    </justification>
  </clause>

  <clause id="4462">
    <literal><![CDATA[
      T(x,y / z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,(z / y) \ 1) = u
    ]]></literal>
    <justification jstring="[para(75(a,1),4454(a,1,2,1))].">
      <j1 rule="para" parents="75 4454"/>
    </justification>
  </clause>

  <clause id="4463">
    <literal><![CDATA[
      L(T(x,y),T(y,x),x) = T(x,y * x)
    ]]></literal>
    <justification jstring="[hyper(1093,a,4256,a),flip(a)].">
      <j1 rule="hyper" parents="1093 4256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4464">
    <literal><![CDATA[
      L(x,T(y,x),x) * y = y * T(x,y * x)
    ]]></literal>
    <justification jstring="[para(4463(a,1),237(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4463 237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4465">
    <literal><![CDATA[
      L(x,T(y,x),x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(30,a,4319,a(flip),b,4464,a),flip(a)].">
      <j1 rule="hyper" parents="30 4319 4464"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4466">
    <literal><![CDATA[
      L(x,(x * y) / x,x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[para(224(a,1),4465(a,1,2)),flip(a)].">
      <j1 rule="para" parents="224 4465"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4467">
    <literal><![CDATA[
      L(x,T(y,x),x) * T(y,x) = y * L(x,y,x)
    ]]></literal>
    <justification jstring="[para(4465(a,2),4371(a,1,1))].">
      <j1 rule="para" parents="4465 4371"/>
    </justification>
  </clause>

  <clause id="4468">
    <literal><![CDATA[
      T(x,y) * T(y,x * y) = x * L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,722,a(flip),b,4467,a)].">
      <j1 rule="hyper" parents="58 722 4467"/>
    </justification>
  </clause>

  <clause id="4469">
    <literal><![CDATA[
      T(x,y) * T(y,y * x) = x * L(y,x,y)
    ]]></literal>
    <justification jstring="[para(4307(a,1),4468(a,1,2))].">
      <j1 rule="para" parents="4307 4468"/>
    </justification>
  </clause>

  <clause id="4470">
    <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(4257(a,1),229(a,1,1,2))].">
      <j1 rule="para" parents="4257 229"/>
    </justification>
  </clause>

  <clause id="4471">
    <literal><![CDATA[
      R(x,y,x) * T(x * y,x) = T(x * y,x) * T(x,y)
    ]]></literal>
    <justification jstring="[para(4241(a,1),4257(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4241 4257"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4472">
    <literal><![CDATA[
      T(x,x * T(T(x,y) \ y,z)) = T(x,x * T(T(y,x) / x,z))
    ]]></literal>
    <justification jstring="[para(4248(a,2),4312(a,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="4248 4312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4473">
    <literal><![CDATA[
      T(x,y) * (T(y,x) / x) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(1385(a,1),4313(a,1,2))].">
      <j1 rule="para" parents="1385 4313"/>
    </justification>
  </clause>

  <clause id="4474">
    <literal><![CDATA[
      T(x,y) * z != x * (y / x)
    ]]></literal>
    <literal><![CDATA[
      T(y,x) / x = z
    ]]></literal>
    <justification jstring="[para(4473(a,1),38(a,1)),flip(a)].">
      <j1 rule="para" parents="4473 38"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4475">
    <literal><![CDATA[
      T(x,y) * (y / T(x,y)) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(4246(a,1),4473(a,1,2))].">
      <j1 rule="para" parents="4246 4473"/>
    </justification>
  </clause>

  <clause id="4476">
    <literal><![CDATA[
      T(x,y) * z != x * (y / x)
    ]]></literal>
    <literal><![CDATA[
      y / T(x,y) = z
    ]]></literal>
    <justification jstring="[para(4475(a,1),38(a,1)),flip(a)].">
      <j1 rule="para" parents="4475 38"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4477">
    <literal><![CDATA[
      ((x \ y) * x) / T(x,y) = x \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(30,a,1379,a(flip),b,4325,a),flip(a)].">
      <j1 rule="hyper" parents="30 1379 4325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4478">
    <literal><![CDATA[
      (x \ T(y,x)) * T(x,y) = (x \ y) * x
    ]]></literal>
    <justification jstring="[hyper(133,a,4477,a)].">
      <j1 rule="hyper" parents="133 4477"/>
    </justification>
  </clause>

  <clause id="4479">
    <literal><![CDATA[
      (T(x,y) \ y) * T(x,y) = (x \ y) * x
    ]]></literal>
    <justification jstring="[hyper(4282,a,4478,a)].">
      <j1 rule="hyper" parents="4282 4478"/>
    </justification>
  </clause>

  <clause id="4480">
    <literal><![CDATA[
      x \ T(x,T(y,y \ x) \ 1) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(4243(a,1),4350(a,1,2,2,1))].">
      <j1 rule="para" parents="4243 4350"/>
    </justification>
  </clause>

  <clause id="4481">
    <literal><![CDATA[
      T(x,T(y,y \ x) \ 1) = x * K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(134,a,4480,a),flip(a)].">
      <j1 rule="hyper" parents="134 4480"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4482">
    <literal><![CDATA[
      K(x,(y \ x) / x) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(3931,a,4481,a)].">
      <j1 rule="hyper" parents="3931 4481"/>
    </justification>
  </clause>

  <clause id="4483">
    <literal><![CDATA[
      K(x \ ((x \ 1) \ y),x) = K(y,(x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,3943,a,b,4482,a)].">
      <j1 rule="hyper" parents="58 3943 4482"/>
    </justification>
  </clause>

  <clause id="4484">
    <literal><![CDATA[
      K(x \ ((x \ 1) \ y),x) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,3554,a(flip),b,4483,a),flip(a)].">
      <j1 rule="hyper" parents="320 3554 4483"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4485">
    <literal><![CDATA[
      K(x \ ((1 / x) \ y),x) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,3987,a,b,4484,a)].">
      <j1 rule="hyper" parents="58 3987 4484"/>
    </justification>
  </clause>

  <clause id="4486">
    <literal><![CDATA[
      K((1 / x) * y,x) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[para(4(a,1),4485(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4 4485"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4487">
    <literal><![CDATA[
      K((1 / x) * (y * x),x) = K(T(y,x),x)
    ]]></literal>
    <justification jstring="[para(17(a,2),4486(a,2,1))].">
      <j1 rule="para" parents="17 4486"/>
    </justification>
  </clause>

  <clause id="4488">
    <literal><![CDATA[
      K((x \ 1) \ y,x \ 1) = K(x * y,x \ 1)
    ]]></literal>
    <justification jstring="[para(72(a,1),4486(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="72 4486"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4489">
    <literal><![CDATA[
      K(T((1 / x) * y,x),x) = K(T(x \ y,x),x)
    ]]></literal>
    <justification jstring="[para(800(a,1),4487(a,1,1))].">
      <j1 rule="para" parents="800 4487"/>
    </justification>
  </clause>

  <clause id="4490">
    <literal><![CDATA[
      ((x \ 1) \ y) * (x \ 1) = y * K(x * y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(119,a,4488,a(flip),b,85,a),flip(a)].">
      <j1 rule="hyper" parents="119 4488 85"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4491">
    <literal><![CDATA[
      K(T((x \ 1) * y,x),x) = K(T(x \ y,x),x)
    ]]></literal>
    <justification jstring="[hyper(58,a,4007,a(flip),b,4489,a)].">
      <j1 rule="hyper" parents="58 4007 4489"/>
    </justification>
  </clause>

  <clause id="4492">
    <literal><![CDATA[
      K(T(x \ y,x),x) \ 1 = K(x,(x \ 1) * y)
    ]]></literal>
    <justification jstring="[para(4491(a,1),4417(a,1,1))].">
      <j1 rule="para" parents="4491 4417"/>
    </justification>
  </clause>

  <clause id="4493">
    <literal><![CDATA[
      K(x,(x \ 1) * y) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,4417,a(flip),b,4492,a),flip(a)].">
      <j1 rule="hyper" parents="58 4417 4492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4494">
    <literal><![CDATA[
      K(x \ 1,(x \ 1) \ y) = K(x \ 1,x * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,3598,a(flip),b,4493,a),flip(a)].">
      <j1 rule="hyper" parents="58 3598 4493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4495">
    <literal><![CDATA[
      K(x * y,T(y,x)) != z
    ]]></literal>
    <literal><![CDATA[
      K(y * x,y) = z
    ]]></literal>
    <justification jstring="[para(4361(a,1),307(a,1))].">
      <j1 rule="para" parents="4361 307"/>
    </justification>
  </clause>

  <clause id="4496">
    <literal><![CDATA[
      (x / y) * (x / (x / y)) = (y \ x) * y
    ]]></literal>
    <justification jstring="[hyper(4400,a,4394,a),flip(a)].">
      <j1 rule="hyper" parents="4400 4394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4497">
    <literal><![CDATA[
      ((x \ y) * x) * x = y * (y / (y / x))
    ]]></literal>
    <justification jstring="[para(4496(a,1),914(a,1,1))].">
      <j1 rule="para" parents="4496 914"/>
    </justification>
  </clause>

  <clause id="4498">
    <literal><![CDATA[
      ((x \ y) * x) * T(x,y) = y * (y / (y / T(x,y)))
    ]]></literal>
    <justification jstring="[para(4479(a,1),4497(a,1,1))].">
      <j1 rule="para" parents="4479 4497"/>
    </justification>
  </clause>

  <clause id="4499">
    <literal><![CDATA[
      T(x,y) / ((y \ 1) \ x) = x / ((x \ ((y \ 1) \ x)) * x)
    ]]></literal>
    <justification jstring="[para(2959(a,1),4407(a,1,1))].">
      <j1 rule="para" parents="2959 4407"/>
    </justification>
  </clause>

  <clause id="4500">
    <literal><![CDATA[
      (T(x,y) / ((y \ 1) \ x)) \ x = (x \ ((y \ 1) \ x)) * x
    ]]></literal>
    <justification jstring="[para(2959(a,1),4413(a,1,1,1))].">
      <j1 rule="para" parents="2959 4413"/>
    </justification>
  </clause>

  <clause id="4501">
    <literal><![CDATA[
      x * (x / (x / T(y,x))) = y * ((y \ x) * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,4324,a(flip),b,4498,a),flip(a)].">
      <j1 rule="hyper" parents="58 4324 4498"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4502">
    <literal><![CDATA[
      x / (x / T(y,x)) = T(x / (x / y),x)
    ]]></literal>
    <justification jstring="[hyper(239,a,4446,a,b,4501,a),flip(a)].">
      <j1 rule="hyper" parents="239 4446 4501"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4503">
    <literal><![CDATA[
      T(x / (x / y),x) \ x = x / T(y,x)
    ]]></literal>
    <justification jstring="[hyper(188,a,4502,a)].">
      <j1 rule="hyper" parents="188 4502"/>
    </justification>
  </clause>

  <clause id="4504">
    <literal><![CDATA[
      x / T(y \ x,x) = T(x / y,x) \ x
    ]]></literal>
    <justification jstring="[para(72(a,1),4503(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="72 4503"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4505">
    <literal><![CDATA[
      L(x,x \ y,x) \ y = y / T(x,y)
    ]]></literal>
    <justification jstring="[para(4401(a,1),4503(a,1,1))].">
      <j1 rule="para" parents="4401 4503"/>
    </justification>
  </clause>

  <clause id="4506">
    <literal><![CDATA[
      L(x,x \ y,x) \ y = T(y,x) / x
    ]]></literal>
    <justification jstring="[hyper(320,a,4246,a,b,4505,a),flip(a)].">
      <j1 rule="hyper" parents="320 4246 4505"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4507">
    <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(2101(a,1),4300(a,1,2,1))].">
      <j1 rule="para" parents="2101 4300"/>
    </justification>
  </clause>

  <clause id="4508">
    <literal><![CDATA[
      T(L(L(x,y,x),z,u) * y,x) = L(x,z,u) * T(y,x)
    ]]></literal>
    <justification jstring="[para(4320(a,1),1928(a,1,1))].">
      <j1 rule="para" parents="4320 1928"/>
    </justification>
  </clause>

  <clause id="4509">
    <literal><![CDATA[
      R(x,y,x) * T(x * y,x) = (x * y) * R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,4342,a(flip),b,4471,a),flip(a)].">
      <j1 rule="hyper" parents="320 4342 4471"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4510">
    <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(4509(a,1),4337(a,1,2))].">
      <j1 rule="para" parents="4509 4337"/>
    </justification>
  </clause>

  <clause id="4511">
    <literal><![CDATA[
      (x \ T(y,x \ 1)) * y = (x \ y) * T(y,x \ 1)
    ]]></literal>
    <justification jstring="[para(4180(a,1),4396(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4180 4396"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4512">
    <literal><![CDATA[
      L(x,K(y,z),L(y,u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(479,a,4421,a)].">
      <j1 rule="hyper" parents="479 4421"/>
    </justification>
  </clause>

  <clause id="4513">
    <literal><![CDATA[
      (K(x,y) * L(x,z,u)) * w = L(x,z,u) * (K(x,y) * w)
    ]]></literal>
    <justification jstring="[para(3336(a,1),4421(a,1,1))].">
      <j1 rule="para" parents="3336 4421"/>
    </justification>
  </clause>

  <clause id="4514">
    <literal><![CDATA[
      L(x,K(y,z),L(y,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      x = v5
    ]]></literal>
    <justification jstring="[para(4512(a,1),45(a,2))].">
      <j1 rule="para" parents="4512 45"/>
    </justification>
  </clause>

  <clause id="4515">
    <literal><![CDATA[
      L(x,K(y,z),y) = x
    ]]></literal>
    <justification jstring="[para(372(a,1),4512(a,1,3))].">
      <j1 rule="para" parents="372 4512"/>
    </justification>
  </clause>

  <clause id="4520">
    <literal><![CDATA[
      (T(x,(y / z) / (1 / z)) \ x) * (y / z) = T(y,x) / z
    ]]></literal>
    <justification jstring="[hyper(58,a,1439,a(flip),b,4441,a),flip(a)].">
      <j1 rule="hyper" parents="58 1439 4441"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4521">
    <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(4431(a,1),4271(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4431 4271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4522">
    <literal><![CDATA[
      R(x,x \ (y \ x),x) = ((y \ x) * T(x,y \ 1)) / (y \ x)
    ]]></literal>
    <justification jstring="[para(4511(a,1),4427(a,2,1))].">
      <j1 rule="para" parents="4511 4427"/>
    </justification>
  </clause>

  <clause id="4523">
    <literal><![CDATA[
      T(x \ T(x,y),T(y,z)) = R(x \ T(x,y),y,u)
    ]]></literal>
    <justification jstring="[para(6(a,1),4461(a,1,1,2,2))].">
      <j1 rule="para" parents="6 4461"/>
    </justification>
  </clause>

  <clause id="4524">
    <literal><![CDATA[
      R(x \ T(x,y),y,z) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,2925,a(flip),b,4523,a),flip(a)].">
      <j1 rule="hyper" parents="58 2925 4523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4525">
    <literal><![CDATA[
      (x \ T(x,y)) \ (((x * y) / x) * z) = y * z
    ]]></literal>
    <justification jstring="[para(4524(a,1),3871(a,1,1))].">
      <j1 rule="para" parents="4524 3871"/>
    </justification>
  </clause>

  <clause id="4526">
    <literal><![CDATA[
      L(x,y \ 1,(z * y) / z) = y * ((y \ 1) * x)
    ]]></literal>
    <justification jstring="[hyper(3888,a,4525,a)].">
      <j1 rule="hyper" parents="3888 4525"/>
    </justification>
  </clause>

  <clause id="4527">
    <literal><![CDATA[
      (x \ T(x,x \ y)) \ y = (x \ y) * x
    ]]></literal>
    <justification jstring="[para(77(a,1),4525(a,1,2))].">
      <j1 rule="para" parents="77 4525"/>
    </justification>
  </clause>

  <clause id="4529">
    <literal><![CDATA[
      (x \ ((x \ y) \ y)) \ y = (x \ y) * x
    ]]></literal>
    <justification jstring="[hyper(58,a,659,a(flip),b,4527,a)].">
      <j1 rule="hyper" parents="58 659 4527"/>
    </justification>
  </clause>

  <clause id="4530">
    <literal><![CDATA[
      x / ((y \ x) * y) = y \ ((y \ x) \ x)
    ]]></literal>
    <justification jstring="[hyper(197,a,4529,a)].">
      <j1 rule="hyper" parents="197 4529"/>
    </justification>
  </clause>

  <clause id="4531">
    <literal><![CDATA[
      (x * (y / x)) / y = y / ((x \ y) * x)
    ]]></literal>
    <justification jstring="[hyper(320,a,4178,a,b,4530,a)].">
      <j1 rule="hyper" parents="320 4178 4530"/>
    </justification>
  </clause>

  <clause id="4532">
    <literal><![CDATA[
      L(x,y \ 1,(z * y) / z) = L(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,257,a(flip),b,4526,a),flip(a)].">
      <j1 rule="hyper" parents="320 257 4526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4533">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) \ 1) * z) = L(z,T(x,y) \ 1,x)
    ]]></literal>
    <justification jstring="[para(225(a,1),4526(a,1,3)),flip(a)].">
      <j1 rule="para" parents="225 4526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4534">
    <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),4532(a,1,3)),flip(a)].">
      <j1 rule="para" parents="225 4532"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4535">
    <literal><![CDATA[
      L(x,1 / T(y,y \ z),(y \ z) \ z) = L(x,T(y,y \ z) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(2864,a,4534,a)].">
      <j1 rule="hyper" parents="2864 4534"/>
    </justification>
  </clause>

  <clause id="4536">
    <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(4301(a,2),4259(a,1))].">
      <j1 rule="para" parents="4301 4259"/>
    </justification>
  </clause>

  <clause id="4537">
    <literal><![CDATA[
      (((x \ 1) * y) \ y) * ((x \ 1) * y) = x * (y / x)
    ]]></literal>
    <justification jstring="[hyper(320,a,4150,a(flip),b,4358,a),flip(a)].">
      <j1 rule="hyper" parents="320 4150 4358"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4538">
    <literal><![CDATA[
      T(x,T(x * T(y / x,z),x)) = T(x,x * T(T(x,y) \ y,z))
    ]]></literal>
    <justification jstring="[para(1550(a,2),4472(a,2,2)),flip(a)].">
      <j1 rule="para" parents="1550 4472"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4539">
    <literal><![CDATA[
      T(x,x * T(T(x,y) \ y,z)) = T(x,x * T(y / x,z))
    ]]></literal>
    <justification jstring="[hyper(4374,a,4538,a),flip(a)].">
      <j1 rule="hyper" parents="4374 4538"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4540">
    <literal><![CDATA[
      T(x,x * T(T(x,y) \ y,z)) = T(x,x * T(x \ y,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,4312,a(flip),b,4539,a),flip(a)].">
      <j1 rule="hyper" parents="320 4312 4539"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4541">
    <literal><![CDATA[
      L(x,(x * y) / x,x) = L(x,y,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,4362,a(flip),b,4106,a),flip(a)].">
      <j1 rule="hyper" parents="58 4362 4106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4542">
    <literal><![CDATA[
      L(x,y,T(x,y)) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,4466,a(flip),b,4541,a),flip(a)].">
      <j1 rule="hyper" parents="58 4466 4541"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4543">
    <literal><![CDATA[
      (x \ T(x,y)) \ z = (T(x,y) \ x) * z
    ]]></literal>
    <justification jstring="[para(4524(a,1),4176(a,1,1))].">
      <j1 rule="para" parents="4524 4176"/>
    </justification>
  </clause>

  <clause id="4544">
    <literal><![CDATA[
      (T(x,y) \ x) * z = x * (T(x,y) \ z)
    ]]></literal>
    <justification jstring="[hyper(4199,a,4543,a),flip(a)].">
      <j1 rule="hyper" parents="4199 4543"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4545">
    <literal><![CDATA[
      (T(x,y) \ x) * (T(x,y) * z) = x * z
    ]]></literal>
    <justification jstring="[hyper(4142,a,4543,a),flip(a)].">
      <j1 rule="hyper" parents="4142 4543"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4546">
    <literal><![CDATA[
      (x \ T(x,y)) \ z = T(y,x) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(320,a,4235,a,b,4543,a),flip(a)].">
      <j1 rule="hyper" parents="320 4235 4543"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4548">
    <literal><![CDATA[
      T(x,y) * (x \ z) = y * (T(y,x) \ z)
    ]]></literal>
    <justification jstring="[hyper(4237,a,4544,a)].">
      <j1 rule="hyper" parents="4237 4544"/>
    </justification>
  </clause>

  <clause id="4549">
    <literal><![CDATA[
      x * (T(x,(y / z) / (1 / z)) \ (y / z)) = T(y,x) / z
    ]]></literal>
    <justification jstring="[hyper(58,a,4520,a(flip),b,4544,a),flip(a)].">
      <j1 rule="hyper" parents="58 4520 4544"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4550">
    <literal><![CDATA[
      x * T(x \ y,z) = z * (T(z,y / x) \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,4389,a(flip),b,4544,a)].">
      <j1 rule="hyper" parents="58 4389 4544"/>
    </justification>
  </clause>

  <clause id="4551">
    <literal><![CDATA[
      T(x,y) * (x \ (T(y,x) * z)) = y * z
    ]]></literal>
    <justification jstring="[hyper(4237,a,4545,a)].">
      <j1 rule="hyper" parents="4237 4545"/>
    </justification>
  </clause>

  <clause id="4552">
    <literal><![CDATA[
      ((x * y) / x) \ (T(x,y) * z) = y \ (x * z)
    ]]></literal>
    <justification jstring="[hyper(116,a,4545,a(flip),b,4165,a),flip(a)].">
      <j1 rule="hyper" parents="116 4545 4165"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4553">
    <literal><![CDATA[
      T(x,y) * (T(y,x) * z) = x * (y * z)
    ]]></literal>
    <justification jstring="[para(4545(a,1),4234(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4545 4234"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4554">
    <literal><![CDATA[
      T(x,y) \ (T(y,x) \ z) = x \ (y \ z)
    ]]></literal>
    <justification jstring="[hyper(116,a,1117,a(flip),b,4548,a)].">
      <j1 rule="hyper" parents="116 1117 4548"/>
    </justification>
  </clause>

  <clause id="4555">
    <literal><![CDATA[
      T(x,y) * (x \ (T(y,x) * z)) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (y * z) = w
    ]]></literal>
    <justification jstring="[para(4548(a,2),615(a,1))].">
      <j1 rule="para" parents="4548 615"/>
    </justification>
  </clause>

  <clause id="4556">
    <literal><![CDATA[
      T(x,y) * (x \ (T(y,x) * z)) != u * w
    ]]></literal>
    <literal><![CDATA[
      (y * z) / w = u
    ]]></literal>
    <justification jstring="[para(4548(a,2),617(a,1))].">
      <j1 rule="para" parents="4548 617"/>
    </justification>
  </clause>

  <clause id="4557">
    <literal><![CDATA[
      x * (T(x,y) \ x) != z
    ]]></literal>
    <literal><![CDATA[
      (y * x) / y = z
    ]]></literal>
    <justification jstring="[para(4548(a,1),4126(a,1))].">
      <j1 rule="para" parents="4548 4126"/>
    </justification>
  </clause>

  <clause id="4558">
    <literal><![CDATA[
      ((x * y) / x) * (x * z) = y * (T(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(119,a,4551,a(flip),b,4442,a)].">
      <j1 rule="hyper" parents="119 4551 4442"/>
    </justification>
  </clause>

  <clause id="4559">
    <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),4551(a,1,2))].">
      <j1 rule="para" parents="474 4551"/>
    </justification>
  </clause>

  <clause id="4560">
    <literal><![CDATA[
      (x * y) \ (x * (y * z)) = L(z,T(y,x),T(x,y))
    ]]></literal>
    <justification jstring="[para(4553(a,1),4273(a,1,2))].">
      <j1 rule="para" parents="4553 4273"/>
    </justification>
  </clause>

  <clause id="4561">
    <literal><![CDATA[
      L(x,y,x) \ (T(x * y,(y * x) / y) \ z) = ((y * x) / y) \ ((x * y) \ z)
    ]]></literal>
    <justification jstring="[para(718(a,1),4554(a,1,1))].">
      <j1 rule="para" parents="718 4554"/>
    </justification>
  </clause>

  <clause id="4562">
    <literal><![CDATA[
      x \ T(x * y,z) = z * (T(z,y / (x \ 1)) \ y)
    ]]></literal>
    <justification jstring="[hyper(1037,a,4550,a)].">
      <j1 rule="hyper" parents="1037 4550"/>
    </justification>
  </clause>

  <clause id="4563">
    <literal><![CDATA[
      x \ (y * ((y \ x) * z)) = L(z,y \ x,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(58,a,4121,a(flip),b,4552,a),flip(a)].">
      <j1 rule="hyper" parents="58 4121 4552"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4564">
    <literal><![CDATA[
      (x \ y) * (T(x,x \ y) * z) = (y / x) * (x * z)
    ]]></literal>
    <justification jstring="[para(5(a,1),4558(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5 4558"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4565">
    <literal><![CDATA[
      ((x * y) / x) * R(x,z,z \ 1) = y * (T(x,y) * a(x,z,z \ 1))
    ]]></literal>
    <justification jstring="[para(706(a,1),4558(a,1,2))].">
      <j1 rule="para" parents="706 4558"/>
    </justification>
  </clause>

  <clause id="4566">
    <literal><![CDATA[
      a((x * y) / x,x,z) = (y * (T(x,y) * z)) \ ((x * y) * z)
    ]]></literal>
    <justification jstring="[para(4558(a,1),83(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4558 83"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4567">
    <literal><![CDATA[
      L(x,T(y,z),T(z,y)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(482,a,4560,a),flip(a)].">
      <j1 rule="hyper" parents="482 4560"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4568">
    <literal><![CDATA[
      L(x,T(y,z),T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(4560(a,1),482(a,1))].">
      <j1 rule="para" parents="4560 482"/>
    </justification>
  </clause>

  <clause id="4569">
    <literal><![CDATA[
      L(x,y \ z,T(y,z / y)) = L(x,z / y,y)
    ]]></literal>
    <justification jstring="[para(107(a,1),4567(a,1,2))].">
      <j1 rule="para" parents="107 4567"/>
    </justification>
  </clause>

  <clause id="4570">
    <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(4184(a,1),4568(a,1,2))].">
      <j1 rule="para" parents="4184 4568"/>
    </justification>
  </clause>

  <clause id="4571">
    <literal><![CDATA[
      L(x,y \ z,T(y,y \ z)) = L(x,z / y,y)
    ]]></literal>
    <justification jstring="[para(4253(a,1),4569(a,1,3))].">
      <j1 rule="para" parents="4253 4569"/>
    </justification>
  </clause>

  <clause id="4572">
    <literal><![CDATA[
      x * (T(x,(y / z) / (z \ 1)) \ (y / z)) = T(y,x) / z
    ]]></literal>
    <justification jstring="[para(3766(a,1),4549(a,1,2,1))].">
      <j1 rule="para" parents="3766 4549"/>
    </justification>
  </clause>

  <clause id="4573">
    <literal><![CDATA[
      x \ T(x * (y / x),z) = T(y,z) / x
    ]]></literal>
    <justification jstring="[hyper(58,a,4562,a,b,4572,a)].">
      <j1 rule="hyper" parents="58 4562 4572"/>
    </justification>
  </clause>

  <clause id="4574">
    <literal><![CDATA[
      T(x * (y / x),z) = x * (T(y,z) / x)
    ]]></literal>
    <justification jstring="[hyper(119,a,4572,a(flip),b,4562,a),flip(a)].">
      <j1 rule="hyper" parents="119 4572 4562"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4575">
    <literal><![CDATA[
      (x \ T(x * (y / x),z)) * x = T(y,z)
    ]]></literal>
    <justification jstring="[hyper(133,a,4573,a(flip))].">
      <j1 rule="hyper" parents="133 4573"/>
    </justification>
  </clause>

  <clause id="4576">
    <literal><![CDATA[
      T(x * y,z) / y = y \ T(y * x,z)
    ]]></literal>
    <justification jstring="[para(6(a,1),4573(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="6 4573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4577">
    <literal><![CDATA[
      (x \ y) \ T((x \ y) * x,z) = T(y,z) / (x \ y)
    ]]></literal>
    <justification jstring="[para(72(a,1),4573(a,1,2,1,2))].">
      <j1 rule="para" parents="72 4573"/>
    </justification>
  </clause>

  <clause id="4578">
    <literal><![CDATA[
      T((x \ y) * x,z) / x = x \ T(y,z)
    ]]></literal>
    <justification jstring="[para(71(a,1),4573(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="71 4573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4579">
    <literal><![CDATA[
      x * (y * (T(z,x) / y)) = (y * (z / y)) * x
    ]]></literal>
    <justification jstring="[para(4573(a,1),227(a,1,2,2))].">
      <j1 rule="para" parents="4573 227"/>
    </justification>
  </clause>

  <clause id="4582">
    <literal><![CDATA[
      x \ T(T(x,y) * y,z) = T(x * y,z) / x
    ]]></literal>
    <justification jstring="[para(4092(a,2),4573(a,1,2,1))].">
      <j1 rule="para" parents="4092 4573"/>
    </justification>
  </clause>

  <clause id="4583">
    <literal><![CDATA[
      x * (T(y * x,z) / x) = T(x * y,z)
    ]]></literal>
    <justification jstring="[para(6(a,1),4574(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6 4574"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4584">
    <literal><![CDATA[
      T(x * (y / x),z) != x * u
    ]]></literal>
    <literal><![CDATA[
      T(y,z) / x = u
    ]]></literal>
    <justification jstring="[para(4574(a,2),38(a,1))].">
      <j1 rule="para" parents="4574 38"/>
    </justification>
  </clause>

  <clause id="4585">
    <literal><![CDATA[
      T(x * (y / x),y) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(104(a,1),4574(a,2,2,1))].">
      <j1 rule="para" parents="104 4574"/>
    </justification>
  </clause>

  <clause id="4586">
    <literal><![CDATA[
      T(x * ((y / z) / x),z) = x * ((z \ y) / x)
    ]]></literal>
    <justification jstring="[para(107(a,1),4574(a,2,2,1))].">
      <j1 rule="para" parents="107 4574"/>
    </justification>
  </clause>

  <clause id="4589">
    <literal><![CDATA[
      T(x * (y / x),K(z,y)) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(2890(a,1),4574(a,2,2,1))].">
      <j1 rule="para" parents="2890 4574"/>
    </justification>
  </clause>

  <clause id="4590">
    <literal><![CDATA[
      T(x * (y / x),K(y,z)) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(3330(a,1),4574(a,2,2,1))].">
      <j1 rule="para" parents="3330 4574"/>
    </justification>
  </clause>

  <clause id="4591">
    <literal><![CDATA[
      T(x * (y / x),z / y) = x * (T(y,y \ z) / x)
    ]]></literal>
    <justification jstring="[para(4253(a,1),4574(a,2,2,1))].">
      <j1 rule="para" parents="4253 4574"/>
    </justification>
  </clause>

  <clause id="4592">
    <literal><![CDATA[
      T(x,y * (x / y)) = x
    ]]></literal>
    <justification jstring="[hyper(49,a,4585,a)].">
      <j1 rule="hyper" parents="49 4585"/>
    </justification>
  </clause>

  <clause id="4593">
    <literal><![CDATA[
      T(x * (y / x),y) / y = y / ((x \ y) * x)
    ]]></literal>
    <justification jstring="[para(4585(a,2),4531(a,1,1))].">
      <j1 rule="para" parents="4585 4531"/>
    </justification>
  </clause>

  <clause id="4594">
    <literal><![CDATA[
      T((x \ y) * x,y) = (x \ y) * x
    ]]></literal>
    <justification jstring="[para(71(a,1),4592(a,1,2))].">
      <j1 rule="para" parents="71 4592"/>
    </justification>
  </clause>

  <clause id="4595">
    <literal><![CDATA[
      K(x \ 1,x) * T(K(x,x \ 1) * y,z) = T(y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,2722,a,b,4575,a)].">
      <j1 rule="hyper" parents="58 2722 4575"/>
    </justification>
  </clause>

  <clause id="4596">
    <literal><![CDATA[
      (x \ T(x * y,z)) * x = T(y * x,z)
    ]]></literal>
    <justification jstring="[para(6(a,1),4575(a,1,1,2,1,2))].">
      <j1 rule="para" parents="6 4575"/>
    </justification>
  </clause>

  <clause id="4597">
    <literal><![CDATA[
      T((x \ y) * x,z) = (x \ T(y,z)) * x
    ]]></literal>
    <justification jstring="[para(71(a,1),4575(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="71 4575"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4598">
    <literal><![CDATA[
      x \ T(x * y,1 / x) = ((1 / x) \ y) * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(1040,a,4576,a),flip(a)].">
      <j1 rule="hyper" parents="1040 4576"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4599">
    <literal><![CDATA[
      (1 / x) * T((1 / x) \ y,z) = x \ T(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(1006,a,4576,a)].">
      <j1 rule="hyper" parents="1006 4576"/>
    </justification>
  </clause>

  <clause id="4600">
    <literal><![CDATA[
      (x \ 1) * T((x \ 1) \ y,z) = T(y * x,z) / x
    ]]></literal>
    <justification jstring="[hyper(320,a,939,a,b,4576,a)].">
      <j1 rule="hyper" parents="320 939 4576"/>
    </justification>
  </clause>

  <clause id="4602">
    <literal><![CDATA[
      T(x \ T(x * y,z),x) = x \ T(y * x,z)
    ]]></literal>
    <justification jstring="[para(4576(a,1),107(a,1,1))].">
      <j1 rule="para" parents="4576 107"/>
    </justification>
  </clause>

  <clause id="4603">
    <literal><![CDATA[
      T(K(x,y) * (y * x),z) / (y * x) = (y * x) \ T(x * y,z)
    ]]></literal>
    <justification jstring="[para(84(a,1),4576(a,2,2,1))].">
      <j1 rule="para" parents="84 4576"/>
    </justification>
  </clause>

  <clause id="4604">
    <literal><![CDATA[
      x * (T(y * x,z) / x) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ T(x * y,z) = w
    ]]></literal>
    <justification jstring="[para(4576(a,2),416(a,1,2))].">
      <j1 rule="para" parents="4576 416"/>
    </justification>
  </clause>

  <clause id="4605">
    <literal><![CDATA[
      x * (y \ T(y * (x \ z),x)) = ((x \ (z * y)) * x) / y
    ]]></literal>
    <justification jstring="[para(4576(a,1),3939(a,1,2))].">
      <j1 rule="para" parents="4576 3939"/>
    </justification>
  </clause>

  <clause id="4607">
    <literal><![CDATA[
      x \ T((x \ y) * x,z) = T(x \ T(y,z),x)
    ]]></literal>
    <justification jstring="[para(4578(a,1),107(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4578 107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4609">
    <literal><![CDATA[
      x \ T(x * y,z) != u
    ]]></literal>
    <literal><![CDATA[
      T(y * x,z) / x = u
    ]]></literal>
    <justification jstring="[para(4583(a,1),287(a,1,2)),flip(b)].">
      <j1 rule="para" parents="4583 287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4610">
    <literal><![CDATA[
      T(x,T(y * x,z)) = T(x,T(x * y,z))
    ]]></literal>
    <justification jstring="[para(4583(a,1),4306(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4583 4306"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4611">
    <literal><![CDATA[
      T(x * ((1 / (1 / y)) / x),K(z,y)) = x * ((1 / (1 / y)) / x)
    ]]></literal>
    <justification jstring="[para(3559(a,1),4589(a,1,2))].">
      <j1 rule="para" parents="3559 4589"/>
    </justification>
  </clause>

  <clause id="4612">
    <literal><![CDATA[
      T(K(x,y),z * (x / z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(49,a,4590,a)].">
      <j1 rule="hyper" parents="49 4590"/>
    </justification>
  </clause>

  <clause id="4613">
    <literal><![CDATA[
      T(K(x * y,z),y * x) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(6(a,1),4612(a,1,2,2))].">
      <j1 rule="para" parents="6 4612"/>
    </justification>
  </clause>

  <clause id="4617">
    <literal><![CDATA[
      x * ((y \ T(z,x)) * y) = ((y \ z) * y) * x
    ]]></literal>
    <justification jstring="[hyper(119,a,4597,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 4597 17"/>
    </justification>
  </clause>

  <clause id="4618">
    <literal><![CDATA[
      T((x \ y) * x,z) != u * x
    ]]></literal>
    <literal><![CDATA[
      x \ T(y,z) = u
    ]]></literal>
    <justification jstring="[para(4597(a,2),39(a,1))].">
      <j1 rule="para" parents="4597 39"/>
    </justification>
  </clause>

  <clause id="4619">
    <literal><![CDATA[
      T((x \ (y / z)) * x,z) = (x \ (z \ y)) * x
    ]]></literal>
    <justification jstring="[para(107(a,1),4597(a,2,1,2))].">
      <j1 rule="para" parents="107 4597"/>
    </justification>
  </clause>

  <clause id="4620">
    <literal><![CDATA[
      T((x \ y) * x,z) \ T(y,z) = K(x,x \ T(y,z))
    ]]></literal>
    <justification jstring="[para(4597(a,2),86(a,1,1))].">
      <j1 rule="para" parents="4597 86"/>
    </justification>
  </clause>

  <clause id="4621">
    <literal><![CDATA[
      ((x * T((y \ z) * y,x)) / x) * (T(x,y) \ x) = (y \ (z * (T(x,y) \ x))) * y
    ]]></literal>
    <justification jstring="[para(4597(a,2),4075(a,1,1,1,2))].">
      <j1 rule="para" parents="4597 4075"/>
    </justification>
  </clause>

  <clause id="4622">
    <literal><![CDATA[
      K(x * y,z) * (y * x) = (y * x) * K(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(119,a,4613,a(flip),b,17,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 4613 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4623">
    <literal><![CDATA[
      (x * ((y / z) / x)) * z = z * (x * ((z \ y) / x))
    ]]></literal>
    <justification jstring="[para(107(a,1),4579(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="107 4579"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4624">
    <literal><![CDATA[
      (x * (((y * z) / y) / x)) * y = y * (x * (z / x))
    ]]></literal>
    <justification jstring="[para(224(a,1),4579(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="224 4579"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4625">
    <literal><![CDATA[
      x / ((((y \ 1) * x) \ x) * ((y \ 1) * x)) = T((y \ x) * y,x) / x
    ]]></literal>
    <justification jstring="[para(3933(a,1),4593(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="3933 4593"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4627">
    <literal><![CDATA[
      ((x \ y) * x) * (y \ 1) = (1 / y) * ((x \ y) * x)
    ]]></literal>
    <justification jstring="[hyper(58,a,3799,a(flip),b,4617,a),flip(a)].">
      <j1 rule="hyper" parents="58 3799 4617"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4628">
    <literal><![CDATA[
      ((x \ (y / z)) * x) * z = z * ((x \ (z \ y)) * x)
    ]]></literal>
    <justification jstring="[para(107(a,1),4617(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="107 4617"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4629">
    <literal><![CDATA[
      (x * ((y \ (x \ z)) * y)) / x = (y \ (z / x)) * y
    ]]></literal>
    <justification jstring="[hyper(271,a,4619,a)].">
      <j1 rule="hyper" parents="271 4619"/>
    </justification>
  </clause>

  <clause id="4630">
    <literal><![CDATA[
      (x \ y) \ T((x \ y) * x,x) = (y * x) / y
    ]]></literal>
    <justification jstring="[hyper(320,a,1157,a(flip),b,4577,a),flip(a)].">
      <j1 rule="hyper" parents="320 1157 4577"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4631">
    <literal><![CDATA[
      T(x * (y / x),z / y) = T(x * (y / x),y \ z)
    ]]></literal>
    <justification jstring="[hyper(320,a,4574,a,b,4591,a),flip(a)].">
      <j1 rule="hyper" parents="320 4574 4591"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4632">
    <literal><![CDATA[
      T(K(x,x \ 1) * y,z) = K(x,x \ 1) * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(2716,a,4595,a),flip(a)].">
      <j1 rule="hyper" parents="2716 4595"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4635">
    <literal><![CDATA[
      T(x * K(y \ 1,y),z) = K(y \ 1,y) * T(x,z)
    ]]></literal>
    <justification jstring="[para(2703(a,1),4595(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2703 4595"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4636">
    <literal><![CDATA[
      T(x,T(K(y,y \ 1) * z,u)) = T(x,T(z,u))
    ]]></literal>
    <justification jstring="[para(4595(a,1),3764(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4595 3764"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4638">
    <literal><![CDATA[
      T(x,T((1 / y) * z,u)) = T(x,T((y \ 1) * z,u))
    ]]></literal>
    <justification jstring="[para(2819(a,1),4636(a,1,2,1))].">
      <j1 rule="para" parents="2819 4636"/>
    </justification>
  </clause>

  <clause id="4639">
    <literal><![CDATA[
      ((1 / x) / y) * T(((1 / x) / y) \ z,u) = (x \ T(x * (z * y),u)) / y
    ]]></literal>
    <justification jstring="[hyper(117,a,4599,a(flip),b,1539,a),flip(a)].">
      <j1 rule="hyper" parents="117 4599 1539"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4640">
    <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(1621(a,1),4600(a,2,1,1))].">
      <j1 rule="para" parents="1621 4600"/>
    </justification>
  </clause>

  <clause id="4641">
    <literal><![CDATA[
      (x * (y \ z)) * (u * (((x * (y \ z)) \ z) / u)) = ((u * ((y / x) / u)) * x) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,4079,a(flip),b,4623,a),flip(a)].">
      <j1 rule="hyper" parents="58 4079 4623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4642">
    <literal><![CDATA[
      (1 / x) * ((y \ x) * y) = ((y \ x) * y) / x
    ]]></literal>
    <justification jstring="[hyper(58,a,3960,a(flip),b,4627,a),flip(a)].">
      <j1 rule="hyper" parents="58 3960 4627"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4643">
    <literal><![CDATA[
      (x * y) * T((x * y) \ z,x) = y * ((x \ (y \ z)) * x)
    ]]></literal>
    <justification jstring="[hyper(1106,a,4628,a)].">
      <j1 rule="hyper" parents="1106 4628"/>
    </justification>
  </clause>

  <clause id="4644">
    <literal><![CDATA[
      ((x \ (y * (z \ 1))) * x) / (z \ 1) = z * ((x \ (z \ y)) * x)
    ]]></literal>
    <justification jstring="[hyper(58,a,3853,a,b,4628,a)].">
      <j1 rule="hyper" parents="58 3853 4628"/>
    </justification>
  </clause>

  <clause id="4645">
    <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),4628(a,1,1,1,2))].">
      <j1 rule="para" parents="219 4628"/>
    </justification>
  </clause>

  <clause id="4646">
    <literal><![CDATA[
      (x * ((y \ z) * y)) / x = (y \ ((x * z) / x)) * y
    ]]></literal>
    <justification jstring="[para(4(a,1),4629(a,1,1,2,1,2))].">
      <j1 rule="para" parents="4 4629"/>
    </justification>
  </clause>

  <clause id="4647">
    <literal><![CDATA[
      ((x \ (y / z)) * x) * z != u
    ]]></literal>
    <literal><![CDATA[
      z * ((x \ (z \ y)) * x) = u
    ]]></literal>
    <justification jstring="[para(4629(a,1),251(a,1,1)),flip(b)].">
      <j1 rule="para" parents="4629 251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4648">
    <literal><![CDATA[
      (x \ ((y * (x * z)) / y)) * x = (y * (z * x)) / y
    ]]></literal>
    <justification jstring="[para(62(a,1),4629(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="62 4629"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4649">
    <literal><![CDATA[
      T(x * (y / x),(y / z) \ 1) = T(x * (y / x),y \ z)
    ]]></literal>
    <justification jstring="[hyper(4462,a,4631,a)].">
      <j1 rule="hyper" parents="4462 4631"/>
    </justification>
  </clause>

  <clause id="4651">
    <literal><![CDATA[
      T(x * K(y,y \ 1),z) = K(y,y \ 1) * T(x,z)
    ]]></literal>
    <justification jstring="[para(2181(a,1),4632(a,1,1))].">
      <j1 rule="para" parents="2181 4632"/>
    </justification>
  </clause>

  <clause id="4652">
    <literal><![CDATA[
      x \ T(y * K(z \ 1,z),u) = (x \ T(y,u)) * K(z \ 1,z)
    ]]></literal>
    <justification jstring="[para(4635(a,2),3415(a,1,2))].">
      <j1 rule="para" parents="4635 3415"/>
    </justification>
  </clause>

  <clause id="4653">
    <literal><![CDATA[
      (x \ ((x * y) / x)) * x = (x \ y) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(4380,a,4646,a),flip(a)].">
      <j1 rule="hyper" parents="4380 4646"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4655">
    <literal><![CDATA[
      ((x \ (y / (z \ 1))) * x) * (z \ 1) = ((x \ (y * z)) * x) / z
    ]]></literal>
    <justification jstring="[hyper(1630,a,4605,a)].">
      <j1 rule="hyper" parents="1630 4605"/>
    </justification>
  </clause>

  <clause id="4656">
    <literal><![CDATA[
      a((x * y) / x,x,z) = a(y,T(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(320,a,229,a(flip),b,4566,a),flip(a)].">
      <j1 rule="hyper" parents="320 229 4566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4657">
    <literal><![CDATA[
      a(x \ y,T(x,x \ y),z) = a(y / x,x,z)
    ]]></literal>
    <justification jstring="[para(5(a,1),4656(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5 4656"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4658">
    <literal><![CDATA[
      (x * y) * T((x * y) \ z,x) != u
    ]]></literal>
    <literal><![CDATA[
      y * ((x \ (y \ z)) * x) = u
    ]]></literal>
    <justification jstring="[para(1105(a,2),4647(a,1))].">
      <j1 rule="para" parents="1105 4647"/>
    </justification>
  </clause>

  <clause id="4659">
    <literal><![CDATA[
      T(x * ((1 / (1 / y)) / x),K(z,y)) = L(x * (y / x),y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,3534,a,b,4611,a),flip(a)].">
      <j1 rule="hyper" parents="320 3534 4611"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4660">
    <literal><![CDATA[
      (x \ 1) * ((y \ ((x \ 1) \ z)) * y) = ((y \ (z * x)) * y) / x
    ]]></literal>
    <justification jstring="[hyper(4647,a,4655,a)].">
      <j1 rule="hyper" parents="4647 4655"/>
    </justification>
  </clause>

  <clause id="4661">
    <literal><![CDATA[
      ((x \ (y * z)) * x) / z = z \ ((x \ (z * y)) * x)
    ]]></literal>
    <justification jstring="[hyper(58,a,3545,a(flip),b,4660,a),flip(a)].">
      <j1 rule="hyper" parents="58 3545 4660"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4662">
    <literal><![CDATA[
      (x \ ((y \ (x * z)) * y)) * x = (y \ (z * x)) * y
    ]]></literal>
    <justification jstring="[hyper(133,a,4661,a)].">
      <j1 rule="hyper" parents="133 4661"/>
    </justification>
  </clause>

  <clause id="4663">
    <literal><![CDATA[
      (x \ ((y \ (x * z)) * y)) * x != u
    ]]></literal>
    <literal><![CDATA[
      (y \ (z * x)) * y = u
    ]]></literal>
    <justification jstring="[para(4661(a,1),251(a,1,1)),flip(b)].">
      <j1 rule="para" parents="4661 251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4664">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * y) * z) = a(T(x,y),T(y,x),z)
    ]]></literal>
    <justification jstring="[para(4553(a,1),4272(a,1,1))].">
      <j1 rule="para" parents="4553 4272"/>
    </justification>
  </clause>

  <clause id="4665">
    <literal><![CDATA[
      a(T(x,y),T(y,x),z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(691,a,4664,a),flip(a)].">
      <j1 rule="hyper" parents="691 4664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4666">
    <literal><![CDATA[
      a(T(x,y),T(y,x),z) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(4664(a,1),691(a,1))].">
      <j1 rule="para" parents="4664 691"/>
    </justification>
  </clause>

  <clause id="4667">
    <literal><![CDATA[
      a(T(x,y),T(T(y,x),x),z) = a(x,T(y,x),z)
    ]]></literal>
    <justification jstring="[para(4233(a,1),4665(a,1,1))].">
      <j1 rule="para" parents="4233 4665"/>
    </justification>
  </clause>

  <clause id="4668">
    <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,4521,a),flip(a)].">
      <j1 rule="hyper" parents="320 514 4521"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4669">
    <literal><![CDATA[
      T(x * y,x) * T(x,y) = (R(x,y,x) * y) * x
    ]]></literal>
    <justification jstring="[para(1325(a,1),4668(a,1,1))].">
      <j1 rule="para" parents="1325 4668"/>
    </justification>
  </clause>

  <clause id="4670">
    <literal><![CDATA[
      (R(x,y,x) * y) * x = (x * y) * R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,4342,a(flip),b,4669,a),flip(a)].">
      <j1 rule="hyper" parents="58 4342 4669"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4671">
    <literal><![CDATA[
      (R(x,y,x) * y) \ (R(x,y,x) * T(x * y,x)) = x
    ]]></literal>
    <justification jstring="[hyper(116,a,4471,a,b,4669,a(flip))].">
      <j1 rule="hyper" parents="116 4471 4669"/>
    </justification>
  </clause>

  <clause id="4672">
    <literal><![CDATA[
      (R(x,y,x) * y) \ ((x * y) * R(x,y,x)) != z
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(4670(a,1),341(a,1,2))].">
      <j1 rule="para" parents="4670 341"/>
    </justification>
  </clause>

  <clause id="4673">
    <literal><![CDATA[
      L(R(x,y,x),y,R(x,y,x)) = x
    ]]></literal>
    <justification jstring="[hyper(4340,a,4671,a)].">
      <j1 rule="hyper" parents="4340 4671"/>
    </justification>
  </clause>

  <clause id="4674">
    <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(4659(a,2),550(a,1))].">
      <j1 rule="para" parents="4659 550"/>
    </justification>
  </clause>

  <clause id="4675">
    <literal><![CDATA[
      T(x \ T(x * y,y),T(x * y,y)) = y
    ]]></literal>
    <justification jstring="[hyper(320,a,4332,a(flip),b,4191,a),flip(a)].">
      <j1 rule="hyper" parents="320 4332 4191"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4677">
    <literal><![CDATA[
      K(x,x \ T(x * y,y)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(4675(a,1),4328(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4675 4328"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4678">
    <literal><![CDATA[
      K(x,y) = (x * R(y,x,y)) \ T(x * y,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,4164,a,b,4677,a),flip(a)].">
      <j1 rule="hyper" parents="58 4164 4677"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4679">
    <literal><![CDATA[
      K(x,y) = T(y * x,y) \ T(x * y,y)
    ]]></literal>
    <justification jstring="[para(4331(a,1),4678(a,2,1))].">
      <j1 rule="para" parents="4331 4678"/>
    </justification>
  </clause>

  <clause id="4680">
    <literal><![CDATA[
      K(x \ T(x * y,x),x) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,1390,a(flip),b,4679,a)].">
      <j1 rule="hyper" parents="320 1390 4679"/>
    </justification>
  </clause>

  <clause id="4681">
    <literal><![CDATA[
      K(x \ T(y,x),x) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[para(5(a,1),4680(a,1,1,2,1))].">
      <j1 rule="para" parents="5 4680"/>
    </justification>
  </clause>

  <clause id="4682">
    <literal><![CDATA[
      T(x,y) * K(y \ x,y) = (T(y,x) \ x) * y
    ]]></literal>
    <justification jstring="[hyper(119,a,4681,a(flip),b,4284,a)].">
      <j1 rule="hyper" parents="119 4681 4284"/>
    </justification>
  </clause>

  <clause id="4683">
    <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(4436(a,2),434(a,1))].">
      <j1 rule="para" parents="4436 434"/>
    </justification>
  </clause>

  <clause id="4684">
    <literal><![CDATA[
      T(x,T(y,z)) / (T(T(y,x),z) \ x) = T(y,T(z,T(y,x)))
    ]]></literal>
    <justification jstring="[para(4438(a,1),4437(a,1,1))].">
      <j1 rule="para" parents="4438 4437"/>
    </justification>
  </clause>

  <clause id="4685">
    <literal><![CDATA[
      T(x,T(y,T(x,z))) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,4280,a(flip),b,4684,a),flip(a)].">
      <j1 rule="hyper" parents="58 4280 4684"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4687">
    <literal><![CDATA[
      T(x,T(y,z)) * T(y,x) = y * T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(119,a,4685,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 4685 17"/>
    </justification>
  </clause>

  <clause id="4689">
    <literal><![CDATA[
      T(x / (x / y),T(z,y)) = T(x / (x / y),z)
    ]]></literal>
    <justification jstring="[para(244(a,1),4685(a,1,2,2))].">
      <j1 rule="para" parents="244 4685"/>
    </justification>
  </clause>

  <clause id="4692">
    <literal><![CDATA[
      T(x,y) \ (x * T(y,T(x,z))) = T(T(y,x),T(x,z))
    ]]></literal>
    <justification jstring="[hyper(116,a,4687,a(flip),b,4255,a)].">
      <j1 rule="hyper" parents="116 4687 4255"/>
    </justification>
  </clause>

  <clause id="4693">
    <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(4689(a,1),4403(a,1,1))].">
      <j1 rule="para" parents="4689 4403"/>
    </justification>
  </clause>

  <clause id="4694">
    <literal><![CDATA[
      ((x / y) \ T(x,y)) * (x / y) = y \ (x * ((y \ x) \ x))
    ]]></literal>
    <justification jstring="[para(7(a,1),4444(a,1,1,2,1))].">
      <j1 rule="para" parents="7 4444"/>
    </justification>
  </clause>

  <clause id="4695">
    <literal><![CDATA[
      x \ (y * ((x \ y) \ y)) = ((y * x) / y) * (y / x)
    ]]></literal>
    <justification jstring="[para(4111(a,1),4694(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4111 4694"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4696">
    <literal><![CDATA[
      ((x * y) / x) * (x / y) = y * (x / T(y,x))
    ]]></literal>
    <justification jstring="[hyper(58,a,4445,a(flip),b,4695,a),flip(a)].">
      <j1 rule="hyper" parents="58 4445 4695"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4697">
    <literal><![CDATA[
      (x \ y) * (y / T(x \ y,y)) = ((y * (x \ y)) / y) * x
    ]]></literal>
    <justification jstring="[para(72(a,1),4696(a,1,2)),flip(a)].">
      <j1 rule="para" parents="72 4696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4698">
    <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),4697(a,1,2,2,1))].">
      <j1 rule="para" parents="106 4697"/>
    </justification>
  </clause>

  <clause id="4699">
    <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,2863,a,b,4535,a),flip(a)].">
      <j1 rule="hyper" parents="58 2863 4535"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4700">
    <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(4565(a,2),38(a,1))].">
      <j1 rule="para" parents="4565 38"/>
    </justification>
  </clause>

  <clause id="4701">
    <literal><![CDATA[
      T((x \ y) * x,y) / y = y / (x * (y / x))
    ]]></literal>
    <justification jstring="[para(4537(a,1),4625(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4537 4625"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4702">
    <literal><![CDATA[
      ((x \ y) * x) / y = y / (x * (y / x))
    ]]></literal>
    <justification jstring="[para(4594(a,1),4701(a,1,1))].">
      <j1 rule="para" parents="4594 4701"/>
    </justification>
  </clause>

  <clause id="4703">
    <literal><![CDATA[
      ((x \ y) * x) / y = x \ (y / (y / x))
    ]]></literal>
    <justification jstring="[hyper(320,a,4387,a(flip),b,4702,a),flip(a)].">
      <j1 rule="hyper" parents="320 4387 4702"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4704">
    <literal><![CDATA[
      (1 / x) * ((y \ x) * y) = y \ (x / (x / y))
    ]]></literal>
    <justification jstring="[hyper(58,a,4642,a,b,4703,a)].">
      <j1 rule="hyper" parents="58 4642 4703"/>
    </justification>
  </clause>

  <clause id="4705">
    <literal><![CDATA[
      L((x \ ((y \ 1) \ 1)) * x,y \ 1,y) = y * (x \ (y / (y / x)))
    ]]></literal>
    <justification jstring="[para(4704(a,1),3793(a,2,2))].">
      <j1 rule="para" parents="4704 3793"/>
    </justification>
  </clause>

  <clause id="4706">
    <literal><![CDATA[
      (x \ (1 \ (y * 1))) * x = y * (x \ (y / (y / x)))
    ]]></literal>
    <justification jstring="[hyper(58,a,3538,a(flip),b,4705,a)].">
      <j1 rule="hyper" parents="58 3538 4705"/>
    </justification>
  </clause>

  <clause id="4707">
    <literal><![CDATA[
      x * (y \ (x / (x / y))) = (y \ x) * y
    ]]></literal>
    <justification jstring="[para(162(a,1),4706(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="162 4706"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4708">
    <literal><![CDATA[
      x \ (y / (y / x)) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(29,a,302,a,b,4707,a),flip(a)].">
      <j1 rule="hyper" parents="29 302 4707"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4709">
    <literal><![CDATA[
      x / (y * (x / y)) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(4388,a,4708,a)].">
      <j1 rule="hyper" parents="4388 4708"/>
    </justification>
  </clause>

  <clause id="4710">
    <literal><![CDATA[
      x / (x / y) = y * K(y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(134,a,4708,a),flip(a)].">
      <j1 rule="hyper" parents="134 4708"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4711">
    <literal><![CDATA[
      T(x,y) / (T(x,y) / y) = y * K(y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,4681,a(flip),b,4708,a),flip(a)].">
      <j1 rule="hyper" parents="119 4681 4708"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4712">
    <literal><![CDATA[
      (1 / x) * ((y \ x) * y) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,4704,a,b,4708,a)].">
      <j1 rule="hyper" parents="58 4704 4708"/>
    </justification>
  </clause>

  <clause id="4713">
    <literal><![CDATA[
      ((x \ y) * x) / y = K(x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,4703,a,b,4708,a)].">
      <j1 rule="hyper" parents="58 4703 4708"/>
    </justification>
  </clause>

  <clause id="4717">
    <literal><![CDATA[
      K(x \ y,x) * (x * (y / x)) = y
    ]]></literal>
    <justification jstring="[hyper(133,a,4709,a)].">
      <j1 rule="hyper" parents="133 4709"/>
    </justification>
  </clause>

  <clause id="4719">
    <literal><![CDATA[
      x \ K((x \ 1) \ y,x \ 1) = y / (y / (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(320,a,2930,a(flip),b,4710,a)].">
      <j1 rule="hyper" parents="320 2930 4710"/>
    </justification>
  </clause>

  <clause id="4720">
    <literal><![CDATA[
      (x * y) * K((x * y) \ y,x * y) = y / R(1 / x,x,y)
    ]]></literal>
    <justification jstring="[para(219(a,2),4710(a,1,2)),flip(a)].">
      <j1 rule="para" parents="219 4710"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4721">
    <literal><![CDATA[
      T(x * K(x \ y,x),y) = L(x,x \ y,x)
    ]]></literal>
    <justification jstring="[para(4710(a,1),4401(a,1,1))].">
      <j1 rule="para" parents="4710 4401"/>
    </justification>
  </clause>

  <clause id="4722">
    <literal><![CDATA[
      K(x \ y,x) * y = (x \ y) * x
    ]]></literal>
    <justification jstring="[hyper(133,a,4713,a)].">
      <j1 rule="hyper" parents="133 4713"/>
    </justification>
  </clause>

  <clause id="4723">
    <literal><![CDATA[
      ((x \ y) * x) * (y \ 1) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,3960,a,b,4713,a)].">
      <j1 rule="hyper" parents="58 3960 4713"/>
    </justification>
  </clause>

  <clause id="4724">
    <literal><![CDATA[
      T(x,K(y \ x,y)) = x
    ]]></literal>
    <justification jstring="[hyper(466,a,4722,a)].">
      <j1 rule="hyper" parents="466 4722"/>
    </justification>
  </clause>

  <clause id="4725">
    <literal><![CDATA[
      T((x \ 1) * ((y \ x) * y),x) = (x \ 1) * ((y \ x) * y)
    ]]></literal>
    <justification jstring="[para(4722(a,1),1985(a,2,2))].">
      <j1 rule="para" parents="4722 1985"/>
    </justification>
  </clause>

  <clause id="4726">
    <literal><![CDATA[
      T(x * y,K(y,x)) = x * y
    ]]></literal>
    <justification jstring="[para(4(a,1),4724(a,1,2,1))].">
      <j1 rule="para" parents="4 4724"/>
    </justification>
  </clause>

  <clause id="4727">
    <literal><![CDATA[
      T(x,K(y,x / y)) = x
    ]]></literal>
    <justification jstring="[para(75(a,1),4724(a,1,2,1))].">
      <j1 rule="para" parents="75 4724"/>
    </justification>
  </clause>

  <clause id="4728">
    <literal><![CDATA[
      T(K(x,y),y * x) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(49,a,4726,a)].">
      <j1 rule="hyper" parents="49 4726"/>
    </justification>
  </clause>

  <clause id="4729">
    <literal><![CDATA[
      K(x,y) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(4351,a,4728,a),flip(a)].">
      <j1 rule="hyper" parents="4351 4728"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4730">
    <literal><![CDATA[
      K(x,y) = T(y,x) \ y
    ]]></literal>
    <justification jstring="[hyper(4169,a,4728,a),flip(a)].">
      <j1 rule="hyper" parents="4169 4728"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4732">
    <literal><![CDATA[
      T(K(x,y),x) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(3342,a,4729,a)].">
      <j1 rule="hyper" parents="3342 4729"/>
    </justification>
  </clause>

  <clause id="4733">
    <literal><![CDATA[
      T(T(x,y),x \ 1) = (x \ 1) \ K(x,y)
    ]]></literal>
    <justification jstring="[hyper(439,a,4729,a,b,993,a)].">
      <j1 rule="hyper" parents="439 4729 993"/>
    </justification>
  </clause>

  <clause id="4734">
    <literal><![CDATA[
      (x * T(x \ y,z)) / y = K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,4156,a,b,4729,a)].">
      <j1 rule="hyper" parents="320 4156 4729"/>
    </justification>
  </clause>

  <clause id="4735">
    <literal><![CDATA[
      (T(x,y) * z) / (x * z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,4140,a,b,4729,a)].">
      <j1 rule="hyper" parents="320 4140 4729"/>
    </justification>
  </clause>

  <clause id="4736">
    <literal><![CDATA[
      L(x \ T(x,y \ 1),z,u) = K(x,L(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,3940,a,b,4729,a)].">
      <j1 rule="hyper" parents="320 3940 4729"/>
    </justification>
  </clause>

  <clause id="4737">
    <literal><![CDATA[
      T(x \ T(x,y \ 1),z) = K(x,T(y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,3930,a,b,4729,a)].">
      <j1 rule="hyper" parents="320 3930 4729"/>
    </justification>
  </clause>

  <clause id="4739">
    <literal><![CDATA[
      K(x,y) = ((x * y) / x) * (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,3869,a,b,4729,a),flip(a)].">
      <j1 rule="hyper" parents="320 3869 4729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4740">
    <literal><![CDATA[
      K(x,y) = ((x * y) / x) / y
    ]]></literal>
    <justification jstring="[hyper(320,a,3866,a,b,4729,a),flip(a)].">
      <j1 rule="hyper" parents="320 3866 4729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4741">
    <literal><![CDATA[
      x * ((y * (x \ 1)) / y) = K(y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,3865,a,b,4729,a)].">
      <j1 rule="hyper" parents="320 3865 4729"/>
    </justification>
  </clause>

  <clause id="4742">
    <literal><![CDATA[
      K(x,y) = y \ ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(320,a,3861,a,b,4729,a),flip(a)].">
      <j1 rule="hyper" parents="320 3861 4729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4743">
    <literal><![CDATA[
      K(x,y) = (1 / x) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,2992,a,b,4729,a),flip(a)].">
      <j1 rule="hyper" parents="320 2992 4729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4744">
    <literal><![CDATA[
      K(x,y) = T(x,y) / x
    ]]></literal>
    <justification jstring="[hyper(320,a,2987,a,b,4729,a),flip(a)].">
      <j1 rule="hyper" parents="320 2987 4729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4745">
    <literal><![CDATA[
      K(x,y) = T(x,y) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,993,a,b,4729,a),flip(a)].">
      <j1 rule="hyper" parents="320 993 4729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4746">
    <literal><![CDATA[
      x * T(x \ 1,y) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,2993,a(flip),b,4729,a)].">
      <j1 rule="hyper" parents="320 2993 4729"/>
    </justification>
  </clause>

  <clause id="4747">
    <literal><![CDATA[
      x * T(x \ 1,y) = K(1 / x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,743,a(flip),b,4729,a)].">
      <j1 rule="hyper" parents="320 743 4729"/>
    </justification>
  </clause>

  <clause id="4749">
    <literal><![CDATA[
      T(x,y) * K(y,x) = x
    ]]></literal>
    <justification jstring="[hyper(119,a,4729,a,b,4230,a)].">
      <j1 rule="hyper" parents="119 4729 4230"/>
    </justification>
  </clause>

  <clause id="4750">
    <literal><![CDATA[
      x * K(y,(x \ z) \ 1) = z * ((y * (z \ x)) / y)
    ]]></literal>
    <justification jstring="[hyper(119,a,4729,a,b,3897,a)].">
      <j1 rule="hyper" parents="119 4729 3897"/>
    </justification>
  </clause>

  <clause id="4751">
    <literal><![CDATA[
      T(x,y) * K(y,T(x,y)) = x
    ]]></literal>
    <justification jstring="[hyper(119,a,4729,a,b,3863,a)].">
      <j1 rule="hyper" parents="119 4729 3863"/>
    </justification>
  </clause>

  <clause id="4752">
    <literal><![CDATA[
      (x * y) / x = y * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,4729,a,b,3861,a),flip(a)].">
      <j1 rule="hyper" parents="119 4729 3861"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4753">
    <literal><![CDATA[
      x / (x / y) = y * K(x / y,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,4729,a,b,3864,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 4729 3864"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4755">
    <literal><![CDATA[
      T(x,y) = x * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,4729,a,b,xx),flip(a)].">
      <j1 rule="hyper" parents="119 4729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4756">
    <literal><![CDATA[
      K(x,y) / T(x,y) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(117,a,4729,a,b,2992,a)].">
      <j1 rule="hyper" parents="117 4729 2992"/>
    </justification>
  </clause>

  <clause id="4757">
    <literal><![CDATA[
      T(x,y) = K(x,y) / (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(117,a,4729,a,b,993,a),flip(a)].">
      <j1 rule="hyper" parents="117 4729 993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4758">
    <literal><![CDATA[
      ((x * y) / x) \ K(x,y) = y \ 1
    ]]></literal>
    <justification jstring="[hyper(116,a,4729,a,b,3869,a)].">
      <j1 rule="hyper" parents="116 4729 3869"/>
    </justification>
  </clause>

  <clause id="4759">
    <literal><![CDATA[
      x \ K(y,x \ 1) = (y * (x \ 1)) / y
    ]]></literal>
    <justification jstring="[hyper(116,a,4729,a,b,3865,a)].">
      <j1 rule="hyper" parents="116 4729 3865"/>
    </justification>
  </clause>

  <clause id="4760">
    <literal><![CDATA[
      T(x,y) \ K(x,y) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(116,a,4729,a,b,993,a)].">
      <j1 rule="hyper" parents="116 4729 993"/>
    </justification>
  </clause>

  <clause id="4762">
    <literal><![CDATA[
      x \ T(x,y \ 1) = K(x,1 / y)
    ]]></literal>
    <justification jstring="[hyper(58,a,3558,a,b,4729,a),flip(a)].">
      <j1 rule="hyper" parents="58 3558 4729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4763">
    <literal><![CDATA[
      (1 / x) * K(x \ 1,y) = T(1 / x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,3312,a(flip),b,4729,a(flip))].">
      <j1 rule="hyper" parents="119 3312 4729"/>
    </justification>
  </clause>

  <clause id="4764">
    <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),4729(a,2,2)),flip(a)].">
      <j1 rule="para" parents="20 4729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4765">
    <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),4729(a,2,2)),flip(a)].">
      <j1 rule="para" parents="22 4729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4766">
    <literal><![CDATA[
      x * K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(4729(a,2),255(a,1,2)),flip(b)].">
      <j1 rule="para" parents="4729 255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4767">
    <literal><![CDATA[
      L(K(x \ y,z),x \ y,x) = y \ (x * T(x \ y,z))
    ]]></literal>
    <justification jstring="[para(4729(a,2),490(a,1,1))].">
      <j1 rule="para" parents="4729 490"/>
    </justification>
  </clause>

  <clause id="4768">
    <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(4729(a,2),587(a,1,1))].">
      <j1 rule="para" parents="4729 587"/>
    </justification>
  </clause>

  <clause id="4769">
    <literal><![CDATA[
      K(x,x * (y \ 1)) = x \ T(x,y \ x)
    ]]></literal>
    <justification jstring="[para(1687(a,1),4729(a,2,2))].">
      <j1 rule="para" parents="1687 4729"/>
    </justification>
  </clause>

  <clause id="4770">
    <literal><![CDATA[
      T(x,y) = K(x,y) * x
    ]]></literal>
    <justification jstring="[para(4729(a,2),2989(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4729 2989"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4771">
    <literal><![CDATA[
      K(x,y) * x != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(4729(a,2),2996(a,1,1))].">
      <j1 rule="para" parents="4729 2996"/>
    </justification>
  </clause>

  <clause id="4772">
    <literal><![CDATA[
      (x \ (y * z)) \ (((x \ (y * z)) \ 1) \ 1) = K(x \ (y * z),z \ (y \ x))
    ]]></literal>
    <justification jstring="[para(3495(a,1),4729(a,2,2)),flip(a)].">
      <j1 rule="para" parents="3495 4729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4773">
    <literal><![CDATA[
      K(x,y * K(z,z \ 1)) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[para(3756(a,1),4729(a,2,2))].">
      <j1 rule="para" parents="3756 4729"/>
    </justification>
  </clause>

  <clause id="4774">
    <literal><![CDATA[
      (x * K(y,x)) * y = y * x
    ]]></literal>
    <justification jstring="[para(4729(a,2),3857(a,1,1,2))].">
      <j1 rule="para" parents="4729 3857"/>
    </justification>
  </clause>

  <clause id="4775">
    <literal><![CDATA[
      (x * y) / x = K(x,y) * y
    ]]></literal>
    <justification jstring="[para(4729(a,2),3860(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4729 3860"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4776">
    <literal><![CDATA[
      (x \ y) * K(x,x \ y) = y / x
    ]]></literal>
    <justification jstring="[para(4729(a,2),3859(a,1,2))].">
      <j1 rule="para" parents="4729 3859"/>
    </justification>
  </clause>

  <clause id="4777">
    <literal><![CDATA[
      x \ (T(x,y) * z) = K(x,y) * z
    ]]></literal>
    <justification jstring="[para(4729(a,2),4086(a,2,1))].">
      <j1 rule="para" parents="4729 4086"/>
    </justification>
  </clause>

  <clause id="4778">
    <literal><![CDATA[
      x * (K(x,y) * z) = T(x,y) * z
    ]]></literal>
    <justification jstring="[para(4729(a,2),4087(a,1,2,1))].">
      <j1 rule="para" parents="4729 4087"/>
    </justification>
  </clause>

  <clause id="4779">
    <literal><![CDATA[
      T(x,y) * (x \ z) = K(x,y) * z
    ]]></literal>
    <justification jstring="[para(4729(a,2),4088(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4729 4088"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4780">
    <literal><![CDATA[
      x * (T(x,y) \ z) = K(x,y) \ z
    ]]></literal>
    <justification jstring="[para(4729(a,2),4098(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4729 4098"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4781">
    <literal><![CDATA[
      K(x,y) * (x * z) = T(x,y) * z
    ]]></literal>
    <justification jstring="[para(4729(a,2),4137(a,1,1))].">
      <j1 rule="para" parents="4729 4137"/>
    </justification>
  </clause>

  <clause id="4782">
    <literal><![CDATA[
      K(x,y) \ (T(x,y) * z) = x * z
    ]]></literal>
    <justification jstring="[para(4729(a,2),4141(a,1,1))].">
      <j1 rule="para" parents="4729 4141"/>
    </justification>
  </clause>

  <clause id="4783">
    <literal><![CDATA[
      K(x,x \ y) * y = x * (y / x)
    ]]></literal>
    <justification jstring="[para(4729(a,2),4150(a,1,1))].">
      <j1 rule="para" parents="4729 4150"/>
    </justification>
  </clause>

  <clause id="4784">
    <literal><![CDATA[
      K(x,y) * z != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) * (x \ z) = u
    ]]></literal>
    <justification jstring="[para(4729(a,2),4095(a,1,1))].">
      <j1 rule="para" parents="4729 4095"/>
    </justification>
  </clause>

  <clause id="4785">
    <literal><![CDATA[
      K(x,y) \ (x \ z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) \ z = u
    ]]></literal>
    <justification jstring="[para(4729(a,2),4143(a,1,1))].">
      <j1 rule="para" parents="4729 4143"/>
    </justification>
  </clause>

  <clause id="4786">
    <literal><![CDATA[
      K(x,y) \ z != u
    ]]></literal>
    <literal><![CDATA[
      x * (T(x,y) \ z) = u
    ]]></literal>
    <justification jstring="[para(4729(a,2),4199(a,1,1))].">
      <j1 rule="para" parents="4729 4199"/>
    </justification>
  </clause>

  <clause id="4787">
    <literal><![CDATA[
      K(x,(y \ z) / z) = x \ T(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(4453(a,1),4729(a,2,2))].">
      <j1 rule="para" parents="4453 4729"/>
    </justification>
  </clause>

  <clause id="4788">
    <literal><![CDATA[
      T(x,y) * (x \ z) = K(y,x) \ z
    ]]></literal>
    <justification jstring="[para(4729(a,2),4546(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4729 4546"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4789">
    <literal><![CDATA[
      T(x,x \ (x / y)) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(4229,a,4730,a),flip(a)].">
      <j1 rule="hyper" parents="4229 4730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4790">
    <literal><![CDATA[
      T(x,y) = K(y,x) \ x
    ]]></literal>
    <justification jstring="[hyper(3067,a,4730,a),flip(a)].">
      <j1 rule="hyper" parents="3067 4730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4791">
    <literal><![CDATA[
      K(x \ (x / y),x) = K(y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,4226,a,b,4730,a)].">
      <j1 rule="hyper" parents="320 4226 4730"/>
    </justification>
  </clause>

  <clause id="4792">
    <literal><![CDATA[
      K(x,y) = ((y * x) / y) \ x
    ]]></literal>
    <justification jstring="[hyper(320,a,3870,a,b,4730,a),flip(a)].">
      <j1 rule="hyper" parents="320 3870 4730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4793">
    <literal><![CDATA[
      (x * T(x \ 1,y)) \ 1 = K(y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,3040,a,b,4730,a)].">
      <j1 rule="hyper" parents="320 3040 4730"/>
    </justification>
  </clause>

  <clause id="4794">
    <literal><![CDATA[
      K(x,y) = y / T(y,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,2879,a,b,4730,a),flip(a)].">
      <j1 rule="hyper" parents="320 2879 4730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4795">
    <literal><![CDATA[
      K(x,y) = (1 / T(y,x)) * y
    ]]></literal>
    <justification jstring="[hyper(320,a,2878,a,b,4730,a),flip(a)].">
      <j1 rule="hyper" parents="320 2878 4730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4796">
    <literal><![CDATA[
      K(x,y) = y * (T(y,x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,1118,a,b,4730,a),flip(a)].">
      <j1 rule="hyper" parents="320 1118 4730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4797">
    <literal><![CDATA[
      T(T(x,y),z) \ T(x,z) = K(y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,154,a,b,4730,a)].">
      <j1 rule="hyper" parents="320 154 4730"/>
    </justification>
  </clause>

  <clause id="4798">
    <literal><![CDATA[
      K(T(x,y),y) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,3875,a(flip),b,4730,a),flip(a)].">
      <j1 rule="hyper" parents="320 3875 4730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4799">
    <literal><![CDATA[
      ((x \ y) \ y) \ x = K(x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,311,a(flip),b,4730,a)].">
      <j1 rule="hyper" parents="320 311 4730"/>
    </justification>
  </clause>

  <clause id="4800">
    <literal><![CDATA[
      ((x * y) / x) * K(y,x) = y
    ]]></literal>
    <justification jstring="[hyper(119,a,4730,a,b,3870,a)].">
      <j1 rule="hyper" parents="119 4730 3870"/>
    </justification>
  </clause>

  <clause id="4801">
    <literal><![CDATA[
      (x \ 1) * K(y,x) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(119,a,4730,a,b,2528,a)].">
      <j1 rule="hyper" parents="119 4730 2528"/>
    </justification>
  </clause>

  <clause id="4802">
    <literal><![CDATA[
      ((x \ y) \ y) * K(x \ y,x) = x
    ]]></literal>
    <justification jstring="[hyper(119,a,4730,a,b,311,a(flip))].">
      <j1 rule="hyper" parents="119 4730 311"/>
    </justification>
  </clause>

  <clause id="4803">
    <literal><![CDATA[
      K(x,y) / y = 1 / T(y,x)
    ]]></literal>
    <justification jstring="[hyper(117,a,4730,a,b,2878,a)].">
      <j1 rule="hyper" parents="117 4730 2878"/>
    </justification>
  </clause>

  <clause id="4804">
    <literal><![CDATA[
      T(x,y) \ 1 = x \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,4730,a,b,1118,a),flip(a)].">
      <j1 rule="hyper" parents="116 4730 1118"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4805">
    <literal><![CDATA[
      T(x,y) = x / K(y,x)
    ]]></literal>
    <justification jstring="[hyper(197,a,4730,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="197 4730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4806">
    <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),4730(a,2,1)),flip(a)].">
      <j1 rule="para" parents="20 4730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4807">
    <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),4730(a,2,1)),flip(a)].">
      <j1 rule="para" parents="22 4730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4809">
    <literal><![CDATA[
      x / K(y,x) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(4730(a,2),330(a,1,2)),flip(b)].">
      <j1 rule="para" parents="4730 330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4810">
    <literal><![CDATA[
      K((1 / x) \ y,y) = T(y,y * x) \ y
    ]]></literal>
    <justification jstring="[para(1688(a,1),4730(a,2,1))].">
      <j1 rule="para" parents="1688 4730"/>
    </justification>
  </clause>

  <clause id="4811">
    <literal><![CDATA[
      K(x,y) * T(y,x) = y
    ]]></literal>
    <justification jstring="[para(4730(a,2),2882(a,1,1))].">
      <j1 rule="para" parents="4730 2882"/>
    </justification>
  </clause>

  <clause id="4812">
    <literal><![CDATA[
      K(x,y) * ((y * x) / y) = x
    ]]></literal>
    <justification jstring="[para(4730(a,2),3867(a,1,1))].">
      <j1 rule="para" parents="4730 3867"/>
    </justification>
  </clause>

  <clause id="4813">
    <literal><![CDATA[
      K(x,y) * (y * x) = x * y
    ]]></literal>
    <justification jstring="[para(4730(a,2),4166(a,1,1))].">
      <j1 rule="para" parents="4730 4166"/>
    </justification>
  </clause>

  <clause id="4814">
    <literal><![CDATA[
      x * (((y * x) / y) \ z) = K(x,y) * z
    ]]></literal>
    <justification jstring="[para(4730(a,2),4165(a,2,1))].">
      <j1 rule="para" parents="4730 4165"/>
    </justification>
  </clause>

  <clause id="4816">
    <literal><![CDATA[
      T(x * K(y,x),y) = x
    ]]></literal>
    <justification jstring="[para(4730(a,2),4344(a,1,1,2))].">
      <j1 rule="para" parents="4730 4344"/>
    </justification>
  </clause>

  <clause id="4817">
    <literal><![CDATA[
      K(x / y,z) * x = y * T(y \ x,z)
    ]]></literal>
    <justification jstring="[para(4730(a,2),4389(a,1,1))].">
      <j1 rule="para" parents="4730 4389"/>
    </justification>
  </clause>

  <clause id="4818">
    <literal><![CDATA[
      x * (T(x,y) \ z) = K(y,x) * z
    ]]></literal>
    <justification jstring="[para(4730(a,2),4544(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4730 4544"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4819">
    <literal><![CDATA[
      K(x,y) * (T(y,x) * z) = y * z
    ]]></literal>
    <justification jstring="[para(4730(a,2),4545(a,1,1))].">
      <j1 rule="para" parents="4730 4545"/>
    </justification>
  </clause>

  <clause id="4820">
    <literal><![CDATA[
      T(x,y) * (x \ y) = y * K(x,y)
    ]]></literal>
    <justification jstring="[para(4730(a,2),4548(a,2,2))].">
      <j1 rule="para" parents="4730 4548"/>
    </justification>
  </clause>

  <clause id="4821">
    <literal><![CDATA[
      x * K(y,x) != z
    ]]></literal>
    <literal><![CDATA[
      (y * x) / y = z
    ]]></literal>
    <justification jstring="[para(4730(a,2),4557(a,1,2))].">
      <j1 rule="para" parents="4730 4557"/>
    </justification>
  </clause>

  <clause id="4823">
    <literal><![CDATA[
      K(x \ (x / L(1 / y,z,u)),x) = L(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(4744(a,2),2496(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4744 2496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4825">
    <literal><![CDATA[
      T(x,y) != x
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = 1
    ]]></literal>
    <justification jstring="[para(4749(a,1),121(a,1)),flip(a),flip(b)].">
      <j1 rule="para" parents="4749 121"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4826">
    <literal><![CDATA[
      (x \ y) * K(x,y / x) = y / x
    ]]></literal>
    <justification jstring="[para(107(a,1),4749(a,1,1))].">
      <j1 rule="para" parents="107 4749"/>
    </justification>
  </clause>

  <clause id="4827">
    <literal><![CDATA[
      T(x,y) \ x != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(4749(a,1),287(a,1,2)),flip(b)].">
      <j1 rule="para" parents="4749 287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4828">
    <literal><![CDATA[
      T(x \ T(y,x),z) * K(z,T(x,y) \ y) = T(x,y) \ y
    ]]></literal>
    <justification jstring="[para(4392(a,1),4749(a,1,1))].">
      <j1 rule="para" parents="4392 4749"/>
    </justification>
  </clause>

  <clause id="4829">
    <literal><![CDATA[
      x * (y * K(x,y)) = T(x,y) * y
    ]]></literal>
    <justification jstring="[para(4749(a,1),4553(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4749 4553"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4830">
    <literal><![CDATA[
      ((x * y) / x) \ x = y \ (x * K(y,x))
    ]]></literal>
    <justification jstring="[para(4749(a,1),4552(a,1,2))].">
      <j1 rule="para" parents="4749 4552"/>
    </justification>
  </clause>

  <clause id="4831">
    <literal><![CDATA[
      (x * y) * L(K(y,z),y,x) = x * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(119,a,4755,a,b,296,a),flip(a)].">
      <j1 rule="hyper" parents="119 4755 296"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4832">
    <literal><![CDATA[
      T(x,T(y,T(x,z))) = x * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,4685,a,b,4755,a)].">
      <j1 rule="hyper" parents="58 4685 4755"/>
    </justification>
  </clause>

  <clause id="4834">
    <literal><![CDATA[
      T(x,T(y,x / y)) = x * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,4296,a,b,4755,a)].">
      <j1 rule="hyper" parents="58 4296 4755"/>
    </justification>
  </clause>

  <clause id="4837">
    <literal><![CDATA[
      T(x,y) != x * z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(4755(a,2),38(a,1))].">
      <j1 rule="para" parents="4755 38"/>
    </justification>
  </clause>

  <clause id="4838">
    <literal><![CDATA[
      x \ T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(4755(a,2),287(a,1,2)),flip(b)].">
      <j1 rule="para" parents="4755 287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4839">
    <literal><![CDATA[
      x / (y * K(y,y \ x)) = y \ x
    ]]></literal>
    <justification jstring="[para(4755(a,1),265(a,1,2))].">
      <j1 rule="para" parents="4755 265"/>
    </justification>
  </clause>

  <clause id="4841">
    <literal><![CDATA[
      K(x,L(x,y,z) \ 1) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(3376,a,4770,a),flip(a)].">
      <j1 rule="hyper" parents="3376 4770"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4842">
    <literal><![CDATA[
      K(T(x,y),z) * T(x,y) = T(T(x,z),y)
    ]]></literal>
    <justification jstring="[hyper(434,a,4770,a),flip(a)].">
      <j1 rule="hyper" parents="434 4770"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4844">
    <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,4770,a),flip(a)].">
      <j1 rule="hyper" parents="58 20 4770"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4847">
    <literal><![CDATA[
      x * (K(y,x) * y) = y * x
    ]]></literal>
    <justification jstring="[hyper(119,a,4770,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 4770 17"/>
    </justification>
  </clause>

  <clause id="4850">
    <literal><![CDATA[
      L(x \ y,x,K(y,z)) = (K(y,z) * x) \ T(y,z)
    ]]></literal>
    <justification jstring="[para(4770(a,2),92(a,2,2))].">
      <j1 rule="para" parents="4770 92"/>
    </justification>
  </clause>

  <clause id="4853">
    <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(4770(a,2),482(a,1,2,2))].">
      <j1 rule="para" parents="4770 482"/>
    </justification>
  </clause>

  <clause id="4854">
    <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(4770(a,2),515(a,2,2))].">
      <j1 rule="para" parents="4770 515"/>
    </justification>
  </clause>

  <clause id="4855">
    <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(4770(a,2),605(a,1,2))].">
      <j1 rule="para" parents="4770 605"/>
    </justification>
  </clause>

  <clause id="4856">
    <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(4770(a,2),690(a,1,1))].">
      <j1 rule="para" parents="4770 690"/>
    </justification>
  </clause>

  <clause id="4857">
    <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(4770(a,2),956(a,1,2,1))].">
      <j1 rule="para" parents="4770 956"/>
    </justification>
  </clause>

  <clause id="4858">
    <literal><![CDATA[
      T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      x * K(x,y) = z
    ]]></literal>
    <justification jstring="[para(4770(a,2),3333(a,1))].">
      <j1 rule="para" parents="4770 3333"/>
    </justification>
  </clause>

  <clause id="4859">
    <literal><![CDATA[
      K(x,y / x) * (x \ y) = y / x
    ]]></literal>
    <justification jstring="[hyper(784,a,4790,a)].">
      <j1 rule="hyper" parents="784 4790"/>
    </justification>
  </clause>

  <clause id="4860">
    <literal><![CDATA[
      T(x,(y \ x) \ 1) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(320,a,4386,a,b,4790,a)].">
      <j1 rule="hyper" parents="320 4386 4790"/>
    </justification>
  </clause>

  <clause id="4862">
    <literal><![CDATA[
      x / T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(4790(a,2),330(a,1,2)),flip(b)].">
      <j1 rule="para" parents="4790 330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4863">
    <literal><![CDATA[
      L(T(x,y),K(y,x),z) = (z * K(y,x)) \ (z * x)
    ]]></literal>
    <justification jstring="[para(4790(a,2),92(a,1,1))].">
      <j1 rule="para" parents="4790 92"/>
    </justification>
  </clause>

  <clause id="4864">
    <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(4790(a,2),2523(a,1,2,1))].">
      <j1 rule="para" parents="4790 2523"/>
    </justification>
  </clause>

  <clause id="4865">
    <literal><![CDATA[
      K(x,y) \ y != z
    ]]></literal>
    <literal><![CDATA[
      T(y,x) = z
    ]]></literal>
    <justification jstring="[para(4794(a,2),267(a,1,1)),flip(b)].">
      <j1 rule="para" parents="4794 267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4866">
    <literal><![CDATA[
      (1 / (1 / x)) \ K(y,x) = 1 / T(x,y)
    ]]></literal>
    <justification jstring="[para(4794(a,2),2257(a,1,2))].">
      <j1 rule="para" parents="4794 2257"/>
    </justification>
  </clause>

  <clause id="4868">
    <literal><![CDATA[
      (1 / (1 / x)) / K(y,x) = T(1 / (1 / x),y)
    ]]></literal>
    <justification jstring="[para(3559(a,1),4805(a,2,2)),flip(a)].">
      <j1 rule="para" parents="3559 4805"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4869">
    <literal><![CDATA[
      K(x,y * K(x,y)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(118,a,4816,a(flip),b,4805,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="118 4816 4805"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4870">
    <literal><![CDATA[
      T(T(x * K(y,x),z),y) = T(x,z)
    ]]></literal>
    <justification jstring="[para(4816(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4816 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4871">
    <literal><![CDATA[
      T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      z * K(y,z) = x
    ]]></literal>
    <justification jstring="[para(4816(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="4816 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4872">
    <literal><![CDATA[
      (x * y) / x != z
    ]]></literal>
    <literal><![CDATA[
      y * K(x,y) = z
    ]]></literal>
    <justification jstring="[para(4816(a,1),331(a,1,1,2)),flip(b)].">
      <j1 rule="para" parents="4816 331"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4873">
    <literal><![CDATA[
      T(x * K(y,x),z) * y = y * T(x,z)
    ]]></literal>
    <justification jstring="[para(4816(a,1),236(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4816 236"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4874">
    <literal><![CDATA[
      T(x * K(y,x),z) = (y * T(x,z)) / y
    ]]></literal>
    <justification jstring="[para(4816(a,1),269(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4816 269"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4875">
    <literal><![CDATA[
      L(x * K(y,x),z,u) * y = y * L(x,z,u)
    ]]></literal>
    <justification jstring="[para(4816(a,1),237(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4816 237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4876">
    <literal><![CDATA[
      R(x * K(y,x),z,u) * y = y * R(x,z,u)
    ]]></literal>
    <justification jstring="[para(4816(a,1),238(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4816 238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4877">
    <literal><![CDATA[
      T((x * (y * K(z,y))) / x,z) = (x * y) / x
    ]]></literal>
    <justification jstring="[para(4816(a,1),460(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4816 460"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4878">
    <literal><![CDATA[
      T(1 / (1 / (x * K(y,x))),y) = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[para(4816(a,1),2166(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4816 2166"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4879">
    <literal><![CDATA[
      T(K(x,y) * y,x) = y
    ]]></literal>
    <justification jstring="[para(2891(a,2),4816(a,1,1))].">
      <j1 rule="para" parents="2891 4816"/>
    </justification>
  </clause>

  <clause id="4880">
    <literal><![CDATA[
      T(x \ K(y,x \ 1),y) = x \ 1
    ]]></literal>
    <justification jstring="[para(2930(a,1),4816(a,1,1))].">
      <j1 rule="para" parents="2930 4816"/>
    </justification>
  </clause>

  <clause id="4881">
    <literal><![CDATA[
      (x * K(y,x)) * ((y \ 1) \ 1) = ((y \ 1) \ 1) * x
    ]]></literal>
    <justification jstring="[para(4816(a,1),2962(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4816 2962"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4882">
    <literal><![CDATA[
      T(K(x,y \ 1) / y,x) = 1 / y
    ]]></literal>
    <justification jstring="[para(3567(a,1),4816(a,1,1))].">
      <j1 rule="para" parents="3567 4816"/>
    </justification>
  </clause>

  <clause id="4883">
    <literal><![CDATA[
      T(x,y * K(x,y)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(4816(a,1),4233(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4816 4233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4884">
    <literal><![CDATA[
      T(x,L(y * K(x,y),z,u)) = T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(4816(a,1),4252(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4816 4252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4885">
    <literal><![CDATA[
      L(x * K(y,x),y,x * K(y,x)) = L(x * K(y,x),y,x)
    ]]></literal>
    <justification jstring="[para(4816(a,1),4542(a,1,3)),flip(a)].">
      <j1 rule="para" parents="4816 4542"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4886">
    <literal><![CDATA[
      ((x \ (y * K(z,y))) * x) * z = z * ((x \ y) * x)
    ]]></literal>
    <justification jstring="[para(4816(a,1),4617(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="4816 4617"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4888">
    <literal><![CDATA[
      T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,z) * z = x
    ]]></literal>
    <justification jstring="[para(4879(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="4879 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4889">
    <literal><![CDATA[
      K(x,y) = (1 / y) * ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(320,a,1472,a,b,4740,a),flip(a)].">
      <j1 rule="hyper" parents="320 1472 4740"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4890">
    <literal><![CDATA[
      R(K(x,y / z),y / z,z) = (((x * (y / z)) / x) * z) / y
    ]]></literal>
    <justification jstring="[para(4740(a,2),525(a,1,1))].">
      <j1 rule="para" parents="4740 525"/>
    </justification>
  </clause>

  <clause id="4891">
    <literal><![CDATA[
      ((x * ((y * z) / y)) / x) / ((x * z) / x) = K(y,(x * z) / x)
    ]]></literal>
    <justification jstring="[para(979(a,1),4740(a,2,1)),flip(a)].">
      <j1 rule="para" parents="979 4740"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4892">
    <literal><![CDATA[
      (x \ T(x * y,y)) / y = K(x * y,y)
    ]]></literal>
    <justification jstring="[para(4129(a,1),4740(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4129 4740"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4894">
    <literal><![CDATA[
      (x \ 1) \ K(y,x) = (y * ((x \ 1) \ 1)) / y
    ]]></literal>
    <justification jstring="[hyper(116,a,4742,a,b,1424,a)].">
      <j1 rule="hyper" parents="116 4742 1424"/>
    </justification>
  </clause>

  <clause id="4895">
    <literal><![CDATA[
      x \ K(y,1 / x) = (y * (x \ 1)) / y
    ]]></literal>
    <justification jstring="[hyper(116,a,4742,a,b,1466,a(flip))].">
      <j1 rule="hyper" parents="116 4742 1466"/>
    </justification>
  </clause>

  <clause id="4896">
    <literal><![CDATA[
      (x \ y) \ (y / x) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[para(5(a,1),4742(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5 4742"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4897">
    <literal><![CDATA[
      x * ((y * z) / y) = x * (z * K(y,z))
    ]]></literal>
    <justification jstring="[para(4742(a,2),151(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4742 151"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4898">
    <literal><![CDATA[
      ((x * y) / x) \ z = (y * K(x,y)) \ z
    ]]></literal>
    <justification jstring="[para(4742(a,2),155(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4742 155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4899">
    <literal><![CDATA[
      x * (y * K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      x * ((z * y) / z) = u
    ]]></literal>
    <justification jstring="[para(4742(a,2),342(a,1,2,2))].">
      <j1 rule="para" parents="4742 342"/>
    </justification>
  </clause>

  <clause id="4900">
    <literal><![CDATA[
      R(x,y,z) \ R((u * x) / u,y,z) = K(u,R(x,y,z))
    ]]></literal>
    <justification jstring="[para(854(a,2),4742(a,2,2)),flip(a)].">
      <j1 rule="para" parents="854 4742"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4901">
    <literal><![CDATA[
      T(x,y) \ ((z * x) / z) = x * (T(x,y) \ K(z,x))
    ]]></literal>
    <justification jstring="[para(4742(a,2),1117(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4742 1117"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4902">
    <literal><![CDATA[
      K(x,y) * K(x \ 1,x) = (x \ 1) * T(x,y)
    ]]></literal>
    <justification jstring="[para(4743(a,2),2847(a,1,1))].">
      <j1 rule="para" parents="4743 2847"/>
    </justification>
  </clause>

  <clause id="4903">
    <literal><![CDATA[
      K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      x \ T(x,y) = z
    ]]></literal>
    <justification jstring="[para(4743(a,2),3018(a,1))].">
      <j1 rule="para" parents="4743 3018"/>
    </justification>
  </clause>

  <clause id="4904">
    <literal><![CDATA[
      K(1 / x,y) / x = T(1 / x,y)
    ]]></literal>
    <justification jstring="[hyper(117,a,4745,a,b,193,a(flip))].">
      <j1 rule="hyper" parents="117 4745 193"/>
    </justification>
  </clause>

  <clause id="4905">
    <literal><![CDATA[
      ((x * y) / x) \ 1 = y \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,4745,a,b,4390,a),flip(a)].">
      <j1 rule="hyper" parents="116 4745 4390"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4906">
    <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(4745(a,2),482(a,1,2,2))].">
      <j1 rule="para" parents="4745 482"/>
    </justification>
  </clause>

  <clause id="4907">
    <literal><![CDATA[
      T(x,y * x) * (x \ 1) = K(x,x * y)
    ]]></literal>
    <justification jstring="[para(4307(a,2),4745(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4307 4745"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4908">
    <literal><![CDATA[
      K(x,T(y,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(29,a,4749,a,b,4751,a),flip(a)].">
      <j1 rule="hyper" parents="29 4749 4751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4910">
    <literal><![CDATA[
      K(x,x \ (y * x)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(17(a,1),4908(a,1,2))].">
      <j1 rule="para" parents="17 4908"/>
    </justification>
  </clause>

  <clause id="4911">
    <literal><![CDATA[
      K(x,L(T(y,x),z,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(20(a,2),4908(a,1,2))].">
      <j1 rule="para" parents="20 4908"/>
    </justification>
  </clause>

  <clause id="4912">
    <literal><![CDATA[
      K(x,y / x) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[para(107(a,1),4908(a,1,2)),flip(a)].">
      <j1 rule="para" parents="107 4908"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4913">
    <literal><![CDATA[
      K(x,L(y / x,z,u)) = K(x,L(x \ y,z,u))
    ]]></literal>
    <justification jstring="[para(247(a,1),4908(a,1,2)),flip(a)].">
      <j1 rule="para" parents="247 4908"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4914">
    <literal><![CDATA[
      K(x,R(y / x,z,u)) = K(x,R(x \ y,z,u))
    ]]></literal>
    <justification jstring="[para(248(a,1),4908(a,1,2)),flip(a)].">
      <j1 rule="para" parents="248 4908"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4915">
    <literal><![CDATA[
      K(x,(x * y) * (x \ 1)) = K(x,R(y,x,x \ 1))
    ]]></literal>
    <justification jstring="[para(788(a,1),4908(a,1,2)),flip(a)].">
      <j1 rule="para" parents="788 4908"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4916">
    <literal><![CDATA[
      K(x,y) \ T(y,x) = T(T(y,x),x)
    ]]></literal>
    <justification jstring="[para(4908(a,1),4790(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4908 4790"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4917">
    <literal><![CDATA[
      (x * y) * K(T(y,x),x * y) = T(y,x * y) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(4536,a,4752,a),flip(a)].">
      <j1 rule="hyper" parents="4536 4752"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4918">
    <literal><![CDATA[
      K(x,y \ 1) / y = (x * (1 / y)) / x
    ]]></literal>
    <justification jstring="[hyper(320,a,3567,a(flip),b,4752,a)].">
      <j1 rule="hyper" parents="320 3567 4752"/>
    </justification>
  </clause>

  <clause id="4919">
    <literal><![CDATA[
      (x * y) \ ((x * y) / x) = L(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[hyper(116,a,4752,a,b,1451,a)].">
      <j1 rule="hyper" parents="116 4752 1451"/>
    </justification>
  </clause>

  <clause id="4920">
    <literal><![CDATA[
      x / ((y * z) / y) = x / (z * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(55,a,4752,a)].">
      <j1 rule="hyper" parents="55 4752"/>
    </justification>
  </clause>

  <clause id="4921">
    <literal><![CDATA[
      (x / ((y * z) / y)) * (z * K(y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(119,a,4752,a(flip),b,75,a)].">
      <j1 rule="hyper" parents="119 4752 75"/>
    </justification>
  </clause>

  <clause id="4922">
    <literal><![CDATA[
      x \ ((y * x) / y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(4752(a,2),287(a,1,2)),flip(b)].">
      <j1 rule="para" parents="4752 287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4923">
    <literal><![CDATA[
      T(x,y) * K(y,T(x,y)) != z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(4752(a,1),331(a,1))].">
      <j1 rule="para" parents="4752 331"/>
    </justification>
  </clause>

  <clause id="4924">
    <literal><![CDATA[
      T(x,y) * K(y,T(x,y)) != z
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(4752(a,1),333(a,1))].">
      <j1 rule="para" parents="4752 333"/>
    </justification>
  </clause>

  <clause id="4925">
    <literal><![CDATA[
      T(x * K(y,x),y) != z
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(4752(a,1),345(a,1,1))].">
      <j1 rule="para" parents="4752 345"/>
    </justification>
  </clause>

  <clause id="4926">
    <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),4752(a,1,1))].">
      <j1 rule="para" parents="101 4752"/>
    </justification>
  </clause>

  <clause id="4927">
    <literal><![CDATA[
      R(x * K(y,x),y,z) = ((y * x) * z) / (y * z)
    ]]></literal>
    <justification jstring="[para(4752(a,1),102(a,1,1))].">
      <j1 rule="para" parents="4752 102"/>
    </justification>
  </clause>

  <clause id="4928">
    <literal><![CDATA[
      (x \ y) * K(x,x \ y) != z
    ]]></literal>
    <literal><![CDATA[
      y / x = z
    ]]></literal>
    <justification jstring="[para(4752(a,1),338(a,1))].">
      <j1 rule="para" parents="4752 338"/>
    </justification>
  </clause>

  <clause id="4929">
    <literal><![CDATA[
      R(x / y,y,K(z,x)) \ ((z * x) / z) = y * K(z,x)
    ]]></literal>
    <justification jstring="[para(4752(a,2),506(a,1,2))].">
      <j1 rule="para" parents="4752 506"/>
    </justification>
  </clause>

  <clause id="4930">
    <literal><![CDATA[
      R(x * K(y,x),y,y \ 1) = (y * x) * (y \ 1)
    ]]></literal>
    <justification jstring="[para(4752(a,1),523(a,1,1))].">
      <j1 rule="para" parents="4752 523"/>
    </justification>
  </clause>

  <clause id="4931">
    <literal><![CDATA[
      T(T(x * K(y,x),z),y) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z) = u
    ]]></literal>
    <justification jstring="[para(4752(a,1),681(a,1,1,1))].">
      <j1 rule="para" parents="4752 681"/>
    </justification>
  </clause>

  <clause id="4932">
    <literal><![CDATA[
      T(x * K(y * x,x),y) = R(x,y,x)
    ]]></literal>
    <justification jstring="[para(4752(a,1),785(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4752 785"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4933">
    <literal><![CDATA[
      L(x * K(y,x),z,u) = (y * L(x,z,u)) / y
    ]]></literal>
    <justification jstring="[para(4752(a,1),848(a,1,1))].">
      <j1 rule="para" parents="4752 848"/>
    </justification>
  </clause>

  <clause id="4934">
    <literal><![CDATA[
      R(x * K(y,x),z,u) = (y * R(x,z,u)) / y
    ]]></literal>
    <justification jstring="[para(4752(a,1),854(a,1,1))].">
      <j1 rule="para" parents="4752 854"/>
    </justification>
  </clause>

  <clause id="4935">
    <literal><![CDATA[
      ((x / y) * (y * K(z,x))) \ ((z * x) / z) = a(x / y,y,K(z,x))
    ]]></literal>
    <justification jstring="[para(4752(a,2),83(a,1,2))].">
      <j1 rule="para" parents="4752 83"/>
    </justification>
  </clause>

  <clause id="4936">
    <literal><![CDATA[
      T(T(x * K(y,x),z),x * y) = L(T(x,z),y,x)
    ]]></literal>
    <justification jstring="[para(4752(a,1),962(a,1,1,1))].">
      <j1 rule="para" parents="4752 962"/>
    </justification>
  </clause>

  <clause id="4937">
    <literal><![CDATA[
      L(x * K(y * z,x),z,y) = (y * (z * x)) / (y * z)
    ]]></literal>
    <justification jstring="[para(4752(a,1),850(a,1,1))].">
      <j1 rule="para" parents="4752 850"/>
    </justification>
  </clause>

  <clause id="4938">
    <literal><![CDATA[
      (x * y) / ((z * y) / z) = (x / (y * K(z,y))) * y
    ]]></literal>
    <justification jstring="[para(4752(a,1),1555(a,2,1,2))].">
      <j1 rule="para" parents="4752 1555"/>
    </justification>
  </clause>

  <clause id="4939">
    <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(1640(a,1),4752(a,1,1))].">
      <j1 rule="para" parents="1640 4752"/>
    </justification>
  </clause>

  <clause id="4940">
    <literal><![CDATA[
      (x * K(y,x)) \ ((y * (x * y)) / y) = L(y,x,y)
    ]]></literal>
    <justification jstring="[para(4752(a,1),1655(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4752 1655"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4941">
    <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(1875(a,1),4752(a,1,1))].">
      <j1 rule="para" parents="1875 4752"/>
    </justification>
  </clause>

  <clause id="4942">
    <literal><![CDATA[
      T(x * y,y * K(x,y)) = T(x * y,y)
    ]]></literal>
    <justification jstring="[para(4752(a,1),4112(a,1,2))].">
      <j1 rule="para" parents="4752 4112"/>
    </justification>
  </clause>

  <clause id="4943">
    <literal><![CDATA[
      T(x * K(y,x),y * x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[para(4752(a,1),4334(a,1,1))].">
      <j1 rule="para" parents="4752 4334"/>
    </justification>
  </clause>

  <clause id="4944">
    <literal><![CDATA[
      (x \ (y * K(x,y))) * x = (x \ y) * T(x,y)
    ]]></literal>
    <justification jstring="[para(4752(a,1),4653(a,1,1,2))].">
      <j1 rule="para" parents="4752 4653"/>
    </justification>
  </clause>

  <clause id="4946">
    <literal><![CDATA[
      T(x,y) * (x \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(4757(a,2),251(a,1,1)),flip(b)].">
      <j1 rule="para" parents="4757 251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4947">
    <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,1894,a,b,4774,a),flip(a)].">
      <j1 rule="hyper" parents="30 1894 4774"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4948">
    <literal><![CDATA[
      (x \ K(y,x \ 1)) * y = y * (x \ 1)
    ]]></literal>
    <justification jstring="[para(2930(a,1),4774(a,1,1))].">
      <j1 rule="para" parents="2930 4774"/>
    </justification>
  </clause>

  <clause id="4949">
    <literal><![CDATA[
      x / ((y * K(x,y)) * ((x \ 1) \ 1)) = (1 / (1 / x)) / (x * y)
    ]]></literal>
    <justification jstring="[para(4774(a,1),3472(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4774 3472"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4950">
    <literal><![CDATA[
      K(x,y) = x / ((y * x) / y)
    ]]></literal>
    <justification jstring="[hyper(320,a,3020,a,b,4792,a),flip(a)].">
      <j1 rule="hyper" parents="320 3020 4792"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4951">
    <literal><![CDATA[
      K(x \ K(x,y),x) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(4792(a,2),2775(a,1,1,2))].">
      <j1 rule="para" parents="4792 2775"/>
    </justification>
  </clause>

  <clause id="4952">
    <literal><![CDATA[
      K(x,y) / x = 1 / ((y * x) / y)
    ]]></literal>
    <justification jstring="[para(4792(a,2),3021(a,1,1))].">
      <j1 rule="para" parents="4792 3021"/>
    </justification>
  </clause>

  <clause id="4953">
    <literal><![CDATA[
      K(x,y) != 1
    ]]></literal>
    <literal><![CDATA[
      T(y,x) = y
    ]]></literal>
    <justification jstring="[para(4795(a,2),125(a,1))].">
      <j1 rule="para" parents="4795 125"/>
    </justification>
  </clause>

  <clause id="4954">
    <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(4795(a,2),518(a,1,2))].">
      <j1 rule="para" parents="4795 518"/>
    </justification>
  </clause>

  <clause id="4955">
    <literal><![CDATA[
      (x * y) \ (x * K(z,y)) = L(T(y,z) \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(4796(a,2),13(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="4796 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4956">
    <literal><![CDATA[
      x * (T(y,z) \ 1) = x * (y \ K(z,y))
    ]]></literal>
    <justification jstring="[para(4796(a,2),152(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4796 152"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4957">
    <literal><![CDATA[
      L(T(x \ y,z) \ 1,x \ y,x) = y \ (x * K(z,x \ y))
    ]]></literal>
    <justification jstring="[para(4796(a,2),91(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4796 91"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4958">
    <literal><![CDATA[
      K(T(x,y),y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,4729,a,b,4798,a),flip(a)].">
      <j1 rule="hyper" parents="320 4729 4798"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4962">
    <literal><![CDATA[
      (T(x,y) * y) / T(x,y) = y * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,4958,a(flip),b,4742,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 4958 4742"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4963">
    <literal><![CDATA[
      K(x \ (y * x),x) = K(y,x)
    ]]></literal>
    <justification jstring="[para(17(a,1),4958(a,1,1))].">
      <j1 rule="para" parents="17 4958"/>
    </justification>
  </clause>

  <clause id="4964">
    <literal><![CDATA[
      K(x / y,y) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[para(107(a,1),4958(a,1,1)),flip(a)].">
      <j1 rule="para" parents="107 4958"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4965">
    <literal><![CDATA[
      K((x \ y) \ y,x \ y) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[para(106(a,1),4958(a,1,1))].">
      <j1 rule="para" parents="106 4958"/>
    </justification>
  </clause>

  <clause id="4966">
    <literal><![CDATA[
      K(R(x,y,x),y * x) = K(T(x,y),y * x)
    ]]></literal>
    <justification jstring="[para(806(a,1),4958(a,1,1)),flip(a)].">
      <j1 rule="para" parents="806 4958"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4967">
    <literal><![CDATA[
      K(x,T(y,x)) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(4958(a,1),4218(a,1))].">
      <j1 rule="para" parents="4958 4218"/>
    </justification>
  </clause>

  <clause id="4968">
    <literal><![CDATA[
      K(x / (x / y),y \ x) = K(y,y \ x)
    ]]></literal>
    <justification jstring="[para(4346(a,1),4958(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4346 4958"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4969">
    <literal><![CDATA[
      K(x,y) \ 1 = K(y,x)
    ]]></literal>
    <justification jstring="[para(4958(a,1),4417(a,1,1))].">
      <j1 rule="para" parents="4958 4417"/>
    </justification>
  </clause>

  <clause id="4970">
    <literal><![CDATA[
      K(x * K(y,x),y) = K(x,y)
    ]]></literal>
    <justification jstring="[para(4816(a,1),4958(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4816 4958"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4971">
    <literal><![CDATA[
      1 / K(x,y) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(2414,a,4969,a)].">
      <j1 rule="hyper" parents="2414 4969"/>
    </justification>
  </clause>

  <clause id="4973">
    <literal><![CDATA[
      K(x,y) * K(y,x) = 1
    ]]></literal>
    <justification jstring="[hyper(134,a,4969,a)].">
      <j1 rule="hyper" parents="134 4969"/>
    </justification>
  </clause>

  <clause id="4974">
    <literal><![CDATA[
      T(K(x,y),z) * K(y,x) = K(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(119,a,4969,a(flip),b,4760,a)].">
      <j1 rule="hyper" parents="119 4969 4760"/>
    </justification>
  </clause>

  <clause id="4975">
    <literal><![CDATA[
      K(x,y) \ x = x * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,4969,a(flip),b,3189,a),flip(a)].">
      <j1 rule="hyper" parents="119 4969 3189"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4976">
    <literal><![CDATA[
      K(x,y) != z \ 1
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(4969(a,1),43(a,1))].">
      <j1 rule="para" parents="4969 43"/>
    </justification>
  </clause>

  <clause id="4977">
    <literal><![CDATA[
      x * K(y,z) != 1
    ]]></literal>
    <literal><![CDATA[
      K(z,y) = x
    ]]></literal>
    <justification jstring="[para(4969(a,1),129(a,1,2))].">
      <j1 rule="para" parents="4969 129"/>
    </justification>
  </clause>

  <clause id="4978">
    <literal><![CDATA[
      1 / K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(4969(a,1),330(a,1,2)),flip(b)].">
      <j1 rule="para" parents="4969 330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4979">
    <literal><![CDATA[
      L(x \ K(y,z),x,K(z,y)) = (K(z,y) * x) \ 1
    ]]></literal>
    <justification jstring="[para(4969(a,1),298(a,1,1,2))].">
      <j1 rule="para" parents="4969 298"/>
    </justification>
  </clause>

  <clause id="4980">
    <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(4969(a,1),2115(a,2,1,2,1))].">
      <j1 rule="para" parents="4969 2115"/>
    </justification>
  </clause>

  <clause id="4982">
    <literal><![CDATA[
      T(x * K(y,z),x \ K(z,y)) = ((x * K(y,z)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(4969(a,1),3803(a,1,2,2))].">
      <j1 rule="para" parents="4969 3803"/>
    </justification>
  </clause>

  <clause id="4983">
    <literal><![CDATA[
      1 / K(x \ 1,y) = K(y,1 / x)
    ]]></literal>
    <justification jstring="[hyper(320,a,3558,a,b,4971,a),flip(a)].">
      <j1 rule="hyper" parents="320 3558 4971"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4984">
    <literal><![CDATA[
      K(x,y) * z != 1
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(4971(a,1),125(a,1,1))].">
      <j1 rule="para" parents="4971 125"/>
    </justification>
  </clause>

  <clause id="4985">
    <literal><![CDATA[
      K(x,y) \ 1 != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(4971(a,1),267(a,1,1)),flip(b)].">
      <j1 rule="para" parents="4971 267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4986">
    <literal><![CDATA[
      K(x,y) \ 1 != z \ u
    ]]></literal>
    <literal><![CDATA[
      z * K(y,x) = u
    ]]></literal>
    <justification jstring="[para(4971(a,1),583(a,1,1))].">
      <j1 rule="para" parents="4971 583"/>
    </justification>
  </clause>

  <clause id="4987">
    <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,4973,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="168 186 4973"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4989">
    <literal><![CDATA[
      ((x * y) / x) \ y != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(4800(a,1),287(a,1,2)),flip(b)].">
      <j1 rule="para" parents="4800 287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4991">
    <literal><![CDATA[
      T(x,y) = (K(y,x) / x) \ 1
    ]]></literal>
    <justification jstring="[hyper(188,a,4803,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="188 4803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4992">
    <literal><![CDATA[
      T(x,y) = 1 / (x \ K(y,x))
    ]]></literal>
    <justification jstring="[hyper(197,a,4804,a),flip(a)].">
      <j1 rule="hyper" parents="197 4804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4993">
    <literal><![CDATA[
      1 / (x \ K(y,x)) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(4804(a,1),330(a,1,2)),flip(b)].">
      <j1 rule="para" parents="4804 330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4994">
    <literal><![CDATA[
      T(x,y) * L(x \ K(y,x),z,u) = T(x * L(x \ 1,z,u),y)
    ]]></literal>
    <justification jstring="[para(4804(a,1),2141(a,1,2,1))].">
      <j1 rule="para" parents="4804 2141"/>
    </justification>
  </clause>

  <clause id="4995">
    <literal><![CDATA[
      T(T(x,x \ 1),y) = (x \ K(y,x)) \ 1
    ]]></literal>
    <justification jstring="[para(4804(a,1),2162(a,2,1))].">
      <j1 rule="para" parents="4804 2162"/>
    </justification>
  </clause>

  <clause id="4996">
    <literal><![CDATA[
      K(x,y) * K(y \ 1,y) = (T(y,x) \ 1) * y
    ]]></literal>
    <justification jstring="[para(4804(a,2),3359(a,2,1))].">
      <j1 rule="para" parents="4804 3359"/>
    </justification>
  </clause>

  <clause id="4997">
    <literal><![CDATA[
      K(x \ y,x) * (y / x) = x \ y
    ]]></literal>
    <justification jstring="[para(5(a,1),4812(a,1,2,1))].">
      <j1 rule="para" parents="5 4812"/>
    </justification>
  </clause>

  <clause id="4999">
    <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),4812(a,1,2,1))].">
      <j1 rule="para" parents="80 4812"/>
    </justification>
  </clause>

  <clause id="5001">
    <literal><![CDATA[
      K(x,y / x) * y = x * (y / x)
    ]]></literal>
    <justification jstring="[para(7(a,1),4813(a,1,2))].">
      <j1 rule="para" parents="7 4813"/>
    </justification>
  </clause>

  <clause id="5002">
    <literal><![CDATA[
      x * (y * z) != z * y
    ]]></literal>
    <literal><![CDATA[
      K(z,y) = x
    ]]></literal>
    <justification jstring="[para(4813(a,1),39(a,1)),flip(a)].">
      <j1 rule="para" parents="4813 39"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5003">
    <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),4813(a,1,2))].">
      <j1 rule="para" parents="90 4813"/>
    </justification>
  </clause>

  <clause id="5004">
    <literal><![CDATA[
      L(x \ (y * z),x,K(z,y)) = (K(z,y) * x) \ (z * y)
    ]]></literal>
    <justification jstring="[para(4813(a,1),92(a,2,2))].">
      <j1 rule="para" parents="4813 92"/>
    </justification>
  </clause>

  <clause id="5005">
    <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(4813(a,1),479(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4813 479"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5006">
    <literal><![CDATA[
      (x * y) \ (K(x,y) * (y * (x * z))) = L(L(z,x,y),y * x,K(x,y))
    ]]></literal>
    <justification jstring="[para(4813(a,1),477(a,1,1))].">
      <j1 rule="para" parents="4813 477"/>
    </justification>
  </clause>

  <clause id="5007">
    <literal><![CDATA[
      T(x * y,z) / (y * x) = (y * x) \ T(x * y,z)
    ]]></literal>
    <justification jstring="[para(4813(a,1),4603(a,1,1,1))].">
      <j1 rule="para" parents="4813 4603"/>
    </justification>
  </clause>

  <clause id="5008">
    <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(4883(a,1),4508(a,2,2))].">
      <j1 rule="para" parents="4883 4508"/>
    </justification>
  </clause>

  <clause id="5011">
    <literal><![CDATA[
      x \ (y * (x / y)) = K(y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,87,a,b,4912,a)].">
      <j1 rule="hyper" parents="58 87 4912"/>
    </justification>
  </clause>

  <clause id="5012">
    <literal><![CDATA[
      K(x,x \ (y \ x)) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,4482,a(flip),b,4912,a),flip(a)].">
      <j1 rule="hyper" parents="58 4482 4912"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5013">
    <literal><![CDATA[
      x * K(y,y \ x) = y * (x / y)
    ]]></literal>
    <justification jstring="[hyper(119,a,4912,a(flip),b,87,a)].">
      <j1 rule="hyper" parents="119 4912 87"/>
    </justification>
  </clause>

  <clause id="5014">
    <literal><![CDATA[
      T(x,K(y,y \ x)) = x
    ]]></literal>
    <justification jstring="[para(4912(a,1),4727(a,1,2))].">
      <j1 rule="para" parents="4912 4727"/>
    </justification>
  </clause>

  <clause id="5016">
    <literal><![CDATA[
      (x \ y) / (y / x) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[para(5(a,1),4950(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5 4950"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5017">
    <literal><![CDATA[
      x / (y / (y / x)) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[para(4343(a,1),4950(a,2,2)),flip(a)].">
      <j1 rule="para" parents="4343 4950"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5018">
    <literal><![CDATA[
      x * K(x / y,y) = (y \ x) * y
    ]]></literal>
    <justification jstring="[hyper(119,a,4964,a,b,85,a)].">
      <j1 rule="hyper" parents="119 4964 85"/>
    </justification>
  </clause>

  <clause id="5023">
    <literal><![CDATA[
      L(x * K(y,x),K(x,y),z) = (z * K(x,y)) \ (z * x)
    ]]></literal>
    <justification jstring="[para(4975(a,1),92(a,1,1))].">
      <j1 rule="para" parents="4975 92"/>
    </justification>
  </clause>

  <clause id="5024">
    <literal><![CDATA[
      (1 / x) * K(x \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      T(1 / x,y) = z
    ]]></literal>
    <justification jstring="[para(3312(a,1),4766(a,1,2))].">
      <j1 rule="para" parents="3312 4766"/>
    </justification>
  </clause>

  <clause id="5025">
    <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),4827(a,1,1))].">
      <j1 rule="para" parents="18 4827"/>
    </justification>
  </clause>

  <clause id="5026">
    <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),4827(a,1,1))].">
      <j1 rule="para" parents="20 4827"/>
    </justification>
  </clause>

  <clause id="5028">
    <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),4827(a,1,1))].">
      <j1 rule="para" parents="317 4827"/>
    </justification>
  </clause>

  <clause id="5029">
    <literal><![CDATA[
      x * T(x \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x \ 1,y) = z
    ]]></literal>
    <justification jstring="[para(4225(a,1),4827(a,1))].">
      <j1 rule="para" parents="4225 4827"/>
    </justification>
  </clause>

  <clause id="5030">
    <literal><![CDATA[
      K(x \ (x / y),x) != z
    ]]></literal>
    <literal><![CDATA[
      K(y \ 1,x) = z
    ]]></literal>
    <justification jstring="[para(4226(a,2),4827(a,1))].">
      <j1 rule="para" parents="4226 4827"/>
    </justification>
  </clause>

  <clause id="5031">
    <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),4838(a,1,2))].">
      <j1 rule="para" parents="20 4838"/>
    </justification>
  </clause>

  <clause id="5033">
    <literal><![CDATA[
      x \ L(T(x,y),y,x) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,x * y) = z
    ]]></literal>
    <justification jstring="[para(711(a,2),4838(a,1,2))].">
      <j1 rule="para" parents="711 4838"/>
    </justification>
  </clause>

  <clause id="5035">
    <literal><![CDATA[
      T(K(x,y),x) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(4732(a,2),4838(a,1))].">
      <j1 rule="para" parents="4732 4838"/>
    </justification>
  </clause>

  <clause id="5036">
    <literal><![CDATA[
      K(x,x \ (y * x)) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(17(a,1),4967(a,1,2))].">
      <j1 rule="para" parents="17 4967"/>
    </justification>
  </clause>

  <clause id="5037">
    <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),4967(a,1,2))].">
      <j1 rule="para" parents="20 4967"/>
    </justification>
  </clause>

  <clause id="5038">
    <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(1096(a,1),4967(a,1,2))].">
      <j1 rule="para" parents="1096 4967"/>
    </justification>
  </clause>

  <clause id="5040">
    <literal><![CDATA[
      K((x \ 1) \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(3328(a,1),5035(a,1))].">
      <j1 rule="para" parents="3328 5035"/>
    </justification>
  </clause>

  <clause id="5041">
    <literal><![CDATA[
      K(x,y) * (x * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) * z = u
    ]]></literal>
    <justification jstring="[para(4735(a,1),251(a,1,1)),flip(b)].">
      <j1 rule="para" parents="4735 251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5042">
    <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),4735(a,1,2))].">
      <j1 rule="para" parents="101 4735"/>
    </justification>
  </clause>

  <clause id="5043">
    <literal><![CDATA[
      (T(x,y) * R(x \ 1,x,z)) / ((z / (x * z)) * x) = K(x,y)
    ]]></literal>
    <justification jstring="[para(652(a,2),4735(a,1,2))].">
      <j1 rule="para" parents="652 4735"/>
    </justification>
  </clause>

  <clause id="5044">
    <literal><![CDATA[
      (x * T(x \ y,y)) * (y \ 1) = K(x \ y,y)
    ]]></literal>
    <justification jstring="[para(1502(a,1),4739(a,2,1)),flip(a)].">
      <j1 rule="para" parents="1502 4739"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5045">
    <literal><![CDATA[
      R(x * T(x \ 1,y),z,u) = K(R(x,z,u) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(2504,a,4746,a)].">
      <j1 rule="hyper" parents="2504 4746"/>
    </justification>
  </clause>

  <clause id="5046">
    <literal><![CDATA[
      x * (y * T(y \ (x \ 1),z)) = K((x * y) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(942,a,4746,a)].">
      <j1 rule="hyper" parents="942 4746"/>
    </justification>
  </clause>

  <clause id="5047">
    <literal><![CDATA[
      T(1 / x,y) * x = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(459,a,4746,a)].">
      <j1 rule="hyper" parents="459 4746"/>
    </justification>
  </clause>

  <clause id="5049">
    <literal><![CDATA[
      (x * T(x \ y,z)) / y = K((x / y) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,1585,a(flip),b,4746,a)].">
      <j1 rule="hyper" parents="58 1585 4746"/>
    </justification>
  </clause>

  <clause id="5050">
    <literal><![CDATA[
      x \ (y * T(y \ x,z)) = K((x \ y) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,1427,a(flip),b,4746,a)].">
      <j1 rule="hyper" parents="58 1427 4746"/>
    </justification>
  </clause>

  <clause id="5051">
    <literal><![CDATA[
      (x \ (x / y)) * x = (x / y) * K(y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,4746,a(flip),b,966,a),flip(a)].">
      <j1 rule="hyper" parents="119 4746 966"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5052">
    <literal><![CDATA[
      ((x * y) \ x) * (x * y) = x * K(y \ 1,x * y)
    ]]></literal>
    <justification jstring="[hyper(119,a,4746,a(flip),b,951,a),flip(a)].">
      <j1 rule="hyper" parents="119 4746 951"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5053">
    <literal><![CDATA[
      L(x \ 1,x,y) * (y * x) = y * K(x \ 1,y * x)
    ]]></literal>
    <justification jstring="[hyper(119,a,4746,a(flip),b,633,a),flip(a)].">
      <j1 rule="hyper" parents="119 4746 633"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5054">
    <literal><![CDATA[
      x * T(x \ y,z) = y * K((y \ x) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(119,a,4746,a(flip),b,1427,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 4746 1427"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5055">
    <literal><![CDATA[
      x \ K((x * y) \ 1,z) = y * T(y \ (x \ 1),z)
    ]]></literal>
    <justification jstring="[hyper(116,a,4746,a(flip),b,924,a(flip))].">
      <j1 rule="hyper" parents="116 4746 924"/>
    </justification>
  </clause>

  <clause id="5056">
    <literal><![CDATA[
      (x * y) * T((x * y) \ y,z) = K(x \ 1,z) * y
    ]]></literal>
    <justification jstring="[para(4746(a,1),1226(a,2,1))].">
      <j1 rule="para" parents="4746 1226"/>
    </justification>
  </clause>

  <clause id="5057">
    <literal><![CDATA[
      K(x \ 1,y) * (x \ z) = z * T(z \ (x \ z),y)
    ]]></literal>
    <justification jstring="[para(4746(a,1),1235(a,1,1))].">
      <j1 rule="para" parents="4746 1235"/>
    </justification>
  </clause>

  <clause id="5058">
    <literal><![CDATA[
      x * (y * T(y \ (x \ y),z)) = K(x \ 1,z) * y
    ]]></literal>
    <justification jstring="[para(4746(a,1),1399(a,2,1))].">
      <j1 rule="para" parents="4746 1399"/>
    </justification>
  </clause>

  <clause id="5059">
    <literal><![CDATA[
      K(x \ (x / T(y,z)),x) = T(K(y \ 1,x),z)
    ]]></literal>
    <justification jstring="[para(4746(a,1),1527(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4746 1527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5060">
    <literal><![CDATA[
      K((x / y) \ 1,z) * y = x * T(x \ y,z)
    ]]></literal>
    <justification jstring="[para(4746(a,1),1584(a,1,1))].">
      <j1 rule="para" parents="4746 1584"/>
    </justification>
  </clause>

  <clause id="5062">
    <literal><![CDATA[
      K((x * y) \ 1,x) != z
    ]]></literal>
    <literal><![CDATA[
      ((x \ (1 / y)) * x) * y = z
    ]]></literal>
    <justification jstring="[para(4746(a,1),1577(a,1))].">
      <j1 rule="para" parents="4746 1577"/>
    </justification>
  </clause>

  <clause id="5063">
    <literal><![CDATA[
      (x * (y * T(y \ 1,z))) * y = (x * y) * K(y \ 1,z)
    ]]></literal>
    <justification jstring="[para(4746(a,1),1713(a,2,2))].">
      <j1 rule="para" parents="4746 1713"/>
    </justification>
  </clause>

  <clause id="5064">
    <literal><![CDATA[
      (x * y) * (z * T(z \ L(y \ z,y,x),u)) = (x * K(y \ 1,u)) * z
    ]]></literal>
    <justification jstring="[para(4746(a,1),2316(a,2,1,2))].">
      <j1 rule="para" parents="4746 2316"/>
    </justification>
  </clause>

  <clause id="5065">
    <literal><![CDATA[
      (x * y) * ((z \ L(y \ z,y,x)) * z) = (x * K(y \ 1,z)) * z
    ]]></literal>
    <justification jstring="[para(4746(a,1),2317(a,2,1,2))].">
      <j1 rule="para" parents="4746 2317"/>
    </justification>
  </clause>

  <clause id="5066">
    <literal><![CDATA[
      K(x \ (x / L(y,z,u)),x) = L(K(y \ 1,x),z,u)
    ]]></literal>
    <justification jstring="[para(4746(a,1),2492(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4746 2492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5068">
    <literal><![CDATA[
      x * ((y \ (x \ y)) * y) = y * K(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(4746(a,1),2976(a,2,2))].">
      <j1 rule="para" parents="4746 2976"/>
    </justification>
  </clause>

  <clause id="5069">
    <literal><![CDATA[
      (x * T(x \ y,z)) / y = K(1 / (x / y),z)
    ]]></literal>
    <justification jstring="[hyper(58,a,1585,a(flip),b,4747,a)].">
      <j1 rule="hyper" parents="58 1585 4747"/>
    </justification>
  </clause>

  <clause id="5070">
    <literal><![CDATA[
      L(K(1 / x,x),y,z) / L(x,y,z) = (x / L(x,y,z)) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(4747(a,1),3225(a,1,1,1))].">
      <j1 rule="para" parents="4747 3225"/>
    </justification>
  </clause>

  <clause id="5071">
    <literal><![CDATA[
      (x * (y / x)) \ x = y \ (y / (y / x))
    ]]></literal>
    <justification jstring="[para(4753(a,2),1452(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4753 1452"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5072">
    <literal><![CDATA[
      K(x,(x / y) / x) = K(x,1 / y)
    ]]></literal>
    <justification jstring="[hyper(3901,a,4762,a)].">
      <j1 rule="hyper" parents="3901 4762"/>
    </justification>
  </clause>

  <clause id="5074">
    <literal><![CDATA[
      x \ (y * ((z * (y \ x)) / z)) = K(z,1 / (x \ y))
    ]]></literal>
    <justification jstring="[hyper(58,a,3897,a,b,4762,a)].">
      <j1 rule="hyper" parents="58 3897 4762"/>
    </justification>
  </clause>

  <clause id="5075">
    <literal><![CDATA[
      K(x,1 / y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ 1) = z
    ]]></literal>
    <justification jstring="[para(4762(a,1),4838(a,1))].">
      <j1 rule="para" parents="4762 4838"/>
    </justification>
  </clause>

  <clause id="5076">
    <literal><![CDATA[
      K(x,x \ y) / (y / x) = 1 / (x \ y)
    ]]></literal>
    <justification jstring="[para(4776(a,1),2927(a,1,2))].">
      <j1 rule="para" parents="4776 2927"/>
    </justification>
  </clause>

  <clause id="5077">
    <literal><![CDATA[
      (x \ y) * K((x \ 1) \ 1,x \ y) = y / x
    ]]></literal>
    <justification jstring="[para(3317(a,2),4776(a,1,2))].">
      <j1 rule="para" parents="3317 4776"/>
    </justification>
  </clause>

  <clause id="5078">
    <literal><![CDATA[
      T(x,y) * T(z,K(x,y)) = x * (z * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(580,a,4777,a),flip(a)].">
      <j1 rule="hyper" parents="580 4777"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5079">
    <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,4260,a,b,4777,a)].">
      <j1 rule="hyper" parents="119 4260 4777"/>
    </justification>
  </clause>

  <clause id="5080">
    <literal><![CDATA[
      T(x,y) \ (K(x,y) * z) = x \ z
    ]]></literal>
    <justification jstring="[hyper(116,a,4777,a(flip),b,1109,a(flip))].">
      <j1 rule="hyper" parents="116 4777 1109"/>
    </justification>
  </clause>

  <clause id="5081">
    <literal><![CDATA[
      K(x,y) * (T(x,y) \ z) = x \ z
    ]]></literal>
    <justification jstring="[para(5(a,1),4777(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5 4777"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5082">
    <literal><![CDATA[
      x \ y != K(x,z) * u
    ]]></literal>
    <literal><![CDATA[
      T(x,z) * u = y
    ]]></literal>
    <justification jstring="[para(4777(a,1),42(a,1)),flip(a)].">
      <j1 rule="para" parents="4777 42"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5083">
    <literal><![CDATA[
      K(x,y) * T(z,T(x,y)) = x \ (z * T(x,y))
    ]]></literal>
    <justification jstring="[para(105(a,1),4777(a,1,2)),flip(a)].">
      <j1 rule="para" parents="105 4777"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5084">
    <literal><![CDATA[
      x * (K(x,y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) * z = u
    ]]></literal>
    <justification jstring="[para(4777(a,1),255(a,1,2)),flip(b)].">
      <j1 rule="para" parents="4777 255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5086">
    <literal><![CDATA[
      x \ ((x * y) / x) = K(x,y) * (x \ y)
    ]]></literal>
    <justification jstring="[para(4102(a,1),4777(a,1,2))].">
      <j1 rule="para" parents="4102 4777"/>
    </justification>
  </clause>

  <clause id="5087">
    <literal><![CDATA[
      K(x,y) \ (x \ z) = T(x,y) \ z
    ]]></literal>
    <justification jstring="[hyper(598,a,4778,a),flip(a)].">
      <j1 rule="hyper" parents="598 4778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5088">
    <literal><![CDATA[
      ((x * y) / x) \ z = K(y,x) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(29,a,4390,a,b,4778,a)].">
      <j1 rule="hyper" parents="29 4390 4778"/>
    </justification>
  </clause>

  <clause id="5089">
    <literal><![CDATA[
      K(x,y) * (z * x) = T(x,y) * T(z,x)
    ]]></literal>
    <justification jstring="[hyper(29,a,1121,a,b,4778,a),flip(a)].">
      <j1 rule="hyper" parents="29 1121 4778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5090">
    <literal><![CDATA[
      K(x,y) * T(y,y * x) = L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(29,a,4469,a(flip),b,4778,a),flip(a)].">
      <j1 rule="hyper" parents="29 4469 4778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5091">
    <literal><![CDATA[
      K(x,y) * T(y,x * y) = L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(29,a,4468,a(flip),b,4778,a),flip(a)].">
      <j1 rule="hyper" parents="29 4468 4778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5092">
    <literal><![CDATA[
      K(x,y) * (T(y,z) * x) = T(y,z) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(29,a,4450,a(flip),b,4778,a),flip(a)].">
      <j1 rule="hyper" parents="29 4450 4778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5093">
    <literal><![CDATA[
      K(x * y,x) * T(x,y) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(29,a,4342,a(flip),b,4778,a),flip(a)].">
      <j1 rule="hyper" parents="29 4342 4778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5094">
    <literal><![CDATA[
      (x * ((K(x,y) * z) * u)) \ ((T(x,y) * z) * u) = a(x,K(x,y) * z,u)
    ]]></literal>
    <justification jstring="[para(4778(a,1),9(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="4778 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5096">
    <literal><![CDATA[
      x \ (T(x,y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * z = u
    ]]></literal>
    <justification jstring="[para(4778(a,1),287(a,1,2)),flip(b)].">
      <j1 rule="para" parents="4778 287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5097">
    <literal><![CDATA[
      T(x,y) * (K(x,y) * z) = T(T(x,y),y) * z
    ]]></literal>
    <justification jstring="[para(4958(a,1),4778(a,1,2,1))].">
      <j1 rule="para" parents="4958 4778"/>
    </justification>
  </clause>

  <clause id="5098">
    <literal><![CDATA[
      (x * y) / (T(x,z) * y) = K(z,x)
    ]]></literal>
    <justification jstring="[hyper(4556,a,4779,a)].">
      <j1 rule="hyper" parents="4556 4779"/>
    </justification>
  </clause>

  <clause id="5099">
    <literal><![CDATA[
      K(x,y) \ (y * z) = T(y,x) * z
    ]]></literal>
    <justification jstring="[hyper(4555,a,4779,a)].">
      <j1 rule="hyper" parents="4555 4779"/>
    </justification>
  </clause>

  <clause id="5100">
    <literal><![CDATA[
      (x \ y) * T((x \ y) \ y,z) = K(x,z) * y
    ]]></literal>
    <justification jstring="[hyper(953,a,4779,a)].">
      <j1 rule="hyper" parents="953 4779"/>
    </justification>
  </clause>

  <clause id="5101">
    <literal><![CDATA[
      T(x,y) * (x \ R(x,z,u)) = R(x,z,u) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,3337,a,b,4779,a),flip(a)].">
      <j1 rule="hyper" parents="320 3337 4779"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5102">
    <literal><![CDATA[
      x * (K(x,y) * (x \ z)) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(58,a,4778,a,b,4779,a)].">
      <j1 rule="hyper" parents="58 4778 4779"/>
    </justification>
  </clause>

  <clause id="5103">
    <literal><![CDATA[
      ((x * y) / x) \ (y * z) = K(y,x) * z
    ]]></literal>
    <justification jstring="[hyper(58,a,4442,a,b,4779,a)].">
      <j1 rule="hyper" parents="58 4442 4779"/>
    </justification>
  </clause>

  <clause id="5104">
    <literal><![CDATA[
      (x \ L(x,y,z)) * T(x,u) = K(x,u) * L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,3524,a(flip),b,4779,a)].">
      <j1 rule="hyper" parents="58 3524 4779"/>
    </justification>
  </clause>

  <clause id="5106">
    <literal><![CDATA[
      x \ (K(y,x) * z) = T(x,y) \ z
    ]]></literal>
    <justification jstring="[hyper(116,a,4779,a(flip),b,4548,a(flip))].">
      <j1 rule="hyper" parents="116 4779 4548"/>
    </justification>
  </clause>

  <clause id="5107">
    <literal><![CDATA[
      (x * T(y,z)) \ (x * (K(y,z) * u)) = L(y \ u,T(y,z),x)
    ]]></literal>
    <justification jstring="[para(4779(a,1),13(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="4779 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5108">
    <literal><![CDATA[
      K(x * y,z) * (x * (y * u)) = T(x * y,z) * L(u,y,x)
    ]]></literal>
    <justification jstring="[para(13(a,2),4779(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13 4779"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5109">
    <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),4779(a,1,2)),flip(a)].">
      <j1 rule="para" parents="110 4779"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5110">
    <literal><![CDATA[
      K(x,y) * (T(x,y) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      x \ z = u
    ]]></literal>
    <justification jstring="[para(4779(a,1),1142(a,1))].">
      <j1 rule="para" parents="4779 1142"/>
    </justification>
  </clause>

  <clause id="5111">
    <literal><![CDATA[
      K(x,y) * T(x,z) = T(x,y) * K(x,z)
    ]]></literal>
    <justification jstring="[para(4729(a,2),4779(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4729 4779"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5112">
    <literal><![CDATA[
      K(x,y / z) \ y = z * T(z \ y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,4550,a,b,4780,a),flip(a)].">
      <j1 rule="hyper" parents="58 4550 4780"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5113">
    <literal><![CDATA[
      K(x,y / (z \ 1)) * (z \ T(z * y,x)) = y
    ]]></literal>
    <justification jstring="[hyper(119,a,4562,a,b,4780,a(flip))].">
      <j1 rule="hyper" parents="119 4562 4780"/>
    </justification>
  </clause>

  <clause id="5114">
    <literal><![CDATA[
      K(x,y) \ (z * T(x,y)) = x * T(z,T(x,y))
    ]]></literal>
    <justification jstring="[para(17(a,2),4780(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17 4780"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5117">
    <literal><![CDATA[
      K(x,x \ y) * (x * z) = ((x \ y) \ y) * z
    ]]></literal>
    <justification jstring="[hyper(320,a,314,a(flip),b,4781,a),flip(a)].">
      <j1 rule="hyper" parents="320 314 4781"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5118">
    <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),4781(a,2,1))].">
      <j1 rule="para" parents="22 4781"/>
    </justification>
  </clause>

  <clause id="5119">
    <literal><![CDATA[
      T(x,y) * (x \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * z = u
    ]]></literal>
    <justification jstring="[para(4781(a,1),342(a,1))].">
      <j1 rule="para" parents="4781 342"/>
    </justification>
  </clause>

  <clause id="5120">
    <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),4781(a,1,2))].">
      <j1 rule="para" parents="237 4781"/>
    </justification>
  </clause>

  <clause id="5121">
    <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(4781(a,1),518(a,1,1,1))].">
      <j1 rule="para" parents="4781 518"/>
    </justification>
  </clause>

  <clause id="5122">
    <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(4781(a,1),477(a,1,1))].">
      <j1 rule="para" parents="4781 477"/>
    </justification>
  </clause>

  <clause id="5123">
    <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(4781(a,1),494(a,1,1))].">
      <j1 rule="para" parents="4781 494"/>
    </justification>
  </clause>

  <clause id="5124">
    <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(4781(a,1),494(a,1,2))].">
      <j1 rule="para" parents="4781 494"/>
    </justification>
  </clause>

  <clause id="5126">
    <literal><![CDATA[
      K(x,y) * (T(x,y) * z) = T(T(x,y),y) * z
    ]]></literal>
    <justification jstring="[para(4958(a,1),4781(a,1,1))].">
      <j1 rule="para" parents="4958 4781"/>
    </justification>
  </clause>

  <clause id="5127">
    <literal><![CDATA[
      T(x * (y / x),z) / T(y,z) = K(x,x \ T(y,z))
    ]]></literal>
    <justification jstring="[hyper(117,a,4574,a,b,4783,a)].">
      <j1 rule="hyper" parents="117 4574 4783"/>
    </justification>
  </clause>

  <clause id="5128">
    <literal><![CDATA[
      K(x,(x \ 1) * y) * y = x * (y / x)
    ]]></literal>
    <justification jstring="[para(4493(a,2),4783(a,1,1))].">
      <j1 rule="para" parents="4493 4783"/>
    </justification>
  </clause>

  <clause id="5129">
    <literal><![CDATA[
      K(x,y) \ (T(y,x) \ z) = y \ z
    ]]></literal>
    <justification jstring="[hyper(1142,a,4788,a),flip(a)].">
      <j1 rule="hyper" parents="1142 4788"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5130">
    <literal><![CDATA[
      K(x,y) \ z = K(y,x) * z
    ]]></literal>
    <justification jstring="[hyper(58,a,4779,a(flip),b,4788,a),flip(a)].">
      <j1 rule="hyper" parents="58 4779 4788"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5131">
    <literal><![CDATA[
      K(x,y) * (y \ z) = T(y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(1141,a,4788,a(flip))].">
      <j1 rule="hyper" parents="1141 4788"/>
    </justification>
  </clause>

  <clause id="5132">
    <literal><![CDATA[
      x \ (K(y,z) \ x) = T(K(z,y),x)
    ]]></literal>
    <justification jstring="[hyper(439,a,4788,a(flip),b,4779,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="439 4788 4779"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5133">
    <literal><![CDATA[
      K(x,y) * (K(y,x) * z) = z
    ]]></literal>
    <justification jstring="[hyper(119,a,4779,a(flip),b,4788,a(flip))].">
      <j1 rule="hyper" parents="119 4779 4788"/>
    </justification>
  </clause>

  <clause id="5134">
    <literal><![CDATA[
      (K(x,y) \ z) / z = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(117,a,4788,a(flip),b,4779,a(flip))].">
      <j1 rule="hyper" parents="117 4788 4779"/>
    </justification>
  </clause>

  <clause id="5135">
    <literal><![CDATA[
      K(x,y) \ (y * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,x) * z = u
    ]]></literal>
    <justification jstring="[para(4788(a,1),585(a,1))].">
      <j1 rule="para" parents="4788 585"/>
    </justification>
  </clause>

  <clause id="5137">
    <literal><![CDATA[
      K(x,y) * (y \ K(y,x)) = y \ 1
    ]]></literal>
    <justification jstring="[hyper(3211,a,5130,a)].">
      <j1 rule="hyper" parents="3211 5130"/>
    </justification>
  </clause>

  <clause id="5138">
    <literal><![CDATA[
      (x \ 1) / (x \ K(x,y)) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(3209,a,5130,a)].">
      <j1 rule="hyper" parents="3209 5130"/>
    </justification>
  </clause>

  <clause id="5139">
    <literal><![CDATA[
      K(x,y) * (K(x,z) * K(y,x)) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(2012,a,5130,a)].">
      <j1 rule="hyper" parents="2012 5130"/>
    </justification>
  </clause>

  <clause id="5140">
    <literal><![CDATA[
      K(x,y) * R(K(y,x),z,z \ 1) = a(K(y,x),z,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(708,a,5130,a),flip(a)].">
      <j1 rule="hyper" parents="708 5130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5141">
    <literal><![CDATA[
      K(x,y) * (z * K(y,x)) = T(z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(580,a,5130,a)].">
      <j1 rule="hyper" parents="580 5130"/>
    </justification>
  </clause>

  <clause id="5142">
    <literal><![CDATA[
      x / (K(y,z) * x) = K(z,y)
    ]]></literal>
    <justification jstring="[hyper(575,a,5130,a)].">
      <j1 rule="hyper" parents="575 5130"/>
    </justification>
  </clause>

  <clause id="5143">
    <literal><![CDATA[
      K(x,y) \ T(T(x,z),u) = T(T(x,z),u) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,2902,a,b,5130,a),flip(a)].">
      <j1 rule="hyper" parents="320 2902 5130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5144">
    <literal><![CDATA[
      K(x,y) * (R(x,z,u) * K(y,x)) = R(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(119,a,2899,a,b,5130,a)].">
      <j1 rule="hyper" parents="119 2899 5130"/>
    </justification>
  </clause>

  <clause id="5145">
    <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,3670,a(flip),b,5130,a),flip(a)].">
      <j1 rule="hyper" parents="58 3670 5130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5146">
    <literal><![CDATA[
      x * (K(y,z) * u) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,y) = x
    ]]></literal>
    <justification jstring="[para(5130(a,1),129(a,1,2))].">
      <j1 rule="para" parents="5130 129"/>
    </justification>
  </clause>

  <clause id="5147">
    <literal><![CDATA[
      K(x,y) * z != u
    ]]></literal>
    <literal><![CDATA[
      K(y,x) * u = z
    ]]></literal>
    <justification jstring="[para(5130(a,1),134(a,1))].">
      <j1 rule="para" parents="5130 134"/>
    </justification>
  </clause>

  <clause id="5148">
    <literal><![CDATA[
      K(x,y) * (K(y,x) * z) != u
    ]]></literal>
    <literal><![CDATA[
      u = z
    ]]></literal>
    <justification jstring="[para(5130(a,1),255(a,1,2))].">
      <j1 rule="para" parents="5130 255"/>
    </justification>
  </clause>

  <clause id="5149">
    <literal><![CDATA[
      K(x,y) * (K(y,x) * z) != u
    ]]></literal>
    <literal><![CDATA[
      z = u
    ]]></literal>
    <justification jstring="[para(5130(a,1),256(a,1,2))].">
      <j1 rule="para" parents="5130 256"/>
    </justification>
  </clause>

  <clause id="5150">
    <literal><![CDATA[
      x / (K(y,z) * x) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,y) = u
    ]]></literal>
    <justification jstring="[para(5130(a,1),330(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5130 330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5151">
    <literal><![CDATA[
      (K(x,y) \ z) * L(u,z,K(y,x)) = K(y,x) * (z * u)
    ]]></literal>
    <justification jstring="[para(5130(a,2),90(a,1,1))].">
      <j1 rule="para" parents="5130 90"/>
    </justification>
  </clause>

  <clause id="5152">
    <literal><![CDATA[
      L(K(x,y) * z,K(y,x),u) = (u * K(y,x)) \ (u * z)
    ]]></literal>
    <justification jstring="[para(5130(a,1),92(a,1,1))].">
      <j1 rule="para" parents="5130 92"/>
    </justification>
  </clause>

  <clause id="5153">
    <literal><![CDATA[
      L(x \ (K(y,z) * u),x,K(z,y)) = (K(z,y) * x) \ u
    ]]></literal>
    <justification jstring="[para(5130(a,1),298(a,1,1,2))].">
      <j1 rule="para" parents="5130 298"/>
    </justification>
  </clause>

  <clause id="5154">
    <literal><![CDATA[
      L(K(x,y) * (z \ u),K(y,x),z) = (z * K(y,x)) \ u
    ]]></literal>
    <justification jstring="[para(5130(a,1),298(a,1,1))].">
      <j1 rule="para" parents="5130 298"/>
    </justification>
  </clause>

  <clause id="5155">
    <literal><![CDATA[
      x \ y != K(z,u) * (K(u,z) * w)
    ]]></literal>
    <literal><![CDATA[
      x * w = y
    ]]></literal>
    <justification jstring="[para(5130(a,1),340(a,2,2))].">
      <j1 rule="para" parents="5130 340"/>
    </justification>
  </clause>

  <clause id="5156">
    <literal><![CDATA[
      T((x \ K(y,z)) \ 1,K(z,y) * x) = (x \ K(y,z)) \ 1
    ]]></literal>
    <justification jstring="[para(5130(a,1),588(a,1,2))].">
      <j1 rule="para" parents="5130 588"/>
    </justification>
  </clause>

  <clause id="5157">
    <literal><![CDATA[
      R(x,K(y,z),K(z,y) * u) * u = (x * K(y,z)) * (K(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(5130(a,1),368(a,1,1,3))].">
      <j1 rule="para" parents="5130 368"/>
    </justification>
  </clause>

  <clause id="5158">
    <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(5130(a,1),564(a,1,1,1))].">
      <j1 rule="para" parents="5130 564"/>
    </justification>
  </clause>

  <clause id="5159">
    <literal><![CDATA[
      (K(x,y) * T(K(y,x) * z,u)) * K(y,x) = T(z * K(y,x),u)
    ]]></literal>
    <justification jstring="[para(5130(a,1),4596(a,1,1))].">
      <j1 rule="para" parents="5130 4596"/>
    </justification>
  </clause>

  <clause id="5160">
    <literal><![CDATA[
      (K(x,y) \ 1) * z = K(x,y) \ z
    ]]></literal>
    <justification jstring="[para(4969(a,2),5130(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4969 5130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5161">
    <literal><![CDATA[
      T(x,y) * (K(y,x) * z) = x * z
    ]]></literal>
    <justification jstring="[hyper(119,a,5133,a(flip),b,4777,a),flip(a)].">
      <j1 rule="hyper" parents="119 5133 4777"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5162">
    <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,5133,a(flip),b,184,a)].">
      <j1 rule="hyper" parents="119 5133 184"/>
    </justification>
  </clause>

  <clause id="5163">
    <literal><![CDATA[
      K(x,y) \ z != u
    ]]></literal>
    <literal><![CDATA[
      K(y,x) * z = u
    ]]></literal>
    <justification jstring="[para(5133(a,1),287(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5133 287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5164">
    <literal><![CDATA[
      L((K(x,y) * z) \ u,K(x,y) * z,K(y,x)) = z \ (K(y,x) * u)
    ]]></literal>
    <justification jstring="[para(5133(a,1),92(a,2,1))].">
      <j1 rule="para" parents="5133 92"/>
    </justification>
  </clause>

  <clause id="5165">
    <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(5133(a,1),477(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5133 477"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5166">
    <literal><![CDATA[
      K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) \ 1 = z
    ]]></literal>
    <justification jstring="[para(5134(a,1),171(a,1)),flip(b)].">
      <j1 rule="para" parents="5134 171"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5167">
    <literal><![CDATA[
      K(x,y) * z != u
    ]]></literal>
    <literal><![CDATA[
      K(y,x) \ z = u
    ]]></literal>
    <justification jstring="[para(5134(a,1),251(a,1,1)),flip(b)].">
      <j1 rule="para" parents="5134 251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5168">
    <literal><![CDATA[
      K(x,y) != z / u
    ]]></literal>
    <literal><![CDATA[
      K(y,x) * z = u
    ]]></literal>
    <justification jstring="[para(5142(a,1),40(a,1))].">
      <j1 rule="para" parents="5142 40"/>
    </justification>
  </clause>

  <clause id="5169">
    <literal><![CDATA[
      (x / y) / T(x,y \ 1) = x \ (x / y)
    ]]></literal>
    <justification jstring="[para(4789(a,1),265(a,1,2))].">
      <j1 rule="para" parents="4789 265"/>
    </justification>
  </clause>

  <clause id="5171">
    <literal><![CDATA[
      (x \ y) * K(((x \ y) \ (x \ 1)) \ 1,z) = x \ T(y,z)
    ]]></literal>
    <justification jstring="[para(4791(a,1),1430(a,1,2))].">
      <j1 rule="para" parents="4791 1430"/>
    </justification>
  </clause>

  <clause id="5172">
    <literal><![CDATA[
      (x / y) * K(((x / y) \ (1 / y)) \ 1,z) = T(x,z) / y
    ]]></literal>
    <justification jstring="[para(4791(a,1),1439(a,1,2))].">
      <j1 rule="para" parents="4791 1439"/>
    </justification>
  </clause>

  <clause id="5174">
    <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(4801(a,1),482(a,1,2,2))].">
      <j1 rule="para" parents="4801 482"/>
    </justification>
  </clause>

  <clause id="5175">
    <literal><![CDATA[
      T(x,y) \ (x * z) = K(y,x) * z
    ]]></literal>
    <justification jstring="[hyper(1180,a,4818,a)].">
      <j1 rule="hyper" parents="1180 4818"/>
    </justification>
  </clause>

  <clause id="5176">
    <literal><![CDATA[
      K(x,y) * (1 / y) = 1 / T(y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,2876,a(flip),b,4818,a),flip(a)].">
      <j1 rule="hyper" parents="58 2876 4818"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5177">
    <literal><![CDATA[
      K((x / y) / (y \ 1),z) = (T(x,z) / y) / (x / y)
    ]]></literal>
    <justification jstring="[hyper(117,a,4572,a(flip),b,4818,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="117 4572 4818"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5178">
    <literal><![CDATA[
      x \ (K(y,x) * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) \ z = u
    ]]></literal>
    <justification jstring="[para(4818(a,1),287(a,1,2)),flip(b)].">
      <j1 rule="para" parents="4818 287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5179">
    <literal><![CDATA[
      L(T(x \ y,z) \ u,x \ y,x) = y \ (x * (K(z,x \ y) * u))
    ]]></literal>
    <justification jstring="[para(4818(a,1),91(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4818 91"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5180">
    <literal><![CDATA[
      K(x,y) * (y \ z) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,x) \ z = u
    ]]></literal>
    <justification jstring="[para(4818(a,1),1143(a,1))].">
      <j1 rule="para" parents="4818 1143"/>
    </justification>
  </clause>

  <clause id="5181">
    <literal><![CDATA[
      K(x,y) * (y \ z) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (T(y,x) \ z) = w
    ]]></literal>
    <justification jstring="[para(4818(a,1),1132(a,1))].">
      <j1 rule="para" parents="4818 1132"/>
    </justification>
  </clause>

  <clause id="5182">
    <literal><![CDATA[
      K(x,y) * T(T(y,x),z) = y * K(T(y,x),z)
    ]]></literal>
    <justification jstring="[para(4729(a,2),4818(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4729 4818"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5183">
    <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,4819,a)].">
      <j1 rule="hyper" parents="117 101 4819"/>
    </justification>
  </clause>

  <clause id="5185">
    <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(4819(a,1),477(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4819 477"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5186">
    <literal><![CDATA[
      K(x,y) * (K(z,T(y,x)) * u) = y * (T(T(y,x),z) \ u)
    ]]></literal>
    <justification jstring="[para(4818(a,1),4819(a,1,2))].">
      <j1 rule="para" parents="4818 4819"/>
    </justification>
  </clause>

  <clause id="5187">
    <literal><![CDATA[
      x \ (y * K(x,y)) = K(x,y) * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(116,a,4820,a(flip),b,4778,a)].">
      <j1 rule="hyper" parents="116 4820 4778"/>
    </justification>
  </clause>

  <clause id="5188">
    <literal><![CDATA[
      ((x * y) * (z * K(y,z))) / (T(y,z) * z) = R(x,y,z * K(y,z))
    ]]></literal>
    <justification jstring="[para(4829(a,1),15(a,2,2)),flip(a)].">
      <j1 rule="para" parents="4829 15"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5189">
    <literal><![CDATA[
      T(x,y * K(x,y)) / (T(x,y) * y) = x / ((y * K(x,y)) * x)
    ]]></literal>
    <justification jstring="[para(4829(a,1),4364(a,1,2))].">
      <j1 rule="para" parents="4829 4364"/>
    </justification>
  </clause>

  <clause id="5190">
    <literal><![CDATA[
      K(x,T(y,T(x,z))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(4837,a,4832,a)].">
      <j1 rule="hyper" parents="4837 4832"/>
    </justification>
  </clause>

  <clause id="5191">
    <literal><![CDATA[
      T(x,y * K(y,z)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(4832(a,1),4438(a,1,2))].">
      <j1 rule="para" parents="4832 4438"/>
    </justification>
  </clause>

  <clause id="5192">
    <literal><![CDATA[
      T(x,T(y,T(x,z))) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = u
    ]]></literal>
    <justification jstring="[para(4832(a,2),4766(a,1))].">
      <j1 rule="para" parents="4832 4766"/>
    </justification>
  </clause>

  <clause id="5193">
    <literal><![CDATA[
      K(x / y,T(z,y \ x)) = K(x / y,z)
    ]]></literal>
    <justification jstring="[para(107(a,1),5190(a,1,2,2))].">
      <j1 rule="para" parents="107 5190"/>
    </justification>
  </clause>

  <clause id="5194">
    <literal><![CDATA[
      K(x,T(y,x / y)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(4837,a,4834,a)].">
      <j1 rule="hyper" parents="4837 4834"/>
    </justification>
  </clause>

  <clause id="5195">
    <literal><![CDATA[
      K(x * y,T(y,x)) = K(x * y,y)
    ]]></literal>
    <justification jstring="[para(6(a,1),5194(a,1,2,2))].">
      <j1 rule="para" parents="6 5194"/>
    </justification>
  </clause>

  <clause id="5196">
    <literal><![CDATA[
      K(x,(y \ x) \ x) = K(x,y)
    ]]></literal>
    <justification jstring="[para(4288(a,1),5194(a,1,2))].">
      <j1 rule="para" parents="4288 5194"/>
    </justification>
  </clause>

  <clause id="5197">
    <literal><![CDATA[
      K(x,x / y) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[para(75(a,1),5196(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="75 5196"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5200">
    <literal><![CDATA[
      T(x,x \ y) / (y \ x) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(4860(a,1),3916(a,1,1))].">
      <j1 rule="para" parents="4860 3916"/>
    </justification>
  </clause>

  <clause id="5201">
    <literal><![CDATA[
      K(x,T(y,z)) * T(y,z) = T(y * K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(4888,a,4870,a)].">
      <j1 rule="hyper" parents="4888 4870"/>
    </justification>
  </clause>

  <clause id="5202">
    <literal><![CDATA[
      T(x,y) * K(z,T(x,y)) = T(x * K(z,x),y)
    ]]></literal>
    <justification jstring="[hyper(4871,a,4870,a)].">
      <j1 rule="hyper" parents="4871 4870"/>
    </justification>
  </clause>

  <clause id="5203">
    <literal><![CDATA[
      T(x * K(x * y,x),y * x) = x
    ]]></literal>
    <justification jstring="[hyper(4318,a,4870,a),flip(a)].">
      <j1 rule="hyper" parents="4318 4870"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5204">
    <literal><![CDATA[
      T(x * K(x * y,x),y) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(4310,a,4870,a),flip(a)].">
      <j1 rule="hyper" parents="4310 4870"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5205">
    <literal><![CDATA[
      T(x,y) != T(z,u)
    ]]></literal>
    <literal><![CDATA[
      T(z * K(y,z),u) = x
    ]]></literal>
    <justification jstring="[para(4870(a,1),44(a,2)),flip(b)].">
      <j1 rule="para" parents="4870 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5206">
    <literal><![CDATA[
      T(1 / x,(y * x) / y) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(239,a,4889,a(flip),b,4739,a(flip))].">
      <j1 rule="hyper" parents="239 4889 4739"/>
    </justification>
  </clause>

  <clause id="5207">
    <literal><![CDATA[
      T(x,x \ K(x,y)) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(4905(a,1),2240(a,1,2))].">
      <j1 rule="para" parents="4905 2240"/>
    </justification>
  </clause>

  <clause id="5208">
    <literal><![CDATA[
      (x * y) \ K(x * y,y) = (L(y,x,y) * x) \ 1
    ]]></literal>
    <justification jstring="[para(4373(a,1),4905(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4373 4905"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5209">
    <literal><![CDATA[
      (x * K(y,x)) \ 1 = x \ K(x,y)
    ]]></literal>
    <justification jstring="[para(4752(a,1),4905(a,1,1))].">
      <j1 rule="para" parents="4752 4905"/>
    </justification>
  </clause>

  <clause id="5210">
    <literal><![CDATA[
      K(x,y) * K(x \ 1,x) = (x \ K(x,y)) * x
    ]]></literal>
    <justification jstring="[hyper(119,a,4951,a(flip),b,85,a)].">
      <j1 rule="hyper" parents="119 4951 85"/>
    </justification>
  </clause>

  <clause id="5211">
    <literal><![CDATA[
      1 / (x * K(y,x)) = K(x,y) / x
    ]]></literal>
    <justification jstring="[para(4752(a,1),4952(a,2,2)),flip(a)].">
      <j1 rule="para" parents="4752 4952"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5213">
    <literal><![CDATA[
      K(x,y \ 1) * (y \ x) = x * ((y \ x) / x)
    ]]></literal>
    <justification jstring="[para(4482(a,1),5001(a,1,1))].">
      <j1 rule="para" parents="4482 5001"/>
    </justification>
  </clause>

  <clause id="5214">
    <literal><![CDATA[
      K(((x / y) \ 1) \ y,(x / y) \ 1) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(3932,a,5011,a)].">
      <j1 rule="hyper" parents="3932 5011"/>
    </justification>
  </clause>

  <clause id="5215">
    <literal><![CDATA[
      x * (K(x \ 1,x) * K(y,y \ (1 / (1 / x)))) = y * ((1 / (1 / x)) / y)
    ]]></literal>
    <justification jstring="[hyper(58,a,2858,a,b,5013,a)].">
      <j1 rule="hyper" parents="58 2858 5013"/>
    </justification>
  </clause>

  <clause id="5216">
    <literal><![CDATA[
      T(x,y) * K(x * y,(x * y) \ T(x,y)) = (x * y) * (x / (y * x))
    ]]></literal>
    <justification jstring="[para(4364(a,1),5013(a,2,2))].">
      <j1 rule="para" parents="4364 5013"/>
    </justification>
  </clause>

  <clause id="5218">
    <literal><![CDATA[
      K(x * y,x / (x * y)) = K(x * y,1 / y)
    ]]></literal>
    <justification jstring="[para(6(a,1),5072(a,1,2,1))].">
      <j1 rule="para" parents="6 5072"/>
    </justification>
  </clause>

  <clause id="5219">
    <literal><![CDATA[
      K(x,1 / (y \ x)) = K(x,y / x)
    ]]></literal>
    <justification jstring="[para(72(a,1),5072(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="72 5072"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5224">
    <literal><![CDATA[
      x \ y != K(x,z) * u
    ]]></literal>
    <literal><![CDATA[
      T(x,z) \ y = u
    ]]></literal>
    <justification jstring="[para(5081(a,1),38(a,1))].">
      <j1 rule="para" parents="5081 38"/>
    </justification>
  </clause>

  <clause id="5225">
    <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(5081(a,1),92(a,2,1))].">
      <j1 rule="para" parents="5081 92"/>
    </justification>
  </clause>

  <clause id="5226">
    <literal><![CDATA[
      L(x \ (T(y,z) \ u),x,K(y,z)) = (K(y,z) * x) \ (y \ u)
    ]]></literal>
    <justification jstring="[para(5081(a,1),92(a,2,2))].">
      <j1 rule="para" parents="5081 92"/>
    </justification>
  </clause>

  <clause id="5227">
    <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),5098(a,1,2,1))].">
      <j1 rule="para" parents="22 5098"/>
    </justification>
  </clause>

  <clause id="5228">
    <literal><![CDATA[
      K(x,T(y,z)) * K(z,y) = T(T(y,z),x) \ y
    ]]></literal>
    <justification jstring="[hyper(119,a,4730,a,b,5129,a)].">
      <j1 rule="hyper" parents="119 4730 5129"/>
    </justification>
  </clause>

  <clause id="5229">
    <literal><![CDATA[
      T(x,y) \ T(x,z) = K(y,x) * K(x,z)
    ]]></literal>
    <justification jstring="[hyper(119,a,4729,a,b,5129,a),flip(a)].">
      <j1 rule="hyper" parents="119 4729 5129"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5230">
    <literal><![CDATA[
      K(x,y \ z) * T(y,y \ z) = T(y \ z,x) \ z
    ]]></literal>
    <justification jstring="[hyper(119,a,106,a,b,5129,a)].">
      <j1 rule="hyper" parents="119 106 5129"/>
    </justification>
  </clause>

  <clause id="5231">
    <literal><![CDATA[
      T(x,y) \ (z * x) = K(y,x) * T(z,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,17,a,b,5129,a),flip(a)].">
      <j1 rule="hyper" parents="119 17 5129"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5232">
    <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,5129,a),flip(a)].">
      <j1 rule="hyper" parents="119 13 5129"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5233">
    <literal><![CDATA[
      T(x,y) \ (T(x,z) * u) = K(y,x) * (K(x,z) * u)
    ]]></literal>
    <justification jstring="[hyper(119,a,4777,a(flip),b,5129,a),flip(a)].">
      <j1 rule="hyper" parents="119 4777 5129"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5234">
    <literal><![CDATA[
      x \ (K(y,x) * z) = K(y,x) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(320,a,5106,a,b,5131,a)].">
      <j1 rule="hyper" parents="320 5106 5131"/>
    </justification>
  </clause>

  <clause id="5235">
    <literal><![CDATA[
      ((x \ y) \ y) \ z = K(x \ y,x) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(320,a,311,a(flip),b,5131,a)].">
      <j1 rule="hyper" parents="320 311 5131"/>
    </justification>
  </clause>

  <clause id="5236">
    <literal><![CDATA[
      x * (K(y,x) * (x \ z)) = K(y,x) * z
    ]]></literal>
    <justification jstring="[hyper(119,a,5131,a,b,5106,a)].">
      <j1 rule="hyper" parents="119 5131 5106"/>
    </justification>
  </clause>

  <clause id="5238">
    <literal><![CDATA[
      K(x,y) * (T(y,x) \ z) = T(T(y,x),x) \ z
    ]]></literal>
    <justification jstring="[para(4908(a,1),5131(a,1,1))].">
      <j1 rule="para" parents="4908 5131"/>
    </justification>
  </clause>

  <clause id="5239">
    <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(5132(a,1),1634(a,1,2,2,1))].">
      <j1 rule="para" parents="5132 1634"/>
    </justification>
  </clause>

  <clause id="5240">
    <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(5132(a,1),1850(a,1,2,2,1))].">
      <j1 rule="para" parents="5132 1850"/>
    </justification>
  </clause>

  <clause id="5241">
    <literal><![CDATA[
      (x \ 1) / (x \ K(x,y)) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(5137(a,1),327(a,1,1)),flip(b)].">
      <j1 rule="para" parents="5137 327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5244">
    <literal><![CDATA[
      L(x,K(y,z) \ 1,K(y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(29,a,437,a(flip),b,5160,a),flip(a)].">
      <j1 rule="hyper" parents="29 437 5160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5245">
    <literal><![CDATA[
      L(x,K(y,z),K(z,y)) = x
    ]]></literal>
    <justification jstring="[para(4969(a,1),5244(a,1,2))].">
      <j1 rule="para" parents="4969 5244"/>
    </justification>
  </clause>

  <clause id="5247">
    <literal><![CDATA[
      L(x,K(y,z),K(z,y)) / (K(u,w) * x) = K(w,u)
    ]]></literal>
    <justification jstring="[hyper(117,a,5245,a,b,5133,a)].">
      <j1 rule="hyper" parents="117 5245 5133"/>
    </justification>
  </clause>

  <clause id="5248">
    <literal><![CDATA[
      K(x,y) * (x / y) = x / T(y,x)
    ]]></literal>
    <justification jstring="[hyper(4476,a,5161,a),flip(a)].">
      <j1 rule="hyper" parents="4476 5161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5249">
    <literal><![CDATA[
      K(x,y) * (x / y) = T(x,y) / y
    ]]></literal>
    <justification jstring="[hyper(4474,a,5161,a),flip(a)].">
      <j1 rule="hyper" parents="4474 5161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5250">
    <literal><![CDATA[
      K(x,y) * (((x * y) / x) \ z) = y \ z
    ]]></literal>
    <justification jstring="[hyper(4443,a,5161,a),flip(a)].">
      <j1 rule="hyper" parents="4443 5161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5251">
    <literal><![CDATA[
      x \ T(x * y,x) = K(x * y,x) * y
    ]]></literal>
    <justification jstring="[hyper(4299,a,5161,a)].">
      <j1 rule="hyper" parents="4299 5161"/>
    </justification>
  </clause>

  <clause id="5253">
    <literal><![CDATA[
      (x * y) / (K(z,x) * y) = T(x,z)
    ]]></literal>
    <justification jstring="[hyper(131,a,5161,a)].">
      <j1 rule="hyper" parents="131 5161"/>
    </justification>
  </clause>

  <clause id="5254">
    <literal><![CDATA[
      T(x,y) / (K(z,x) * K(x,y)) = T(x,z)
    ]]></literal>
    <justification jstring="[hyper(117,a,4755,a,b,5161,a)].">
      <j1 rule="hyper" parents="117 4755 5161"/>
    </justification>
  </clause>

  <clause id="5255">
    <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,5161,a)].">
      <j1 rule="hyper" parents="117 101 5161"/>
    </justification>
  </clause>

  <clause id="5256">
    <literal><![CDATA[
      K(x,y) * (y * z) = y * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(119,a,5161,a(flip),b,5099,a)].">
      <j1 rule="hyper" parents="119 5161 5099"/>
    </justification>
  </clause>

  <clause id="5257">
    <literal><![CDATA[
      (x * y) / (K(z,x) * y) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z) = u
    ]]></literal>
    <justification jstring="[para(5161(a,1),327(a,1,1)),flip(b)].">
      <j1 rule="para" parents="5161 327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5258">
    <literal><![CDATA[
      x * (y * (K(x,y) * z)) = T(x,y) * (y * z)
    ]]></literal>
    <justification jstring="[para(5161(a,1),4553(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5161 4553"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5259">
    <literal><![CDATA[
      K(x,y) * T(x,T(y,z)) = T(T(x,y),T(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,4692,a(flip),b,5175,a),flip(a)].">
      <j1 rule="hyper" parents="58 4692 5175"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5260">
    <literal><![CDATA[
      x * (K(x * y,x) * y) = T(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,5175,a(flip),b,4248,a(flip))].">
      <j1 rule="hyper" parents="119 5175 4248"/>
    </justification>
  </clause>

  <clause id="5261">
    <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),5175(a,1,1))].">
      <j1 rule="para" parents="20 5175"/>
    </justification>
  </clause>

  <clause id="5262">
    <literal><![CDATA[
      T(x,y) * (K(y,x) * z) != u
    ]]></literal>
    <literal><![CDATA[
      x * z = u
    ]]></literal>
    <justification jstring="[para(5175(a,1),255(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5175 255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5263">
    <literal><![CDATA[
      K(x,y) * z != u
    ]]></literal>
    <literal><![CDATA[
      y * (T(y,x) \ z) = u
    ]]></literal>
    <justification jstring="[para(5175(a,1),1139(a,1))].">
      <j1 rule="para" parents="5175 1139"/>
    </justification>
  </clause>

  <clause id="5264">
    <literal><![CDATA[
      T(x,y) * (1 / y) = x * (1 / T(y,x))
    ]]></literal>
    <justification jstring="[hyper(119,a,5176,a(flip),b,4777,a),flip(a)].">
      <j1 rule="hyper" parents="119 5176 4777"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5266">
    <literal><![CDATA[
      K(x * y,y) = K(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(4495,a,5195,a),flip(a)].">
      <j1 rule="hyper" parents="4495 5195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5267">
    <literal><![CDATA[
      (x \ K(x,y)) * T((x \ 1) \ 1,z) = T(x,z) * (x \ K(x,y))
    ]]></literal>
    <justification jstring="[para(5207(a,1),236(a,1,2,1))].">
      <j1 rule="para" parents="5207 236"/>
    </justification>
  </clause>

  <clause id="5268">
    <literal><![CDATA[
      1 / (x \ K(x,y)) = x * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(197,a,5209,a)].">
      <j1 rule="hyper" parents="197 5209"/>
    </justification>
  </clause>

  <clause id="5269">
    <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(5209(a,1),3129(a,2,2,2))].">
      <j1 rule="para" parents="5209 3129"/>
    </justification>
  </clause>

  <clause id="5270">
    <literal><![CDATA[
      (K(x,y) / x) \ 1 = x * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(188,a,5211,a)].">
      <j1 rule="hyper" parents="188 5211"/>
    </justification>
  </clause>

  <clause id="5271">
    <literal><![CDATA[
      1 / ((x \ 1) * K(y,x \ 1)) = K(1 / x,y) / (x \ 1)
    ]]></literal>
    <justification jstring="[para(3312(a,2),5211(a,2,1))].">
      <j1 rule="para" parents="3312 5211"/>
    </justification>
  </clause>

  <clause id="5272">
    <literal><![CDATA[
      K(1 / x,y) / (1 / x) = 1 / (K(y,x \ 1) / x)
    ]]></literal>
    <justification jstring="[para(3567(a,1),5211(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3567 5211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5273">
    <literal><![CDATA[
      K(((x * K(y,x)) \ 1) * z,u) = K((K(x,y) / x) * z,u)
    ]]></literal>
    <justification jstring="[para(5211(a,1),3981(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5211 3981"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5274">
    <literal><![CDATA[
      (x / T(y,x)) * L(z,x / y,K(x,y)) = K(x,y) * ((x / y) * z)
    ]]></literal>
    <justification jstring="[para(5248(a,1),90(a,1,1))].">
      <j1 rule="para" parents="5248 90"/>
    </justification>
  </clause>

  <clause id="5275">
    <literal><![CDATA[
      R(K(x,y),x / y,z) \ ((x / T(y,x)) * z) = (x / y) * z
    ]]></literal>
    <justification jstring="[para(5248(a,1),184(a,1,2,1))].">
      <j1 rule="para" parents="5248 184"/>
    </justification>
  </clause>

  <clause id="5276">
    <literal><![CDATA[
      1 / x != y * K(z,y)
    ]]></literal>
    <literal><![CDATA[
      y \ K(y,z) = x
    ]]></literal>
    <justification jstring="[para(5268(a,1),40(a,1)),flip(a)].">
      <j1 rule="para" parents="5268 40"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5277">
    <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,4841,a,b,3396,a)].">
      <j1 rule="hyper" parents="116 4841 3396"/>
    </justification>
  </clause>

  <clause id="5278">
    <literal><![CDATA[
      L(x,y,z) \ K(x,L(x,u,w) \ 1) = 1 / L(x,y,z)
    ]]></literal>
    <justification jstring="[para(4841(a,2),3796(a,1,2))].">
      <j1 rule="para" parents="4841 3796"/>
    </justification>
  </clause>

  <clause id="5280">
    <literal><![CDATA[
      (x \ 1) * ((y * ((x \ 1) \ 1)) / y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(1424(a,2),4922(a,1))].">
      <j1 rule="para" parents="1424 4922"/>
    </justification>
  </clause>

  <clause id="5281">
    <literal><![CDATA[
      T(K(x * (1 / y),y \ 1) / y,x) = R(1 / y,x,1 / y)
    ]]></literal>
    <justification jstring="[para(3567(a,1),4932(a,1,1))].">
      <j1 rule="para" parents="3567 4932"/>
    </justification>
  </clause>

  <clause id="5282">
    <literal><![CDATA[
      K(x \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(1 / x,y) = z
    ]]></literal>
    <justification jstring="[para(75(a,1),5040(a,1,1,1))].">
      <j1 rule="para" parents="75 5040"/>
    </justification>
  </clause>

  <clause id="5283">
    <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(3298(a,1),5040(a,1,1))].">
      <j1 rule="para" parents="3298 5040"/>
    </justification>
  </clause>

  <clause id="5284">
    <literal><![CDATA[
      T(x,x * y) * K(y,x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(2900,a,5090,a)].">
      <j1 rule="hyper" parents="2900 5090"/>
    </justification>
  </clause>

  <clause id="5285">
    <literal><![CDATA[
      K(x,y) = T(y,y * x) \ L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(116,a,5090,a(flip),b,2897,a),flip(a)].">
      <j1 rule="hyper" parents="116 5090 2897"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5286">
    <literal><![CDATA[
      T(x,y) * K(x * y,x) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(2900,a,5093,a)].">
      <j1 rule="hyper" parents="2900 5093"/>
    </justification>
  </clause>

  <clause id="5287">
    <literal><![CDATA[
      T(x,x * y) \ T(x,y) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,5093,a(flip),b,4818,a),flip(a)].">
      <j1 rule="hyper" parents="116 5093 4818"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5288">
    <literal><![CDATA[
      T(x,y) \ R(x,y,x) = K(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,5093,a(flip),b,2897,a)].">
      <j1 rule="hyper" parents="116 5093 2897"/>
    </justification>
  </clause>

  <clause id="5289">
    <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),5163(a,1))].">
      <j1 rule="para" parents="17 5163"/>
    </justification>
  </clause>

  <clause id="5290">
    <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),5192(a,1,2))].">
      <j1 rule="para" parents="248 5192"/>
    </justification>
  </clause>

  <clause id="5291">
    <literal><![CDATA[
      T(T(x * K(x * y,x),z),y) = T(R(x,y,x),z)
    ]]></literal>
    <justification jstring="[para(5204(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5204 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5292">
    <literal><![CDATA[
      K(x,x * y) * K(y,x) = x \ L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,5284,a(flip),b,4778,a),flip(a)].">
      <j1 rule="hyper" parents="116 5284 4778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5293">
    <literal><![CDATA[
      K(x,y) * K(x * y,x) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,5286,a(flip),b,4778,a),flip(a)].">
      <j1 rule="hyper" parents="116 5286 4778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5294">
    <literal><![CDATA[
      (x * T(y,z)) \ (x * R(y,z,y)) = L(K(y * z,y),T(y,z),x)
    ]]></literal>
    <justification jstring="[para(5286(a,1),13(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="5286 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5295">
    <literal><![CDATA[
      x \ R(y,z,y) != K(y * z,y)
    ]]></literal>
    <literal><![CDATA[
      T(y,z) = x
    ]]></literal>
    <justification jstring="[para(5288(a,1),43(a,1)),flip(a)].">
      <j1 rule="para" parents="5288 43"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5296">
    <literal><![CDATA[
      K(x \ y,x) != 1
    ]]></literal>
    <literal><![CDATA[
      (x \ y) * x = y
    ]]></literal>
    <justification jstring="[para(4712(a,1),125(a,1)),flip(b)].">
      <j1 rule="para" parents="4712 125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5297">
    <literal><![CDATA[
      K(x \ (x * y),x) = (y * x) * ((x * y) \ 1)
    ]]></literal>
    <justification jstring="[para(4(a,1),4723(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4 4723"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5298">
    <literal><![CDATA[
      (x * (y * T(y \ z,u))) / (x * z) = K((x * z) / (x * y),u)
    ]]></literal>
    <justification jstring="[para(923(a,1),4734(a,1,1))].">
      <j1 rule="para" parents="923 4734"/>
    </justification>
  </clause>

  <clause id="5300">
    <literal><![CDATA[
      (x * ((y * (x \ z)) / y)) / z = K(y,(x / z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,2433,a(flip),b,4741,a)].">
      <j1 rule="hyper" parents="58 2433 4741"/>
    </justification>
  </clause>

  <clause id="5302">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ x)) / z) = x * K(z,y \ 1)
    ]]></literal>
    <justification jstring="[para(4741(a,1),1097(a,2,2))].">
      <j1 rule="para" parents="4741 1097"/>
    </justification>
  </clause>

  <clause id="5303">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ y)) / z) = K(z,x \ 1) * y
    ]]></literal>
    <justification jstring="[para(4741(a,1),1721(a,2,1))].">
      <j1 rule="para" parents="4741 1721"/>
    </justification>
  </clause>

  <clause id="5304">
    <literal><![CDATA[
      K(x,(y * x) \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      y * (x * ((y \ 1) / x)) = z
    ]]></literal>
    <justification jstring="[para(4741(a,1),971(a,1))].">
      <j1 rule="para" parents="4741 971"/>
    </justification>
  </clause>

  <clause id="5305">
    <literal><![CDATA[
      K(x,R(y,z,u) \ 1) * (z * u) = ((y * z) * ((x * ((y * z) \ z)) / x)) * u
    ]]></literal>
    <justification jstring="[para(4741(a,1),3262(a,1,1))].">
      <j1 rule="para" parents="4741 3262"/>
    </justification>
  </clause>

  <clause id="5306">
    <literal><![CDATA[
      L(x,y,z) \ K(x,L(x,y,z) \ 1) = (L(x,y,z) \ x) / x
    ]]></literal>
    <justification jstring="[para(1413(a,1),4759(a,2,1))].">
      <j1 rule="para" parents="1413 4759"/>
    </justification>
  </clause>

  <clause id="5307">
    <literal><![CDATA[
      K(x,x * (y \ 1)) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[hyper(320,a,4729,a,b,4769,a),flip(a)].">
      <j1 rule="hyper" parents="320 4729 4769"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5308">
    <literal><![CDATA[
      K(x,y * K(z,z \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,4729,a,b,4773,a),flip(a)].">
      <j1 rule="hyper" parents="320 4729 4773"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5309">
    <literal><![CDATA[
      K(x,y * K(z,1 / z)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(1791(a,2),5308(a,1,2,2))].">
      <j1 rule="para" parents="1791 5308"/>
    </justification>
  </clause>

  <clause id="5310">
    <literal><![CDATA[
      K(x,y * K(z \ 1,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(1798(a,1),5308(a,1,2,2))].">
      <j1 rule="para" parents="1798 5308"/>
    </justification>
  </clause>

  <clause id="5311">
    <literal><![CDATA[
      K(x,K(y,y \ 1) * z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(2181(a,2),5308(a,1,2))].">
      <j1 rule="para" parents="2181 5308"/>
    </justification>
  </clause>

  <clause id="5312">
    <literal><![CDATA[
      K(x,y * ((z \ 1) \ 1)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(2677(a,1),5308(a,1,2))].">
      <j1 rule="para" parents="2677 5308"/>
    </justification>
  </clause>

  <clause id="5313">
    <literal><![CDATA[
      K(x,y * T(z,z \ 1)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(2678(a,1),5308(a,1,2))].">
      <j1 rule="para" parents="2678 5308"/>
    </justification>
  </clause>

  <clause id="5314">
    <literal><![CDATA[
      K(x,K(y \ 1,y) * z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(2692(a,1),5308(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2692 5308"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5315">
    <literal><![CDATA[
      K(x,y * (1 / z)) = K(x,y * (z \ 1))
    ]]></literal>
    <justification jstring="[para(2691(a,1),5308(a,1,2))].">
      <j1 rule="para" parents="2691 5308"/>
    </justification>
  </clause>

  <clause id="5316">
    <literal><![CDATA[
      K(x,y / (1 / z)) = K(x,y / (z \ 1))
    ]]></literal>
    <justification jstring="[para(2701(a,1),5308(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2701 5308"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5317">
    <literal><![CDATA[
      K(x,(y / (z \ 1)) * (1 / z)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(2718(a,2),5308(a,1,2))].">
      <j1 rule="para" parents="2718 5308"/>
    </justification>
  </clause>

  <clause id="5318">
    <literal><![CDATA[
      K(x,(y \ 1) * (y * z)) = K(x,L(z,y,y \ 1))
    ]]></literal>
    <justification jstring="[para(2699(a,1),5308(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2699 5308"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5319">
    <literal><![CDATA[
      K(x,T(y,y \ 1) * z) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(2802(a,1),5308(a,1,2))].">
      <j1 rule="para" parents="2802 5308"/>
    </justification>
  </clause>

  <clause id="5321">
    <literal><![CDATA[
      K(x,((y \ 1) \ 1) \ z) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(2839(a,1),5308(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2839 5308"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5322">
    <literal><![CDATA[
      K(x,(1 / y) * z) = K(x,(y \ 1) * z)
    ]]></literal>
    <justification jstring="[para(2846(a,1),5308(a,1,2))].">
      <j1 rule="para" parents="2846 5308"/>
    </justification>
  </clause>

  <clause id="5323">
    <literal><![CDATA[
      K(x,(1 / y) \ z) = K(x,(y \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(2948(a,1),5308(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2948 5308"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5324">
    <literal><![CDATA[
      K(x,y \ (K(z,z \ 1) * u)) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[para(3423(a,2),5308(a,1,2))].">
      <j1 rule="para" parents="3423 5308"/>
    </justification>
  </clause>

  <clause id="5325">
    <literal><![CDATA[
      K(x,(K(y \ 1,y) * z) \ u) = K(x,z \ u)
    ]]></literal>
    <justification jstring="[para(3739(a,2),5308(a,1,2))].">
      <j1 rule="para" parents="3739 5308"/>
    </justification>
  </clause>

  <clause id="5326">
    <literal><![CDATA[
      K(x,((1 / y) * z) \ u) = K(x,((y \ 1) * z) \ u)
    ]]></literal>
    <justification jstring="[para(3752(a,1),5308(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3752 5308"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5327">
    <literal><![CDATA[
      K(x,y * (z * K(u,1 / u))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(3418(a,1),5309(a,1,2))].">
      <j1 rule="para" parents="3418 5309"/>
    </justification>
  </clause>

  <clause id="5328">
    <literal><![CDATA[
      K(x,y * (z * K(u \ 1,u))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(3380(a,1),5310(a,1,2))].">
      <j1 rule="para" parents="3380 5310"/>
    </justification>
  </clause>

  <clause id="5329">
    <literal><![CDATA[
      K(x,y \ (z / (1 / u))) = K(x,y \ (z / (u \ 1)))
    ]]></literal>
    <justification jstring="[para(3434(a,1),5310(a,1,2))].">
      <j1 rule="para" parents="3434 5310"/>
    </justification>
  </clause>

  <clause id="5330">
    <literal><![CDATA[
      K(x,y / (K(z,z \ 1) * u)) = K(x,y / u)
    ]]></literal>
    <justification jstring="[para(3813(a,2),5310(a,1,2))].">
      <j1 rule="para" parents="3813 5310"/>
    </justification>
  </clause>

  <clause id="5331">
    <literal><![CDATA[
      K(x,y / T(1 / z,u)) = K(x,y / T(z \ 1,u))
    ]]></literal>
    <justification jstring="[para(3814(a,1),5310(a,1,2))].">
      <j1 rule="para" parents="3814 5310"/>
    </justification>
  </clause>

  <clause id="5332">
    <literal><![CDATA[
      K(x,K(y,1 / y) * z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(1791(a,2),5311(a,1,2,1))].">
      <j1 rule="para" parents="1791 5311"/>
    </justification>
  </clause>

  <clause id="5333">
    <literal><![CDATA[
      K(x,y * (z * ((u \ 1) \ 1))) = K(x,y * (z * u))
    ]]></literal>
    <justification jstring="[para(3456(a,1),5311(a,1,2))].">
      <j1 rule="para" parents="3456 5311"/>
    </justification>
  </clause>

  <clause id="5334">
    <literal><![CDATA[
      K(x,y * (z * (1 / u))) = K(x,y * (z * (u \ 1)))
    ]]></literal>
    <justification jstring="[para(3457(a,1),5311(a,1,2))].">
      <j1 rule="para" parents="3457 5311"/>
    </justification>
  </clause>

  <clause id="5335">
    <literal><![CDATA[
      K(x,y * (z / (1 / u))) = K(x,y * (z / (u \ 1)))
    ]]></literal>
    <justification jstring="[para(3458(a,1),5311(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3458 5311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5336">
    <literal><![CDATA[
      K(x,y * ((1 / z) * u)) = K(x,y * ((z \ 1) * u))
    ]]></literal>
    <justification jstring="[para(3459(a,1),5311(a,1,2))].">
      <j1 rule="para" parents="3459 5311"/>
    </justification>
  </clause>

  <clause id="5337">
    <literal><![CDATA[
      K(x,y * ((1 / z) \ u)) = K(x,y * ((z \ 1) \ u))
    ]]></literal>
    <justification jstring="[para(3460(a,1),5311(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3460 5311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5338">
    <literal><![CDATA[
      K(x,y \ ((1 / z) * u)) = K(x,y \ ((z \ 1) * u))
    ]]></literal>
    <justification jstring="[para(3461(a,1),5311(a,1,2))].">
      <j1 rule="para" parents="3461 5311"/>
    </justification>
  </clause>

  <clause id="5339">
    <literal><![CDATA[
      K(x,y \ (z * ((1 / u) \ w))) = K(x,y \ (z * ((u \ 1) \ w)))
    ]]></literal>
    <justification jstring="[para(3474(a,1),5311(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3474 5311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5340">
    <literal><![CDATA[
      K(x,(y * (z / (1 / u))) \ w) = K(x,(y * (z / (u \ 1))) \ w)
    ]]></literal>
    <justification jstring="[para(3809(a,1),5311(a,1,2))].">
      <j1 rule="para" parents="3809 5311"/>
    </justification>
  </clause>

  <clause id="5341">
    <literal><![CDATA[
      K(x,T(y * K(z,z \ 1),u)) = K(x,T(y,u))
    ]]></literal>
    <justification jstring="[para(4651(a,2),5311(a,1,2))].">
      <j1 rule="para" parents="4651 5311"/>
    </justification>
  </clause>

  <clause id="5342">
    <literal><![CDATA[
      K(x,y \ (z * (1 / u))) = K(x,y \ (z * (u \ 1)))
    ]]></literal>
    <justification jstring="[para(3454(a,1),5314(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3454 5314"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5343">
    <literal><![CDATA[
      K(x,(K(y \ 1,y) * z) / u) = K(x,z / u)
    ]]></literal>
    <justification jstring="[para(3674(a,2),5314(a,1,2))].">
      <j1 rule="para" parents="3674 5314"/>
    </justification>
  </clause>

  <clause id="5344">
    <literal><![CDATA[
      K(x,R(1 / y,z,u) \ w) = K(x,R(y \ 1,z,u) \ w)
    ]]></literal>
    <justification jstring="[para(3830(a,1),5314(a,1,2))].">
      <j1 rule="para" parents="3830 5314"/>
    </justification>
  </clause>

  <clause id="5345">
    <literal><![CDATA[
      K(x,K(y,1 / y) / z) = K(x,1 / z)
    ]]></literal>
    <justification jstring="[para(3647(a,1),5332(a,1,2))].">
      <j1 rule="para" parents="3647 5332"/>
    </justification>
  </clause>

  <clause id="5346">
    <literal><![CDATA[
      K(x,(y \ z) / z) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,4729,a,b,4787,a),flip(a)].">
      <j1 rule="hyper" parents="320 4729 4787"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5347">
    <literal><![CDATA[
      K(x,(y \ z) / z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ 1) = u
    ]]></literal>
    <justification jstring="[para(4787(a,2),4838(a,1))].">
      <j1 rule="para" parents="4787 4838"/>
    </justification>
  </clause>

  <clause id="5350">
    <literal><![CDATA[
      K(x,y / (z * y)) = K(x,z \ 1)
    ]]></literal>
    <justification jstring="[para(4(a,1),5346(a,1,2,1))].">
      <j1 rule="para" parents="4 5346"/>
    </justification>
  </clause>

  <clause id="5351">
    <literal><![CDATA[
      K(x,(y / z) \ 1) = K(x,z / y)
    ]]></literal>
    <justification jstring="[para(75(a,1),5346(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="75 5346"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5352">
    <literal><![CDATA[
      K(x,y \ 1) * (((y \ z) / z) \ u) = T((y \ z) / z,x) \ u
    ]]></literal>
    <justification jstring="[para(5346(a,1),5131(a,1,1))].">
      <j1 rule="para" parents="5346 5131"/>
    </justification>
  </clause>

  <clause id="5353">
    <literal><![CDATA[
      K(x,y / (z * y)) = K(x,1 / z)
    ]]></literal>
    <justification jstring="[hyper(320,a,3558,a,b,5350,a),flip(a)].">
      <j1 rule="hyper" parents="320 3558 5350"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5354">
    <literal><![CDATA[
      K(x * y,x \ 1) * ((x * y) \ y) = y / (x * y)
    ]]></literal>
    <justification jstring="[para(5350(a,1),4859(a,1,1))].">
      <j1 rule="para" parents="5350 4859"/>
    </justification>
  </clause>

  <clause id="5355">
    <literal><![CDATA[
      K(x,(y / z) \ 1) = K(z / y,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(320,a,4969,a,b,5351,a),flip(a)].">
      <j1 rule="hyper" parents="320 4969 5351"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5356">
    <literal><![CDATA[
      K(x,1 / (y / z)) = K(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(58,a,3558,a,b,5351,a)].">
      <j1 rule="hyper" parents="58 3558 5351"/>
    </justification>
  </clause>

  <clause id="5357">
    <literal><![CDATA[
      K(x,y / (z * y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ 1) = u
    ]]></literal>
    <justification jstring="[para(5353(a,2),5075(a,1))].">
      <j1 rule="para" parents="5353 5075"/>
    </justification>
  </clause>

  <clause id="5358">
    <literal><![CDATA[
      K((x * y) / x,1 / ((x * y) / x)) = K(y,1 / y)
    ]]></literal>
    <justification jstring="[hyper(320,a,3037,a(flip),b,5356,a),flip(a)].">
      <j1 rule="hyper" parents="320 3037 5356"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5359">
    <literal><![CDATA[
      K(x,y / z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,(z / y) \ 1) = u
    ]]></literal>
    <justification jstring="[para(5356(a,1),5075(a,1))].">
      <j1 rule="para" parents="5356 5075"/>
    </justification>
  </clause>

  <clause id="5360">
    <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(4793(a,1),3603(a,2,1,2,1))].">
      <j1 rule="para" parents="4793 3603"/>
    </justification>
  </clause>

  <clause id="5361">
    <literal><![CDATA[
      K((1 / x) \ y,y) = K(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,4730,a,b,4810,a),flip(a)].">
      <j1 rule="hyper" parents="320 4730 4810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5362">
    <literal><![CDATA[
      K((x \ 1) \ y,y) = K(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,3982,a(flip),b,5361,a)].">
      <j1 rule="hyper" parents="58 3982 5361"/>
    </justification>
  </clause>

  <clause id="5363">
    <literal><![CDATA[
      K(x * (y \ 1),x) = K(y \ x,x)
    ]]></literal>
    <justification jstring="[para(72(a,1),5361(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="72 5361"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5364">
    <literal><![CDATA[
      K((x \ 1) \ y,y) = K(x * y,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,5266,a,b,5362,a),flip(a)].">
      <j1 rule="hyper" parents="320 5266 5362"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5365">
    <literal><![CDATA[
      K((x \ 1) * y,y) = K(x \ y,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,5266,a,b,5363,a)].">
      <j1 rule="hyper" parents="58 5266 5363"/>
    </justification>
  </clause>

  <clause id="5366">
    <literal><![CDATA[
      K(((x * y) / x) \ z,z) = K(z * (y \ K(y,x)),z)
    ]]></literal>
    <justification jstring="[para(4905(a,1),5363(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4905 5363"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5367">
    <literal><![CDATA[
      T(x * K(y \ x,x),y \ 1) = R(x,y \ 1,x)
    ]]></literal>
    <justification jstring="[para(5363(a,1),5204(a,1,1,2))].">
      <j1 rule="para" parents="5363 5204"/>
    </justification>
  </clause>

  <clause id="5368">
    <literal><![CDATA[
      ((x \ 1) \ y) * K(x * y,y) = T((x \ 1) \ y,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,5364,a(flip),b,4729,a(flip))].">
      <j1 rule="hyper" parents="119 5364 4729"/>
    </justification>
  </clause>

  <clause id="5369">
    <literal><![CDATA[
      K((1 / x) * y,y) = K(x \ y,y)
    ]]></literal>
    <justification jstring="[para(75(a,1),5364(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="75 5364"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5370">
    <literal><![CDATA[
      (x * y) / (((z * x) / z) * y) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(617,a,4814,a)].">
      <j1 rule="hyper" parents="617 4814"/>
    </justification>
  </clause>

  <clause id="5371">
    <literal><![CDATA[
      K(x,y) * (((y * x) / y) * z) = x * z
    ]]></literal>
    <justification jstring="[hyper(585,a,4814,a),flip(a)].">
      <j1 rule="hyper" parents="585 4814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5372">
    <literal><![CDATA[
      (x \ y) * ((y / x) \ z) = K(x \ y,x) * z
    ]]></literal>
    <justification jstring="[para(5(a,1),4814(a,1,2,1,1))].">
      <j1 rule="para" parents="5 4814"/>
    </justification>
  </clause>

  <clause id="5373">
    <literal><![CDATA[
      x * ((y / (y / x)) \ z) = K(x,x \ y) * z
    ]]></literal>
    <justification jstring="[para(4343(a,1),4814(a,1,2,1))].">
      <j1 rule="para" parents="4343 4814"/>
    </justification>
  </clause>

  <clause id="5374">
    <literal><![CDATA[
      x / (y * T(y \ x,z)) = K(z,x / y)
    ]]></literal>
    <justification jstring="[para(4817(a,1),5142(a,1,2))].">
      <j1 rule="para" parents="4817 5142"/>
    </justification>
  </clause>

  <clause id="5375">
    <literal><![CDATA[
      x / (y * T(y \ x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,x / y) = u
    ]]></literal>
    <justification jstring="[para(4817(a,1),5150(a,1,2))].">
      <j1 rule="para" parents="4817 5150"/>
    </justification>
  </clause>

  <clause id="5376">
    <literal><![CDATA[
      (x * K(y,x)) \ y = x \ (y * K(x,y))
    ]]></literal>
    <justification jstring="[para(4752(a,1),4830(a,1,1))].">
      <j1 rule="para" parents="4752 4830"/>
    </justification>
  </clause>

  <clause id="5377">
    <literal><![CDATA[
      K(x,y) / (1 / T(y,x)) = 1 / (1 / y)
    ]]></literal>
    <justification jstring="[hyper(197,a,4866,a)].">
      <j1 rule="hyper" parents="197 4866"/>
    </justification>
  </clause>

  <clause id="5378">
    <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,1894,a,b,4873,a),flip(a)].">
      <j1 rule="hyper" parents="30 1894 4873"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5379">
    <literal><![CDATA[
      T(x * K(y \ x,x),y \ 1) = R(x,x \ (y \ x),x)
    ]]></literal>
    <justification jstring="[hyper(320,a,4522,a,b,4874,a),flip(a)].">
      <j1 rule="hyper" parents="320 4522 4874"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5380">
    <literal><![CDATA[
      T(x,y) \ T(x * K(z,x),y) = K(z,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(116,a,4874,a,b,4752,a(flip))].">
      <j1 rule="hyper" parents="116 4874 4752"/>
    </justification>
  </clause>

  <clause id="5381">
    <literal><![CDATA[
      T(x * K(y,x),z) \ T(x,z) = K(T(x,z),y)
    ]]></literal>
    <justification jstring="[para(4874(a,2),4792(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4874 4792"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5382">
    <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(4874(a,2),4872(a,1))].">
      <j1 rule="para" parents="4874 4872"/>
    </justification>
  </clause>

  <clause id="5383">
    <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(4874(a,2),4922(a,1,2))].">
      <j1 rule="para" parents="4874 4922"/>
    </justification>
  </clause>

  <clause id="5384">
    <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(4892(a,1),768(a,1,1))].">
      <j1 rule="para" parents="4892 768"/>
    </justification>
  </clause>

  <clause id="5385">
    <literal><![CDATA[
      K(x,y * x) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(4946,a,4907,a)].">
      <j1 rule="hyper" parents="4946 4907"/>
    </justification>
  </clause>

  <clause id="5386">
    <literal><![CDATA[
      K(x,x * (y / x)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(7(a,1),5385(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7 5385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5387">
    <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),5385(a,2,2))].">
      <j1 rule="para" parents="80 5385"/>
    </justification>
  </clause>

  <clause id="5388">
    <literal><![CDATA[
      K(x,T(y * x,z)) = K(x,T(x * y,z))
    ]]></literal>
    <justification jstring="[para(4583(a,1),5386(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4583 5386"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5389">
    <literal><![CDATA[
      K(x,(1 / x) * (y * x)) = K(x,L(y,x,x \ 1))
    ]]></literal>
    <justification jstring="[para(2821(a,1),4911(a,1,2))].">
      <j1 rule="para" parents="2821 4911"/>
    </justification>
  </clause>

  <clause id="5390">
    <literal><![CDATA[
      L(x * K(y,x),z,u) * T(y,x) = T(y,x) * L(x,z,u)
    ]]></literal>
    <justification jstring="[para(4962(a,1),637(a,1,1,1))].">
      <j1 rule="para" parents="4962 637"/>
    </justification>
  </clause>

  <clause id="5391">
    <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(4962(a,1),1468(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4962 1468"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5395">
    <literal><![CDATA[
      x * ((y * (x / y)) \ y) = x / (x / y)
    ]]></literal>
    <justification jstring="[hyper(119,a,5071,a,b,xx)].">
      <j1 rule="hyper" parents="119 5071"/>
    </justification>
  </clause>

  <clause id="5396">
    <literal><![CDATA[
      x \ (y \ ((y * z) / y)) = x \ (K(y,z) * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(116,a,5086,a,b,5,a)].">
      <j1 rule="hyper" parents="116 5086 5"/>
    </justification>
  </clause>

  <clause id="5397">
    <literal><![CDATA[
      L(x \ (y \ z),x,K(y,z)) = (K(y,z) * x) \ (y \ ((y * z) / y))
    ]]></literal>
    <justification jstring="[para(5086(a,2),92(a,2,2))].">
      <j1 rule="para" parents="5086 92"/>
    </justification>
  </clause>

  <clause id="5398">
    <literal><![CDATA[
      (x * K(y,x)) \ z = K(x,y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,4898,a(flip),b,5088,a)].">
      <j1 rule="hyper" parents="58 4898 5088"/>
    </justification>
  </clause>

  <clause id="5399">
    <literal><![CDATA[
      K(x \ y,x) * ((x \ y) \ z) = (y / x) \ z
    ]]></literal>
    <justification jstring="[para(5(a,1),5088(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5 5088"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5401">
    <literal><![CDATA[
      (x / (x / y)) \ z = K(y,y \ x) * (y \ z)
    ]]></literal>
    <justification jstring="[para(4343(a,1),5088(a,1,1))].">
      <j1 rule="para" parents="4343 5088"/>
    </justification>
  </clause>

  <clause id="5404">
    <literal><![CDATA[
      ((x * y) / x) * z = y * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(119,a,5133,a(flip),b,5103,a)].">
      <j1 rule="hyper" parents="119 5133 5103"/>
    </justification>
  </clause>

  <clause id="5405">
    <literal><![CDATA[
      K(x,y) * T(x,z) = K(x,z) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,3334,a(flip),b,5111,a)].">
      <j1 rule="hyper" parents="320 3334 5111"/>
    </justification>
  </clause>

  <clause id="5406">
    <literal><![CDATA[
      (K(x,y) * T(x,z)) / T(x,y) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(117,a,3334,a(flip),b,5111,a)].">
      <j1 rule="hyper" parents="117 3334 5111"/>
    </justification>
  </clause>

  <clause id="5407">
    <literal><![CDATA[
      K(x,y) * T(x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) * T(x,y) = u
    ]]></literal>
    <justification jstring="[para(5111(a,2),3341(a,1))].">
      <j1 rule="para" parents="5111 3341"/>
    </justification>
  </clause>

  <clause id="5408">
    <literal><![CDATA[
      K(x,(y \ z) / (y \ 1)) * (y \ T(z,x)) = y \ z
    ]]></literal>
    <justification jstring="[hyper(1051,a,5112,a)].">
      <j1 rule="hyper" parents="1051 5112"/>
    </justification>
  </clause>

  <clause id="5409">
    <literal><![CDATA[
      T(x,x \ (y * x)) / ((y * x) \ x) = x * y
    ]]></literal>
    <justification jstring="[para(6(a,1),5200(a,2,2))].">
      <j1 rule="para" parents="6 5200"/>
    </justification>
  </clause>

  <clause id="5410">
    <literal><![CDATA[
      T(x,y) \ T(x,z) = K(x,z) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,2003,a,b,5229,a),flip(a)].">
      <j1 rule="hyper" parents="320 2003 5229"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5411">
    <literal><![CDATA[
      x * (K(y,x) * T(z,x)) = K(y,x) * (z * x)
    ]]></literal>
    <justification jstring="[hyper(119,a,5231,a(flip),b,5106,a)].">
      <j1 rule="hyper" parents="119 5231 5106"/>
    </justification>
  </clause>

  <clause id="5412">
    <literal><![CDATA[
      x * (K(y,x) * (x \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,x) * z = u
    ]]></literal>
    <justification jstring="[para(5234(a,1),255(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5234 255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5413">
    <literal><![CDATA[
      x \ (((y * x) / y) * z) = K(y,x) * z
    ]]></literal>
    <justification jstring="[hyper(585,a,5250,a),flip(a)].">
      <j1 rule="hyper" parents="585 5250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5414">
    <literal><![CDATA[
      K(x,x \ y) * ((y / x) \ z) = (x \ y) \ z
    ]]></literal>
    <justification jstring="[para(5(a,1),5250(a,1,2,1,1))].">
      <j1 rule="para" parents="5 5250"/>
    </justification>
  </clause>

  <clause id="5415">
    <literal><![CDATA[
      K(x \ y,x) * ((y / (y / x)) \ z) = x \ z
    ]]></literal>
    <justification jstring="[para(4343(a,1),5250(a,1,2,1))].">
      <j1 rule="para" parents="4343 5250"/>
    </justification>
  </clause>

  <clause id="5416">
    <literal><![CDATA[
      K(x,y) * (K((x * y) / x,z) * u) = y \ (T((x * y) / x,z) * u)
    ]]></literal>
    <justification jstring="[para(4777(a,1),5250(a,1,2))].">
      <j1 rule="para" parents="4777 5250"/>
    </justification>
  </clause>

  <clause id="5417">
    <literal><![CDATA[
      x \ T(x * y,x) != y * z
    ]]></literal>
    <literal><![CDATA[
      T(K(x * y,x),y) = z
    ]]></literal>
    <justification jstring="[para(5251(a,2),240(a,2)),flip(a)].">
      <j1 rule="para" parents="5251 240"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5418">
    <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(4816(a,1),5254(a,1,1))].">
      <j1 rule="para" parents="4816 5254"/>
    </justification>
  </clause>

  <clause id="5419">
    <literal><![CDATA[
      R(K(x,y),y * z,u) * ((y * z) * u) = (y * (K(x,y) * z)) * u
    ]]></literal>
    <justification jstring="[para(5256(a,1),101(a,2,1))].">
      <j1 rule="para" parents="5256 101"/>
    </justification>
  </clause>

  <clause id="5421">
    <literal><![CDATA[
      x * (K(y \ x,x) * (y \ 1)) = T(x * (y \ 1),x)
    ]]></literal>
    <justification jstring="[para(5363(a,1),5260(a,1,2,1))].">
      <j1 rule="para" parents="5363 5260"/>
    </justification>
  </clause>

  <clause id="5422">
    <literal><![CDATA[
      K(x,(y \ 1) \ x) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,5307,a(flip),b,5312,a)].">
      <j1 rule="hyper" parents="58 5307 5312"/>
    </justification>
  </clause>

  <clause id="5423">
    <literal><![CDATA[
      K(x \ (y \ 1),z * T(u,u \ 1)) = K(x \ (1 / y),z * u)
    ]]></literal>
    <justification jstring="[hyper(320,a,3985,a,b,5313,a),flip(a)].">
      <j1 rule="hyper" parents="320 3985 5313"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5426">
    <literal><![CDATA[
      K(x,(1 / x) * y) * y = x * (y / x)
    ]]></literal>
    <justification jstring="[para(5322(a,2),5128(a,1,1))].">
      <j1 rule="para" parents="5322 5128"/>
    </justification>
  </clause>

  <clause id="5427">
    <literal><![CDATA[
      K((x / y) \ 1,z) = K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(4976,a,5355,a)].">
      <j1 rule="hyper" parents="4976 5355"/>
    </justification>
  </clause>

  <clause id="5428">
    <literal><![CDATA[
      K(x,(y / z) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(5355(a,2),4985(a,1))].">
      <j1 rule="para" parents="5355 4985"/>
    </justification>
  </clause>

  <clause id="5429">
    <literal><![CDATA[
      K(1 / (x / y),z) = K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(5282,a,5427,a)].">
      <j1 rule="hyper" parents="5282 5427"/>
    </justification>
  </clause>

  <clause id="5430">
    <literal><![CDATA[
      R(K(x / y,z),x / y,u) = K((y / x) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,4204,a,b,5427,a)].">
      <j1 rule="hyper" parents="320 4204 5427"/>
    </justification>
  </clause>

  <clause id="5431">
    <literal><![CDATA[
      K((x / y) \ 1,x) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,4964,a(flip),b,5427,a),flip(a)].">
      <j1 rule="hyper" parents="320 4964 5427"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5432">
    <literal><![CDATA[
      K(x / (y * x),z) = K(y \ 1,z)
    ]]></literal>
    <justification jstring="[para(6(a,1),5427(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6 5427"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5434">
    <literal><![CDATA[
      K((x \ y) / y,z) = K(x \ 1,z)
    ]]></literal>
    <justification jstring="[para(72(a,1),5427(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="72 5427"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5435">
    <literal><![CDATA[
      K((x / ((1 / x) \ y)) \ 1,x) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,4485,a(flip),b,5431,a),flip(a)].">
      <j1 rule="hyper" parents="320 4485 5431"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5436">
    <literal><![CDATA[
      (x / y) \ K(x \ y,x) = T((x / y) \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,5431,a(flip),b,4746,a)].">
      <j1 rule="hyper" parents="116 5431 4746"/>
    </justification>
  </clause>

  <clause id="5437">
    <literal><![CDATA[
      K((x * y) \ y,x * y) = K(x \ 1,x * y)
    ]]></literal>
    <justification jstring="[para(6(a,1),5431(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6 5431"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5438">
    <literal><![CDATA[
      K(x \ (y \ x),x) = K(y \ 1,x)
    ]]></literal>
    <justification jstring="[para(72(a,1),5431(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="72 5431"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5439">
    <literal><![CDATA[
      ((x * y) \ y) * (x * y) = y * K(x \ 1,x * y)
    ]]></literal>
    <justification jstring="[para(5432(a,1),5018(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5432 5018"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5440">
    <literal><![CDATA[
      K(x / (y * x),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(1 / y,z) = u
    ]]></literal>
    <justification jstring="[para(5432(a,2),5282(a,1))].">
      <j1 rule="para" parents="5432 5282"/>
    </justification>
  </clause>

  <clause id="5442">
    <literal><![CDATA[
      K(x,y) * (y * z) = ((x * y) / x) * z
    ]]></literal>
    <justification jstring="[hyper(31,a,5142,a,b,5370,a)].">
      <j1 rule="hyper" parents="31 5142 5370"/>
    </justification>
  </clause>

  <clause id="5443">
    <literal><![CDATA[
      K(x \ y,x) * ((y / x) * z) = (x \ y) * z
    ]]></literal>
    <justification jstring="[para(5(a,1),5371(a,1,2,1,1))].">
      <j1 rule="para" parents="5 5371"/>
    </justification>
  </clause>

  <clause id="5445">
    <literal><![CDATA[
      x / (((y \ (x * z)) * y) / z) = K(y,x / (y / z))
    ]]></literal>
    <justification jstring="[para(1583(a,1),5374(a,1,2))].">
      <j1 rule="para" parents="1583 5374"/>
    </justification>
  </clause>

  <clause id="5446">
    <literal><![CDATA[
      K(x,y) / (K(x,y) / y) = 1 / (1 / y)
    ]]></literal>
    <justification jstring="[para(4803(a,2),5377(a,1,2))].">
      <j1 rule="para" parents="4803 5377"/>
    </justification>
  </clause>

  <clause id="5447">
    <literal><![CDATA[
      (x * K(y,x)) \ z = K(y,x) \ (x \ z)
    ]]></literal>
    <justification jstring="[hyper(320,a,5130,a,b,5398,a),flip(a)].">
      <j1 rule="hyper" parents="320 5130 5398"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5448">
    <literal><![CDATA[
      ((x * y) / x) * (y \ z) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(1459,a,5404,a)].">
      <j1 rule="hyper" parents="1459 5404"/>
    </justification>
  </clause>

  <clause id="5449">
    <literal><![CDATA[
      (x \ y) * (K(x,x \ y) * z) = (y / x) * z
    ]]></literal>
    <justification jstring="[para(5(a,1),5404(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5 5404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5450">
    <literal><![CDATA[
      (x * (K(y * z,x) * y)) * z = (y * z) * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(5404(a,1),853(a,1,1))].">
      <j1 rule="para" parents="5404 853"/>
    </justification>
  </clause>

  <clause id="5451">
    <literal><![CDATA[
      (x / (x / y)) * z = y * (K(y \ x,y) * z)
    ]]></literal>
    <justification jstring="[para(4343(a,1),5404(a,1,1))].">
      <j1 rule="para" parents="4343 5404"/>
    </justification>
  </clause>

  <clause id="5452">
    <literal><![CDATA[
      (x * K(y,x)) * z = x * (K(y,x) * z)
    ]]></literal>
    <justification jstring="[para(4752(a,1),5404(a,1,1))].">
      <j1 rule="para" parents="4752 5404"/>
    </justification>
  </clause>

  <clause id="5453">
    <literal><![CDATA[
      (x / y) * (K(y,y \ x) * z) = ((y * (x / y)) / y) * z
    ]]></literal>
    <justification jstring="[para(4912(a,1),5404(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="4912 5404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5454">
    <literal><![CDATA[
      K(x,y) * (K(y,z) * T(y,x)) = T(y,z)
    ]]></literal>
    <justification jstring="[hyper(5147,a,5405,a)].">
      <j1 rule="hyper" parents="5147 5405"/>
    </justification>
  </clause>

  <clause id="5455">
    <literal><![CDATA[
      (x / (K(y,z) * T(y,u))) \ x = K(y,u) * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(364,a,5405,a)].">
      <j1 rule="hyper" parents="364 5405"/>
    </justification>
  </clause>

  <clause id="5456">
    <literal><![CDATA[
      K(x / (x / y),y \ x) * K(z,x / (x / y)) = T(x / (x / y),z) \ y
    ]]></literal>
    <justification jstring="[para(4346(a,1),5410(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4346 5410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5457">
    <literal><![CDATA[
      (x \ y) \ ((y / x) * z) = K(x,x \ y) * z
    ]]></literal>
    <justification jstring="[para(5(a,1),5413(a,1,2,1,1))].">
      <j1 rule="para" parents="5 5413"/>
    </justification>
  </clause>

  <clause id="5458">
    <literal><![CDATA[
      x \ ((y / (y / x)) * z) = K(x \ y,x) * z
    ]]></literal>
    <justification jstring="[para(4343(a,1),5413(a,1,2,1))].">
      <j1 rule="para" parents="4343 5413"/>
    </justification>
  </clause>

  <clause id="5459">
    <literal><![CDATA[
      K(x,x \ y) * ((x \ y) * z) = (y / x) * z
    ]]></literal>
    <justification jstring="[para(5(a,1),5442(a,2,1,1))].">
      <j1 rule="para" parents="5 5442"/>
    </justification>
  </clause>

  <clause id="5460">
    <literal><![CDATA[
      (x * K(y,x)) * z = K(y,x) * (x * z)
    ]]></literal>
    <justification jstring="[para(4752(a,1),5442(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4752 5442"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5461">
    <literal><![CDATA[
      (K(x,y) * y) * z = K(x,y) * (y * z)
    ]]></literal>
    <justification jstring="[para(4775(a,1),5442(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4775 5442"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5462">
    <literal><![CDATA[
      (x * K(y,x)) \ z != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * (x \ z) = u
    ]]></literal>
    <justification jstring="[para(5447(a,2),5163(a,1))].">
      <j1 rule="para" parents="5447 5163"/>
    </justification>
  </clause>

  <clause id="5463">
    <literal><![CDATA[
      (x \ y) * ((z * ((x \ y) \ y)) / z) = K(z,x) * y
    ]]></literal>
    <justification jstring="[hyper(1357,a,5448,a)].">
      <j1 rule="hyper" parents="1357 5448"/>
    </justification>
  </clause>

  <clause id="5464">
    <literal><![CDATA[
      R(x,K(y,x),z) = x
    ]]></literal>
    <justification jstring="[hyper(3476,a,5452,a)].">
      <j1 rule="hyper" parents="3476 5452"/>
    </justification>
  </clause>

  <clause id="5465">
    <literal><![CDATA[
      L(x,K(y,z),z) = x
    ]]></literal>
    <justification jstring="[hyper(479,a,5452,a)].">
      <j1 rule="hyper" parents="479 5452"/>
    </justification>
  </clause>

  <clause id="5466">
    <literal><![CDATA[
      (T(x,y) * K(z,x)) * u = T(x,y) * (K(z,x) * u)
    ]]></literal>
    <justification jstring="[para(5464(a,1),512(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5464 512"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5467">
    <literal><![CDATA[
      (R(x,y,z) * K(u,x)) * w = R(x,y,z) * (K(u,x) * w)
    ]]></literal>
    <justification jstring="[para(5464(a,1),514(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5464 514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5468">
    <literal><![CDATA[
      L(x,K(y,z),z) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(5465(a,1),45(a,2))].">
      <j1 rule="para" parents="5465 45"/>
    </justification>
  </clause>

  <clause id="5469">
    <literal><![CDATA[
      (x * K(y,x)) * z != u
    ]]></literal>
    <literal><![CDATA[
      x * (K(y,x) * z) = u
    ]]></literal>
    <justification jstring="[para(5465(a,1),286(a,1,2))].">
      <j1 rule="para" parents="5465 286"/>
    </justification>
  </clause>

  <clause id="5471">
    <literal><![CDATA[
      (x * K(y,x)) * K(x,z) = K(y,x) * T(x,z)
    ]]></literal>
    <justification jstring="[para(4755(a,2),5460(a,2,2))].">
      <j1 rule="para" parents="4755 5460"/>
    </justification>
  </clause>

  <clause id="5472">
    <literal><![CDATA[
      R(K(x,y),y,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(3476,a,5461,a)].">
      <j1 rule="hyper" parents="3476 5461"/>
    </justification>
  </clause>

  <clause id="5473">
    <literal><![CDATA[
      L(x,y,K(z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(479,a,5461,a)].">
      <j1 rule="hyper" parents="479 5461"/>
    </justification>
  </clause>

  <clause id="5474">
    <literal><![CDATA[
      a(K(x,y),y,z) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,5461,a(flip),b,80,a),flip(a)].">
      <j1 rule="hyper" parents="115 5461 80"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5475">
    <literal><![CDATA[
      L(x,y,K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(5473(a,1),45(a,2))].">
      <j1 rule="para" parents="5473 45"/>
    </justification>
  </clause>

  <clause id="5476">
    <literal><![CDATA[
      R(K(x,y / (z * y)),y / (z * y),u) = K(x,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,5350,a(flip),b,5472,a),flip(a)].">
      <j1 rule="hyper" parents="320 5350 5472"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5477">
    <literal><![CDATA[
      K(x / y,z) \ y != u
    ]]></literal>
    <literal><![CDATA[
      T(x / y,z) \ x = u
    ]]></literal>
    <justification jstring="[para(75(a,1),4785(a,1,2))].">
      <j1 rule="para" parents="75 4785"/>
    </justification>
  </clause>

  <clause id="5478">
    <literal><![CDATA[
      L(x \ 1,T(x,y),y) = L(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,3868,a(flip),b,4919,a)].">
      <j1 rule="hyper" parents="58 3868 4919"/>
    </justification>
  </clause>

  <clause id="5479">
    <literal><![CDATA[
      T(x * L(x \ 1,x,y),y) = T(x,y) * ((x * y) \ y)
    ]]></literal>
    <justification jstring="[para(5478(a,1),1851(a,1,1,2))].">
      <j1 rule="para" parents="5478 1851"/>
    </justification>
  </clause>

  <clause id="5480">
    <literal><![CDATA[
      x \ (y * T(y \ x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K((x \ y) \ 1,z) = u
    ]]></literal>
    <justification jstring="[para(1427(a,1),5029(a,1))].">
      <j1 rule="para" parents="1427 5029"/>
    </justification>
  </clause>

  <clause id="5481">
    <literal><![CDATA[
      x \ R(x,y,x) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * K(x * y,x) = z
    ]]></literal>
    <justification jstring="[para(5286(a,1),5096(a,1,2))].">
      <j1 rule="para" parents="5286 5096"/>
    </justification>
  </clause>

  <clause id="5482">
    <literal><![CDATA[
      K(x,x * y) * K(y,x) != z
    ]]></literal>
    <literal><![CDATA[
      x \ L(x,y,x) = z
    ]]></literal>
    <justification jstring="[para(5285(a,2),5110(a,1,2))].">
      <j1 rule="para" parents="5285 5110"/>
    </justification>
  </clause>

  <clause id="5483">
    <literal><![CDATA[
      K(x,y) * K(x * y,x) != z
    ]]></literal>
    <literal><![CDATA[
      x \ R(x,y,x) = z
    ]]></literal>
    <justification jstring="[para(5288(a,1),5110(a,1,2))].">
      <j1 rule="para" parents="5288 5110"/>
    </justification>
  </clause>

  <clause id="5484">
    <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),5119(a,1,2))].">
      <j1 rule="para" parents="17 5119"/>
    </justification>
  </clause>

  <clause id="5485">
    <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(5106(a,1),5119(a,1,2))].">
      <j1 rule="para" parents="5106 5119"/>
    </justification>
  </clause>

  <clause id="5486">
    <literal><![CDATA[
      K(x,y) * K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,x) \ T(y,z) = u
    ]]></literal>
    <justification jstring="[para(4729(a,2),5180(a,1,2))].">
      <j1 rule="para" parents="4729 5180"/>
    </justification>
  </clause>

  <clause id="5487">
    <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(2292(a,1),5262(a,1,2))].">
      <j1 rule="para" parents="2292 5262"/>
    </justification>
  </clause>

  <clause id="5488">
    <literal><![CDATA[
      T(x,y) * z != u
    ]]></literal>
    <literal><![CDATA[
      x * (K(x,y) * z) = u
    ]]></literal>
    <justification jstring="[para(5133(a,1),5262(a,1,2))].">
      <j1 rule="para" parents="5133 5262"/>
    </justification>
  </clause>

  <clause id="5489">
    <literal><![CDATA[
      K(x * y,x) * K(x,y) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,5229,a(flip),b,5287,a)].">
      <j1 rule="hyper" parents="58 5229 5287"/>
    </justification>
  </clause>

  <clause id="5490">
    <literal><![CDATA[
      K(x,y) * K(y,y * x) = y \ L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(2005,a,5292,a)].">
      <j1 rule="hyper" parents="2005 5292"/>
    </justification>
  </clause>

  <clause id="5491">
    <literal><![CDATA[
      x \ R(x,y,x) != z
    ]]></literal>
    <literal><![CDATA[
      K(x * y,x) * K(x,y) = z
    ]]></literal>
    <justification jstring="[para(5293(a,1),2005(a,1))].">
      <j1 rule="para" parents="5293 2005"/>
    </justification>
  </clause>

  <clause id="5492">
    <literal><![CDATA[
      K(x,y) * K(y * x,x) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[para(5266(a,2),5293(a,1,2))].">
      <j1 rule="para" parents="5266 5293"/>
    </justification>
  </clause>

  <clause id="5493">
    <literal><![CDATA[
      K(x,x * y) * (x \ R(x,y,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(5293(a,1),5139(a,1,2))].">
      <j1 rule="para" parents="5293 5139"/>
    </justification>
  </clause>

  <clause id="5494">
    <literal><![CDATA[
      R(K(x,y / z),y / z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z / y) \ 1) = w
    ]]></literal>
    <justification jstring="[para(5472(a,2),5359(a,1))].">
      <j1 rule="para" parents="5472 5359"/>
    </justification>
  </clause>

  <clause id="5495">
    <literal><![CDATA[
      K(x,y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,1 / y) = z
    ]]></literal>
    <justification jstring="[para(70(a,1),5428(a,1,2,1))].">
      <j1 rule="para" parents="70 5428"/>
    </justification>
  </clause>

  <clause id="5496">
    <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),5428(a,1,2,1))].">
      <j1 rule="para" parents="102 5428"/>
    </justification>
  </clause>

  <clause id="5498">
    <literal><![CDATA[
      K(x,y / (z * y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,1 / z) = u
    ]]></literal>
    <justification jstring="[para(5350(a,2),5495(a,1))].">
      <j1 rule="para" parents="5350 5495"/>
    </justification>
  </clause>

  <clause id="5499">
    <literal><![CDATA[
      x \ R(x,x \ y,x) = K(y,x) * K(x,x \ y)
    ]]></literal>
    <justification jstring="[para(5(a,1),5489(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5 5489"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5500">
    <literal><![CDATA[
      K(x * y,y) * K(y,x) = y \ R(y,x,y)
    ]]></literal>
    <justification jstring="[para(5266(a,2),5489(a,1,1))].">
      <j1 rule="para" parents="5266 5489"/>
    </justification>
  </clause>

  <clause id="5501">
    <literal><![CDATA[
      K(x,y) * K(y,x * y) = y \ L(y,x,y)
    ]]></literal>
    <justification jstring="[para(5385(a,2),5490(a,1,2))].">
      <j1 rule="para" parents="5385 5490"/>
    </justification>
  </clause>

  <clause id="5502">
    <literal><![CDATA[
      x \ y != K(x,z) * K(z * x,x)
    ]]></literal>
    <literal><![CDATA[
      R(x,z,x) = y
    ]]></literal>
    <justification jstring="[para(5492(a,2),42(a,1)),flip(a)].">
      <j1 rule="para" parents="5492 42"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5503">
    <literal><![CDATA[
      x \ R(x,y,x) != z
    ]]></literal>
    <literal><![CDATA[
      K(y * x,x) * K(x,y) = z
    ]]></literal>
    <justification jstring="[para(5492(a,1),2005(a,1))].">
      <j1 rule="para" parents="5492 2005"/>
    </justification>
  </clause>

  <clause id="5504">
    <literal><![CDATA[
      x \ R(x,y,x) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * K(y * x,x) = z
    ]]></literal>
    <justification jstring="[para(5500(a,1),2009(a,1))].">
      <j1 rule="para" parents="5500 2009"/>
    </justification>
  </clause>

  <clause id="5505">
    <literal><![CDATA[
      T(T(x * K(x \ y,x),y),z) = L(T(x,z),x \ T(y,x),x)
    ]]></literal>
    <justification jstring="[para(4711(a,1),4693(a,1,1,1))].">
      <j1 rule="para" parents="4711 4693"/>
    </justification>
  </clause>

  <clause id="5506">
    <literal><![CDATA[
      K(x,T(y,z) \ 1) = T(K(x,y \ 1),z)
    ]]></literal>
    <justification jstring="[para(4729(a,2),4737(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4729 4737"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5508">
    <literal><![CDATA[
      x * K(y,T(z,x) \ 1) = K(y,z \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(119,a,5506,a,b,17,a(flip))].">
      <j1 rule="hyper" parents="119 5506 17"/>
    </justification>
  </clause>

  <clause id="5510">
    <literal><![CDATA[
      K(x,T(1 / y,z) \ 1) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(75(a,1),5506(a,2,1,2))].">
      <j1 rule="para" parents="75 5506"/>
    </justification>
  </clause>

  <clause id="5511">
    <literal><![CDATA[
      K(x,T(y \ 1,z) \ 1) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(3554(a,1),5506(a,2,1))].">
      <j1 rule="para" parents="3554 5506"/>
    </justification>
  </clause>

  <clause id="5512">
    <literal><![CDATA[
      x * T(K(x,y \ 1),z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z) \ 1) = u
    ]]></literal>
    <justification jstring="[para(5506(a,1),4766(a,1,2))].">
      <j1 rule="para" parents="5506 4766"/>
    </justification>
  </clause>

  <clause id="5513">
    <literal><![CDATA[
      K(x,1 / T(1 / y,z)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(5495,a,5510,a)].">
      <j1 rule="hyper" parents="5495 5510"/>
    </justification>
  </clause>

  <clause id="5514">
    <literal><![CDATA[
      K(x,1 / T(y,z)) = T(K(x,1 / y),z)
    ]]></literal>
    <justification jstring="[para(2163(a,1),5510(a,1,2))].">
      <j1 rule="para" parents="2163 5510"/>
    </justification>
  </clause>

  <clause id="5515">
    <literal><![CDATA[
      K(x,R(T(K(x,y),z),u,w)) = 1
    ]]></literal>
    <justification jstring="[para(5510(a,1),3350(a,1,2,1))].">
      <j1 rule="para" parents="5510 3350"/>
    </justification>
  </clause>

  <clause id="5516">
    <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,4875,a),flip(a)].">
      <j1 rule="hyper" parents="320 149 4875"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5517">
    <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,4774,a,b,4875,a)].">
      <j1 rule="hyper" parents="30 4774 4875"/>
    </justification>
  </clause>

  <clause id="5518">
    <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,4774,a,b,4876,a)].">
      <j1 rule="hyper" parents="30 4774 4876"/>
    </justification>
  </clause>

  <clause id="5519">
    <literal><![CDATA[
      T(1 / (K(x,y) / x),y) = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[para(5211(a,1),4878(a,1,1,2))].">
      <j1 rule="para" parents="5211 4878"/>
    </justification>
  </clause>

  <clause id="5520">
    <literal><![CDATA[
      (1 / (K(x,y) / x)) * y = y * (1 / (1 / x))
    ]]></literal>
    <justification jstring="[hyper(119,a,5519,a(flip),b,17,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 5519 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5521">
    <literal><![CDATA[
      (((x * y) / x) \ 1) \ 1 = (y \ 1) \ K(x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,2247,a(flip),b,4894,a)].">
      <j1 rule="hyper" parents="320 2247 4894"/>
    </justification>
  </clause>

  <clause id="5522">
    <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,4933,a,b,4775,a(flip))].">
      <j1 rule="hyper" parents="117 4933 4775"/>
    </justification>
  </clause>

  <clause id="5523">
    <literal><![CDATA[
      L(x,y,z) / L(x * K(u,x),y,z) = K(L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(4933(a,2),4950(a,2,2)),flip(a)].">
      <j1 rule="para" parents="4933 4950"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5524">
    <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,4934,a,b,4752,a(flip))].">
      <j1 rule="hyper" parents="116 4934 4752"/>
    </justification>
  </clause>

  <clause id="5525">
    <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(4934(a,2),4345(a,1,1))].">
      <j1 rule="para" parents="4934 4345"/>
    </justification>
  </clause>

  <clause id="5526">
    <literal><![CDATA[
      R(x * K(y,x),z,u) \ R(x,z,u) = K(R(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(4934(a,2),4792(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4934 4792"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5527">
    <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(4934(a,2),4989(a,1,1))].">
      <j1 rule="para" parents="4934 4989"/>
    </justification>
  </clause>

  <clause id="5528">
    <literal><![CDATA[
      K(x \ 1,x) * K(y,x) = (T(x,y) \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(2201,a,4996,a)].">
      <j1 rule="hyper" parents="2201 4996"/>
    </justification>
  </clause>

  <clause id="5529">
    <literal><![CDATA[
      K((x / y) \ 1,z) \ (x * T(x \ y,z)) = y
    ]]></literal>
    <justification jstring="[hyper(188,a,5049,a)].">
      <j1 rule="hyper" parents="188 5049"/>
    </justification>
  </clause>

  <clause id="5530">
    <literal><![CDATA[
      (x * (y * T(y \ (x \ z),u))) / z = K(((x * y) / z) \ 1,u)
    ]]></literal>
    <justification jstring="[para(924(a,1),5049(a,1,1))].">
      <j1 rule="para" parents="924 5049"/>
    </justification>
  </clause>

  <clause id="5531">
    <literal><![CDATA[
      x \ (((y \ (x / z)) * y) * z) = K((x \ (y * z)) \ 1,y)
    ]]></literal>
    <justification jstring="[para(1105(a,1),5050(a,1,2))].">
      <j1 rule="para" parents="1105 5050"/>
    </justification>
  </clause>

  <clause id="5532">
    <literal><![CDATA[
      x \ (y * (z * T(z \ (y \ x),u))) = K((x \ (y * z)) \ 1,u)
    ]]></literal>
    <justification jstring="[para(924(a,1),5050(a,1,2))].">
      <j1 rule="para" parents="924 5050"/>
    </justification>
  </clause>

  <clause id="5533">
    <literal><![CDATA[
      x \ (((y \ (x * z)) * y) / z) = K((x \ (y / z)) \ 1,y)
    ]]></literal>
    <justification jstring="[para(1583(a,1),5050(a,1,2))].">
      <j1 rule="para" parents="1583 5050"/>
    </justification>
  </clause>

  <clause id="5534">
    <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(1963(a,1),5050(a,1,2))].">
      <j1 rule="para" parents="1963 5050"/>
    </justification>
  </clause>

  <clause id="5535">
    <literal><![CDATA[
      (x \ (x / (y \ 1))) * x = (x / (y \ 1)) * K(y,x)
    ]]></literal>
    <justification jstring="[para(3317(a,1),5051(a,2,2))].">
      <j1 rule="para" parents="3317 5051"/>
    </justification>
  </clause>

  <clause id="5536">
    <literal><![CDATA[
      x * K((x \ (y * z)) \ 1,y) = z * ((y \ (z \ x)) * y)
    ]]></literal>
    <justification jstring="[hyper(4658,a,5054,a),flip(a)].">
      <j1 rule="hyper" parents="4658 5054"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5537">
    <literal><![CDATA[
      x \ T(x * y,z) = y * K((y \ (x \ 1)) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(1037,a,5054,a)].">
      <j1 rule="hyper" parents="1037 5054"/>
    </justification>
  </clause>

  <clause id="5538">
    <literal><![CDATA[
      x * K((x \ (y * z)) \ 1,u) = y * (z * T(z \ (y \ x),u))
    ]]></literal>
    <justification jstring="[hyper(942,a,5054,a),flip(a)].">
      <j1 rule="hyper" parents="942 5054"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5539">
    <literal><![CDATA[
      (x * y) * K(((x * y) \ y) \ 1,z) = T(x,z) * y
    ]]></literal>
    <justification jstring="[hyper(741,a,5054,a),flip(a)].">
      <j1 rule="hyper" parents="741 5054"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5540">
    <literal><![CDATA[
      T(K(x / y,z),x) = K((x \ y) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(239,a,4817,a,b,5054,a(flip))].">
      <j1 rule="hyper" parents="239 4817 5054"/>
    </justification>
  </clause>

  <clause id="5541">
    <literal><![CDATA[
      x * (y * K((y \ (x \ 1)) \ 1,z)) = T(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(119,a,5054,a(flip),b,939,a(flip))].">
      <j1 rule="hyper" parents="119 5054 939"/>
    </justification>
  </clause>

  <clause id="5542">
    <literal><![CDATA[
      (x * K((x \ y) \ 1,z)) / y = T(x / y,z)
    ]]></literal>
    <justification jstring="[hyper(117,a,5054,a(flip),b,453,a)].">
      <j1 rule="hyper" parents="117 5054 453"/>
    </justification>
  </clause>

  <clause id="5544">
    <literal><![CDATA[
      K(T(x,y) \ 1,z) = T(K(x \ 1,z),y)
    ]]></literal>
    <justification jstring="[hyper(5030,a,5059,a)].">
      <j1 rule="hyper" parents="5030 5059"/>
    </justification>
  </clause>

  <clause id="5546">
    <literal><![CDATA[
      T(K(x \ 1,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(T(x,z) \ 1,y) = u
    ]]></literal>
    <justification jstring="[para(5059(a,1),5030(a,1))].">
      <j1 rule="para" parents="5059 5030"/>
    </justification>
  </clause>

  <clause id="5547">
    <literal><![CDATA[
      K(T(1 / x,y) \ 1,z) = T(K(x,z),y)
    ]]></literal>
    <justification jstring="[para(75(a,1),5544(a,2,1,1))].">
      <j1 rule="para" parents="75 5544"/>
    </justification>
  </clause>

  <clause id="5548">
    <literal><![CDATA[
      K(T(x \ 1,y) \ 1,z) = T(K(x,z),y)
    ]]></literal>
    <justification jstring="[para(3317(a,1),5544(a,2,1))].">
      <j1 rule="para" parents="3317 5544"/>
    </justification>
  </clause>

  <clause id="5549">
    <literal><![CDATA[
      K(1 / T(x,y),z) = T(K(1 / x,z),y)
    ]]></literal>
    <justification jstring="[para(2163(a,1),5547(a,1,1))].">
      <j1 rule="para" parents="2163 5547"/>
    </justification>
  </clause>

  <clause id="5550">
    <literal><![CDATA[
      K(x,T(y \ 1,z) \ 1) = 1 / T(K(y,x),z)
    ]]></literal>
    <justification jstring="[para(5548(a,1),4971(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5548 4971"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5551">
    <literal><![CDATA[
      T(x,y) != K(1 / T(z,y),u)
    ]]></literal>
    <literal><![CDATA[
      K(1 / z,u) = x
    ]]></literal>
    <justification jstring="[para(5549(a,2),44(a,1)),flip(a)].">
      <j1 rule="para" parents="5549 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5552">
    <literal><![CDATA[
      T(x * y,z) / y = K(((1 / y) / x) \ 1,z) * x
    ]]></literal>
    <justification jstring="[hyper(320,a,1001,a(flip),b,5060,a)].">
      <j1 rule="hyper" parents="320 1001 5060"/>
    </justification>
  </clause>

  <clause id="5553">
    <literal><![CDATA[
      K(((x \ 1) / (x \ y)) \ 1,z) * (x \ y) = x \ T(y,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,992,a(flip),b,5060,a),flip(a)].">
      <j1 rule="hyper" parents="320 992 5060"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5555">
    <literal><![CDATA[
      K((x / (x * y)) \ 1,z) * (x * y) = x * T(y,z)
    ]]></literal>
    <justification jstring="[para(4(a,1),5060(a,2,2,1))].">
      <j1 rule="para" parents="4 5060"/>
    </justification>
  </clause>

  <clause id="5556">
    <literal><![CDATA[
      K(1 / ((1 / x) / y),z) = (T(y * x,z) / x) / y
    ]]></literal>
    <justification jstring="[para(1001(a,1),5069(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1001 5069"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5557">
    <literal><![CDATA[
      ((x \ y) \ ((x \ 1) \ (x \ y))) * (x \ y) = (x \ 1) \ (y / x)
    ]]></literal>
    <justification jstring="[hyper(116,a,5077,a(flip),b,5068,a),flip(a)].">
      <j1 rule="hyper" parents="116 5077 5068"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5558">
    <literal><![CDATA[
      K(x,y) * (T(y,z) * x) = K(y,z) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(320,a,5089,a,b,5092,a),flip(a)].">
      <j1 rule="hyper" parents="320 5089 5092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5559">
    <literal><![CDATA[
      T(T(x,y),z) * K(y,x) = x * K(T(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(2919,a,5182,a)].">
      <j1 rule="hyper" parents="2919 5182"/>
    </justification>
  </clause>

  <clause id="5560">
    <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(5182(a,1),2919(a,1))].">
      <j1 rule="para" parents="5182 2919"/>
    </justification>
  </clause>

  <clause id="5561">
    <literal><![CDATA[
      (x \ K(x,y)) * T(x,x \ 1) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(2666,a,5210,a)].">
      <j1 rule="hyper" parents="2666 5210"/>
    </justification>
  </clause>

  <clause id="5562">
    <literal><![CDATA[
      (x \ K(x,y)) * x = (x \ 1) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,4902,a(flip),b,5210,a),flip(a)].">
      <j1 rule="hyper" parents="58 4902 5210"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5563">
    <literal><![CDATA[
      (x \ T(y,x \ 1)) / (x \ y) = K(y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(117,a,3913,a,b,5213,a)].">
      <j1 rule="hyper" parents="117 3913 5213"/>
    </justification>
  </clause>

  <clause id="5564">
    <literal><![CDATA[
      (x * y) * (x / (x * y)) = x * K(x * y,1 / y)
    ]]></literal>
    <justification jstring="[hyper(119,a,5218,a(flip),b,87,a),flip(a)].">
      <j1 rule="hyper" parents="119 5218 87"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5565">
    <literal><![CDATA[
      T(T(x,y),y) \ x = K(y,x) * K(y,x)
    ]]></literal>
    <justification jstring="[para(4908(a,1),5228(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4908 5228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5566">
    <literal><![CDATA[
      K(T(x,T(y,z)),y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(30,a,4842,a,b,5259,a)].">
      <j1 rule="hyper" parents="30 4842 5259"/>
    </justification>
  </clause>

  <clause id="5567">
    <literal><![CDATA[
      K(x / T(y,z),y) = K(T(y,z) \ x,y)
    ]]></literal>
    <justification jstring="[para(107(a,1),5566(a,1,1)),flip(a)].">
      <j1 rule="para" parents="107 5566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5568">
    <literal><![CDATA[
      K(x,y) = (x * y) * ((y * x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(1359,a,5297,a)].">
      <j1 rule="hyper" parents="1359 5297"/>
    </justification>
  </clause>

  <clause id="5569">
    <literal><![CDATA[
      (x * y) \ K(x,y) = (y * x) \ 1
    ]]></literal>
    <justification jstring="[hyper(116,a,673,a(flip),b,5297,a(flip))].">
      <j1 rule="hyper" parents="116 673 5297"/>
    </justification>
  </clause>

  <clause id="5570">
    <literal><![CDATA[
      ((x \ y) * x) \ 1 = y \ K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(116,a,5568,a,b,148,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="116 5568 148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5572">
    <literal><![CDATA[
      K(x,y) != 1
    ]]></literal>
    <literal><![CDATA[
      x * y = y * x
    ]]></literal>
    <justification jstring="[para(5568(a,2),130(a,1))].">
      <j1 rule="para" parents="5568 130"/>
    </justification>
  </clause>

  <clause id="5573">
    <literal><![CDATA[
      K(x,y \ (((z \ 1) \ 1) * u)) = K(x,y \ (z * u))
    ]]></literal>
    <justification jstring="[para(2803(a,1),5324(a,1,2,2))].">
      <j1 rule="para" parents="2803 5324"/>
    </justification>
  </clause>

  <clause id="5574">
    <literal><![CDATA[
      K(x,((y \ 1) * (y * z)) \ u) = K(x,L(z,y,y \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(484(a,1),5325(a,1,2,1))].">
      <j1 rule="para" parents="484 5325"/>
    </justification>
  </clause>

  <clause id="5575">
    <literal><![CDATA[
      K(x,((((y \ 1) \ 1) * z) \ u) \ w) = K(x,((y * z) \ u) \ w)
    ]]></literal>
    <justification jstring="[para(3736(a,1),5325(a,1,2,1))].">
      <j1 rule="para" parents="3736 5325"/>
    </justification>
  </clause>

  <clause id="5576">
    <literal><![CDATA[
      K(x,y * (z / ((u \ 1) \ 1))) = K(x,y * (z / u))
    ]]></literal>
    <justification jstring="[para(2653(a,1),5328(a,1,2,2))].">
      <j1 rule="para" parents="2653 5328"/>
    </justification>
  </clause>

  <clause id="5577">
    <literal><![CDATA[
      K(x,y * (((z \ 1) \ 1) \ u)) = K(x,y * (z \ u))
    ]]></literal>
    <justification jstring="[para(2837(a,1),5328(a,1,2,2))].">
      <j1 rule="para" parents="2837 5328"/>
    </justification>
  </clause>

  <clause id="5578">
    <literal><![CDATA[
      K(x,y / (z * (1 / u))) = K(x,y / (z * (u \ 1)))
    ]]></literal>
    <justification jstring="[para(2714(a,1),5330(a,1,2,2))].">
      <j1 rule="para" parents="2714 5330"/>
    </justification>
  </clause>

  <clause id="5579">
    <literal><![CDATA[
      K(x,y / (((z \ 1) \ 1) * u)) = K(x,y / (z * u))
    ]]></literal>
    <justification jstring="[para(2803(a,1),5330(a,1,2,2))].">
      <j1 rule="para" parents="2803 5330"/>
    </justification>
  </clause>

  <clause id="5580">
    <literal><![CDATA[
      K(x,T((1 / y) * z,u)) = K(x,T((y \ 1) * z,u))
    ]]></literal>
    <justification jstring="[para(2846(a,1),5341(a,1,2,1))].">
      <j1 rule="para" parents="2846 5341"/>
    </justification>
  </clause>

  <clause id="5581">
    <literal><![CDATA[
      K(x,((1 / y) * z) / u) = K(x,((y \ 1) * z) / u)
    ]]></literal>
    <justification jstring="[para(2814(a,1),5343(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2814 5343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5583">
    <literal><![CDATA[
      K(x \ y,x) * (z * (y / x)) = (x \ y) * T(z,y / x)
    ]]></literal>
    <justification jstring="[para(17(a,2),5372(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17 5372"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5586">
    <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(5380(a,1),255(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5380 255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5587">
    <literal><![CDATA[
      T(x,y) \ T(x * K(x * z,x),y) = K(z * x,T(x,y))
    ]]></literal>
    <justification jstring="[para(5266(a,1),5380(a,1,2,1,2))].">
      <j1 rule="para" parents="5266 5380"/>
    </justification>
  </clause>

  <clause id="5588">
    <literal><![CDATA[
      T(x,y) \ T(z * T(z \ x,x),y) = K((x \ z) \ 1,T(x,y))
    ]]></literal>
    <justification jstring="[para(5054(a,2),5380(a,1,2,1))].">
      <j1 rule="para" parents="5054 5380"/>
    </justification>
  </clause>

  <clause id="5589">
    <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(5202(a,1),5381(a,1,1,1))].">
      <j1 rule="para" parents="5202 5381"/>
    </justification>
  </clause>

  <clause id="5590">
    <literal><![CDATA[
      K(x \ y,x) \ ((y / x) \ z) = (x \ y) \ z
    ]]></literal>
    <justification jstring="[hyper(123,a,5399,a)].">
      <j1 rule="hyper" parents="123 5399"/>
    </justification>
  </clause>

  <clause id="5592">
    <literal><![CDATA[
      T(x,x \ y) \ ((x \ y) \ z) = x \ ((y / x) \ z)
    ]]></literal>
    <justification jstring="[hyper(116,a,5399,a(flip),b,4818,a),flip(a)].">
      <j1 rule="hyper" parents="116 5399 4818"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5593">
    <literal><![CDATA[
      K(x \ y,x) * T(z,x \ y) = (y / x) \ (z * (x \ y))
    ]]></literal>
    <justification jstring="[para(17(a,2),5399(a,1,2))].">
      <j1 rule="para" parents="17 5399"/>
    </justification>
  </clause>

  <clause id="5595">
    <literal><![CDATA[
      T(x,T(y,x)) / ((y * x) \ x) = x * y
    ]]></literal>
    <justification jstring="[para(17(a,2),5409(a,1,1,2))].">
      <j1 rule="para" parents="17 5409"/>
    </justification>
  </clause>

  <clause id="5596">
    <literal><![CDATA[
      T(x,y) / ((y * x) \ x) = x * y
    ]]></literal>
    <justification jstring="[para(4233(a,1),5595(a,1,1))].">
      <j1 rule="para" parents="4233 5595"/>
    </justification>
  </clause>

  <clause id="5597">
    <literal><![CDATA[
      ((x \ y) * x) \ x = y \ T(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(349,a,5596,a),flip(a)].">
      <j1 rule="hyper" parents="349 5596"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5598">
    <literal><![CDATA[
      (x * y) \ T(x,y) = (y * x) \ x
    ]]></literal>
    <justification jstring="[hyper(188,a,5596,a)].">
      <j1 rule="hyper" parents="188 5596"/>
    </justification>
  </clause>

  <clause id="5599">
    <literal><![CDATA[
      T(x,y) = (x * y) * ((y * x) \ x)
    ]]></literal>
    <justification jstring="[hyper(133,a,5596,a),flip(a)].">
      <j1 rule="hyper" parents="133 5596"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5600">
    <literal><![CDATA[
      T(x * y,z) * ((y * x) \ x) = K(x * y,z) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,5598,a(flip),b,5080,a)].">
      <j1 rule="hyper" parents="119 5598 5080"/>
    </justification>
  </clause>

  <clause id="5601">
    <literal><![CDATA[
      ((x * y) \ y) * T(y * x,x \ 1) = T(y,x)
    ]]></literal>
    <justification jstring="[para(5598(a,1),4222(a,1,1))].">
      <j1 rule="para" parents="5598 4222"/>
    </justification>
  </clause>

  <clause id="5602">
    <literal><![CDATA[
      (x / (x / y)) \ ((x / y) \ z) = y \ ((y \ x) \ z)
    ]]></literal>
    <justification jstring="[hyper(116,a,5414,a(flip),b,5373,a),flip(a)].">
      <j1 rule="hyper" parents="116 5414 5373"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5609">
    <literal><![CDATA[
      (x \ y) * (K(x,x \ y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      (y / x) * z = u
    ]]></literal>
    <justification jstring="[para(5457(a,1),255(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5457 255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5610">
    <literal><![CDATA[
      (x * K(y,x)) \ L(x,y,x) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(116,a,5090,a(flip),b,5471,a)].">
      <j1 rule="hyper" parents="116 5090 5471"/>
    </justification>
  </clause>

  <clause id="5611">
    <literal><![CDATA[
      K(x,(y / z) \ 1) * z = z * K(x,(z \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(107(a,1),5508(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="107 5508"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5612">
    <literal><![CDATA[
      ((x * K(y,x)) \ 1) \ 1 = (x \ 1) \ K(y,x)
    ]]></literal>
    <justification jstring="[para(4752(a,1),5521(a,1,1,1))].">
      <j1 rule="para" parents="4752 5521"/>
    </justification>
  </clause>

  <clause id="5613">
    <literal><![CDATA[
      (x \ K(x,y)) \ 1 = (x \ 1) \ K(y,x)
    ]]></literal>
    <justification jstring="[para(4905(a,1),5521(a,1,1))].">
      <j1 rule="para" parents="4905 5521"/>
    </justification>
  </clause>

  <clause id="5614">
    <literal><![CDATA[
      (x \ 1) * (x * K(y,x)) = (T(x,y) \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(3097,a,5528,a)].">
      <j1 rule="hyper" parents="3097 5528"/>
    </justification>
  </clause>

  <clause id="5615">
    <literal><![CDATA[
      1 / T(K(x,y),z) = T(K(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(58,a,5511,a(flip),b,5550,a),flip(a)].">
      <j1 rule="hyper" parents="58 5511 5550"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5616">
    <literal><![CDATA[
      T(K(x,y),z) \ 1 = T(K(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(188,a,5615,a)].">
      <j1 rule="hyper" parents="188 5615"/>
    </justification>
  </clause>

  <clause id="5617">
    <literal><![CDATA[
      T(K(x,y),z) * T(K(y,x),z) = 1
    ]]></literal>
    <justification jstring="[hyper(133,a,5615,a)].">
      <j1 rule="hyper" parents="133 5615"/>
    </justification>
  </clause>

  <clause id="5618">
    <literal><![CDATA[
      T(K(x,y),z) * K(y,x) = K(z,K(y,x))
    ]]></literal>
    <justification jstring="[para(5615(a,1),4795(a,2,1)),flip(a)].">
      <j1 rule="para" parents="5615 4795"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5619">
    <literal><![CDATA[
      K(x,y) * T(K(y,x),z) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(119,a,5616,a(flip),b,4804,a(flip))].">
      <j1 rule="hyper" parents="119 5616 4804"/>
    </justification>
  </clause>

  <clause id="5620">
    <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(841,a,5617,a)].">
      <j1 rule="hyper" parents="841 5617"/>
    </justification>
  </clause>

  <clause id="5621">
    <literal><![CDATA[
      K(K(x,y),z) = K(z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(58,a,4974,a(flip),b,5618,a)].">
      <j1 rule="hyper" parents="58 4974 5618"/>
    </justification>
  </clause>

  <clause id="5622">
    <literal><![CDATA[
      K(x,K(y,z)) \ 1 = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(5166,a,5621,a)].">
      <j1 rule="hyper" parents="5166 5621"/>
    </justification>
  </clause>

  <clause id="5623">
    <literal><![CDATA[
      x * K(K(y,z),x) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(119,a,5621,a,b,4729,a(flip))].">
      <j1 rule="hyper" parents="119 5621 4729"/>
    </justification>
  </clause>

  <clause id="5624">
    <literal><![CDATA[
      K(x,y) * K(z,K(y,x)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(119,a,5621,a(flip),b,4729,a(flip))].">
      <j1 rule="hyper" parents="119 5621 4729"/>
    </justification>
  </clause>

  <clause id="5625">
    <literal><![CDATA[
      K(x,K(y,z)) * K(z,y) = T(K(z,y),x)
    ]]></literal>
    <justification jstring="[para(5621(a,1),4770(a,2,1)),flip(a)].">
      <j1 rule="para" parents="5621 4770"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5626">
    <literal><![CDATA[
      K(x,K(y,z)) \ 1 != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y)) = u
    ]]></literal>
    <justification jstring="[para(5621(a,1),4985(a,1,1))].">
      <j1 rule="para" parents="5621 4985"/>
    </justification>
  </clause>

  <clause id="5627">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(z,y) * u) = T(K(z,y),x) * u
    ]]></literal>
    <justification jstring="[para(5621(a,1),4781(a,1,1))].">
      <j1 rule="para" parents="5621 4781"/>
    </justification>
  </clause>

  <clause id="5628">
    <literal><![CDATA[
      K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(K(z,y),x) = u
    ]]></literal>
    <justification jstring="[para(5622(a,1),4985(a,1))].">
      <j1 rule="para" parents="5622 4985"/>
    </justification>
  </clause>

  <clause id="5629">
    <literal><![CDATA[
      T(K(x,y) \ z,K(y,x)) = z / K(x,y)
    ]]></literal>
    <justification jstring="[hyper(4928,a,5623,a),flip(a)].">
      <j1 rule="hyper" parents="4928 5623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5630">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(4924,a,5623,a),flip(a)].">
      <j1 rule="hyper" parents="4924 5623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5631">
    <literal><![CDATA[
      T(x,K(y,z)) * K(z,y) = K(z,y) * x
    ]]></literal>
    <justification jstring="[para(5623(a,1),4774(a,1,1))].">
      <j1 rule="para" parents="5623 4774"/>
    </justification>
  </clause>

  <clause id="5632">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(5623(a,1),4925(a,1,1))].">
      <j1 rule="para" parents="5623 4925"/>
    </justification>
  </clause>

  <clause id="5633">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      u = x
    ]]></literal>
    <justification jstring="[para(5623(a,1),4923(a,1))].">
      <j1 rule="para" parents="5623 4923"/>
    </justification>
  </clause>

  <clause id="5634">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(z,y) * x) = L(x,K(z,y),x)
    ]]></literal>
    <justification jstring="[para(5623(a,1),4943(a,1,1))].">
      <j1 rule="para" parents="5623 4943"/>
    </justification>
  </clause>

  <clause id="5635">
    <literal><![CDATA[
      T(K(x,y) * z,T(z,K(y,x))) = T(K(x,y) * z,z)
    ]]></literal>
    <justification jstring="[para(5623(a,1),4942(a,1,2))].">
      <j1 rule="para" parents="5623 4942"/>
    </justification>
  </clause>

  <clause id="5636">
    <literal><![CDATA[
      T(K(x,y),K(x,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(2008,a,5630,a),flip(a)].">
      <j1 rule="hyper" parents="2008 5630"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5637">
    <literal><![CDATA[
      T(K(x,y),K(z,y)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(2004,a,5630,a),flip(a)].">
      <j1 rule="hyper" parents="2004 5630"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5638">
    <literal><![CDATA[
      T(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(u,K(z,y)) = x
    ]]></literal>
    <justification jstring="[para(5630(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="5630 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5639">
    <literal><![CDATA[
      K(x,y) * K(x,z) = K(x,z) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,5636,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 5636 17"/>
    </justification>
  </clause>

  <clause id="5640">
    <literal><![CDATA[
      K(x,y) * K(x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) * K(x,y) = u
    ]]></literal>
    <justification jstring="[para(5636(a,1),284(a,1,2))].">
      <j1 rule="para" parents="5636 284"/>
    </justification>
  </clause>

  <clause id="5641">
    <literal><![CDATA[
      K(x,y) \ K(z,x) = K(z,x) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,5637,a(flip),b,5132,a),flip(a)].">
      <j1 rule="hyper" parents="119 5637 5132"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5642">
    <literal><![CDATA[
      K(x,y) * K(z,y) = K(z,y) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,5637,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 5637 17"/>
    </justification>
  </clause>

  <clause id="5643">
    <literal><![CDATA[
      K(x,y) * T(K(y,x),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,K(x,y)) = u
    ]]></literal>
    <justification jstring="[para(5624(a,1),5148(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5624 5148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5644">
    <literal><![CDATA[
      T(K(x,y) * z,K(x,y)) = z / K(y,x)
    ]]></literal>
    <justification jstring="[para(5130(a,1),5629(a,1,1))].">
      <j1 rule="para" parents="5130 5629"/>
    </justification>
  </clause>

  <clause id="5645">
    <literal><![CDATA[
      (x * T(x \ y,z)) / K((x / y) \ 1,z) = T(y,K(z,(x / y) \ 1))
    ]]></literal>
    <justification jstring="[para(5529(a,1),5629(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5529 5629"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5646">
    <literal><![CDATA[
      K(x,1 / x) * y = y * K(x,1 / x)
    ]]></literal>
    <justification jstring="[para(2187(a,1),5631(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2187 5631"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5647">
    <literal><![CDATA[
      K(x \ y,z) * (y \ x) = (y \ x) * K(x \ y,z)
    ]]></literal>
    <justification jstring="[para(2291(a,1),5631(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2291 5631"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5648">
    <literal><![CDATA[
      T(x,y) * (x \ K(x,z)) = K(x,z) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(4784,a,5639,a)].">
      <j1 rule="hyper" parents="4784 5639"/>
    </justification>
  </clause>

  <clause id="5649">
    <literal><![CDATA[
      K(x,y) * K(x,z) != K(x,z) * u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(5639(a,1),38(a,1))].">
      <j1 rule="para" parents="5639 38"/>
    </justification>
  </clause>

  <clause id="5650">
    <literal><![CDATA[
      x * (T(x,y) \ K(z,x)) = K(z,x) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(4786,a,5641,a)].">
      <j1 rule="hyper" parents="4786 5641"/>
    </justification>
  </clause>

  <clause id="5651">
    <literal><![CDATA[
      (K(x,1 / x) * y) * z = (y * z) * K(x,1 / x)
    ]]></literal>
    <justification jstring="[hyper(3650,a,5646,a)].">
      <j1 rule="hyper" parents="3650 5646"/>
    </justification>
  </clause>

  <clause id="5652">
    <literal><![CDATA[
      K(x,1 / x) * (y * z) = y * (z * K(x,1 / x))
    ]]></literal>
    <justification jstring="[hyper(320,a,3418,a(flip),b,5646,a),flip(a)].">
      <j1 rule="hyper" parents="320 3418 5646"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5653">
    <literal><![CDATA[
      K(x,y * (K(z,1 / z) * u)) = K(x,y * u)
    ]]></literal>
    <justification jstring="[para(5646(a,2),5327(a,1,2,2))].">
      <j1 rule="para" parents="5646 5327"/>
    </justification>
  </clause>

  <clause id="5654">
    <literal><![CDATA[
      K(K(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,K(y,x)) = u
    ]]></literal>
    <justification jstring="[para(4969(a,1),5626(a,1))].">
      <j1 rule="para" parents="4969 5626"/>
    </justification>
  </clause>

  <clause id="5655">
    <literal><![CDATA[
      T(K(x,y),z) * K(y,x) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,K(y,x)) = u
    ]]></literal>
    <justification jstring="[para(4974(a,2),5654(a,1))].">
      <j1 rule="para" parents="4974 5654"/>
    </justification>
  </clause>

  <clause id="5656">
    <literal><![CDATA[
      K(x,y) * (K(x,z) * (y * x)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z) * y = u
    ]]></literal>
    <justification jstring="[para(5558(a,1),5148(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5558 5148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5657">
    <literal><![CDATA[
      (x \ 1) * ((y * x) / y) = (T(x,y) \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(58,a,4897,a,b,5614,a)].">
      <j1 rule="hyper" parents="58 4897 5614"/>
    </justification>
  </clause>

  <clause id="5658">
    <literal><![CDATA[
      T(x,y) \ K(z,x) = T(x,z) \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(29,a,4818,a,b,5650,a)].">
      <j1 rule="hyper" parents="29 4818 5650"/>
    </justification>
  </clause>

  <clause id="5659">
    <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(5650(a,1),4015(a,2,3))].">
      <j1 rule="para" parents="5650 4015"/>
    </justification>
  </clause>

  <clause id="5660">
    <literal><![CDATA[
      T(x,y) \ K(z,x) != T(x,z) \ u
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = u
    ]]></literal>
    <justification jstring="[para(5658(a,1),42(a,1))].">
      <j1 rule="para" parents="5658 42"/>
    </justification>
  </clause>

  <clause id="5661">
    <literal><![CDATA[
      K(x,y * (((1 / (1 / z)) \ u) * w)) = K(x,y * ((z \ u) * w))
    ]]></literal>
    <justification jstring="[para(3662(a,1),5653(a,1,2,2))].">
      <j1 rule="para" parents="3662 5653"/>
    </justification>
  </clause>

  <clause id="5663">
    <literal><![CDATA[
      ((x * K(y,x)) \ ((y * (x * y)) / y)) \ ((y * (x * y)) / y) = x
    ]]></literal>
    <justification jstring="[para(4940(a,2),4372(a,1,1))].">
      <j1 rule="para" parents="4940 4372"/>
    </justification>
  </clause>

  <clause id="5664">
    <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(5247(a,1),251(a,1,1)),flip(b)].">
      <j1 rule="para" parents="5247 251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5665">
    <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,5291,a),flip(a)].">
      <j1 rule="hyper" parents="320 22 5291"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5666">
    <literal><![CDATA[
      x / (y * ((z \ (y \ x)) * z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,x / (z * y)) = u
    ]]></literal>
    <justification jstring="[para(4643(a,1),5375(a,1,2))].">
      <j1 rule="para" parents="4643 5375"/>
    </justification>
  </clause>

  <clause id="5667">
    <literal><![CDATA[
      K(x,L(y,x,x \ 1)) * (y * x) = x * ((y * x) / x)
    ]]></literal>
    <justification jstring="[para(5389(a,1),5426(a,1,1))].">
      <j1 rule="para" parents="5389 5426"/>
    </justification>
  </clause>

  <clause id="5668">
    <literal><![CDATA[
      K((x / y) \ 1,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y / x,z) = u
    ]]></literal>
    <justification jstring="[para(5430(a,1),384(a,1)),flip(b)].">
      <j1 rule="para" parents="5430 384"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5669">
    <literal><![CDATA[
      K(1 / (x / y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y / x,z) = u
    ]]></literal>
    <justification jstring="[para(3312(a,2),5668(a,1))].">
      <j1 rule="para" parents="3312 5668"/>
    </justification>
  </clause>

  <clause id="5670">
    <literal><![CDATA[
      ((x * y) / x) * z != u
    ]]></literal>
    <literal><![CDATA[
      y * (K(x,y) * z) = u
    ]]></literal>
    <justification jstring="[para(4752(a,2),5469(a,1,1))].">
      <j1 rule="para" parents="4752 5469"/>
    </justification>
  </clause>

  <clause id="5671">
    <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),5484(a,1,2))].">
      <j1 rule="para" parents="20 5484"/>
    </justification>
  </clause>

  <clause id="5672">
    <literal><![CDATA[
      K(x,y) * K(z,x) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z) \ T(x,y) = u
    ]]></literal>
    <justification jstring="[para(2003(a,2),5486(a,1))].">
      <j1 rule="para" parents="2003 5486"/>
    </justification>
  </clause>

  <clause id="5673">
    <literal><![CDATA[
      x \ K(x * y,x \ 1) = y / (y / (x \ 1))
    ]]></literal>
    <justification jstring="[para(4488(a,1),4719(a,1,2))].">
      <j1 rule="para" parents="4488 4719"/>
    </justification>
  </clause>

  <clause id="5674">
    <literal><![CDATA[
      (x \ K(x * y,x \ 1)) \ y = y / (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(188,a,5673,a(flip))].">
      <j1 rule="hyper" parents="188 5673"/>
    </justification>
  </clause>

  <clause id="5675">
    <literal><![CDATA[
      L(K(x,y \ 1),z,u) = K(x,L(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(4729(a,2),4736(a,1,1))].">
      <j1 rule="para" parents="4729 4736"/>
    </justification>
  </clause>

  <clause id="5677">
    <literal><![CDATA[
      K(x,L(1 / y,z,u) \ 1) = L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(75(a,1),5675(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="75 5675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5678">
    <literal><![CDATA[
      K(x,L(y \ 1,z,u) \ 1) = L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(3554(a,1),5675(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3554 5675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5679">
    <literal><![CDATA[
      K(x,L(K(y,z),u,w) \ 1) = L(K(x,K(z,y)),u,w)
    ]]></literal>
    <justification jstring="[para(4969(a,1),5675(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4969 5675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5680">
    <literal><![CDATA[
      K(x,L(T(y \ 1,z),u,w) \ 1) = L(T(K(x,y),z),u,w)
    ]]></literal>
    <justification jstring="[para(5511(a,1),5675(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5511 5675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5681">
    <literal><![CDATA[
      L(K(x,y \ z),y \ z,y) = K(x,(z \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(390(a,1),5678(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="390 5678"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5682">
    <literal><![CDATA[
      K(L(x \ 1,y,z) \ 1,u) * w = L(K(u,x),y,z) \ w
    ]]></literal>
    <justification jstring="[para(5678(a,1),5130(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5678 5130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5683">
    <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(5678(a,1),5675(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5678 5675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5684">
    <literal><![CDATA[
      x * ((x \ y) * K(z,x \ y)) = y * K(z,(y \ x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(119,a,5681,a(flip),b,91,a),flip(a)].">
      <j1 rule="hyper" parents="119 5681 91"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5685">
    <literal><![CDATA[
      K(L(1 / x,y,z) \ 1,u) = L(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[hyper(5030,a,4823,a)].">
      <j1 rule="hyper" parents="5030 4823"/>
    </justification>
  </clause>

  <clause id="5686">
    <literal><![CDATA[
      K(1 / L(1 / x,y,z),u) = L(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[hyper(5282,a,5685,a)].">
      <j1 rule="hyper" parents="5282 5685"/>
    </justification>
  </clause>

  <clause id="5687">
    <literal><![CDATA[
      K(L(x \ 1,y,z) \ 1,u) = L(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,3997,a(flip),b,5685,a)].">
      <j1 rule="hyper" parents="58 3997 5685"/>
    </justification>
  </clause>

  <clause id="5688">
    <literal><![CDATA[
      L(K(x \ 1,y),z,u) = K(L(x,z,u) \ 1,y)
    ]]></literal>
    <justification jstring="[para(72(a,1),5685(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="72 5685"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5689">
    <literal><![CDATA[
      L(K(1 / x,y),z,u) = K(1 / L(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(3291(a,1),5685(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3291 5685"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5690">
    <literal><![CDATA[
      K(L(K(x,y),z,u) \ 1,w) = L(K(K(y,x),w),z,u)
    ]]></literal>
    <justification jstring="[para(4971(a,1),5685(a,1,1,1,1))].">
      <j1 rule="para" parents="4971 5685"/>
    </justification>
  </clause>

  <clause id="5691">
    <literal><![CDATA[
      K(x,1 / L(1 / y,z,u)) = 1 / L(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(5685(a,1),4983(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5685 4983"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5692">
    <literal><![CDATA[
      K(x,L(y \ 1,z,u) \ 1) = L(K(y,x),z,u) \ 1
    ]]></literal>
    <justification jstring="[para(5687(a,1),4969(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5687 4969"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5694">
    <literal><![CDATA[
      K(L(x,y,z) \ 1,(x \ 1) * L((x \ 1) \ 1,u,w)) = L(1,y,z)
    ]]></literal>
    <justification jstring="[para(1757(a,1),5688(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1757 5688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5695">
    <literal><![CDATA[
      K(L(T(1 / x,y),z,u) \ 1,w) = L(T(K(x,w),y),z,u)
    ]]></literal>
    <justification jstring="[para(5547(a,1),5688(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5547 5688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5696">
    <literal><![CDATA[
      K(L(T(x \ 1,y),z,u) \ 1,w) = L(T(K(x,w),y),z,u)
    ]]></literal>
    <justification jstring="[para(5548(a,1),5688(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5548 5688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5697">
    <literal><![CDATA[
      ((x \ y) * x) * K(z,(x \ y) * x) = (x \ (y * K(z,y))) * x
    ]]></literal>
    <justification jstring="[hyper(30,a,4774,a,b,4886,a)].">
      <j1 rule="hyper" parents="30 4774 4886"/>
    </justification>
  </clause>

  <clause id="5698">
    <literal><![CDATA[
      T(x,y) \ ((z * x) / z) = K(z,x) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,5650,a(flip),b,4901,a),flip(a)].">
      <j1 rule="hyper" parents="320 5650 4901"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5699">
    <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(5698(a,1),91(a,1,2,2,1))].">
      <j1 rule="para" parents="5698 91"/>
    </justification>
  </clause>

  <clause id="5700">
    <literal><![CDATA[
      (x * y) / (y * K(z,y)) = (x / (y * K(z,y))) * y
    ]]></literal>
    <justification jstring="[hyper(58,a,4920,a(flip),b,4938,a)].">
      <j1 rule="hyper" parents="58 4920 4938"/>
    </justification>
  </clause>

  <clause id="5701">
    <literal><![CDATA[
      ((x * y) \ T(y * x,z)) * (x * y) = T(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(133,a,5007,a)].">
      <j1 rule="hyper" parents="133 5007"/>
    </justification>
  </clause>

  <clause id="5702">
    <literal><![CDATA[
      a(1 / R(x,y,z),x,x \ 1) = K(R(x,y,z) \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,3607,a,b,5045,a)].">
      <j1 rule="hyper" parents="58 3607 5045"/>
    </justification>
  </clause>

  <clause id="5703">
    <literal><![CDATA[
      R(K(x \ 1,y),z,u) = K(R(x,z,u) \ 1,y)
    ]]></literal>
    <justification jstring="[para(4746(a,1),5045(a,1,1))].">
      <j1 rule="para" parents="4746 5045"/>
    </justification>
  </clause>

  <clause id="5704">
    <literal><![CDATA[
      K(R(x,y,z) \ 1,R(x,y,z)) = K(x \ 1,R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(3655,a,5703,a)].">
      <j1 rule="hyper" parents="3655 5703"/>
    </justification>
  </clause>

  <clause id="5705">
    <literal><![CDATA[
      K(R(x,y,z) \ 1,y) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,5472,a(flip),b,5703,a),flip(a)].">
      <j1 rule="hyper" parents="58 5472 5703"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5706">
    <literal><![CDATA[
      K(R(1 / x,y,z) \ 1,u) = R(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(75(a,1),5703(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="75 5703"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5707">
    <literal><![CDATA[
      K(R(x,y,z) \ 1,u) * (y * z) = (K(x \ 1,u) * y) * z
    ]]></literal>
    <justification jstring="[para(5703(a,1),101(a,1,1))].">
      <j1 rule="para" parents="5703 101"/>
    </justification>
  </clause>

  <clause id="5708">
    <literal><![CDATA[
      R(K((x / y) \ 1,z),y,u) = K(((x * u) / (y * u)) \ 1,z)
    ]]></literal>
    <justification jstring="[para(102(a,1),5703(a,2,1,1))].">
      <j1 rule="para" parents="102 5703"/>
    </justification>
  </clause>

  <clause id="5709">
    <literal><![CDATA[
      K(R(x \ 1,y,z) \ 1,u) = R(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(3317(a,1),5703(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3317 5703"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5710">
    <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(767(a,1),5705(a,1,1,1))].">
      <j1 rule="para" parents="767 5705"/>
    </justification>
  </clause>

  <clause id="5711">
    <literal><![CDATA[
      K(x,R(y \ 1,z,u) \ 1) * w = R(K(y,x),z,u) \ w
    ]]></literal>
    <justification jstring="[para(5709(a,1),5130(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5709 5130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5712">
    <literal><![CDATA[
      (x * T(x \ y,z)) * (y \ 1) = K((x * (y \ 1)) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(1949,a,5046,a)].">
      <j1 rule="hyper" parents="1949 5046"/>
    </justification>
  </clause>

  <clause id="5713">
    <literal><![CDATA[
      (1 / x) * (y * T(y \ x,z)) = K(((1 / x) * y) \ 1,z)
    ]]></literal>
    <justification jstring="[para(75(a,1),5046(a,1,2,2,1,2))].">
      <j1 rule="para" parents="75 5046"/>
    </justification>
  </clause>

  <clause id="5714">
    <literal><![CDATA[
      x * ((y \ (x \ 1)) * y) = K((x * y) \ 1,y)
    ]]></literal>
    <justification jstring="[para(105(a,1),5046(a,1,2))].">
      <j1 rule="para" parents="105 5046"/>
    </justification>
  </clause>

  <clause id="5715">
    <literal><![CDATA[
      x * (y \ T(y * (x \ 1),z)) = K((x * (y \ 1)) \ 1,z)
    ]]></literal>
    <justification jstring="[para(939(a,1),5046(a,1,2))].">
      <j1 rule="para" parents="939 5046"/>
    </justification>
  </clause>

  <clause id="5716">
    <literal><![CDATA[
      ((1 / x) * y) * T(((1 / x) * y) \ y,z) = K(x,z) * y
    ]]></literal>
    <justification jstring="[para(75(a,1),5056(a,2,1,1))].">
      <j1 rule="para" parents="75 5056"/>
    </justification>
  </clause>

  <clause id="5717">
    <literal><![CDATA[
      K(x \ 1,x) * (x \ y) = y * T(y \ (x \ y),T(x,z))
    ]]></literal>
    <justification jstring="[para(3043(a,1),5057(a,1,1))].">
      <j1 rule="para" parents="3043 5057"/>
    </justification>
  </clause>

  <clause id="5718">
    <literal><![CDATA[
      K(x \ 1,y) * (x \ K(x,z)) = K(x,z) * T(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(3207(a,1),5057(a,2,2,1))].">
      <j1 rule="para" parents="3207 5057"/>
    </justification>
  </clause>

  <clause id="5719">
    <literal><![CDATA[
      x * (y \ T(y * (x \ (y \ 1)),z)) = K(x \ 1,z) * (y \ 1)
    ]]></literal>
    <justification jstring="[para(939(a,1),5058(a,1,2))].">
      <j1 rule="para" parents="939 5058"/>
    </justification>
  </clause>

  <clause id="5720">
    <literal><![CDATA[
      x * (K(x \ 1,y) * (x \ z)) = K(x \ 1,y) * z
    ]]></literal>
    <justification jstring="[para(5057(a,2),5058(a,1,2))].">
      <j1 rule="para" parents="5057 5058"/>
    </justification>
  </clause>

  <clause id="5721">
    <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(5066(a,1),5030(a,1))].">
      <j1 rule="para" parents="5066 5030"/>
    </justification>
  </clause>

  <clause id="5722">
    <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(406(a,1),5074(a,1,2,2,1,2))].">
      <j1 rule="para" parents="406 5074"/>
    </justification>
  </clause>

  <clause id="5723">
    <literal><![CDATA[
      K(((x \ 1) / (y / x)) \ 1,z) = (T(y,z) / x) / (y / x)
    ]]></literal>
    <justification jstring="[hyper(58,a,5427,a,b,5177,a)].">
      <j1 rule="hyper" parents="58 5427 5177"/>
    </justification>
  </clause>

  <clause id="5724">
    <literal><![CDATA[
      (x * ((y * (x \ z)) / y)) / z = K(y,z / x)
    ]]></literal>
    <justification jstring="[hyper(320,a,5351,a(flip),b,5300,a),flip(a)].">
      <j1 rule="hyper" parents="320 5351 5300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5725">
    <literal><![CDATA[
      K(x,(y / z) \ 1) * z = y * ((x * (y \ z)) / x)
    ]]></literal>
    <justification jstring="[hyper(133,a,5300,a)].">
      <j1 rule="hyper" parents="133 5300"/>
    </justification>
  </clause>

  <clause id="5726">
    <literal><![CDATA[
      (x * (y * ((x \ z) / y))) / z = K(y,((x * y) / z) \ 1)
    ]]></literal>
    <justification jstring="[para(968(a,1),5300(a,1,1))].">
      <j1 rule="para" parents="968 5300"/>
    </justification>
  </clause>

  <clause id="5727">
    <literal><![CDATA[
      T(x * ((y * (x \ z)) / y),z) / z = K(y,(T(x,z) / z) \ 1)
    ]]></literal>
    <justification jstring="[para(2310(a,1),5300(a,1,1))].">
      <j1 rule="para" parents="2310 5300"/>
    </justification>
  </clause>

  <clause id="5728">
    <literal><![CDATA[
      (x * (y * ((x \ z) / y))) / z = K(y,z / (x * y))
    ]]></literal>
    <justification jstring="[para(968(a,1),5724(a,1,1))].">
      <j1 rule="para" parents="968 5724"/>
    </justification>
  </clause>

  <clause id="5729">
    <literal><![CDATA[
      K(x,y * (((1 / z) * (u * z)) \ (u * (u * z)))) = K(x,y * ((z \ 1) \ u))
    ]]></literal>
    <justification jstring="[para(2759(a,2),5337(a,1,2,2))].">
      <j1 rule="para" parents="2759 5337"/>
    </justification>
  </clause>

  <clause id="5730">
    <literal><![CDATA[
      K(x,y * (((z * (u \ 1)) / z) \ 1)) = K(x,y * ((1 / u) \ K(u \ 1,z)))
    ]]></literal>
    <justification jstring="[para(4905(a,2),5337(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="4905 5337"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5731">
    <literal><![CDATA[
      K(x,y \ ((z \ 1) * (z * u))) = K(x,y \ L(u,z,z \ 1))
    ]]></literal>
    <justification jstring="[para(2820(a,1),5338(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2820 5338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5732">
    <literal><![CDATA[
      (((x * y) / x) \ z) * K(y,1 / y) = (1 / (1 / ((x * y) / x))) \ z
    ]]></literal>
    <justification jstring="[para(5358(a,1),3036(a,1,2))].">
      <j1 rule="para" parents="5358 3036"/>
    </justification>
  </clause>

  <clause id="5733">
    <literal><![CDATA[
      x / (y * ((z \ (y \ x)) * z)) = K(z,x / (z / (y \ 1)))
    ]]></literal>
    <justification jstring="[para(4644(a,1),5445(a,1,2))].">
      <j1 rule="para" parents="4644 5445"/>
    </justification>
  </clause>

  <clause id="5734">
    <literal><![CDATA[
      L(x,K(y,z),T(z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(479,a,5466,a)].">
      <j1 rule="hyper" parents="479 5466"/>
    </justification>
  </clause>

  <clause id="5735">
    <literal><![CDATA[
      L(x,K(y,z),T(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(5734(a,1),45(a,2))].">
      <j1 rule="para" parents="5734 45"/>
    </justification>
  </clause>

  <clause id="5736">
    <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,5537,a)].">
      <j1 rule="hyper" parents="58 310 5537"/>
    </justification>
  </clause>

  <clause id="5737">
    <literal><![CDATA[
      K(x,y) * (z * K((z \ K(y,x)) \ 1,u)) = T(K(x,y) * z,u)
    ]]></literal>
    <justification jstring="[para(4969(a,1),5541(a,1,2,2,1,1,2))].">
      <j1 rule="para" parents="4969 5541"/>
    </justification>
  </clause>

  <clause id="5738">
    <literal><![CDATA[
      K(((1 / x) / (y / x)) \ 1,z) * (y / x) = T(y,z) / x
    ]]></literal>
    <justification jstring="[para(7(a,1),5552(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7 5552"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5739">
    <literal><![CDATA[
      (x * y) * (x / (x * y)) = x * K(x * y,y \ 1)
    ]]></literal>
    <justification jstring="[para(3558(a,1),5564(a,2,2))].">
      <j1 rule="para" parents="3558 5564"/>
    </justification>
  </clause>

  <clause id="5740">
    <literal><![CDATA[
      (x * (1 / y)) * (x / (x * (1 / y))) = x * K(x * (1 / y),y)
    ]]></literal>
    <justification jstring="[para(3559(a,1),5564(a,2,2))].">
      <j1 rule="para" parents="3559 5564"/>
    </justification>
  </clause>

  <clause id="5741">
    <literal><![CDATA[
      K(x,y \ (T(1 / z,u) * w)) = K(x,y \ (T(z \ 1,u) * w))
    ]]></literal>
    <justification jstring="[para(2165(a,1),5573(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="2165 5573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5742">
    <literal><![CDATA[
      K(x,T((y \ 1) * ((z \ y) * z),u)) = K(x,T(K(z \ y,z),u))
    ]]></literal>
    <justification jstring="[para(4712(a,1),5580(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4712 5580"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5743">
    <literal><![CDATA[
      K(x,y \ K(y,z)) * z = z * K(x,(z \ (z * y)) \ 1)
    ]]></literal>
    <justification jstring="[para(4905(a,1),5611(a,1,1,2))].">
      <j1 rule="para" parents="4905 5611"/>
    </justification>
  </clause>

  <clause id="5744">
    <literal><![CDATA[
      x * K(y,(x \ z) \ 1) = K(y,x / z) * x
    ]]></literal>
    <justification jstring="[para(5351(a,1),5611(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5351 5611"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5745">
    <literal><![CDATA[
      T(K(x,y / z),y) = K(x,(y \ z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(240,a,5744,a)].">
      <j1 rule="hyper" parents="240 5744"/>
    </justification>
  </clause>

  <clause id="5746">
    <literal><![CDATA[
      T(x,y) != K(z,(y \ u) \ 1)
    ]]></literal>
    <literal><![CDATA[
      K(z,y / u) = x
    ]]></literal>
    <justification jstring="[para(5745(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="5745 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5747">
    <literal><![CDATA[
      (K(x,1 / x) * y) * z = y * (z * K(x,1 / x))
    ]]></literal>
    <justification jstring="[hyper(320,a,3418,a(flip),b,5651,a),flip(a)].">
      <j1 rule="hyper" parents="320 3418 5651"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5748">
    <literal><![CDATA[
      (x * K(y,1 / y)) / z = K(y,1 / y) * (x / z)
    ]]></literal>
    <justification jstring="[hyper(117,a,147,a(flip),b,5651,a)].">
      <j1 rule="hyper" parents="117 147 5651"/>
    </justification>
  </clause>

  <clause id="5749">
    <literal><![CDATA[
      K(x,1 / x) * (y * L(x,z,u)) = y * L((x \ 1) \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(3514(a,1),5652(a,2,2))].">
      <j1 rule="para" parents="3514 5652"/>
    </justification>
  </clause>

  <clause id="5750">
    <literal><![CDATA[
      L(K(x,y),z,u) \ 1 = L(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,5678,a(flip),b,5692,a),flip(a)].">
      <j1 rule="hyper" parents="58 5678 5692"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5751">
    <literal><![CDATA[
      1 / L(K(x,y),z,u) = L(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(197,a,5750,a)].">
      <j1 rule="hyper" parents="197 5750"/>
    </justification>
  </clause>

  <clause id="5752">
    <literal><![CDATA[
      L(K(x,K(y,z)),u,w) = K(x,L(K(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(5750(a,1),5679(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5750 5679"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5753">
    <literal><![CDATA[
      L(K(x,y),z,u) \ 1 != w
    ]]></literal>
    <literal><![CDATA[
      L(K(y,x),z,u) = w
    ]]></literal>
    <justification jstring="[para(5751(a,1),267(a,1,1)),flip(b)].">
      <j1 rule="para" parents="5751 267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5754">
    <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,5752,a,b,4729,a(flip))].">
      <j1 rule="hyper" parents="119 5752 4729"/>
    </justification>
  </clause>

  <clause id="5755">
    <literal><![CDATA[
      ((x * K(y,z)) / (z * K(y,z))) * z = R(x,K(y,z),z)
    ]]></literal>
    <justification jstring="[hyper(2917,a,5700,a),flip(a)].">
      <j1 rule="hyper" parents="2917 5700"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5758">
    <literal><![CDATA[
      (1 / x) * (K(x,y) * ((1 / x) \ z)) = K((1 / x) \ 1,y) * z
    ]]></literal>
    <justification jstring="[para(75(a,1),5720(a,1,2,1,1))].">
      <j1 rule="para" parents="75 5720"/>
    </justification>
  </clause>

  <clause id="5759">
    <literal><![CDATA[
      K(x,y \ 1) * (y \ z) = z * ((x * (z \ (y \ z))) / x)
    ]]></literal>
    <justification jstring="[para(72(a,1),5725(a,1,1,2,1))].">
      <j1 rule="para" parents="72 5725"/>
    </justification>
  </clause>

  <clause id="5760">
    <literal><![CDATA[
      R(K(x,(y / z) / (u * x)),y / z,z) = ((u * (x * ((u \ (y / z)) / x))) * z) / y
    ]]></literal>
    <justification jstring="[para(5728(a,1),525(a,1,1))].">
      <j1 rule="para" parents="5728 525"/>
    </justification>
  </clause>

  <clause id="5761">
    <literal><![CDATA[
      (x / y) * (z * K(y,1 / y)) = (x / (1 / (1 / y))) * z
    ]]></literal>
    <justification jstring="[para(2633(a,1),5747(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2633 5747"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5762">
    <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,5748,a)].">
      <j1 rule="hyper" parents="58 525 5748"/>
    </justification>
  </clause>

  <clause id="5763">
    <literal><![CDATA[
      L(x \ (y * z),x,K(z,y)) = (K(y,z) \ x) \ (z * y)
    ]]></literal>
    <justification jstring="[para(5130(a,2),5004(a,2,1))].">
      <j1 rule="para" parents="5130 5004"/>
    </justification>
  </clause>

  <clause id="5764">
    <literal><![CDATA[
      L(x * K(y,x),K(x * K(y,x),y),z) = (z * K(x,y)) \ (z * x)
    ]]></literal>
    <justification jstring="[para(4970(a,2),5023(a,1,2))].">
      <j1 rule="para" parents="4970 5023"/>
    </justification>
  </clause>

  <clause id="5765">
    <literal><![CDATA[
      (K(x,y) \ z) \ (K(x,y) \ (z * u)) = L(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(116,a,5130,a,b,5151,a)].">
      <j1 rule="hyper" parents="116 5130 5151"/>
    </justification>
  </clause>

  <clause id="5766">
    <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(5133(a,1),5152(a,2,2))].">
      <j1 rule="para" parents="5133 5152"/>
    </justification>
  </clause>

  <clause id="5767">
    <literal><![CDATA[
      L(K(x \ y,x) * z,K(x,x \ y),y) = (x * (y / x)) \ (y * z)
    ]]></literal>
    <justification jstring="[para(5013(a,1),5152(a,2,1))].">
      <j1 rule="para" parents="5013 5152"/>
    </justification>
  </clause>

  <clause id="5768">
    <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(5153(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="5153 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5769">
    <literal><![CDATA[
      (T(x,y) * K(z,x)) \ u = K(x,z) * (T(x,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(5735,a,5154,a),flip(a)].">
      <j1 rule="hyper" parents="5735 5154"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5770">
    <literal><![CDATA[
      (L(x,y,z) * K(x,u)) \ w = K(u,x) * (L(x,y,z) \ w)
    ]]></literal>
    <justification jstring="[hyper(4514,a,5154,a),flip(a)].">
      <j1 rule="hyper" parents="4514 5154"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5771">
    <literal><![CDATA[
      (K(x,y) * T(y,z)) \ u = K(y,x) * (T(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(2897(a,1),5769(a,1,1))].">
      <j1 rule="para" parents="2897 5769"/>
    </justification>
  </clause>

  <clause id="5772">
    <literal><![CDATA[
      K(x,y) * (T(x,x * y) \ z) = L(x,y,x) \ z
    ]]></literal>
    <justification jstring="[para(5284(a,1),5769(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5284 5769"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5773">
    <literal><![CDATA[
      K(x,x * y) * (T(x,y) \ z) = R(x,y,x) \ z
    ]]></literal>
    <justification jstring="[para(5286(a,1),5769(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5286 5769"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5774">
    <literal><![CDATA[
      K(x,x * y) * K(y,x) = R(x,y,x) \ x
    ]]></literal>
    <justification jstring="[para(4730(a,2),5773(a,1,2))].">
      <j1 rule="para" parents="4730 5773"/>
    </justification>
  </clause>

  <clause id="5775">
    <literal><![CDATA[
      R(x,y,x) \ x = x \ L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(5482,a,5774,a),flip(a)].">
      <j1 rule="hyper" parents="5482 5774"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5776">
    <literal><![CDATA[
      x \ (x \ L(x,y,x)) = R(x,y,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(116,a,5775,a(flip),b,1316,a)].">
      <j1 rule="hyper" parents="116 5775 1316"/>
    </justification>
  </clause>

  <clause id="5777">
    <literal><![CDATA[
      x \ ((x \ L(x,y,x)) * T(x,z)) = T(x,z) * (R(x,y,x) \ 1)
    ]]></literal>
    <justification jstring="[para(5776(a,1),3539(a,2,2))].">
      <j1 rule="para" parents="5776 3539"/>
    </justification>
  </clause>

  <clause id="5778">
    <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),5181(a,1,2))].">
      <j1 rule="para" parents="75 5181"/>
    </justification>
  </clause>

  <clause id="5779">
    <literal><![CDATA[
      K(x,(y \ 1) \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(4741(a,1),5280(a,1))].">
      <j1 rule="para" parents="4741 5280"/>
    </justification>
  </clause>

  <clause id="5780">
    <literal><![CDATA[
      K(x,T(y,y \ 1)) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(106(a,2),5779(a,1,2))].">
      <j1 rule="para" parents="106 5779"/>
    </justification>
  </clause>

  <clause id="5781">
    <literal><![CDATA[
      K(x,T(y / z,z / y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y / z) = u
    ]]></literal>
    <justification jstring="[para(2069(a,2),5779(a,1,2))].">
      <j1 rule="para" parents="2069 5779"/>
    </justification>
  </clause>

  <clause id="5782">
    <literal><![CDATA[
      K(x,T(y \ 1,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(1 / y,z)) = u
    ]]></literal>
    <justification jstring="[para(2165(a,1),5779(a,1,2))].">
      <j1 rule="para" parents="2165 5779"/>
    </justification>
  </clause>

  <clause id="5783">
    <literal><![CDATA[
      K(x,T(y \ z,z \ y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(2375(a,2),5779(a,1,2))].">
      <j1 rule="para" parents="2375 5779"/>
    </justification>
  </clause>

  <clause id="5784">
    <literal><![CDATA[
      K(x,T(y / z,y \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y / z) = u
    ]]></literal>
    <justification jstring="[para(2403(a,2),5779(a,1,2))].">
      <j1 rule="para" parents="2403 5779"/>
    </justification>
  </clause>

  <clause id="5785">
    <literal><![CDATA[
      K(x,T(y,L(y,z,u) \ 1)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = w
    ]]></literal>
    <justification jstring="[para(3373(a,2),5779(a,1,2))].">
      <j1 rule="para" parents="3373 5779"/>
    </justification>
  </clause>

  <clause id="5786">
    <literal><![CDATA[
      K(((x \ 1) \ 1) \ y,(z \ 1) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,z) = u
    ]]></literal>
    <justification jstring="[para(3980(a,2),5779(a,1))].">
      <j1 rule="para" parents="3980 5779"/>
    </justification>
  </clause>

  <clause id="5788">
    <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),5283(a,1,1))].">
      <j1 rule="para" parents="217 5283"/>
    </justification>
  </clause>

  <clause id="5789">
    <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),5378(a,2,3))].">
      <j1 rule="para" parents="219 5378"/>
    </justification>
  </clause>

  <clause id="5790">
    <literal><![CDATA[
      R(x,x \ (y \ x),x) = R(x,y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,5367,a(flip),b,5379,a),flip(a)].">
      <j1 rule="hyper" parents="58 5367 5379"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5791">
    <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),5476(a,1,2))].">
      <j1 rule="para" parents="219 5476"/>
    </justification>
  </clause>

  <clause id="5792">
    <literal><![CDATA[
      K(x \ y,L(y \ x,z,u)) = K(x \ y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(29,a,3576,a(flip),b,5517,a),flip(a)].">
      <j1 rule="hyper" parents="29 3576 5517"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5793">
    <literal><![CDATA[
      K(1 / x,L(x,y,z)) = K(1 / x,x)
    ]]></literal>
    <justification jstring="[hyper(29,a,3549,a(flip),b,5517,a),flip(a)].">
      <j1 rule="hyper" parents="29 3549 5517"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5794">
    <literal><![CDATA[
      K(x \ 1,L(x,y,z)) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(29,a,3498,a(flip),b,5517,a),flip(a)].">
      <j1 rule="hyper" parents="29 3498 5517"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5795">
    <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(5517(a,1),2893(a,1,1))].">
      <j1 rule="para" parents="5517 2893"/>
    </justification>
  </clause>

  <clause id="5796">
    <literal><![CDATA[
      K(1 / L(x,y,z),L(x,u,w)) = L(K(1 / x,x),y,z)
    ]]></literal>
    <justification jstring="[para(5793(a,1),5689(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5793 5689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5797">
    <literal><![CDATA[
      K(L(x,y,z) \ 1,x) = K(x \ 1,L(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(320,a,3378,a,b,5794,a)].">
      <j1 rule="hyper" parents="320 3378 5794"/>
    </justification>
  </clause>

  <clause id="5798">
    <literal><![CDATA[
      L(K(x \ 1,L(x,y,z)),u,w) = K(L(x,u,w) \ 1,x)
    ]]></literal>
    <justification jstring="[para(5794(a,2),2519(a,1,1))].">
      <j1 rule="para" parents="5794 2519"/>
    </justification>
  </clause>

  <clause id="5799">
    <literal><![CDATA[
      K(x \ (y \ 1),(y \ 1) \ x) = K(x \ (y \ 1),y * x)
    ]]></literal>
    <justification jstring="[para(489(a,1),5792(a,1,2)),flip(a)].">
      <j1 rule="para" parents="489 5792"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5800">
    <literal><![CDATA[
      K(x \ 1,R(x,y,z)) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(29,a,3831,a(flip),b,5518,a),flip(a)].">
      <j1 rule="hyper" parents="29 3831 5518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5801">
    <literal><![CDATA[
      (x \ R(x,y,z)) * K(x \ 1,x) = (x \ 1) * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(5800(a,1),1212(a,1,2))].">
      <j1 rule="para" parents="5800 1212"/>
    </justification>
  </clause>

  <clause id="5802">
    <literal><![CDATA[
      (x \ y) * (((x \ y) \ y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      (y / x) * (x * z) = u
    ]]></literal>
    <justification jstring="[para(5117(a,1),5609(a,1,2))].">
      <j1 rule="para" parents="5117 5609"/>
    </justification>
  </clause>

  <clause id="5803">
    <literal><![CDATA[
      K(x,L(y,x,x \ 1)) * (y * x) = x * y
    ]]></literal>
    <justification jstring="[para(6(a,1),5667(a,2,2))].">
      <j1 rule="para" parents="6 5667"/>
    </justification>
  </clause>

  <clause id="5804">
    <literal><![CDATA[
      K(x,L(y,x,x \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(5002,a,5803,a),flip(a)].">
      <j1 rule="hyper" parents="5002 5803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5805">
    <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,5702,a(flip),b,216,a)].">
      <j1 rule="hyper" parents="119 5702 216"/>
    </justification>
  </clause>

  <clause id="5806">
    <literal><![CDATA[
      K(R(x,y,z) \ 1,R(x,y,z)) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,5800,a(flip),b,5704,a),flip(a)].">
      <j1 rule="hyper" parents="320 5800 5704"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5807">
    <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,5704,a(flip),b,4708,a)].">
      <j1 rule="hyper" parents="119 5704 4708"/>
    </justification>
  </clause>

  <clause id="5809">
    <literal><![CDATA[
      (x \ (1 / R(y,z,u))) * K(y \ 1,y) = x \ (R(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(5806(a,1),3431(a,1,2))].">
      <j1 rule="para" parents="5806 3431"/>
    </justification>
  </clause>

  <clause id="5810">
    <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(3317(a,1),5721(a,1,1))].">
      <j1 rule="para" parents="3317 5721"/>
    </justification>
  </clause>

  <clause id="5811">
    <literal><![CDATA[
      R(x * y,K(z,y),y) = R(x,y,K(z,y)) * y
    ]]></literal>
    <justification jstring="[para(15(a,2),5755(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15 5755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5812">
    <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(5811(a,2),39(a,1))].">
      <j1 rule="para" parents="5811 39"/>
    </justification>
  </clause>

  <clause id="5813">
    <literal><![CDATA[
      L(x \ y,x,K(z,u)) = (K(u,z) \ x) \ (K(u,z) \ y)
    ]]></literal>
    <justification jstring="[hyper(1907,a,5765,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="1907 5765"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5814">
    <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),5765(a,1,2,2))].">
      <j1 rule="para" parents="90 5765"/>
    </justification>
  </clause>

  <clause id="5815">
    <literal><![CDATA[
      K(1 / L(x,y,z),L(x,u,w)) = K(1 / x,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,3394,a(flip),b,5796,a),flip(a)].">
      <j1 rule="hyper" parents="320 3394 5796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5817">
    <literal><![CDATA[
      L(x,y,z) * K(1 / x,x) = 1 / (1 / L(x,y,z))
    ]]></literal>
    <justification jstring="[para(5815(a,1),4753(a,2,2)),flip(a)].">
      <j1 rule="para" parents="5815 4753"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5818">
    <literal><![CDATA[
      K(L(x,y,z) \ 1,L(x,u,w)) = K(L(x,y,z) \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(5721,a,5798,a)].">
      <j1 rule="hyper" parents="5721 5798"/>
    </justification>
  </clause>

  <clause id="5820">
    <literal><![CDATA[
      L(x \ T(y,z),x,K(y,z)) = (K(z,y) \ x) \ T(T(y,z),z)
    ]]></literal>
    <justification jstring="[para(4916(a,1),5813(a,2,2))].">
      <j1 rule="para" parents="4916 5813"/>
    </justification>
  </clause>

  <clause id="5821">
    <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,5797,a(flip),b,5818,a),flip(a)].">
      <j1 rule="hyper" parents="320 5797 5818"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5823">
    <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),5821(a,1,1,1))].">
      <j1 rule="para" parents="298 5821"/>
    </justification>
  </clause>

  <clause id="5824">
    <literal><![CDATA[
      T(x * K(y,x),x \ K(x,y)) = (x \ 1) \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,5612,a(flip),b,4982,a),flip(a)].">
      <j1 rule="hyper" parents="320 5612 4982"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5825">
    <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(5639(a,1),4982(a,2,1,1))].">
      <j1 rule="para" parents="5639 4982"/>
    </justification>
  </clause>

  <clause id="5826">
    <literal><![CDATA[
      (x * K(y \ 1,z)) * y = (x * y) * K(y \ 1,z)
    ]]></literal>
    <justification jstring="[para(4746(a,1),5063(a,1,1,2))].">
      <j1 rule="para" parents="4746 5063"/>
    </justification>
  </clause>

  <clause id="5829">
    <literal><![CDATA[
      (x * K(y \ 1,z)) \ ((x * y) * K(y \ 1,z)) = y
    ]]></literal>
    <justification jstring="[hyper(123,a,5826,a)].">
      <j1 rule="hyper" parents="123 5826"/>
    </justification>
  </clause>

  <clause id="5830">
    <literal><![CDATA[
      (x * K(y \ 1,z)) / y = (x / y) * K(y \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(117,a,147,a(flip),b,5826,a)].">
      <j1 rule="hyper" parents="117 147 5826"/>
    </justification>
  </clause>

  <clause id="5831">
    <literal><![CDATA[
      R(T(x,y * K(x \ 1,z)),y,K(x \ 1,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(5829(a,1),1096(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5829 1096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5832">
    <literal><![CDATA[
      (T(x,y \ 1) / y) * K(y \ 1,x) = x / y
    ]]></literal>
    <justification jstring="[para(4749(a,1),5830(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4749 5830"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5833">
    <literal><![CDATA[
      (T(x,y \ 1) / y) \ (x / y) = K(y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(123,a,5832,a)].">
      <j1 rule="hyper" parents="123 5832"/>
    </justification>
  </clause>

  <clause id="5834">
    <literal><![CDATA[
      K(x \ 1,(1 / x) \ (y / x)) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,3364,a,b,5833,a)].">
      <j1 rule="hyper" parents="58 3364 5833"/>
    </justification>
  </clause>

  <clause id="5835">
    <literal><![CDATA[
      K(x \ 1,(1 / x) \ y) = K(x \ 1,y * x)
    ]]></literal>
    <justification jstring="[para(6(a,1),5834(a,1,2,2))].">
      <j1 rule="para" parents="6 5834"/>
    </justification>
  </clause>

  <clause id="5836">
    <literal><![CDATA[
      K(1 / x,(1 / x) \ y) = K(x \ 1,y * x)
    ]]></literal>
    <justification jstring="[hyper(5282,a,5835,a)].">
      <j1 rule="hyper" parents="5282 5835"/>
    </justification>
  </clause>

  <clause id="5837">
    <literal><![CDATA[
      K(x \ 1,(x \ 1) \ y) = K(x \ 1,y * x)
    ]]></literal>
    <justification jstring="[hyper(58,a,5323,a(flip),b,5835,a)].">
      <j1 rule="hyper" parents="58 5323 5835"/>
    </justification>
  </clause>

  <clause id="5838">
    <literal><![CDATA[
      (1 / x) * (y / (1 / x)) = y * K(x \ 1,y * x)
    ]]></literal>
    <justification jstring="[hyper(119,a,5836,a(flip),b,5011,a),flip(a)].">
      <j1 rule="hyper" parents="119 5836 5011"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5839">
    <literal><![CDATA[
      K(x \ 1,y * x) = K(x \ 1,x * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,4494,a(flip),b,5837,a),flip(a)].">
      <j1 rule="hyper" parents="58 4494 5837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5840">
    <literal><![CDATA[
      (x \ 1) * (y / (x \ 1)) = y * K(x \ 1,y * x)
    ]]></literal>
    <justification jstring="[hyper(119,a,5837,a(flip),b,5011,a),flip(a)].">
      <j1 rule="hyper" parents="119 5837 5011"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5841">
    <literal><![CDATA[
      T(x \ 1,y * x) = T(x \ 1,x * y)
    ]]></literal>
    <justification jstring="[hyper(118,a,5839,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 5839 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5842">
    <literal><![CDATA[
      ((x * y) \ y) * (x * y) = y * K(x \ 1,y * x)
    ]]></literal>
    <justification jstring="[para(5839(a,2),5439(a,2,2))].">
      <j1 rule="para" parents="5839 5439"/>
    </justification>
  </clause>

  <clause id="5843">
    <literal><![CDATA[
      T(x \ 1,y * x) = ((x \ 1) \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(320,a,4409,a(flip),b,5841,a),flip(a)].">
      <j1 rule="hyper" parents="320 4409 5841"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5844">
    <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(5841(a,1),2141(a,1,2,1,1))].">
      <j1 rule="para" parents="5841 2141"/>
    </justification>
  </clause>

  <clause id="5845">
    <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(5841(a,2),2141(a,1,1))].">
      <j1 rule="para" parents="5841 2141"/>
    </justification>
  </clause>

  <clause id="5846">
    <literal><![CDATA[
      T((x \ y) \ 1,y) = (((x \ y) \ 1) \ x) \ x
    ]]></literal>
    <justification jstring="[para(5(a,1),5843(a,1,2))].">
      <j1 rule="para" parents="5 5843"/>
    </justification>
  </clause>

  <clause id="5847">
    <literal><![CDATA[
      K(T(1 / x,y * x),z) = K(((x \ 1) \ y) \ y,z)
    ]]></literal>
    <justification jstring="[para(5843(a,1),3319(a,2,1))].">
      <j1 rule="para" parents="5843 3319"/>
    </justification>
  </clause>

  <clause id="5848">
    <literal><![CDATA[
      x * K((1 / y) \ 1,x * (1 / y)) = y * (x / y)
    ]]></literal>
    <justification jstring="[hyper(58,a,2857,a(flip),b,5838,a),flip(a)].">
      <j1 rule="hyper" parents="58 2857 5838"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5849">
    <literal><![CDATA[
      (x \ 1) * ((y / x) / (x \ 1)) = (y / x) * K(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(7(a,1),5840(a,2,2,2))].">
      <j1 rule="para" parents="7 5840"/>
    </justification>
  </clause>

  <clause id="5850">
    <literal><![CDATA[
      x * K(y,x * (1 / y)) = y * (x / y)
    ]]></literal>
    <justification jstring="[para(75(a,1),5848(a,1,2,1))].">
      <j1 rule="para" parents="75 5848"/>
    </justification>
  </clause>

  <clause id="5851">
    <literal><![CDATA[
      K(x,y * (1 / x)) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(29,a,5013,a,b,5850,a),flip(a)].">
      <j1 rule="hyper" parents="29 5013 5850"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5852">
    <literal><![CDATA[
      (x / y) * z != x * K(y,x * (1 / y))
    ]]></literal>
    <literal><![CDATA[
      T(y,x / y) = z
    ]]></literal>
    <justification jstring="[para(5850(a,2),240(a,2))].">
      <j1 rule="para" parents="5850 240"/>
    </justification>
  </clause>

  <clause id="5854">
    <literal><![CDATA[
      (x / (y \ 1)) * K(y,x) = y * ((x / (y \ 1)) / y)
    ]]></literal>
    <justification jstring="[para(5317(a,1),5850(a,1,2))].">
      <j1 rule="para" parents="5317 5850"/>
    </justification>
  </clause>

  <clause id="5855">
    <literal><![CDATA[
      K(x,y * (x \ 1)) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,5315,a(flip),b,5851,a)].">
      <j1 rule="hyper" parents="58 5315 5851"/>
    </justification>
  </clause>

  <clause id="5856">
    <literal><![CDATA[
      K(x * (1 / y),y) = 1 / K(y,y \ x)
    ]]></literal>
    <justification jstring="[para(5851(a,1),4971(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5851 4971"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5857">
    <literal><![CDATA[
      K(x,R(y,x,x \ 1)) = K(x,x \ (x * y))
    ]]></literal>
    <justification jstring="[hyper(58,a,4915,a(flip),b,5855,a)].">
      <j1 rule="hyper" parents="58 4915 5855"/>
    </justification>
  </clause>

  <clause id="5858">
    <literal><![CDATA[
      K(x * (1 / y),y) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,4971,a(flip),b,5856,a),flip(a)].">
      <j1 rule="hyper" parents="320 4971 5856"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5859">
    <literal><![CDATA[
      K(x * (1 / y),y) = K(x / y,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,4964,a,b,5858,a),flip(a)].">
      <j1 rule="hyper" parents="320 4964 5858"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5860">
    <literal><![CDATA[
      K((1 / x) * y,x) = K(y * (1 / x),x)
    ]]></literal>
    <justification jstring="[hyper(320,a,4486,a,b,5858,a)].">
      <j1 rule="hyper" parents="320 4486 5858"/>
    </justification>
  </clause>

  <clause id="5861">
    <literal><![CDATA[
      K(x * (y \ 1),y) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,3975,a(flip),b,5858,a)].">
      <j1 rule="hyper" parents="58 3975 5858"/>
    </justification>
  </clause>

  <clause id="5862">
    <literal><![CDATA[
      K((x \ 1) \ y,x \ 1) = K(y * x,x \ 1)
    ]]></literal>
    <justification jstring="[para(72(a,1),5858(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="72 5858"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5863">
    <literal><![CDATA[
      K(x \ y,x) * (y * (1 / x)) = T(y * (1 / x),x)
    ]]></literal>
    <justification jstring="[para(5858(a,1),4770(a,2,1)),flip(a)].">
      <j1 rule="para" parents="5858 4770"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5864">
    <literal><![CDATA[
      K(x / (1 / y),1 / y) = K(x * y,1 / y)
    ]]></literal>
    <justification jstring="[hyper(58,a,3979,a(flip),b,5859,a),flip(a)].">
      <j1 rule="hyper" parents="58 3979 5859"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5865">
    <literal><![CDATA[
      x * K(x * (y \ 1),y) = (y \ x) * y
    ]]></literal>
    <justification jstring="[hyper(119,a,5861,a,b,85,a)].">
      <j1 rule="hyper" parents="119 5861 85"/>
    </justification>
  </clause>

  <clause id="5866">
    <literal><![CDATA[
      K((1 / (1 / x)) * y,1 / x) = K(y * x,1 / x)
    ]]></literal>
    <justification jstring="[hyper(320,a,3979,a(flip),b,5860,a),flip(a)].">
      <j1 rule="hyper" parents="320 3979 5860"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5867">
    <literal><![CDATA[
      ((1 / x) \ y) * (1 / x) = y * K(y * x,1 / x)
    ]]></literal>
    <justification jstring="[para(75(a,1),5865(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="75 5865"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5868">
    <literal><![CDATA[
      K(x,R(y,x,x \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(4(a,1),5857(a,2,2))].">
      <j1 rule="para" parents="4 5857"/>
    </justification>
  </clause>

  <clause id="5869">
    <literal><![CDATA[
      K(x,y) = x \ T(x,R(y,x,x \ 1))
    ]]></literal>
    <justification jstring="[hyper(4903,a,5868,a),flip(a)].">
      <j1 rule="hyper" parents="4903 5868"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5870">
    <literal><![CDATA[
      R(x,y,y \ 1) * K(y,x) = (y * x) * (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(119,a,5869,a,b,3862,a)].">
      <j1 rule="hyper" parents="119 5869 3862"/>
    </justification>
  </clause>

  <clause id="5871">
    <literal><![CDATA[
      K(x * y,y \ 1) = K(y * x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,4488,a(flip),b,5862,a),flip(a)].">
      <j1 rule="hyper" parents="58 4488 5862"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5872">
    <literal><![CDATA[
      K(x,y) * ((y * x) * (y \ 1)) = R(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[para(5870(a,1),5144(a,1,2))].">
      <j1 rule="para" parents="5870 5144"/>
    </justification>
  </clause>

  <clause id="5873">
    <literal><![CDATA[
      K(x * y,1 / y) = K(y * x,1 / y)
    ]]></literal>
    <justification jstring="[hyper(58,a,3573,a(flip),b,5866,a),flip(a)].">
      <j1 rule="hyper" parents="58 3573 5866"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5874">
    <literal><![CDATA[
      K((x \ y) * x,1 / x) = K(y,1 / x)
    ]]></literal>
    <justification jstring="[para(5(a,1),5873(a,2,1))].">
      <j1 rule="para" parents="5 5873"/>
    </justification>
  </clause>

  <clause id="5875">
    <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,4327,a(flip),b,5109,a),flip(a)].">
      <j1 rule="hyper" parents="320 4327 5109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5876">
    <literal><![CDATA[
      K(x,y) * (R(y,z,u) * x) = R(y,z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,4257,a(flip),b,5109,a),flip(a)].">
      <j1 rule="hyper" parents="320 4257 5109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5877">
    <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,4326,a(flip),b,5120,a),flip(a)].">
      <j1 rule="hyper" parents="320 4326 5120"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5878">
    <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),5171(a,2,2))].">
      <j1 rule="para" parents="22 5171"/>
    </justification>
  </clause>

  <clause id="5879">
    <literal><![CDATA[
      K(x,y) * (K(x,y) * z) = y * (T(T(y,x),x) \ z)
    ]]></literal>
    <justification jstring="[para(4908(a,1),5186(a,1,2,1))].">
      <j1 rule="para" parents="4908 5186"/>
    </justification>
  </clause>

  <clause id="5880">
    <literal><![CDATA[
      K(1 / x,y) / (x \ 1) = 1 / (x \ K(y,1 / x))
    ]]></literal>
    <justification jstring="[para(3568(a,1),5271(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3568 5271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5881">
    <literal><![CDATA[
      K((K(x,y) / x) * z,u) = K((x \ K(x,y)) * z,u)
    ]]></literal>
    <justification jstring="[para(5209(a,1),5273(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5209 5273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5882">
    <literal><![CDATA[
      ((x * y) * ((z * ((x * y) \ x)) / z)) * y = (x * y) * K(z,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,2298,a(flip),b,5302,a)].">
      <j1 rule="hyper" parents="58 2298 5302"/>
    </justification>
  </clause>

  <clause id="5883">
    <literal><![CDATA[
      (x * (y \ 1)) * ((z * ((x * (y \ 1)) \ x)) / z) = x * K(z,y)
    ]]></literal>
    <justification jstring="[para(3554(a,1),5302(a,2,2))].">
      <j1 rule="para" parents="3554 5302"/>
    </justification>
  </clause>

  <clause id="5884">
    <literal><![CDATA[
      x * (y * ((z * (y \ (x \ y))) / z)) = K(z,x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(1342,a,5303,a)].">
      <j1 rule="hyper" parents="1342 5303"/>
    </justification>
  </clause>

  <clause id="5885">
    <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(5453(a,2),5334(a,1,2,2))].">
      <j1 rule="para" parents="5453 5334"/>
    </justification>
  </clause>

  <clause id="5886">
    <literal><![CDATA[
      (K(x,y) * R(y,z,u)) * w = R(y,z,u) * (K(x,y) * w)
    ]]></literal>
    <justification jstring="[para(2899(a,1),5467(a,1,1))].">
      <j1 rule="para" parents="2899 5467"/>
    </justification>
  </clause>

  <clause id="5887">
    <literal><![CDATA[
      K((x \ (y / (z \ 1))) \ 1,y) = x \ (((y \ (x / z)) * y) * z)
    ]]></literal>
    <justification jstring="[para(3853(a,1),5533(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3853 5533"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5888">
    <literal><![CDATA[
      K(x * y,T(y,z)) = K(y * x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(5383,a,5587,a),flip(a)].">
      <j1 rule="hyper" parents="5383 5587"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5889">
    <literal><![CDATA[
      L(K(x,y),z,u) \ w = L(K(y,x),z,u) * w
    ]]></literal>
    <justification jstring="[para(5687(a,1),5682(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5687 5682"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5890">
    <literal><![CDATA[
      L(K(x,y),z,u) * K(y,x) = a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(1935,a,5889,a)].">
      <j1 rule="hyper" parents="1935 5889"/>
    </justification>
  </clause>

  <clause id="5891">
    <literal><![CDATA[
      L(K(x,y),z,u) * (L(K(y,x),z,u) * w) = w
    ]]></literal>
    <justification jstring="[hyper(341,a,5889,a),flip(a)].">
      <j1 rule="hyper" parents="341 5889"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5892">
    <literal><![CDATA[
      K(x,y) * L(K(y,x),z,u) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,2010,a(flip),b,5890,a)].">
      <j1 rule="hyper" parents="58 2010 5890"/>
    </justification>
  </clause>

  <clause id="5893">
    <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(5890(a,1),4977(a,1)),flip(b)].">
      <j1 rule="para" parents="5890 4977"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5894">
    <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(5891(a,1),287(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5891 287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5895">
    <literal><![CDATA[
      K(x,y) \ L(K(x,y),z,u) = a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(5167,a,5892,a)].">
      <j1 rule="hyper" parents="5167 5892"/>
    </justification>
  </clause>

  <clause id="5896">
    <literal><![CDATA[
      K(x,y) * a(z,u,K(y,x)) = L(K(x,y),u,z)
    ]]></literal>
    <justification jstring="[hyper(5147,a,5892,a)].">
      <j1 rule="hyper" parents="5147 5892"/>
    </justification>
  </clause>

  <clause id="5897">
    <literal><![CDATA[
      (K(x,y) / z) * (z * K(y,x)) = a(K(x,y) / z,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(697,a,5892,a)].">
      <j1 rule="hyper" parents="697 5892"/>
    </justification>
  </clause>

  <clause id="5898">
    <literal><![CDATA[
      K(x \ 1,y) * K(y,L(x,z,u) \ 1) = a(u,z,K(x \ 1,y))
    ]]></literal>
    <justification jstring="[para(5675(a,1),5892(a,1,2))].">
      <j1 rule="para" parents="5675 5892"/>
    </justification>
  </clause>

  <clause id="5899">
    <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(5896(a,1),5148(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5896 5148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5900">
    <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(2006(a,2),5899(a,1))].">
      <j1 rule="para" parents="2006 5899"/>
    </justification>
  </clause>

  <clause id="5901">
    <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(5696(a,1),5130(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5696 5130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5902">
    <literal><![CDATA[
      K((x * (y \ 1)) \ 1,y) = K(x \ y,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,5044,a(flip),b,5712,a),flip(a)].">
      <j1 rule="hyper" parents="58 5044 5712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5903">
    <literal><![CDATA[
      (x * K((x \ y) \ 1,z)) * (x \ 1) = K((y * (x \ 1)) \ 1,z)
    ]]></literal>
    <justification jstring="[para(5054(a,1),5712(a,1,1))].">
      <j1 rule="para" parents="5054 5712"/>
    </justification>
  </clause>

  <clause id="5904">
    <literal><![CDATA[
      K(((1 / x) * (y \ 1)) \ 1,z) = (1 / x) * (y \ T(y * x,z))
    ]]></literal>
    <justification jstring="[para(939(a,1),5713(a,1,2)),flip(a)].">
      <j1 rule="para" parents="939 5713"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5905">
    <literal><![CDATA[
      K(x \ y,y) / (y \ T(y * (x \ 1),y)) = x
    ]]></literal>
    <justification jstring="[hyper(117,a,5902,a(flip),b,5715,a)].">
      <j1 rule="hyper" parents="117 5902 5715"/>
    </justification>
  </clause>

  <clause id="5906">
    <literal><![CDATA[
      x \ T(x * (y \ 1),x) = y \ K(y \ x,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,5902,a(flip),b,5715,a),flip(a)].">
      <j1 rule="hyper" parents="116 5902 5715"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5907">
    <literal><![CDATA[
      x * (y \ K(y \ x,x)) = T(x * (y \ 1),x)
    ]]></literal>
    <justification jstring="[para(5905(a,1),195(a,1,2,1))].">
      <j1 rule="para" parents="5905 195"/>
    </justification>
  </clause>

  <clause id="5908">
    <literal><![CDATA[
      (x \ K(x \ y,y)) * y = T((x \ 1) * y,y)
    ]]></literal>
    <justification jstring="[para(5906(a,1),4596(a,1,1))].">
      <j1 rule="para" parents="5906 4596"/>
    </justification>
  </clause>

  <clause id="5909">
    <literal><![CDATA[
      ((x * (K(y \ x,x) * (y \ 1))) / x) / (y \ 1) = y * (T(x * (y \ 1),x) / x)
    ]]></literal>
    <justification jstring="[para(5907(a,1),1483(a,2,2,1))].">
      <j1 rule="para" parents="5907 1483"/>
    </justification>
  </clause>

  <clause id="5910">
    <literal><![CDATA[
      x * T(x \ (y \ x),T(y,z)) = ((y \ 1) \ 1) \ x
    ]]></literal>
    <justification jstring="[hyper(3025,a,5717,a),flip(a)].">
      <j1 rule="hyper" parents="3025 5717"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5911">
    <literal><![CDATA[
      K(((1 / x) / (y / x)) \ 1,z) = (T(y,z) / x) / (y / x)
    ]]></literal>
    <justification jstring="[hyper(58,a,4004,a,b,5723,a)].">
      <j1 rule="hyper" parents="58 4004 5723"/>
    </justification>
  </clause>

  <clause id="5912">
    <literal><![CDATA[
      (x * (y * ((x \ z) / y))) / z != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z / (x * y)) = u
    ]]></literal>
    <justification jstring="[para(5726(a,2),5428(a,1))].">
      <j1 rule="para" parents="5726 5428"/>
    </justification>
  </clause>

  <clause id="5913">
    <literal><![CDATA[
      K(x,y \ K(y,z)) * z = z * K(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(4(a,1),5743(a,2,2,2,1))].">
      <j1 rule="para" parents="4 5743"/>
    </justification>
  </clause>

  <clause id="5914">
    <literal><![CDATA[
      K(x,(y / (1 / (1 / z))) * u) = K(x,(y / z) * u)
    ]]></literal>
    <justification jstring="[para(5761(a,1),5327(a,1,2))].">
      <j1 rule="para" parents="5761 5327"/>
    </justification>
  </clause>

  <clause id="5915">
    <literal><![CDATA[
      (1 / x) * R(x,y,z) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(30,a,2847,a,b,5801,a)].">
      <j1 rule="hyper" parents="30 2847 5801"/>
    </justification>
  </clause>

  <clause id="5917">
    <literal><![CDATA[
      R(x,y,z) / x = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(1888,a,5915,a)].">
      <j1 rule="hyper" parents="1888 5915"/>
    </justification>
  </clause>

  <clause id="5919">
    <literal><![CDATA[
      x \ R(x,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) / x = u
    ]]></literal>
    <justification jstring="[para(5915(a,1),1888(a,1))].">
      <j1 rule="para" parents="5915 1888"/>
    </justification>
  </clause>

  <clause id="5921">
    <literal><![CDATA[
      (x \ R(x,y,z)) * x = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(133,a,5917,a)].">
      <j1 rule="hyper" parents="133 5917"/>
    </justification>
  </clause>

  <clause id="5922">
    <literal><![CDATA[
      T(x,x \ R(x,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(31,a,265,a,b,5917,a)].">
      <j1 rule="hyper" parents="31 265 5917"/>
    </justification>
  </clause>

  <clause id="5923">
    <literal><![CDATA[
      R(x \ R(x,y,z),x,y * z) = ((x * y) * z) / (x * (y * z))
    ]]></literal>
    <justification jstring="[para(5917(a,1),532(a,1,1))].">
      <j1 rule="para" parents="5917 532"/>
    </justification>
  </clause>

  <clause id="5924">
    <literal><![CDATA[
      K(R(x,y,z),x \ R(x,u,w)) = R(x,y,z) \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(5922(a,1),4765(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5922 4765"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5925">
    <literal><![CDATA[
      (x \ 1) \ ((y \ (y / x)) * y) = (y / x) / (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(116,a,5051,a,b,5849,a)].">
      <j1 rule="hyper" parents="116 5051 5849"/>
    </justification>
  </clause>

  <clause id="5926">
    <literal><![CDATA[
      (x / (y \ x)) / ((y \ x) \ 1) = ((y \ x) \ 1) \ ((x \ y) * x)
    ]]></literal>
    <justification jstring="[para(72(a,1),5925(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="72 5925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5927">
    <literal><![CDATA[
      x * (K(y,x \ 1) * (x \ z)) = K(y,x \ 1) * z
    ]]></literal>
    <justification jstring="[para(5759(a,2),5884(a,1,2))].">
      <j1 rule="para" parents="5759 5884"/>
    </justification>
  </clause>

  <clause id="5929">
    <literal><![CDATA[
      K(x,y \ 1) * (y * z) = y * (K(x,y \ 1) * z)
    ]]></literal>
    <justification jstring="[para(4(a,1),5927(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 5927"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5932">
    <literal><![CDATA[
      1 \ (x * (K(y,x \ 1) * z)) = K(y,x \ 1) * (x * z)
    ]]></literal>
    <justification jstring="[hyper(320,a,60,a,b,5929,a)].">
      <j1 rule="hyper" parents="320 60 5929"/>
    </justification>
  </clause>

  <clause id="5933">
    <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(5886(a,1),515(a,1))].">
      <j1 rule="para" parents="5886 515"/>
    </justification>
  </clause>

  <clause id="5934">
    <literal><![CDATA[
      K(R(x,y,z),x \ R(x,u,w)) = 1
    ]]></literal>
    <justification jstring="[hyper(320,a,61,a(flip),b,5924,a),flip(a)].">
      <j1 rule="hyper" parents="320 61 5924"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5936">
    <literal><![CDATA[
      (x * y) * K(x \ 1,x * y) = y / R(1 / x,x,y)
    ]]></literal>
    <justification jstring="[para(5437(a,1),4720(a,1,2))].">
      <j1 rule="para" parents="5437 4720"/>
    </justification>
  </clause>

  <clause id="5937">
    <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(1502(a,1),4890(a,2,1,1))].">
      <j1 rule="para" parents="1502 4890"/>
    </justification>
  </clause>

  <clause id="5938">
    <literal><![CDATA[
      T(x \ y,z) \ T((x \ y) * (y \ x),z) = y \ (x * K(z,x \ y))
    ]]></literal>
    <justification jstring="[hyper(58,a,2146,a,b,4957,a)].">
      <j1 rule="hyper" parents="58 2146 4957"/>
    </justification>
  </clause>

  <clause id="5939">
    <literal><![CDATA[
      ((x \ y) * T(x,x \ y)) \ ((y / x) * z) = L(x \ z,T(x,x \ y),x \ y)
    ]]></literal>
    <justification jstring="[para(5449(a,1),5107(a,1,2))].">
      <j1 rule="para" parents="5449 5107"/>
    </justification>
  </clause>

  <clause id="5940">
    <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(5118(a,1),5150(a,1,2))].">
      <j1 rule="para" parents="5118 5150"/>
    </justification>
  </clause>

  <clause id="5941">
    <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,5892,a(flip),b,5232,a)].">
      <j1 rule="hyper" parents="119 5892 5232"/>
    </justification>
  </clause>

  <clause id="5942">
    <literal><![CDATA[
      T(K(x * (y \ 1),y \ 1) / y,x) = R(1 / y,x,1 / y)
    ]]></literal>
    <justification jstring="[para(3975(a,1),5281(a,1,1,1))].">
      <j1 rule="para" parents="3975 5281"/>
    </justification>
  </clause>

  <clause id="5943">
    <literal><![CDATA[
      (L(x,y,z) \ x) / x = 1 / L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,5278,a(flip),b,5306,a),flip(a)].">
      <j1 rule="hyper" parents="58 5278 5306"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5945">
    <literal><![CDATA[
      (1 / L(x,y,z)) * x = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(133,a,5943,a)].">
      <j1 rule="hyper" parents="133 5943"/>
    </justification>
  </clause>

  <clause id="5946">
    <literal><![CDATA[
      x / L(x,y,z) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(58,a,1643,a(flip),b,5945,a)].">
      <j1 rule="hyper" parents="58 1643 5945"/>
    </justification>
  </clause>

  <clause id="5947">
    <literal><![CDATA[
      (L(x,y,z) \ x) * L(x,y,z) = x
    ]]></literal>
    <justification jstring="[para(5945(a,1),1645(a,1,1))].">
      <j1 rule="para" parents="5945 1645"/>
    </justification>
  </clause>

  <clause id="5948">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ x = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(188,a,5946,a)].">
      <j1 rule="hyper" parents="188 5946"/>
    </justification>
  </clause>

  <clause id="5949">
    <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,5946,a)].">
      <j1 rule="hyper" parents="31 265 5946"/>
    </justification>
  </clause>

  <clause id="5950">
    <literal><![CDATA[
      L(x / L(x,y,z),L(x,y,z),z * y) = (z * (y * x)) \ ((z * y) * x)
    ]]></literal>
    <justification jstring="[para(5946(a,2),501(a,1,1))].">
      <j1 rule="para" parents="5946 501"/>
    </justification>
  </clause>

  <clause id="5951">
    <literal><![CDATA[
      x / L(x,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) \ x = u
    ]]></literal>
    <justification jstring="[para(5947(a,1),327(a,1,1)),flip(b)].">
      <j1 rule="para" parents="5947 327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5952">
    <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(5947(a,1),92(a,2,2))].">
      <j1 rule="para" parents="5947 92"/>
    </justification>
  </clause>

  <clause id="5953">
    <literal><![CDATA[
      a(x,y,K(z,u)) * L(K(z,u),y,x) = K(z,u)
    ]]></literal>
    <justification jstring="[para(1932(a,1),5947(a,1,1))].">
      <j1 rule="para" parents="1932 5947"/>
    </justification>
  </clause>

  <clause id="5954">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * y) * z) = T(a(x,y,z),L(z,y,x))
    ]]></literal>
    <justification jstring="[para(5947(a,1),3240(a,1,2,2))].">
      <j1 rule="para" parents="5947 3240"/>
    </justification>
  </clause>

  <clause id="5955">
    <literal><![CDATA[
      a(x \ 1,x,y) * L(y,x,x \ 1) = y
    ]]></literal>
    <justification jstring="[para(4066(a,1),5947(a,1,1))].">
      <j1 rule="para" parents="4066 5947"/>
    </justification>
  </clause>

  <clause id="5956">
    <literal><![CDATA[
      a(x \ 1,x,y) \ y = L(y,x,x \ 1)
    ]]></literal>
    <justification jstring="[para(4066(a,1),5948(a,1,1))].">
      <j1 rule="para" parents="4066 5948"/>
    </justification>
  </clause>

  <clause id="5957">
    <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(5953(a,1),38(a,1)),flip(a)].">
      <j1 rule="para" parents="5953 38"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5958">
    <literal><![CDATA[
      T(a(x,y,z),L(z,y,x)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(691,a,5954,a),flip(a)].">
      <j1 rule="hyper" parents="691 5954"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5959">
    <literal><![CDATA[
      L(T(x,y),x \ T(z,x),x) = T(L(x,x \ z,x),y)
    ]]></literal>
    <justification jstring="[para(4721(a,1),5505(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4721 5505"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5960">
    <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,5959,a),flip(a)].">
      <j1 rule="hyper" parents="320 20 5959"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5961">
    <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(5960(a,1),24(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5960 24"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5962">
    <literal><![CDATA[
      K(x,y / (x / (z \ 1))) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (x * z)) = u
    ]]></literal>
    <justification jstring="[para(5733(a,1),5666(a,1))].">
      <j1 rule="para" parents="5733 5666"/>
    </justification>
  </clause>

  <clause id="5963">
    <literal><![CDATA[
      R(K(x \ y,x),y,z) = K(((x * z) / (y * z)) \ 1,x)
    ]]></literal>
    <justification jstring="[para(5431(a,1),5708(a,1,1))].">
      <j1 rule="para" parents="5431 5708"/>
    </justification>
  </clause>

  <clause id="5964">
    <literal><![CDATA[
      R(K(x \ (y / z),x),y / z,z) = K(((x * z) / y) \ 1,x)
    ]]></literal>
    <justification jstring="[para(7(a,1),5963(a,2,1,1,2))].">
      <j1 rule="para" parents="7 5963"/>
    </justification>
  </clause>

  <clause id="5965">
    <literal><![CDATA[
      K(x / y,z) \ y != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (T(x / y,z) \ x) = w
    ]]></literal>
    <justification jstring="[para(5130(a,2),5778(a,1))].">
      <j1 rule="para" parents="5130 5778"/>
    </justification>
  </clause>

  <clause id="5966">
    <literal><![CDATA[
      K(((x \ 1) \ 1) \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,z) = u
    ]]></literal>
    <justification jstring="[para(3554(a,1),5786(a,1))].">
      <j1 rule="para" parents="3554 5786"/>
    </justification>
  </clause>

  <clause id="5967">
    <literal><![CDATA[
      K((x \ 1) \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K((1 / x) \ y,z) = u
    ]]></literal>
    <justification jstring="[para(75(a,1),5966(a,1,1,1,1))].">
      <j1 rule="para" parents="75 5966"/>
    </justification>
  </clause>

  <clause id="5968">
    <literal><![CDATA[
      K(x * (y \ 1),x) != z
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,x) = z
    ]]></literal>
    <justification jstring="[para(5362(a,1),5966(a,1))].">
      <j1 rule="para" parents="5362 5966"/>
    </justification>
  </clause>

  <clause id="5969">
    <literal><![CDATA[
      R(x,y,z) \ K(R(x,y,z),x \ 1) = 1 / R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(5276,a,5807,a(flip))].">
      <j1 rule="hyper" parents="5276 5807"/>
    </justification>
  </clause>

  <clause id="5970">
    <literal><![CDATA[
      R(x,y,z) * (1 / R(x,y,z)) = K(R(x,y,z),x \ 1)
    ]]></literal>
    <justification jstring="[hyper(134,a,5969,a)].">
      <j1 rule="hyper" parents="134 5969"/>
    </justification>
  </clause>

  <clause id="5971">
    <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(4147(a,1),5820(a,1,1,2))].">
      <j1 rule="para" parents="4147 5820"/>
    </justification>
  </clause>

  <clause id="5972">
    <literal><![CDATA[
      T(K(x * (y \ 1),y \ 1) / y,x) = R(1 / y,x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,3419,a(flip),b,5942,a),flip(a)].">
      <j1 rule="hyper" parents="320 3419 5942"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5973">
    <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(5964(a,2),5668(a,1))].">
      <j1 rule="para" parents="5964 5668"/>
    </justification>
  </clause>

  <clause id="5974">
    <literal><![CDATA[
      (x * y) * K(R(y,x,y),x * y) = ((y * x) / R(y,x,y)) * y
    ]]></literal>
    <justification jstring="[hyper(1889,a,4926,a),flip(a)].">
      <j1 rule="hyper" parents="1889 4926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5975">
    <literal><![CDATA[
      (1 / (1 / x)) / (x * y) = x / (((x \ 1) \ 1) * y)
    ]]></literal>
    <justification jstring="[para(4881(a,1),4949(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4881 4949"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5976">
    <literal><![CDATA[
      (1 / (1 / x)) / (x * (T(x,y) \ 1)) = x / (T(x,y) \ ((x \ 1) \ 1))
    ]]></literal>
    <justification jstring="[para(1711(a,1),5975(a,2,2))].">
      <j1 rule="para" parents="1711 5975"/>
    </justification>
  </clause>

  <clause id="5977">
    <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(4994(a,1),5488(a,1))].">
      <j1 rule="para" parents="4994 5488"/>
    </justification>
  </clause>

  <clause id="5978">
    <literal><![CDATA[
      ((T(x,y) * z) * u) / ((x * z) * u) = K(R(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(512(a,1),5042(a,1,1))].">
      <j1 rule="para" parents="512 5042"/>
    </justification>
  </clause>

  <clause id="5979">
    <literal><![CDATA[
      (K(x,y) * T(K(x,y) \ z,u)) * K(y,x) = T(z * K(y,x),u)
    ]]></literal>
    <justification jstring="[para(5130(a,2),5159(a,1,1,2,1))].">
      <j1 rule="para" parents="5130 5159"/>
    </justification>
  </clause>

  <clause id="5980">
    <literal><![CDATA[
      T((K(x,y) * z) * K(y,x),u) = (K(x,y) * T(z,u)) * K(y,x)
    ]]></literal>
    <justification jstring="[para(5133(a,1),5159(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5133 5159"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5981">
    <literal><![CDATA[
      ((x * y) * z) / ((T(x,u) * y) * z) = K(u,R(x,y,z))
    ]]></literal>
    <justification jstring="[para(512(a,1),5183(a,1,2))].">
      <j1 rule="para" parents="512 5183"/>
    </justification>
  </clause>

  <clause id="5982">
    <literal><![CDATA[
      T(x,y) / (T(x,y) * y) = x / ((y * K(x,y)) * x)
    ]]></literal>
    <justification jstring="[para(4883(a,1),5189(a,1,1))].">
      <j1 rule="para" parents="4883 5189"/>
    </justification>
  </clause>

  <clause id="5983">
    <literal><![CDATA[
      T(x,y) / (T(x,y) * y) = x / (x * y)
    ]]></literal>
    <justification jstring="[para(4774(a,1),5982(a,2,2))].">
      <j1 rule="para" parents="4774 5982"/>
    </justification>
  </clause>

  <clause id="5984">
    <literal><![CDATA[
      (x / (x * y)) \ T(x,y) = T(x,y) * y
    ]]></literal>
    <justification jstring="[hyper(188,a,5983,a)].">
      <j1 rule="hyper" parents="188 5983"/>
    </justification>
  </clause>

  <clause id="5985">
    <literal><![CDATA[
      (x \ K(x,y)) * T((x \ 1) \ 1,z) = K(x,y) * K(x,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,5648,a(flip),b,5267,a),flip(a)].">
      <j1 rule="hyper" parents="320 5648 5267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5986">
    <literal><![CDATA[
      K(x \ 1,x) * (K(x,y) * K(x,z)) = (x \ K(x,y)) * T(x,z)
    ]]></literal>
    <justification jstring="[para(5985(a,1),3701(a,1,2))].">
      <j1 rule="para" parents="5985 3701"/>
    </justification>
  </clause>

  <clause id="5987">
    <literal><![CDATA[
      K((x * y) / (x * (z \ y)),u) = (x * (K(z,u) * y)) / (x * y)
    ]]></literal>
    <justification jstring="[para(5100(a,1),5298(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5100 5298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5988">
    <literal><![CDATA[
      ((x \ T(x * (y / z),u)) * z) / y = K((((x \ 1) * z) / y) \ 1,u)
    ]]></literal>
    <justification jstring="[para(1600(a,1),5530(a,1,1))].">
      <j1 rule="para" parents="1600 5530"/>
    </justification>
  </clause>

  <clause id="5989">
    <literal><![CDATA[
      x * K((x \ (y * z)) \ 1,z) = y * ((z \ (y \ x)) * z)
    ]]></literal>
    <justification jstring="[para(105(a,1),5538(a,2,2))].">
      <j1 rule="para" parents="105 5538"/>
    </justification>
  </clause>

  <clause id="5990">
    <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),5538(a,2,2,2,1))].">
      <j1 rule="para" parents="62 5538"/>
    </justification>
  </clause>

  <clause id="5991">
    <literal><![CDATA[
      T(x \ y,x) / ((x \ 1) \ (x \ y)) = (x \ y) / ((x \ 1) \ (y / x))
    ]]></literal>
    <justification jstring="[para(5557(a,1),4499(a,2,2))].">
      <j1 rule="para" parents="5557 4499"/>
    </justification>
  </clause>

  <clause id="5992">
    <literal><![CDATA[
      K(x,y * ((z \ L(u,1 / z,z)) * w)) = K(x,y * (((1 / z) * u) * w))
    ]]></literal>
    <justification jstring="[para(2831(a,1),5661(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="2831 5661"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5993">
    <literal><![CDATA[
      K(x,(T(y \ z,z) / z) \ 1) = T(K(x,y) * z,z) / z
    ]]></literal>
    <justification jstring="[para(5463(a,1),5727(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5463 5727"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5994">
    <literal><![CDATA[
      K(x,(T(y \ z,z) / z) \ 1) = z \ T(z * K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(320,a,4576,a(flip),b,5993,a),flip(a)].">
      <j1 rule="hyper" parents="320 4576 5993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5995">
    <literal><![CDATA[
      K(x,y / T(z \ y,y)) = y \ T(y * K(x,z),y)
    ]]></literal>
    <justification jstring="[hyper(5428,a,5994,a)].">
      <j1 rule="hyper" parents="5428 5994"/>
    </justification>
  </clause>

  <clause id="5996">
    <literal><![CDATA[
      K(x,T(y / z,y) \ y) = y \ T(y * K(x,z),y)
    ]]></literal>
    <justification jstring="[para(4504(a,1),5995(a,1,2))].">
      <j1 rule="para" parents="4504 5995"/>
    </justification>
  </clause>

  <clause id="5997">
    <literal><![CDATA[
      K(x,y) * (K(y,x) * T(K(y,x) \ z,u)) = T(K(x,y) * z,u)
    ]]></literal>
    <justification jstring="[para(5054(a,2),5737(a,1,2))].">
      <j1 rule="para" parents="5054 5737"/>
    </justification>
  </clause>

  <clause id="5998">
    <literal><![CDATA[
      T(K(x,y) * (z * K(y,x)),u) = K(x,y) * (T(z,u) * K(y,x))
    ]]></literal>
    <justification jstring="[para(5539(a,1),5737(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5539 5737"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5999">
    <literal><![CDATA[
      (x * (1 / y)) * (x / (x * (1 / y))) = x * K(y \ x,y)
    ]]></literal>
    <justification jstring="[para(5858(a,1),5740(a,2,2))].">
      <j1 rule="para" parents="5858 5740"/>
    </justification>
  </clause>

  <clause id="6000">
    <literal><![CDATA[
      (x * (1 / y)) * (x / (x * (1 / y))) = (y \ x) * y
    ]]></literal>
    <justification jstring="[hyper(320,a,302,a(flip),b,5999,a),flip(a)].">
      <j1 rule="hyper" parents="320 302 5999"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6001">
    <literal><![CDATA[
      (1 / x) * (K(x,y) * ((1 / x) \ z)) = K(x,y) * z
    ]]></literal>
    <justification jstring="[para(75(a,1),5758(a,2,1,1))].">
      <j1 rule="para" parents="75 5758"/>
    </justification>
  </clause>

  <clause id="6002">
    <literal><![CDATA[
      (x \ 1) * (K(x,y) * ((x \ 1) \ z)) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(58,a,3473,a(flip),b,6001,a)].">
      <j1 rule="hyper" parents="58 3473 6001"/>
    </justification>
  </clause>

  <clause id="6003">
    <literal><![CDATA[
      K(x,y) * ((1 / x) * z) = (1 / x) * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(4(a,1),6001(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 6001"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6005">
    <literal><![CDATA[
      K(x,y) * ((x \ 1) * z) = (x \ 1) * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(4(a,1),6002(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 6002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6006">
    <literal><![CDATA[
      (x \ 1) * (K(x,y) * T(z,x \ 1)) = K(x,y) * (z * (x \ 1))
    ]]></literal>
    <justification jstring="[para(17(a,2),6002(a,1,2,2))].">
      <j1 rule="para" parents="17 6002"/>
    </justification>
  </clause>

  <clause id="6007">
    <literal><![CDATA[
      (K(x,y) * z) \ (K(x,y) * ((1 / x) * z)) = T(1 / x,K(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(439,a,6003,a,b,xx),flip(a)].">
      <j1 rule="hyper" parents="439 6003"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6008">
    <literal><![CDATA[
      (1 / x) * (K(x,y) * ((1 / x) \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * z = u
    ]]></literal>
    <justification jstring="[para(6003(a,1),342(a,1))].">
      <j1 rule="para" parents="6003 342"/>
    </justification>
  </clause>

  <clause id="6009">
    <literal><![CDATA[
      x * (K(x,y) * ((x \ 1) * z)) = L(K(x,y) * z,x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,6005,a,b,437,a)].">
      <j1 rule="hyper" parents="119 6005 437"/>
    </justification>
  </clause>

  <clause id="6010">
    <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),6005(a,2,2))].">
      <j1 rule="para" parents="105 6005"/>
    </justification>
  </clause>

  <clause id="6011">
    <literal><![CDATA[
      ((x \ 1) * y) / ((x \ 1) * (K(x,z) * y)) = K(z,x)
    ]]></literal>
    <justification jstring="[para(6005(a,1),5142(a,1,2))].">
      <j1 rule="para" parents="6005 5142"/>
    </justification>
  </clause>

  <clause id="6012">
    <literal><![CDATA[
      ((x \ 1) * (K(y,x) * z)) / ((x \ 1) * z) = K(y,x)
    ]]></literal>
    <justification jstring="[para(5133(a,1),6011(a,1,2,2))].">
      <j1 rule="para" parents="5133 6011"/>
    </justification>
  </clause>

  <clause id="6013">
    <literal><![CDATA[
      L(K(x,y) * z,x \ 1,x) = T(x,y) * ((x \ 1) * z)
    ]]></literal>
    <justification jstring="[hyper(5084,a,6009,a),flip(a)].">
      <j1 rule="hyper" parents="5084 6009"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6014">
    <literal><![CDATA[
      T(x,y) * ((x \ 1) * (K(y,x) * z)) = L(z,x \ 1,x)
    ]]></literal>
    <justification jstring="[para(5133(a,1),6013(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5133 6013"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6015">
    <literal><![CDATA[
      x \ ((x \ L(x,y,x)) * T(x,z)) = R(x,y,x) \ T(x,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,2129,a(flip),b,5777,a),flip(a)].">
      <j1 rule="hyper" parents="320 2129 5777"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6016">
    <literal><![CDATA[
      x \ (K(x,y) * L(x,z,x)) = R(x,z,x) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(5104(a,1),6015(a,1,2))].">
      <j1 rule="para" parents="5104 6015"/>
    </justification>
  </clause>

  <clause id="6017">
    <literal><![CDATA[
      (1 / x) \ (1 / R(x,y,z)) = (x \ 1) \ (R(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(3027,a,5809,a)].">
      <j1 rule="hyper" parents="3027 5809"/>
    </justification>
  </clause>

  <clause id="6018">
    <literal><![CDATA[
      (1 / x) \ (1 / R(x,y,z)) = (x \ R(x,y,z)) \ 1
    ]]></literal>
    <justification jstring="[hyper(320,a,3611,a(flip),b,6017,a),flip(a)].">
      <j1 rule="hyper" parents="320 3611 6017"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6019">
    <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(4331(a,1),5875(a,1,2))].">
      <j1 rule="para" parents="4331 5875"/>
    </justification>
  </clause>

  <clause id="6020">
    <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(4331(a,1),5877(a,1,2))].">
      <j1 rule="para" parents="4331 5877"/>
    </justification>
  </clause>

  <clause id="6021">
    <literal><![CDATA[
      K((x \ (y / (z \ 1))) \ 1,y) = K((x \ (y * z)) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,5531,a(flip),b,5887,a),flip(a)].">
      <j1 rule="hyper" parents="320 5531 5887"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6022">
    <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(5687(a,1),5898(a,1,1))].">
      <j1 rule="para" parents="5687 5898"/>
    </justification>
  </clause>

  <clause id="6023">
    <literal><![CDATA[
      K((x * ((1 / y) \ 1)) \ 1,z) / y = (1 / y) * K(((1 / y) \ x) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(353,a,5903,a)].">
      <j1 rule="hyper" parents="353 5903"/>
    </justification>
  </clause>

  <clause id="6024">
    <literal><![CDATA[
      ((1 / x) * T((1 / x) \ y,z)) * (y \ 1) = (1 / x) * (y \ T(y * x,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,5712,a,b,5904,a)].">
      <j1 rule="hyper" parents="58 5712 5904"/>
    </justification>
  </clause>

  <clause id="6025">
    <literal><![CDATA[
      K(((x \ 1) * (y \ 1)) \ 1,z) = (1 / x) * (y \ T(y * x,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,3989,a(flip),b,5904,a)].">
      <j1 rule="hyper" parents="58 3989 5904"/>
    </justification>
  </clause>

  <clause id="6026">
    <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(5923(a,2),2168(a,1,1,1,1))].">
      <j1 rule="para" parents="5923 2168"/>
    </justification>
  </clause>

  <clause id="6027">
    <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(5130(a,1),5923(a,1,1))].">
      <j1 rule="para" parents="5130 5923"/>
    </justification>
  </clause>

  <clause id="6028">
    <literal><![CDATA[
      ((x \ y) \ 1) \ ((y \ x) * y) = x / ((x \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(72(a,1),5926(a,1,1)),flip(a)].">
      <j1 rule="para" parents="72 5926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6030">
    <literal><![CDATA[
      x / ((x \ L(x,y,z)) \ 1) = ((x \ L(x,y,z)) \ 1) \ x
    ]]></literal>
    <justification jstring="[para(5947(a,1),6028(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5947 6028"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6031">
    <literal><![CDATA[
      ((x * y) / R(x,y,x)) * x = (y * x) * K(T(x,y),y * x)
    ]]></literal>
    <justification jstring="[para(4966(a,1),5974(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4966 5974"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6032">
    <literal><![CDATA[
      ((x * y) / R(x,y,x)) * x = T(x,y * x) * T(y,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,4917,a(flip),b,6031,a),flip(a)].">
      <j1 rule="hyper" parents="320 4917 6031"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6033">
    <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),6032(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5 6032"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6034">
    <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(5979(a,1),39(a,1))].">
      <j1 rule="para" parents="5979 39"/>
    </justification>
  </clause>

  <clause id="6035">
    <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(5980(a,2),39(a,1))].">
      <j1 rule="para" parents="5980 39"/>
    </justification>
  </clause>

  <clause id="6036">
    <literal><![CDATA[
      (K(x,y) * K(x,z)) \ K(x,x \ 1) = ((x \ K(x,y)) * T(x,z)) \ 1
    ]]></literal>
    <justification jstring="[para(5986(a,1),3726(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5986 3726"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6037">
    <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(5986(a,1),4022(a,1,2))].">
      <j1 rule="para" parents="5986 4022"/>
    </justification>
  </clause>

  <clause id="6038">
    <literal><![CDATA[
      K(x,(y * z) / (y * (u \ z))) * (y * (K(u,x) * z)) = y * z
    ]]></literal>
    <justification jstring="[hyper(5168,a,5987,a)].">
      <j1 rule="hyper" parents="5168 5987"/>
    </justification>
  </clause>

  <clause id="6039">
    <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(5664,a,5997,a)].">
      <j1 rule="hyper" parents="5664 5997"/>
    </justification>
  </clause>

  <clause id="6040">
    <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,4987,a,b,6039,a)].">
      <j1 rule="hyper" parents="58 4987 6039"/>
    </justification>
  </clause>

  <clause id="6041">
    <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(5998(a,2),38(a,1))].">
      <j1 rule="para" parents="5998 38"/>
    </justification>
  </clause>

  <clause id="6042">
    <literal><![CDATA[
      K((((x \ y) \ 1) * (x \ 1)) \ 1,z) = (1 / (x \ y)) * (x \ T(y,z))
    ]]></literal>
    <justification jstring="[para(5(a,1),6025(a,2,2,2,1))].">
      <j1 rule="para" parents="5 6025"/>
    </justification>
  </clause>

  <clause id="6043">
    <literal><![CDATA[
      1 / ((1 / x) * (y \ T(y * x,z))) = K(z,((x \ 1) * (y \ 1)) \ 1)
    ]]></literal>
    <justification jstring="[para(6025(a,1),4971(a,1,2))].">
      <j1 rule="para" parents="6025 4971"/>
    </justification>
  </clause>

  <clause id="6044">
    <literal><![CDATA[
      K(x,(y * z) / (y * (u \ z))) = (y * z) / (y * (K(u,x) * z))
    ]]></literal>
    <justification jstring="[hyper(131,a,6038,a),flip(a)].">
      <j1 rule="hyper" parents="131 6038"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6045">
    <literal><![CDATA[
      K(x,y) * (R(y,z,u) * (K(y,x) * w)) = R(y,z,u) * w
    ]]></literal>
    <justification jstring="[para(1313(a,1),6038(a,1,1,2))].">
      <j1 rule="para" parents="1313 6038"/>
    </justification>
  </clause>

  <clause id="6046">
    <literal><![CDATA[
      R(x,y,z) * (K(u,x) * w) = K(u,x) * (R(x,y,z) * w)
    ]]></literal>
    <justification jstring="[para(5133(a,1),6045(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5133 6045"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6047">
    <literal><![CDATA[
      K(x,y) * (R(y,z,u) * (y \ w)) = R(y,z,u) * (T(y,x) \ w)
    ]]></literal>
    <justification jstring="[para(5081(a,1),6045(a,1,2,2))].">
      <j1 rule="para" parents="5081 6045"/>
    </justification>
  </clause>

  <clause id="6048">
    <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(6040(a,1),38(a,1))].">
      <j1 rule="para" parents="6040 38"/>
    </justification>
  </clause>

  <clause id="6049">
    <literal><![CDATA[
      (x * y) * L((z \ (y \ z)) * z,y,x) = (x * K(y \ 1,z)) * z
    ]]></literal>
    <justification jstring="[para(3531(a,2),5065(a,1,2))].">
      <j1 rule="para" parents="3531 5065"/>
    </justification>
  </clause>

  <clause id="6050">
    <literal><![CDATA[
      K(1 / x,x) / L(x,y,z) = (x / L(x,y,z)) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(3394(a,1),5070(a,1,1))].">
      <j1 rule="para" parents="3394 5070"/>
    </justification>
  </clause>

  <clause id="6051">
    <literal><![CDATA[
      (x / L(x,y,z)) * (x \ 1) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(58,a,3552,a(flip),b,6050,a),flip(a)].">
      <j1 rule="hyper" parents="58 3552 6050"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6053">
    <literal><![CDATA[
      (L(x,y,z) \ x) * (x \ 1) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(5946(a,1),6051(a,1,1))].">
      <j1 rule="para" parents="5946 6051"/>
    </justification>
  </clause>

  <clause id="6054">
    <literal><![CDATA[
      (L(1 / x,y,z) \ 1) / x = L(1 / x,y,z) \ (1 / x)
    ]]></literal>
    <justification jstring="[hyper(353,a,6053,a)].">
      <j1 rule="hyper" parents="353 6053"/>
    </justification>
  </clause>

  <clause id="6055">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ (L(x,y,z) \ 1) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(123,a,6053,a)].">
      <j1 rule="hyper" parents="123 6053"/>
    </justification>
  </clause>

  <clause id="6056">
    <literal><![CDATA[
      (L(1 / x,y,z) \ 1) / x = x \ (L(1 / x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,3791,a(flip),b,6054,a),flip(a)].">
      <j1 rule="hyper" parents="320 3791 6054"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6057">
    <literal><![CDATA[
      T(x,x \ (L(x \ 1,y,z) \ 1)) = x
    ]]></literal>
    <justification jstring="[hyper(31,a,3817,a,b,6056,a)].">
      <j1 rule="hyper" parents="31 3817 6056"/>
    </justification>
  </clause>

  <clause id="6058">
    <literal><![CDATA[
      T(x,x \ (((y * x) \ y) \ 1)) = x
    ]]></literal>
    <justification jstring="[para(217(a,1),6057(a,1,2,2,1))].">
      <j1 rule="para" parents="217 6057"/>
    </justification>
  </clause>

  <clause id="6059">
    <literal><![CDATA[
      (1 / ((x * y) \ x)) / y = y \ (1 / ((x * y) \ x))
    ]]></literal>
    <justification jstring="[para(6058(a,1),3784(a,1,2))].">
      <j1 rule="para" parents="6058 3784"/>
    </justification>
  </clause>

  <clause id="6060">
    <literal><![CDATA[
      (((x * y) \ x) \ 1) / ((y \ 1) \ 1) = y \ (1 / ((x * y) \ x))
    ]]></literal>
    <justification jstring="[hyper(58,a,3842,a,b,6059,a)].">
      <j1 rule="hyper" parents="58 3842 6059"/>
    </justification>
  </clause>

  <clause id="6061">
    <literal><![CDATA[
      L(T(x \ 1,y) \ z,x \ 1,x) = K(y,x \ 1) * (x * z)
    ]]></literal>
    <justification jstring="[hyper(320,a,5932,a(flip),b,5179,a),flip(a)].">
      <j1 rule="hyper" parents="320 5932 5179"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6062">
    <literal><![CDATA[
      (1 / x) * (L(x,y,z) \ x) = 1 / L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,5278,a(flip),b,5277,a),flip(a)].">
      <j1 rule="hyper" parents="58 5278 5277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6063">
    <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,5694,a),flip(a)].">
      <j1 rule="hyper" parents="320 179 5694"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6065">
    <literal><![CDATA[
      K(L(x,y,z) \ 1,x \ L(x,u,w)) = 1
    ]]></literal>
    <justification jstring="[para(1193(a,1),6063(a,1,2))].">
      <j1 rule="para" parents="1193 6063"/>
    </justification>
  </clause>

  <clause id="6066">
    <literal><![CDATA[
      T(x \ L(x,y,z),L(x,u,w) \ 1) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(4953,a,6065,a)].">
      <j1 rule="hyper" parents="4953 6065"/>
    </justification>
  </clause>

  <clause id="6067">
    <literal><![CDATA[
      T(L(x,y,z) * (x \ 1),L(x,u,w) \ 1) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[para(1194(a,2),6066(a,1,1))].">
      <j1 rule="para" parents="1194 6066"/>
    </justification>
  </clause>

  <clause id="6068">
    <literal><![CDATA[
      (L(x,y,z) * (x \ 1)) \ (x \ 1) = (x \ 1) / (x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[para(6067(a,1),4193(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6067 4193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6069">
    <literal><![CDATA[
      (L(x,y,z) * (x \ 1)) \ (x \ 1) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(320,a,3228,a(flip),b,6068,a),flip(a)].">
      <j1 rule="hyper" parents="320 3228 6068"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6070">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ (x \ 1) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(1194(a,1),6069(a,1,1))].">
      <j1 rule="para" parents="1194 6069"/>
    </justification>
  </clause>

  <clause id="6071">
    <literal><![CDATA[
      (x \ 1) * (L(x,y,z) \ x) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(58,a,3586,a(flip),b,6070,a)].">
      <j1 rule="hyper" parents="58 3586 6070"/>
    </justification>
  </clause>

  <clause id="6072">
    <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(6070(a,1),1699(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6070 1699"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6073">
    <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(6070(a,1),3532(a,2,2,1))].">
      <j1 rule="para" parents="6070 3532"/>
    </justification>
  </clause>

  <clause id="6074">
    <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(6070(a,1),5054(a,2,2,1,1)),flip(a)].">
      <j1 rule="para" parents="6070 5054"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6075">
    <literal><![CDATA[
      T(L(x,y,z) \ x,x \ 1) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(239,a,6053,a,b,6071,a)].">
      <j1 rule="hyper" parents="239 6053 6071"/>
    </justification>
  </clause>

  <clause id="6076">
    <literal><![CDATA[
      (x / R(y,y \ x,y)) * y = T(y,x) * T(y \ x,y)
    ]]></literal>
    <justification jstring="[para(4311(a,1),6033(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4311 6033"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6077">
    <literal><![CDATA[
      (x / R(y,y \ x,y)) * y = (y \ x) * T(y,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,4132,a(flip),b,6076,a),flip(a)].">
      <j1 rule="hyper" parents="320 4132 6076"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6078">
    <literal><![CDATA[
      x / R(y,y \ x,y) = y \ (x * K(y,x))
    ]]></literal>
    <justification jstring="[hyper(30,a,4944,a,b,6077,a),flip(a)].">
      <j1 rule="hyper" parents="30 4944 6077"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6079">
    <literal><![CDATA[
      x / R(y,y \ x,y) = (y * K(x,y)) \ x
    ]]></literal>
    <justification jstring="[hyper(320,a,5376,a,b,6078,a),flip(a)].">
      <j1 rule="hyper" parents="320 5376 6078"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6080">
    <literal><![CDATA[
      x / R(y,y \ x,y) = K(y,x) * (y \ x)
    ]]></literal>
    <justification jstring="[hyper(320,a,5187,a(flip),b,6078,a),flip(a)].">
      <j1 rule="hyper" parents="320 5187 6078"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6081">
    <literal><![CDATA[
      x / ((y \ x) \ T(x,y)) = (y * K(x,y)) \ x
    ]]></literal>
    <justification jstring="[para(4335(a,1),6079(a,1,2))].">
      <j1 rule="para" parents="4335 6079"/>
    </justification>
  </clause>

  <clause id="6082">
    <literal><![CDATA[
      ((x * K(y,x)) \ y) \ y = (x \ y) \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(188,a,6081,a)].">
      <j1 rule="hyper" parents="188 6081"/>
    </justification>
  </clause>

  <clause id="6083">
    <literal><![CDATA[
      (x \ (y * K(x,y))) \ y = (x \ y) \ T(y,x)
    ]]></literal>
    <justification jstring="[para(5376(a,1),6082(a,1,1))].">
      <j1 rule="para" parents="5376 6082"/>
    </justification>
  </clause>

  <clause id="6084">
    <literal><![CDATA[
      (x \ ((x * y) / x)) \ y = (x \ y) \ T(y,x)
    ]]></literal>
    <justification jstring="[para(4752(a,2),6083(a,1,1,2))].">
      <j1 rule="para" parents="4752 6083"/>
    </justification>
  </clause>

  <clause id="6085">
    <literal><![CDATA[
      x * (y * ((z \ (y \ z)) * z)) = (x * K(y \ 1,z)) * z
    ]]></literal>
    <justification jstring="[hyper(286,a,6049,a)].">
      <j1 rule="hyper" parents="286 6049"/>
    </justification>
  </clause>

  <clause id="6086">
    <literal><![CDATA[
      (x * K(y \ 1,z)) * z = x * (z * K(y \ 1,z))
    ]]></literal>
    <justification jstring="[para(5068(a,1),6085(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5068 6085"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6087">
    <literal><![CDATA[
      R(x,K(y \ 1,z),z) = x
    ]]></literal>
    <justification jstring="[hyper(2916,a,6086,a)].">
      <j1 rule="hyper" parents="2916 6086"/>
    </justification>
  </clause>

  <clause id="6088">
    <literal><![CDATA[
      R(x,K(y,z),z) = x
    ]]></literal>
    <justification jstring="[para(75(a,1),6087(a,1,2,1))].">
      <j1 rule="para" parents="75 6087"/>
    </justification>
  </clause>

  <clause id="6089">
    <literal><![CDATA[
      R(x,y,K(z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(5812,a,6088,a)].">
      <j1 rule="hyper" parents="5812 6088"/>
    </justification>
  </clause>

  <clause id="6090">
    <literal><![CDATA[
      (x * K(y,z)) * z = x * (z * K(y,z))
    ]]></literal>
    <justification jstring="[para(6088(a,1),2915(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6088 2915"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6091">
    <literal><![CDATA[
      (x * y) * K(z,y) = x * (y * K(z,y))
    ]]></literal>
    <justification jstring="[para(6089(a,1),101(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6089 101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6092">
    <literal><![CDATA[
      (x * (y * K(z,y))) / y = x * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(131,a,6090,a)].">
      <j1 rule="hyper" parents="131 6090"/>
    </justification>
  </clause>

  <clause id="6093">
    <literal><![CDATA[
      (x / ((y * z) / y)) * K(y,z) = x / z
    ]]></literal>
    <justification jstring="[hyper(117,a,4921,a(flip),b,6090,a),flip(a)].">
      <j1 rule="hyper" parents="117 4921 6090"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6094">
    <literal><![CDATA[
      L(K(x,y),y,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(479,a,6091,a)].">
      <j1 rule="hyper" parents="479 6091"/>
    </justification>
  </clause>

  <clause id="6095">
    <literal><![CDATA[
      (x / y) * (y * K(z,y)) = x * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(326,a,6091,a),flip(a)].">
      <j1 rule="hyper" parents="326 6091"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6096">
    <literal><![CDATA[
      (x * K(y,z)) * z = (x * z) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,6090,a,b,6091,a)].">
      <j1 rule="hyper" parents="320 6090 6091"/>
    </justification>
  </clause>

  <clause id="6097">
    <literal><![CDATA[
      (x * y) * K(z,y) = x * ((z * y) / z)
    ]]></literal>
    <justification jstring="[hyper(320,a,4897,a,b,6091,a),flip(a)].">
      <j1 rule="hyper" parents="320 4897 6091"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6098">
    <literal><![CDATA[
      (x / (y * K(z,y))) * y = x / K(z,y)
    ]]></literal>
    <justification jstring="[hyper(117,a,7,a(flip),b,6091,a),flip(a)].">
      <j1 rule="hyper" parents="117 7 6091"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6099">
    <literal><![CDATA[
      a(x,y,K(z,y)) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,6091,a(flip),b,80,a),flip(a)].">
      <j1 rule="hyper" parents="115 6091 80"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6101">
    <literal><![CDATA[
      (x * (y \ z)) * K(y,y \ z) = x * (z / y)
    ]]></literal>
    <justification jstring="[para(4776(a,1),6091(a,2,2))].">
      <j1 rule="para" parents="4776 6091"/>
    </justification>
  </clause>

  <clause id="6102">
    <literal><![CDATA[
      L(K(x,y),x,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(5893,a,6099,a)].">
      <j1 rule="hyper" parents="5893 6099"/>
    </justification>
  </clause>

  <clause id="6103">
    <literal><![CDATA[
      a(x,1,y) = a(z,u,K(w,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,375,a,b,6099,a)].">
      <j1 rule="hyper" parents="320 375 6099"/>
    </justification>
  </clause>

  <clause id="6104">
    <literal><![CDATA[
      L(K(x,y),x,z) = K(y,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(116,a,6099,a(flip),b,5892,a),flip(a)].">
      <j1 rule="hyper" parents="116 6099 5892"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6105">
    <literal><![CDATA[
      a(x,T(y,z),K(z,y)) = 1
    ]]></literal>
    <justification jstring="[para(4158(a,1),6099(a,1,3))].">
      <j1 rule="para" parents="4158 6099"/>
    </justification>
  </clause>

  <clause id="6106">
    <literal><![CDATA[
      L(K(x,y),y,z) = L(K(x,y),y,u)
    ]]></literal>
    <justification jstring="[hyper(320,a,6094,a,b,6094,a)].">
      <j1 rule="hyper" parents="320 6094 6094"/>
    </justification>
  </clause>

  <clause id="6108">
    <literal><![CDATA[
      K(x,(y \ z) \ 1) = K(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,5681,a(flip),b,6094,a)].">
      <j1 rule="hyper" parents="58 5681 6094"/>
    </justification>
  </clause>

  <clause id="6110">
    <literal><![CDATA[
      K(L(x \ 1,x,y) \ 1,z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(5810,a,6102,a)].">
      <j1 rule="hyper" parents="5810 6102"/>
    </justification>
  </clause>

  <clause id="6111">
    <literal><![CDATA[
      x \ (y * T(y \ x,z)) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(4768,a,6102,a)].">
      <j1 rule="hyper" parents="4768 6102"/>
    </justification>
  </clause>

  <clause id="6112">
    <literal><![CDATA[
      L(K(x,y),x,z) = K(u \ (u * x),y)
    ]]></literal>
    <justification jstring="[hyper(320,a,673,a,b,6102,a),flip(a)].">
      <j1 rule="hyper" parents="320 673 6102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6114">
    <literal><![CDATA[
      x * T(x \ y,z) = y * K(x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(119,a,6102,a(flip),b,4767,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 6102 4767"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6115">
    <literal><![CDATA[
      (x * y) * K(y,z) = x * (y * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(119,a,6102,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="119 6102 13"/>
    </justification>
  </clause>

  <clause id="6116">
    <literal><![CDATA[
      (x * y) * K(y,z) = x * T(y,z)
    ]]></literal>
    <justification jstring="[para(6102(a,1),4831(a,1,2))].">
      <j1 rule="para" parents="6102 4831"/>
    </justification>
  </clause>

  <clause id="6117">
    <literal><![CDATA[
      L(K(x,y),T(y,x),z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(47,a,6105,a)].">
      <j1 rule="hyper" parents="47 6105"/>
    </justification>
  </clause>

  <clause id="6118">
    <literal><![CDATA[
      L(K(x,y),x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(6104(a,2),4985(a,1))].">
      <j1 rule="para" parents="6104 4985"/>
    </justification>
  </clause>

  <clause id="6119">
    <literal><![CDATA[
      L(K(x,y),T(y,x),z) \ u = T(y,x) * (y \ u)
    ]]></literal>
    <justification jstring="[para(6117(a,2),4788(a,2,1)),flip(a)].">
      <j1 rule="para" parents="6117 4788"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6121">
    <literal><![CDATA[
      L(K(x,y \ z),y \ z,u) = K(x,(z \ y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,5681,a(flip),b,6106,a),flip(a)].">
      <j1 rule="hyper" parents="320 5681 6106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6122">
    <literal><![CDATA[
      L(K(x,y),y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(6106(a,1),3666(a,1))].">
      <j1 rule="para" parents="6106 3666"/>
    </justification>
  </clause>

  <clause id="6123">
    <literal><![CDATA[
      K(x,1 / (y \ z)) = K(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(5495,a,6108,a)].">
      <j1 rule="hyper" parents="5495 6108"/>
    </justification>
  </clause>

  <clause id="6124">
    <literal><![CDATA[
      K((x \ y) \ 1,(y \ x) \ 1) = K(y \ x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(320,a,2583,a(flip),b,6108,a),flip(a)].">
      <j1 rule="hyper" parents="320 2583 6108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6125">
    <literal><![CDATA[
      T(x,(y \ z) \ 1) = T(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(118,a,6108,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 6108 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6126">
    <literal><![CDATA[
      T(K(x,y / z),y) = K(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,5745,a,b,6108,a)].">
      <j1 rule="hyper" parents="58 5745 6108"/>
    </justification>
  </clause>

  <clause id="6127">
    <literal><![CDATA[
      K(x,(y * z) \ y) = K(x,z \ 1)
    ]]></literal>
    <justification jstring="[para(4(a,1),6108(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4 6108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6129">
    <literal><![CDATA[
      K(x,((y * z) * u) \ (y * (z * u))) = K(x,a(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(9(a,2),6108(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 6108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6131">
    <literal><![CDATA[
      K(x,(y \ (y / z)) \ 1) = K(x,z)
    ]]></literal>
    <justification jstring="[para(75(a,1),6108(a,2,2))].">
      <j1 rule="para" parents="75 6108"/>
    </justification>
  </clause>

  <clause id="6132">
    <literal><![CDATA[
      K(x,L(y \ z,y,u) \ 1) = K(x,(u * z) \ (u * y))
    ]]></literal>
    <justification jstring="[para(92(a,2),6108(a,1,2,1))].">
      <j1 rule="para" parents="92 6108"/>
    </justification>
  </clause>

  <clause id="6133">
    <literal><![CDATA[
      K(x,R(y,z,z \ 1) \ y) = K(x,a(y,z,z \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(705(a,1),6108(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="705 6108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6134">
    <literal><![CDATA[
      K(x,(T(y,z) * (y \ u)) \ 1) = K(x,(T(y,z) * u) \ y)
    ]]></literal>
    <justification jstring="[para(1109(a,1),6108(a,1,2,1))].">
      <j1 rule="para" parents="1109 6108"/>
    </justification>
  </clause>

  <clause id="6137">
    <literal><![CDATA[
      (((x \ y) \ 1) \ z) * ((x \ y) \ 1) = z * K((x \ y) * z,y \ x)
    ]]></literal>
    <justification jstring="[para(6108(a,1),4490(a,2,2))].">
      <j1 rule="para" parents="6108 4490"/>
    </justification>
  </clause>

  <clause id="6138">
    <literal><![CDATA[
      K((x \ y) \ 1,z) = K(z,y \ x) \ 1
    ]]></literal>
    <justification jstring="[para(6108(a,1),4969(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6108 4969"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6139">
    <literal><![CDATA[
      K(x,(T(y,z) * (y \ u)) \ 1) = K(x,u \ K(z,y))
    ]]></literal>
    <justification jstring="[para(4788(a,2),6108(a,1,2,1))].">
      <j1 rule="para" parents="4788 6108"/>
    </justification>
  </clause>

  <clause id="6140">
    <literal><![CDATA[
      K(x,(K(y,z) * u) \ 1) = K(x,u \ K(z,y))
    ]]></literal>
    <justification jstring="[para(5130(a,1),6108(a,1,2,1))].">
      <j1 rule="para" parents="5130 6108"/>
    </justification>
  </clause>

  <clause id="6141">
    <literal><![CDATA[
      K(x,(y \ K(z,u)) \ 1) = K(x,K(u,z) * y)
    ]]></literal>
    <justification jstring="[para(5130(a,1),6108(a,2,2))].">
      <j1 rule="para" parents="5130 6108"/>
    </justification>
  </clause>

  <clause id="6142">
    <literal><![CDATA[
      K(x,(K(y,z) * u) \ 1) = K(x,(z * u) \ T(z,y))
    ]]></literal>
    <justification jstring="[para(5175(a,1),6108(a,1,2,1))].">
      <j1 rule="para" parents="5175 6108"/>
    </justification>
  </clause>

  <clause id="6143">
    <literal><![CDATA[
      K(x,y \ z) * K(x * ((z \ y) \ 1),x) = x \ R(x,(z \ y) \ 1,x)
    ]]></literal>
    <justification jstring="[para(6108(a,1),5293(a,1,1))].">
      <j1 rule="para" parents="6108 5293"/>
    </justification>
  </clause>

  <clause id="6144">
    <literal><![CDATA[
      K(x,L(y \ z,u,w) \ 1) = L(K(x,z \ y),u,w)
    ]]></literal>
    <justification jstring="[para(6108(a,1),5675(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6108 5675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6145">
    <literal><![CDATA[
      x * K(y,z \ x) = z * ((y * (z \ x)) / y)
    ]]></literal>
    <justification jstring="[para(6108(a,1),4750(a,1,2))].">
      <j1 rule="para" parents="6108 4750"/>
    </justification>
  </clause>

  <clause id="6146">
    <literal><![CDATA[
      T(x,y) != K(z,u \ y)
    ]]></literal>
    <literal><![CDATA[
      K(z,y / u) = x
    ]]></literal>
    <justification jstring="[para(6108(a,1),5746(a,2))].">
      <j1 rule="para" parents="6108 5746"/>
    </justification>
  </clause>

  <clause id="6147">
    <literal><![CDATA[
      x \ (y * K(x \ y,z)) = T(x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(614,a,6116,a)].">
      <j1 rule="hyper" parents="614 6116"/>
    </justification>
  </clause>

  <clause id="6148">
    <literal><![CDATA[
      (x * K(y,z)) / T(y,z) = x / y
    ]]></literal>
    <justification jstring="[hyper(596,a,6116,a)].">
      <j1 rule="hyper" parents="596 6116"/>
    </justification>
  </clause>

  <clause id="6149">
    <literal><![CDATA[
      (x / y) \ (x * K(y,z)) = T(y,z)
    ]]></literal>
    <justification jstring="[hyper(571,a,6116,a)].">
      <j1 rule="hyper" parents="571 6116"/>
    </justification>
  </clause>

  <clause id="6150">
    <literal><![CDATA[
      K(x,y) \ (z * T(x,y)) = T(z * x,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(439,a,xx,b,6116,a),flip(a)].">
      <j1 rule="hyper" parents="439 6116"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6151">
    <literal><![CDATA[
      (x / y) * T(y,z) = x * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(326,a,6116,a),flip(a)].">
      <j1 rule="hyper" parents="326 6116"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6153">
    <literal><![CDATA[
      K(x,y) * (z * T(y,x)) = T(z * y,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(239,a,6116,a,b,5133,a),flip(a)].">
      <j1 rule="hyper" parents="239 6116 5133"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6154">
    <literal><![CDATA[
      (x * y) \ (x * T(y,z)) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(123,a,6116,a)].">
      <j1 rule="hyper" parents="123 6116"/>
    </justification>
  </clause>

  <clause id="6155">
    <literal><![CDATA[
      x * T(x \ y,z) != y * u
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,z) = u
    ]]></literal>
    <justification jstring="[para(6116(a,1),322(a,1)),flip(b)].">
      <j1 rule="para" parents="6116 322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6156">
    <literal><![CDATA[
      R(x,T(y,x),K(x,z)) \ (y * T(x,z)) = T(y,x) * K(x,z)
    ]]></literal>
    <justification jstring="[para(6116(a,1),540(a,1,2))].">
      <j1 rule="para" parents="6116 540"/>
    </justification>
  </clause>

  <clause id="6157">
    <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(6116(a,1),541(a,1,2))].">
      <j1 rule="para" parents="6116 541"/>
    </justification>
  </clause>

  <clause id="6158">
    <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(6116(a,1),510(a,1,1))].">
      <j1 rule="para" parents="6116 510"/>
    </justification>
  </clause>

  <clause id="6160">
    <literal><![CDATA[
      K(x,y) * T(y * x,z) = (x * y) * K(y * x,z)
    ]]></literal>
    <justification jstring="[para(4813(a,1),6116(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4813 6116"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6161">
    <literal><![CDATA[
      (x * y) * (z * K(y,z)) = (x * T(y,z)) * z
    ]]></literal>
    <justification jstring="[para(6116(a,1),6090(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6116 6090"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6165">
    <literal><![CDATA[
      x \ (y * T(y \ x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(4767(a,1),6118(a,1))].">
      <j1 rule="para" parents="4767 6118"/>
    </justification>
  </clause>

  <clause id="6166">
    <literal><![CDATA[
      K(x,(y \ z) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(5681(a,1),6122(a,1))].">
      <j1 rule="para" parents="5681 6122"/>
    </justification>
  </clause>

  <clause id="6167">
    <literal><![CDATA[
      K(x,(y * (z * u)) \ (y * z)) = K(x,1 / L(u,z,y))
    ]]></literal>
    <justification jstring="[para(13(a,2),6123(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="13 6123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6168">
    <literal><![CDATA[
      K(x,y \ (y / z)) = K(x,1 / z)
    ]]></literal>
    <justification jstring="[para(75(a,1),6123(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="75 6123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6169">
    <literal><![CDATA[
      ((1 / (x \ y)) \ z) * (1 / (x \ y)) = z * K(z * (x \ y),y \ x)
    ]]></literal>
    <justification jstring="[para(6123(a,1),5867(a,2,2))].">
      <j1 rule="para" parents="6123 5867"/>
    </justification>
  </clause>

  <clause id="6171">
    <literal><![CDATA[
      T(x,(y \ z) \ 1) = K(z \ y,x) \ x
    ]]></literal>
    <justification jstring="[hyper(320,a,4790,a(flip),b,6125,a),flip(a)].">
      <j1 rule="hyper" parents="320 4790 6125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6172">
    <literal><![CDATA[
      (1 / (x \ y)) * T(z,y \ x) = z * (1 / (x \ y))
    ]]></literal>
    <justification jstring="[hyper(119,a,6125,a(flip),b,2954,a)].">
      <j1 rule="hyper" parents="119 6125 2954"/>
    </justification>
  </clause>

  <clause id="6173">
    <literal><![CDATA[
      ((x \ y) \ 1) * T(z,y \ x) = z * ((x \ y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(119,a,6125,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 6125 17"/>
    </justification>
  </clause>

  <clause id="6174">
    <literal><![CDATA[
      T(x,(y * z) \ y) = T(x,z \ 1)
    ]]></literal>
    <justification jstring="[para(4(a,1),6125(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4 6125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6175">
    <literal><![CDATA[
      T(x,((y * z) \ y) \ 1) = T(x,z)
    ]]></literal>
    <justification jstring="[para(4(a,1),6125(a,2,2))].">
      <j1 rule="para" parents="4 6125"/>
    </justification>
  </clause>

  <clause id="6177">
    <literal><![CDATA[
      T(x,y \ (y / z)) = T(x,z \ 1)
    ]]></literal>
    <justification jstring="[para(75(a,1),6125(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="75 6125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6178">
    <literal><![CDATA[
      T(x \ y,y \ x) != z
    ]]></literal>
    <literal><![CDATA[
      ((x \ y) \ 1) \ 1 = z
    ]]></literal>
    <justification jstring="[para(6125(a,1),427(a,1))].">
      <j1 rule="para" parents="6125 427"/>
    </justification>
  </clause>

  <clause id="6179">
    <literal><![CDATA[
      T(x,y \ z) / ((z \ y) \ x) = x / ((x \ ((z \ y) \ x)) * x)
    ]]></literal>
    <justification jstring="[para(6125(a,1),4407(a,1,1))].">
      <j1 rule="para" parents="6125 4407"/>
    </justification>
  </clause>

  <clause id="6180">
    <literal><![CDATA[
      K(x,(y \ z) \ z) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(72(a,1),6126(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="72 6126"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6181">
    <literal><![CDATA[
      T(x,K(y,x / z)) = T(x,K(y,z \ x))
    ]]></literal>
    <justification jstring="[para(6126(a,1),4233(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6126 4233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6182">
    <literal><![CDATA[
      T(K(x / (y / z),y / z),y) = K(x * (1 / (y / z)),z \ y)
    ]]></literal>
    <justification jstring="[para(5859(a,1),6126(a,1,1))].">
      <j1 rule="para" parents="5859 6126"/>
    </justification>
  </clause>

  <clause id="6184">
    <literal><![CDATA[
      (((x * y) \ x) * z) * K(z,y \ 1) = z * ((x * y) \ x)
    ]]></literal>
    <justification jstring="[hyper(119,a,6127,a(flip),b,11,a(flip))].">
      <j1 rule="hyper" parents="119 6127 11"/>
    </justification>
  </clause>

  <clause id="6188">
    <literal><![CDATA[
      (x / T(y,z)) * K(y,z) = x / y
    ]]></literal>
    <justification jstring="[hyper(32,a,1496,a(flip),b,6148,a),flip(a)].">
      <j1 rule="hyper" parents="32 1496 6148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6189">
    <literal><![CDATA[
      (x / y) * ((y \ z) \ z) = x * K(y,y \ z)
    ]]></literal>
    <justification jstring="[para(6148(a,1),369(a,1,1))].">
      <j1 rule="para" parents="6148 369"/>
    </justification>
  </clause>

  <clause id="6190">
    <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(6149(a,1),1020(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6149 1020"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6191">
    <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(6149(a,1),5563(a,1,2))].">
      <j1 rule="para" parents="6149 5563"/>
    </justification>
  </clause>

  <clause id="6192">
    <literal><![CDATA[
      T(x,y * (1 / x)) = T(x,y / x)
    ]]></literal>
    <justification jstring="[hyper(5852,a,6151,a),flip(a)].">
      <j1 rule="hyper" parents="5852 6151"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6193">
    <literal><![CDATA[
      (x * T(y,z)) / y = x * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(1513,a,6151,a)].">
      <j1 rule="hyper" parents="1513 6151"/>
    </justification>
  </clause>

  <clause id="6194">
    <literal><![CDATA[
      (x * K(y,z)) / (x / y) = T(x / (x / y),z)
    ]]></literal>
    <justification jstring="[hyper(117,a,6151,a(flip),b,456,a)].">
      <j1 rule="hyper" parents="117 6151 456"/>
    </justification>
  </clause>

  <clause id="6195">
    <literal><![CDATA[
      x * K(y \ x,z) != u
    ]]></literal>
    <literal><![CDATA[
      y * T(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(6151(a,1),348(a,1))].">
      <j1 rule="para" parents="6151 348"/>
    </justification>
  </clause>

  <clause id="6196">
    <literal><![CDATA[
      (x * K(y,z)) * y = x * T(y,z)
    ]]></literal>
    <justification jstring="[para(6151(a,1),1491(a,1,1))].">
      <j1 rule="para" parents="6151 1491"/>
    </justification>
  </clause>

  <clause id="6197">
    <literal><![CDATA[
      T(x * K(y,z),y) = y \ (x * T(y,z))
    ]]></literal>
    <justification jstring="[para(6151(a,1),1489(a,1,1))].">
      <j1 rule="para" parents="6151 1489"/>
    </justification>
  </clause>

  <clause id="6198">
    <literal><![CDATA[
      (x / T(y,z)) * K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x / y = u
    ]]></literal>
    <justification jstring="[para(6151(a,1),1509(a,1))].">
      <j1 rule="para" parents="6151 1509"/>
    </justification>
  </clause>

  <clause id="6199">
    <literal><![CDATA[
      (x * y) * K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x * T(y,z) = u
    ]]></literal>
    <justification jstring="[para(6154(a,1),255(a,1,2)),flip(b)].">
      <j1 rule="para" parents="6154 255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6202">
    <literal><![CDATA[
      (x * (y / x)) \ (K(x,x \ y) * T(y,z)) = K(y,z)
    ]]></literal>
    <justification jstring="[para(4783(a,1),6154(a,1,1))].">
      <j1 rule="para" parents="4783 6154"/>
    </justification>
  </clause>

  <clause id="6203">
    <literal><![CDATA[
      T(x,y \ (y / z)) = T(x,1 / z)
    ]]></literal>
    <justification jstring="[hyper(118,a,6168,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 6168 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6204">
    <literal><![CDATA[
      K(x,y \ (y / z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ 1) = u
    ]]></literal>
    <justification jstring="[para(6168(a,2),5075(a,1))].">
      <j1 rule="para" parents="6168 5075"/>
    </justification>
  </clause>

  <clause id="6205">
    <literal><![CDATA[
      T(x * y,y \ 1) = ((x * y) \ x) \ x
    ]]></literal>
    <justification jstring="[hyper(427,a,6174,a),flip(a)].">
      <j1 rule="hyper" parents="427 6174"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6206">
    <literal><![CDATA[
      T(x,L(y \ 1,y,z)) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,1370,a,b,6174,a)].">
      <j1 rule="hyper" parents="58 1370 6174"/>
    </justification>
  </clause>

  <clause id="6207">
    <literal><![CDATA[
      ((x * y) \ x) * T(z,y \ 1) = z * ((x * y) \ x)
    ]]></literal>
    <justification jstring="[hyper(119,a,6174,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 6174 17"/>
    </justification>
  </clause>

  <clause id="6208">
    <literal><![CDATA[
      x / T(x * y,y \ 1) = (x * y) \ x
    ]]></literal>
    <justification jstring="[para(6174(a,1),265(a,1,2))].">
      <j1 rule="para" parents="6174 265"/>
    </justification>
  </clause>

  <clause id="6210">
    <literal><![CDATA[
      (1 / ((x * y) \ x)) * T(z,y) = z * (1 / ((x * y) \ x))
    ]]></literal>
    <justification jstring="[hyper(119,a,6175,a(flip),b,2954,a)].">
      <j1 rule="hyper" parents="119 6175 2954"/>
    </justification>
  </clause>

  <clause id="6212">
    <literal><![CDATA[
      T(x,L(y \ 1,y,z) \ 1) = T(x,y)
    ]]></literal>
    <justification jstring="[para(217(a,2),6175(a,1,2,1))].">
      <j1 rule="para" parents="217 6175"/>
    </justification>
  </clause>

  <clause id="6213">
    <literal><![CDATA[
      T(x,y \ (y / z)) = T(x,(z \ u) / u)
    ]]></literal>
    <justification jstring="[hyper(320,a,4453,a,b,6177,a),flip(a)].">
      <j1 rule="hyper" parents="320 4453 6177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6216">
    <literal><![CDATA[
      K(x,T(y,y \ z)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(1939,a,6180,a)].">
      <j1 rule="hyper" parents="1939 6180"/>
    </justification>
  </clause>

  <clause id="6217">
    <literal><![CDATA[
      K(x,T(y,z / y)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(4288(a,2),6180(a,1,2))].">
      <j1 rule="para" parents="4288 6180"/>
    </justification>
  </clause>

  <clause id="6218">
    <literal><![CDATA[
      T(K(x,y),z * y) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(4268(a,2),6180(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4268 6180"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6219">
    <literal><![CDATA[
      (T(x,y) / y) * K(y,x) = x / y
    ]]></literal>
    <justification jstring="[hyper(4302,a,6188,a)].">
      <j1 rule="hyper" parents="4302 6188"/>
    </justification>
  </clause>

  <clause id="6220">
    <literal><![CDATA[
      T(x / T(y,z),K(y,z)) = K(z,y) * (x / y)
    ]]></literal>
    <justification jstring="[hyper(239,a,6188,a,b,5133,a)].">
      <j1 rule="hyper" parents="239 6188 5133"/>
    </justification>
  </clause>

  <clause id="6221">
    <literal><![CDATA[
      (x / (y \ z)) * K(z / y,y) = x / (z / y)
    ]]></literal>
    <justification jstring="[para(107(a,1),6188(a,1,1,2))].">
      <j1 rule="para" parents="107 6188"/>
    </justification>
  </clause>

  <clause id="6222">
    <literal><![CDATA[
      (1 / x) * K(x,y) = K(x,y) / x
    ]]></literal>
    <justification jstring="[para(4756(a,1),6188(a,1,1))].">
      <j1 rule="para" parents="4756 6188"/>
    </justification>
  </clause>

  <clause id="6223">
    <literal><![CDATA[
      (x * K(y,x)) * K(y,x) = (T(y,x) * x) / y
    ]]></literal>
    <justification jstring="[para(4962(a,1),6188(a,1,1))].">
      <j1 rule="para" parents="4962 6188"/>
    </justification>
  </clause>

  <clause id="6224">
    <literal><![CDATA[
      (x * K(y,z)) / y = (x / y) * K(y,z)
    ]]></literal>
    <justification jstring="[para(6148(a,1),6188(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6148 6188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6225">
    <literal><![CDATA[
      T(x,(y / (1 / x)) / x) = T(x,y)
    ]]></literal>
    <justification jstring="[para(7(a,1),6192(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7 6192"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6226">
    <literal><![CDATA[
      (x * K(y,z)) \ (x * T(y,z)) = y
    ]]></literal>
    <justification jstring="[hyper(188,a,6193,a)].">
      <j1 rule="hyper" parents="188 6193"/>
    </justification>
  </clause>

  <clause id="6227">
    <literal><![CDATA[
      (x * K(y,z)) * y != u
    ]]></literal>
    <literal><![CDATA[
      x * T(y,z) = u
    ]]></literal>
    <justification jstring="[para(6193(a,1),251(a,1,1)),flip(b)].">
      <j1 rule="para" parents="6193 251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6228">
    <literal><![CDATA[
      R(x,K(y,z),y) = x
    ]]></literal>
    <justification jstring="[hyper(4854,a,6196,a)].">
      <j1 rule="hyper" parents="4854 6196"/>
    </justification>
  </clause>

  <clause id="6230">
    <literal><![CDATA[
      (x * K(y,z)) * y = (x * y) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,6116,a,b,6196,a),flip(a)].">
      <j1 rule="hyper" parents="320 6116 6196"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6231">
    <literal><![CDATA[
      (K(x,y) * K(y,z)) * y = T(y,z) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,2897,a,b,6196,a),flip(a)].">
      <j1 rule="hyper" parents="320 2897 6196"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6233">
    <literal><![CDATA[
      (x * K(y,z)) \ ((x * y) * K(y,z)) = y
    ]]></literal>
    <justification jstring="[hyper(116,a,6116,a,b,6196,a)].">
      <j1 rule="hyper" parents="116 6116 6196"/>
    </justification>
  </clause>

  <clause id="6234">
    <literal><![CDATA[
      ((x / y) * K(y,z)) \ (x * K(y,z)) = y
    ]]></literal>
    <justification jstring="[hyper(116,a,6151,a(flip),b,6196,a)].">
      <j1 rule="hyper" parents="116 6151 6196"/>
    </justification>
  </clause>

  <clause id="6235">
    <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,6196,a)].">
      <j1 rule="hyper" parents="116 449 6196"/>
    </justification>
  </clause>

  <clause id="6236">
    <literal><![CDATA[
      (x * y) * K(T(x,y),z) = T(x,z) * y
    ]]></literal>
    <justification jstring="[hyper(30,a,1348,a,b,6196,a),flip(a)].">
      <j1 rule="hyper" parents="30 1348 6196"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6237">
    <literal><![CDATA[
      (x * (y * T(z,u))) \ ((x * (y * K(z,u))) * z) = a(x,y * K(z,u),z)
    ]]></literal>
    <justification jstring="[para(6196(a,1),9(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="6196 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6238">
    <literal><![CDATA[
      L(x \ 1,x,y * K(x,z)) = (y * T(x,z)) \ (y * K(x,z))
    ]]></literal>
    <justification jstring="[para(6196(a,1),217(a,2,1))].">
      <j1 rule="para" parents="6196 217"/>
    </justification>
  </clause>

  <clause id="6239">
    <literal><![CDATA[
      x \ (y * T(x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(y * K(x,z),x) = u
    ]]></literal>
    <justification jstring="[para(6196(a,1),288(a,1,2))].">
      <j1 rule="para" parents="6196 288"/>
    </justification>
  </clause>

  <clause id="6240">
    <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(6196(a,1),482(a,1,2,2))].">
      <j1 rule="para" parents="6196 482"/>
    </justification>
  </clause>

  <clause id="6241">
    <literal><![CDATA[
      (T(x,y) \ 1) * y = (x \ 1) * T(y,x)
    ]]></literal>
    <justification jstring="[para(4801(a,1),6196(a,1,1))].">
      <j1 rule="para" parents="4801 6196"/>
    </justification>
  </clause>

  <clause id="6242">
    <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(6196(a,1),5492(a,1,2,1))].">
      <j1 rule="para" parents="6196 5492"/>
    </justification>
  </clause>

  <clause id="6243">
    <literal><![CDATA[
      (x * (y * K(z,y))) * z = (x * y) * T(z,y)
    ]]></literal>
    <justification jstring="[para(6091(a,1),6196(a,1,1))].">
      <j1 rule="para" parents="6091 6196"/>
    </justification>
  </clause>

  <clause id="6244">
    <literal><![CDATA[
      T(K(x,y),y * z) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(4(a,1),6216(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 6216"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6245">
    <literal><![CDATA[
      K(x,y) * (1 / x) = K(x,y) / x
    ]]></literal>
    <justification jstring="[hyper(1298,a,6222,a)].">
      <j1 rule="hyper" parents="1298 6222"/>
    </justification>
  </clause>

  <clause id="6246">
    <literal><![CDATA[
      (K(x,y) / x) * L(z,K(x,y),x \ 1) = (1 / x) * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(6222(a,1),3688(a,1,1))].">
      <j1 rule="para" parents="6222 3688"/>
    </justification>
  </clause>

  <clause id="6247">
    <literal><![CDATA[
      L(x,K(x,y),z) = x
    ]]></literal>
    <justification jstring="[hyper(4853,a,6226,a)].">
      <j1 rule="hyper" parents="4853 6226"/>
    </justification>
  </clause>

  <clause id="6248">
    <literal><![CDATA[
      (x * K(y,z)) \ (x * y) = y * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,5764,a(flip),b,6247,a)].">
      <j1 rule="hyper" parents="58 5764 6247"/>
    </justification>
  </clause>

  <clause id="6249">
    <literal><![CDATA[
      (x * K(y,z)) * L(y,u,w) = x * (K(y,z) * L(y,u,w))
    ]]></literal>
    <justification jstring="[para(6247(a,1),446(a,1,2,1))].">
      <j1 rule="para" parents="6247 446"/>
    </justification>
  </clause>

  <clause id="6251">
    <literal><![CDATA[
      L(x * y,K(y * x,z),u) = (y \ (y * x)) * y
    ]]></literal>
    <justification jstring="[para(6247(a,1),3529(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6247 3529"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6252">
    <literal><![CDATA[
      L(x,x \ T(x,y),z) = x
    ]]></literal>
    <justification jstring="[para(4729(a,1),6247(a,1,2))].">
      <j1 rule="para" parents="4729 6247"/>
    </justification>
  </clause>

  <clause id="6255">
    <literal><![CDATA[
      T(K(x,y),z * y) = T(K(x,y),y * z)
    ]]></literal>
    <justification jstring="[hyper(320,a,6218,a,b,6244,a)].">
      <j1 rule="hyper" parents="320 6218 6244"/>
    </justification>
  </clause>

  <clause id="6256">
    <literal><![CDATA[
      (x * y) * K(z,T(x,y)) = K(z,x) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(119,a,6244,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 6244 17"/>
    </justification>
  </clause>

  <clause id="6257">
    <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(6244(a,1),5643(a,1,2))].">
      <j1 rule="para" parents="6244 5643"/>
    </justification>
  </clause>

  <clause id="6258">
    <literal><![CDATA[
      K(((x * y) \ x) \ 1,z) = K(y,z)
    ]]></literal>
    <justification jstring="[para(217(a,1),6110(a,1,1,1))].">
      <j1 rule="para" parents="217 6110"/>
    </justification>
  </clause>

  <clause id="6259">
    <literal><![CDATA[
      K((x \ y) \ 1,z) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[para(390(a,1),6110(a,1,1,1))].">
      <j1 rule="para" parents="390 6110"/>
    </justification>
  </clause>

  <clause id="6264">
    <literal><![CDATA[
      T(((x * y) \ x) \ 1,z) = ((x * y) \ x) \ K(y,z)
    ]]></literal>
    <justification jstring="[hyper(116,a,6258,a(flip),b,4746,a),flip(a)].">
      <j1 rule="hyper" parents="116 6258 4746"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6265">
    <literal><![CDATA[
      (1 / ((x * y) \ x)) * K(y,z) = T(1 / ((x * y) \ x),z)
    ]]></literal>
    <justification jstring="[para(6258(a,1),4763(a,1,2))].">
      <j1 rule="para" parents="6258 4763"/>
    </justification>
  </clause>

  <clause id="6266">
    <literal><![CDATA[
      K(1 / (x \ y),z) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(5282,a,6259,a)].">
      <j1 rule="hyper" parents="5282 6259"/>
    </justification>
  </clause>

  <clause id="6268">
    <literal><![CDATA[
      T(K(x / y,z),x) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,5540,a,b,6259,a)].">
      <j1 rule="hyper" parents="58 5540 6259"/>
    </justification>
  </clause>

  <clause id="6269">
    <literal><![CDATA[
      x \ (((y \ (x * z)) * y) / z) = K((y / z) \ x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,5533,a,b,6259,a)].">
      <j1 rule="hyper" parents="58 5533 6259"/>
    </justification>
  </clause>

  <clause id="6270">
    <literal><![CDATA[
      K((x \ (y * z)) \ 1,y) = K((y / (z \ 1)) \ x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,6021,a(flip),b,6259,a)].">
      <j1 rule="hyper" parents="58 6021 6259"/>
    </justification>
  </clause>

  <clause id="6271">
    <literal><![CDATA[
      (x \ y) \ K(y \ x,z) = T((x \ y) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(116,a,6259,a(flip),b,4746,a)].">
      <j1 rule="hyper" parents="116 6259 4746"/>
    </justification>
  </clause>

  <clause id="6272">
    <literal><![CDATA[
      K((x * y) \ x,z) = K(y \ 1,z)
    ]]></literal>
    <justification jstring="[para(4(a,1),6259(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4 6259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6273">
    <literal><![CDATA[
      K(T(x,y) \ 1,z) = K((x * y) \ y,z)
    ]]></literal>
    <justification jstring="[para(17(a,2),6259(a,1,1,1))].">
      <j1 rule="para" parents="17 6259"/>
    </justification>
  </clause>

  <clause id="6277">
    <literal><![CDATA[
      K((K(x,y) * z) \ 1,u) = K(z \ K(y,x),u)
    ]]></literal>
    <justification jstring="[para(5130(a,1),6259(a,1,1,1))].">
      <j1 rule="para" parents="5130 6259"/>
    </justification>
  </clause>

  <clause id="6279">
    <literal><![CDATA[
      (x * K(y \ x,z)) / y = T(x / y,z)
    ]]></literal>
    <justification jstring="[para(6259(a,1),5542(a,1,1,2))].">
      <j1 rule="para" parents="6259 5542"/>
    </justification>
  </clause>

  <clause id="6280">
    <literal><![CDATA[
      (((x \ y) * z) \ z) * ((x \ y) * z) = z * K(y \ x,(x \ y) * z)
    ]]></literal>
    <justification jstring="[para(6259(a,1),5439(a,2,2))].">
      <j1 rule="para" parents="6259 5439"/>
    </justification>
  </clause>

  <clause id="6281">
    <literal><![CDATA[
      x \ T(x * y,z) = y * K((x \ 1) \ y,z)
    ]]></literal>
    <justification jstring="[para(6259(a,1),5537(a,2,2))].">
      <j1 rule="para" parents="6259 5537"/>
    </justification>
  </clause>

  <clause id="6282">
    <literal><![CDATA[
      (1 / (x \ y)) * (z / (1 / (x \ y))) = z * K(y \ x,z * (x \ y))
    ]]></literal>
    <justification jstring="[para(6259(a,1),5838(a,2,2))].">
      <j1 rule="para" parents="6259 5838"/>
    </justification>
  </clause>

  <clause id="6283">
    <literal><![CDATA[
      (x \ y) * K((x \ 1) \ (x \ y),z) = x \ T(y,z)
    ]]></literal>
    <justification jstring="[para(6259(a,1),5171(a,1,2))].">
      <j1 rule="para" parents="6259 5171"/>
    </justification>
  </clause>

  <clause id="6284">
    <literal><![CDATA[
      x * K((y * z) \ x,y) = z * ((y \ (z \ x)) * y)
    ]]></literal>
    <justification jstring="[para(6259(a,1),5536(a,1,2))].">
      <j1 rule="para" parents="6259 5536"/>
    </justification>
  </clause>

  <clause id="6285">
    <literal><![CDATA[
      x * K((y * z) \ x,z) = y * ((z \ (y \ x)) * z)
    ]]></literal>
    <justification jstring="[para(6259(a,1),5989(a,1,2))].">
      <j1 rule="para" parents="6259 5989"/>
    </justification>
  </clause>

  <clause id="6286">
    <literal><![CDATA[
      K(1 / L(x \ y,z,u),w) = L(K(y \ x,w),z,u)
    ]]></literal>
    <justification jstring="[para(6266(a,1),5689(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6266 5689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6287">
    <literal><![CDATA[
      K(x / y,x) = K(y \ x,x)
    ]]></literal>
    <justification jstring="[hyper(2913,a,6268,a)].">
      <j1 rule="hyper" parents="2913 6268"/>
    </justification>
  </clause>

  <clause id="6288">
    <literal><![CDATA[
      K(x,K(y,x / z)) * K(x / z,y) = K(z \ x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,5625,a,b,6268,a)].">
      <j1 rule="hyper" parents="58 5625 6268"/>
    </justification>
  </clause>

  <clause id="6289">
    <literal><![CDATA[
      K(L(x,y,z) / u,x) = K(u \ L(x,y,z),x)
    ]]></literal>
    <justification jstring="[hyper(58,a,2975,a(flip),b,6268,a)].">
      <j1 rule="hyper" parents="58 2975 6268"/>
    </justification>
  </clause>

  <clause id="6290">
    <literal><![CDATA[
      K(x / y,z) * x = x * K(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(119,a,6268,a(flip),b,17,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 6268 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6291">
    <literal><![CDATA[
      T(x,y) != K(z \ y,u)
    ]]></literal>
    <literal><![CDATA[
      K(y / z,u) = x
    ]]></literal>
    <justification jstring="[para(6268(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="6268 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6292">
    <literal><![CDATA[
      K((x \ y) \ y,z) = T(K(x,z),y)
    ]]></literal>
    <justification jstring="[para(72(a,1),6268(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="72 6268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6293">
    <literal><![CDATA[
      K((x \ y) \ y,y) = K(x,y)
    ]]></literal>
    <justification jstring="[para(72(a,1),6287(a,1,1)),flip(a)].">
      <j1 rule="para" parents="72 6287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6294">
    <literal><![CDATA[
      K(L(1 / x,x,y),z) = K(x \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(5788,a,6272,a)].">
      <j1 rule="hyper" parents="5788 6272"/>
    </justification>
  </clause>

  <clause id="6297">
    <literal><![CDATA[
      K(T(x,x \ y),z) = T(K(x,z),y)
    ]]></literal>
    <justification jstring="[para(106(a,2),6292(a,1,1))].">
      <j1 rule="para" parents="106 6292"/>
    </justification>
  </clause>

  <clause id="6298">
    <literal><![CDATA[
      K((x \ y) \ y,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(6292(a,2),2913(a,1))].">
      <j1 rule="para" parents="6292 2913"/>
    </justification>
  </clause>

  <clause id="6299">
    <literal><![CDATA[
      K(x \ (x * y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) = u
    ]]></literal>
    <justification jstring="[para(6112(a,1),3666(a,1))].">
      <j1 rule="para" parents="6112 3666"/>
    </justification>
  </clause>

  <clause id="6300">
    <literal><![CDATA[
      L(x \ 1,x,y) \ y = T(y * x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(429,a,6206,a)].">
      <j1 rule="hyper" parents="429 6206"/>
    </justification>
  </clause>

  <clause id="6302">
    <literal><![CDATA[
      K(L(1 / x,x,y),z) = K(1 / x,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,3312,a,b,6294,a),flip(a)].">
      <j1 rule="hyper" parents="320 3312 6294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6303">
    <literal><![CDATA[
      K((x / y) \ x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) = u
    ]]></literal>
    <justification jstring="[para(7(a,1),6299(a,1,1,2))].">
      <j1 rule="para" parents="7 6299"/>
    </justification>
  </clause>

  <clause id="6304">
    <literal><![CDATA[
      K(1 / ((x * y) \ x),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) = u
    ]]></literal>
    <justification jstring="[para(6266(a,2),6299(a,1))].">
      <j1 rule="para" parents="6266 6299"/>
    </justification>
  </clause>

  <clause id="6305">
    <literal><![CDATA[
      K(L(x,x \ 1,y),z) = K(1 / (x \ 1),z)
    ]]></literal>
    <justification jstring="[para(72(a,1),6302(a,1,1,1))].">
      <j1 rule="para" parents="72 6302"/>
    </justification>
  </clause>

  <clause id="6306">
    <literal><![CDATA[
      L(T(x,K(y,x)),K(y,x),z) = x
    ]]></literal>
    <justification jstring="[hyper(772,a,6092,a)].">
      <j1 rule="hyper" parents="772 6092"/>
    </justification>
  </clause>

  <clause id="6307">
    <literal><![CDATA[
      L(x,K(y,x),z) = x
    ]]></literal>
    <justification jstring="[para(2890(a,1),6306(a,1,1))].">
      <j1 rule="para" parents="2890 6306"/>
    </justification>
  </clause>

  <clause id="6308">
    <literal><![CDATA[
      L(T(x,y),K(z,x),u) = T(x,y)
    ]]></literal>
    <justification jstring="[para(6307(a,1),20(a,2,1))].">
      <j1 rule="para" parents="6307 20"/>
    </justification>
  </clause>

  <clause id="6309">
    <literal><![CDATA[
      L((x \ y) \ y,K(z,x),u) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(6307(a,1),317(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6307 317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6310">
    <literal><![CDATA[
      (x * K(y,z)) * T(z,u) = x * (K(y,z) * T(z,u))
    ]]></literal>
    <justification jstring="[para(6307(a,1),449(a,1,2,1))].">
      <j1 rule="para" parents="6307 449"/>
    </justification>
  </clause>

  <clause id="6311">
    <literal><![CDATA[
      (x * K(y,z)) * L(z,u,w) = x * (K(y,z) * L(z,u,w))
    ]]></literal>
    <justification jstring="[para(6307(a,1),446(a,1,2,1))].">
      <j1 rule="para" parents="6307 446"/>
    </justification>
  </clause>

  <clause id="6312">
    <literal><![CDATA[
      (x * K(y,z)) * R(z,u,w) = x * (K(y,z) * R(z,u,w))
    ]]></literal>
    <justification jstring="[para(6307(a,1),447(a,1,2,1))].">
      <j1 rule="para" parents="6307 447"/>
    </justification>
  </clause>

  <clause id="6315">
    <literal><![CDATA[
      (x * K(y,z)) \ (x * z) = T(z,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,4863,a(flip),b,6308,a)].">
      <j1 rule="hyper" parents="58 4863 6308"/>
    </justification>
  </clause>

  <clause id="6316">
    <literal><![CDATA[
      (x * K(y,z)) * T(z,y) = x * z
    ]]></literal>
    <justification jstring="[hyper(119,a,6308,a(flip),b,4863,a(flip))].">
      <j1 rule="hyper" parents="119 6308 4863"/>
    </justification>
  </clause>

  <clause id="6317">
    <literal><![CDATA[
      x / T(y \ x,z) = y * K(z,y \ x)
    ]]></literal>
    <justification jstring="[hyper(366,a,6315,a)].">
      <j1 rule="hyper" parents="366 6315"/>
    </justification>
  </clause>

  <clause id="6319">
    <literal><![CDATA[
      (x * y) / T(y,z) = x * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(197,a,6315,a)].">
      <j1 rule="hyper" parents="197 6315"/>
    </justification>
  </clause>

  <clause id="6321">
    <literal><![CDATA[
      (x * K(y,x \ z)) \ z = T(x \ z,y)
    ]]></literal>
    <justification jstring="[para(5(a,1),6315(a,1,2))].">
      <j1 rule="para" parents="5 6315"/>
    </justification>
  </clause>

  <clause id="6322">
    <literal><![CDATA[
      (x / y) * K(z,y) = x / T(y,z)
    ]]></literal>
    <justification jstring="[para(6315(a,1),324(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6315 324"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6324">
    <literal><![CDATA[
      (x * T(y,z)) \ ((x * y) * z) = T(z,y)
    ]]></literal>
    <justification jstring="[para(6116(a,1),6315(a,1,1))].">
      <j1 rule="para" parents="6116 6315"/>
    </justification>
  </clause>

  <clause id="6325">
    <literal><![CDATA[
      (x / T(y,z)) * y = x * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(1498,a,6316,a)].">
      <j1 rule="hyper" parents="1498 6316"/>
    </justification>
  </clause>

  <clause id="6326">
    <literal><![CDATA[
      (x / T(y,z)) / K(z,y) = x / y
    ]]></literal>
    <justification jstring="[hyper(595,a,6316,a),flip(a)].">
      <j1 rule="hyper" parents="595 6316"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6327">
    <literal><![CDATA[
      (x \ y) * K(y,x) = x \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(30,a,4478,a,b,6316,a),flip(a)].">
      <j1 rule="hyper" parents="30 4478 6316"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6329">
    <literal><![CDATA[
      (x * K(y,z)) * K(z,y) = x
    ]]></literal>
    <justification jstring="[hyper(30,a,6196,a(flip),b,6316,a),flip(a)].">
      <j1 rule="hyper" parents="30 6196 6316"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6330">
    <literal><![CDATA[
      (x \ K(x,y)) * K(y,x) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(30,a,5562,a(flip),b,6316,a),flip(a)].">
      <j1 rule="hyper" parents="30 5562 6316"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6331">
    <literal><![CDATA[
      (x * T(y,z)) * K(z,y) = x * y
    ]]></literal>
    <justification jstring="[hyper(30,a,1487,a(flip),b,6316,a),flip(a)].">
      <j1 rule="hyper" parents="30 1487 6316"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6332">
    <literal><![CDATA[
      (x * K(y,z)) \ (x * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(z,y) = u
    ]]></literal>
    <justification jstring="[para(6316(a,1),287(a,1,2)),flip(b)].">
      <j1 rule="para" parents="6316 287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6333">
    <literal><![CDATA[
      (x * T(y,z)) * T(z,y) = (x * y) * z
    ]]></literal>
    <justification jstring="[para(6116(a,1),6316(a,1,1))].">
      <j1 rule="para" parents="6116 6316"/>
    </justification>
  </clause>

  <clause id="6334">
    <literal><![CDATA[
      T(x * K(y,z),K(z,y)) = K(z,y) \ x
    ]]></literal>
    <justification jstring="[hyper(439,a,xx,b,6329,a)].">
      <j1 rule="hyper" parents="439 6329"/>
    </justification>
  </clause>

  <clause id="6335">
    <literal><![CDATA[
      x / K(y,z) = x * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(326,a,6329,a),flip(a)].">
      <j1 rule="hyper" parents="326 6329"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6337">
    <literal><![CDATA[
      T(x * K(y,z),K(z,y)) = K(y,z) * x
    ]]></literal>
    <justification jstring="[hyper(239,a,6329,a,b,5133,a)].">
      <j1 rule="hyper" parents="239 6329 5133"/>
    </justification>
  </clause>

  <clause id="6338">
    <literal><![CDATA[
      (x * K(y,z)) \ x = K(z,y)
    ]]></literal>
    <justification jstring="[hyper(123,a,6329,a)].">
      <j1 rule="hyper" parents="123 6329"/>
    </justification>
  </clause>

  <clause id="6339">
    <literal><![CDATA[
      (x / y) * K(x,y) = T(x,y) / y
    ]]></literal>
    <justification jstring="[hyper(30,a,6219,a,b,6329,a),flip(a)].">
      <j1 rule="hyper" parents="30 6219 6329"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6340">
    <literal><![CDATA[
      (K(x,y) * z) * K(y,x) = T(z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(30,a,5631,a,b,6329,a),flip(a)].">
      <j1 rule="hyper" parents="30 5631 6329"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6341">
    <literal><![CDATA[
      (K(x,y) * K(y,z)) * K(y,x) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(30,a,2003,a,b,6329,a),flip(a)].">
      <j1 rule="hyper" parents="30 2003 6329"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6342">
    <literal><![CDATA[
      (x * K(y,z)) / z = x / T(z,y)
    ]]></literal>
    <justification jstring="[hyper(117,a,6329,a(flip),b,6151,a),flip(a)].">
      <j1 rule="hyper" parents="117 6329 6151"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6343">
    <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(6329(a,1),9(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="6329 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6344">
    <literal><![CDATA[
      x * K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      u * K(z,y) = x
    ]]></literal>
    <justification jstring="[para(6329(a,1),39(a,1)),flip(a)].">
      <j1 rule="para" parents="6329 39"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6345">
    <literal><![CDATA[
      (x * K(y,z)) \ x != u
    ]]></literal>
    <literal><![CDATA[
      K(z,y) = u
    ]]></literal>
    <justification jstring="[para(6329(a,1),287(a,1,2)),flip(b)].">
      <j1 rule="para" parents="6329 287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6346">
    <literal><![CDATA[
      x / K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x * K(z,y) = u
    ]]></literal>
    <justification jstring="[para(6329(a,1),327(a,1,1)),flip(b)].">
      <j1 rule="para" parents="6329 327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6347">
    <literal><![CDATA[
      x * L(y,K(z,u),x * K(u,z)) = (x * K(u,z)) * (K(z,u) * y)
    ]]></literal>
    <justification jstring="[para(6329(a,1),90(a,1,1))].">
      <j1 rule="para" parents="6329 90"/>
    </justification>
  </clause>

  <clause id="6348">
    <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(6329(a,1),482(a,1,1))].">
      <j1 rule="para" parents="6329 482"/>
    </justification>
  </clause>

  <clause id="6349">
    <literal><![CDATA[
      (x * y) / K(z,y) = x * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,6116,a(flip),b,6335,a),flip(a)].">
      <j1 rule="hyper" parents="320 6116 6335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6350">
    <literal><![CDATA[
      T(x,K(y,z)) / K(y,z) = K(z,y) * x
    ]]></literal>
    <justification jstring="[hyper(320,a,5631,a(flip),b,6335,a),flip(a)].">
      <j1 rule="hyper" parents="320 5631 6335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6351">
    <literal><![CDATA[
      T(K(x,y) * z,K(x,y)) = z * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,5644,a,b,6335,a)].">
      <j1 rule="hyper" parents="58 5644 6335"/>
    </justification>
  </clause>

  <clause id="6352">
    <literal><![CDATA[
      (x * K(y,z)) * K(z,y) != u
    ]]></literal>
    <literal><![CDATA[
      u = x
    ]]></literal>
    <justification jstring="[para(6335(a,1),251(a,1,1))].">
      <j1 rule="para" parents="6335 251"/>
    </justification>
  </clause>

  <clause id="6354">
    <literal><![CDATA[
      R((x / y) * K(z,u),K(u,z),y) = x / (K(u,z) * y)
    ]]></literal>
    <justification jstring="[para(6335(a,1),301(a,1,1))].">
      <j1 rule="para" parents="6335 301"/>
    </justification>
  </clause>

  <clause id="6355">
    <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(6335(a,1),622(a,1,1,1))].">
      <j1 rule="para" parents="6335 622"/>
    </justification>
  </clause>

  <clause id="6356">
    <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(6335(a,1),622(a,1,1))].">
      <j1 rule="para" parents="6335 622"/>
    </justification>
  </clause>

  <clause id="6357">
    <literal><![CDATA[
      ((K(x,y) / z) * (z * K(y,x))) \ (K(x,y) / z) = 1 / (z / K(x,y))
    ]]></literal>
    <justification jstring="[para(6335(a,1),2051(a,1,1,2))].">
      <j1 rule="para" parents="6335 2051"/>
    </justification>
  </clause>

  <clause id="6359">
    <literal><![CDATA[
      K(x,1 / (K(y,z) / u)) = K(x,u * K(z,y))
    ]]></literal>
    <justification jstring="[para(6335(a,1),5356(a,2,2))].">
      <j1 rule="para" parents="6335 5356"/>
    </justification>
  </clause>

  <clause id="6360">
    <literal><![CDATA[
      (x * K(L(y \ 1,z,u) \ 1,w)) \ x = L(K(w,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(320,a,5678,a(flip),b,6338,a),flip(a)].">
      <j1 rule="hyper" parents="320 5678 6338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6361">
    <literal><![CDATA[
      ((x * K(y,z)) \ x) \ u = K(y,z) * u
    ]]></literal>
    <justification jstring="[para(6338(a,2),5130(a,1,1))].">
      <j1 rule="para" parents="6338 5130"/>
    </justification>
  </clause>

  <clause id="6362">
    <literal><![CDATA[
      (x \ R(x,y,x)) \ K(x,y) = K(x,x * y)
    ]]></literal>
    <justification jstring="[para(5293(a,1),6338(a,1,1))].">
      <j1 rule="para" parents="5293 6338"/>
    </justification>
  </clause>

  <clause id="6363">
    <literal><![CDATA[
      (x \ R(x,y,x)) \ K(x * y,x) = K(y,x)
    ]]></literal>
    <justification jstring="[para(5489(a,1),6338(a,1,1))].">
      <j1 rule="para" parents="5489 6338"/>
    </justification>
  </clause>

  <clause id="6364">
    <literal><![CDATA[
      (x / y) \ (x / T(y,z)) = K(z,y)
    ]]></literal>
    <justification jstring="[para(6188(a,1),6338(a,1,1))].">
      <j1 rule="para" parents="6188 6338"/>
    </justification>
  </clause>

  <clause id="6365">
    <literal><![CDATA[
      R(x * K(y,z),K(u,w),u) = (x * z) / T(z,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,6228,a,b,6319,a)].">
      <j1 rule="hyper" parents="320 6228 6319"/>
    </justification>
  </clause>

  <clause id="6366">
    <literal><![CDATA[
      T(x / T(y,z),y) = y \ (x * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(439,a,6319,a(flip),b,1488,a(flip))].">
      <j1 rule="hyper" parents="439 6319 1488"/>
    </justification>
  </clause>

  <clause id="6367">
    <literal><![CDATA[
      (x / y) * K(z,y) != u
    ]]></literal>
    <literal><![CDATA[
      x / T(y,z) = u
    ]]></literal>
    <justification jstring="[para(6319(a,1),576(a,1))].">
      <j1 rule="para" parents="6319 576"/>
    </justification>
  </clause>

  <clause id="6369">
    <literal><![CDATA[
      x * (K(y,x) * K(z,y)) = (y * x) / T(y,z)
    ]]></literal>
    <justification jstring="[hyper(5670,a,6322,a)].">
      <j1 rule="hyper" parents="5670 6322"/>
    </justification>
  </clause>

  <clause id="6371">
    <literal><![CDATA[
      T(x / y,K(x,y)) = x / y
    ]]></literal>
    <justification jstring="[hyper(239,a,6322,a,b,5248,a)].">
      <j1 rule="hyper" parents="239 6322 5248"/>
    </justification>
  </clause>

  <clause id="6372">
    <literal><![CDATA[
      K(x \ y,x) * K(z,y / x) = x \ (y / T(y / x,z))
    ]]></literal>
    <justification jstring="[hyper(116,a,6322,a(flip),b,5451,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="116 6322 5451"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6373">
    <literal><![CDATA[
      x \ (y / T(x \ y,z)) = K(z,x \ y)
    ]]></literal>
    <justification jstring="[hyper(116,a,6322,a(flip),b,183,a(flip))].">
      <j1 rule="hyper" parents="116 6322 183"/>
    </justification>
  </clause>

  <clause id="6374">
    <literal><![CDATA[
      T(x / y,K(y,x)) = x / y
    ]]></literal>
    <justification jstring="[hyper(5638,a,6371,a)].">
      <j1 rule="hyper" parents="5638 6371"/>
    </justification>
  </clause>

  <clause id="6375">
    <literal><![CDATA[
      K(x,y) * (y / x) = (y / x) * K(x,y)
    ]]></literal>
    <justification jstring="[para(6371(a,1),5631(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6371 5631"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6376">
    <literal><![CDATA[
      T((x * y) / T(z,y),z) = z \ (x * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(439,a,6116,a(flip),b,6325,a)].">
      <j1 rule="hyper" parents="439 6116 6325"/>
    </justification>
  </clause>

  <clause id="6377">
    <literal><![CDATA[
      x / T(x * y,y \ 1) = L(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[hyper(30,a,5053,a,b,6325,a),flip(a)].">
      <j1 rule="hyper" parents="30 5053 6325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6378">
    <literal><![CDATA[
      (x / ((y \ z) \ z)) * y = x * K(y \ z,y)
    ]]></literal>
    <justification jstring="[para(106(a,1),6325(a,1,1,2))].">
      <j1 rule="para" parents="106 6325"/>
    </justification>
  </clause>

  <clause id="6379">
    <literal><![CDATA[
      x \ (y * K(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      T(y / T(x,z),x) = u
    ]]></literal>
    <justification jstring="[para(6325(a,1),288(a,1,2))].">
      <j1 rule="para" parents="6325 288"/>
    </justification>
  </clause>

  <clause id="6380">
    <literal><![CDATA[
      x \ y != (z * K(u,w)) / w
    ]]></literal>
    <literal><![CDATA[
      x * (z / T(w,u)) = y
    ]]></literal>
    <justification jstring="[para(6325(a,1),623(a,2,1))].">
      <j1 rule="para" parents="6325 623"/>
    </justification>
  </clause>

  <clause id="6381">
    <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(6325(a,1),521(a,1,1))].">
      <j1 rule="para" parents="6325 521"/>
    </justification>
  </clause>

  <clause id="6382">
    <literal><![CDATA[
      (x / T(y,z)) * T(y,u) = (x * K(z,y)) * K(y,u)
    ]]></literal>
    <justification jstring="[para(6325(a,1),6116(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6325 6116"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6384">
    <literal><![CDATA[
      x \ T(x * y,x) = y * K(x * y,x)
    ]]></literal>
    <justification jstring="[para(4(a,1),6327(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4 6327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6385">
    <literal><![CDATA[
      (x \ T(y,x)) \ ((x \ y) * (K(y,x) * z)) = L(z,K(y,x),x \ y)
    ]]></literal>
    <justification jstring="[para(6327(a,1),13(a,2,1)),flip(a)].">
      <j1 rule="para" parents="6327 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6386">
    <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(6330(a,1),102(a,2,2))].">
      <j1 rule="para" parents="6330 102"/>
    </justification>
  </clause>

  <clause id="6387">
    <literal><![CDATA[
      (x * T(x \ y,z)) \ y = K(z,x \ y)
    ]]></literal>
    <justification jstring="[hyper(116,a,5,a(flip),b,6331,a)].">
      <j1 rule="hyper" parents="116 5 6331"/>
    </justification>
  </clause>

  <clause id="6388">
    <literal><![CDATA[
      x * K(y,z) != u * z
    ]]></literal>
    <literal><![CDATA[
      u * T(z,y) = x
    ]]></literal>
    <justification jstring="[para(6331(a,1),39(a,1)),flip(a)].">
      <j1 rule="para" parents="6331 39"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6390">
    <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(6331(a,1),510(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6331 510"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6391">
    <literal><![CDATA[
      x * (K(y,x) * K(y * x,y)) = T(y * x,y) / y
    ]]></literal>
    <justification jstring="[hyper(5670,a,6339,a)].">
      <j1 rule="hyper" parents="5670 6339"/>
    </justification>
  </clause>

  <clause id="6392">
    <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(6342(a,1),4401(a,1,1,2))].">
      <j1 rule="para" parents="6342 4401"/>
    </justification>
  </clause>

  <clause id="6393">
    <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(6342(a,1),4403(a,1,1,1,2))].">
      <j1 rule="para" parents="6342 4403"/>
    </justification>
  </clause>

  <clause id="6394">
    <literal><![CDATA[
      (x \ K(y,x)) \ (x \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(3161(a,1),6345(a,1,1))].">
      <j1 rule="para" parents="3161 6345"/>
    </justification>
  </clause>

  <clause id="6395">
    <literal><![CDATA[
      T(K(x,y) * z,K(x,y)) != u
    ]]></literal>
    <literal><![CDATA[
      z * K(x,y) = u
    ]]></literal>
    <justification jstring="[para(5644(a,2),6346(a,1))].">
      <j1 rule="para" parents="5644 6346"/>
    </justification>
  </clause>

  <clause id="6396">
    <literal><![CDATA[
      x * K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x / K(z,y) = u
    ]]></literal>
    <justification jstring="[para(7(a,1),6352(a,1,1)),flip(b)].">
      <j1 rule="para" parents="7 6352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6397">
    <literal><![CDATA[
      x / ((y * z) / y) = (x / z) * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(6344,a,6093,a),flip(a)].">
      <j1 rule="hyper" parents="6344 6093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6398">
    <literal><![CDATA[
      (x / (y / z)) * K(z,z \ y) = x / (z \ y)
    ]]></literal>
    <justification jstring="[para(5(a,1),6093(a,1,1,2,1))].">
      <j1 rule="para" parents="5 6093"/>
    </justification>
  </clause>

  <clause id="6399">
    <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(6093(a,1),967(a,2,1,2))].">
      <j1 rule="para" parents="6093 967"/>
    </justification>
  </clause>

  <clause id="6401">
    <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(6093(a,1),4598(a,1,2,1))].">
      <j1 rule="para" parents="6093 4598"/>
    </justification>
  </clause>

  <clause id="6402">
    <literal><![CDATA[
      (x / (y \ z)) * (z / y) = x * K(y,y \ z)
    ]]></literal>
    <justification jstring="[para(4776(a,1),6095(a,1,2))].">
      <j1 rule="para" parents="4776 6095"/>
    </justification>
  </clause>

  <clause id="6404">
    <literal><![CDATA[
      T(K(x \ 1,y) * y,K(x \ 1,y)) = x * ((y \ (x \ y)) * y)
    ]]></literal>
    <justification jstring="[hyper(239,a,6096,a(flip),b,6085,a)].">
      <j1 rule="hyper" parents="239 6096 6085"/>
    </justification>
  </clause>

  <clause id="6405">
    <literal><![CDATA[
      (x * ((y * z) / y)) * K(z,y) = x * z
    ]]></literal>
    <justification jstring="[hyper(6344,a,6097,a)].">
      <j1 rule="hyper" parents="6344 6097"/>
    </justification>
  </clause>

  <clause id="6406">
    <literal><![CDATA[
      (x * ((y * z) / y)) * y = (x * z) * T(y,z)
    ]]></literal>
    <justification jstring="[para(6097(a,1),6196(a,1,1))].">
      <j1 rule="para" parents="6097 6196"/>
    </justification>
  </clause>

  <clause id="6407">
    <literal><![CDATA[
      (x / (y * K(z,y))) * y = x * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,6335,a(flip),b,6098,a),flip(a)].">
      <j1 rule="hyper" parents="320 6335 6098"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6409">
    <literal><![CDATA[
      L(K(x \ (y \ z),u),y \ z,y) = z \ (y * (x * T(x \ (y \ z),u)))
    ]]></literal>
    <justification jstring="[para(6111(a,1),490(a,1,1))].">
      <j1 rule="para" parents="6111 490"/>
    </justification>
  </clause>

  <clause id="6410">
    <literal><![CDATA[
      x \ (y \ T(y * x,z)) = K((y \ 1) \ x,z)
    ]]></literal>
    <justification jstring="[para(939(a,1),6111(a,1,2))].">
      <j1 rule="para" parents="939 6111"/>
    </justification>
  </clause>

  <clause id="6411">
    <literal><![CDATA[
      x \ (y \ ((z \ (y * x)) * z)) = K((y \ z) \ x,z)
    ]]></literal>
    <justification jstring="[para(965(a,1),6111(a,1,2))].">
      <j1 rule="para" parents="965 6111"/>
    </justification>
  </clause>

  <clause id="6413">
    <literal><![CDATA[
      K(x \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K((y \ x) \ 1,z) = u
    ]]></literal>
    <justification jstring="[para(6111(a,1),5480(a,1))].">
      <j1 rule="para" parents="6111 5480"/>
    </justification>
  </clause>

  <clause id="6415">
    <literal><![CDATA[
      x * (y * K((x \ z) \ y,z)) = (z \ (x * y)) * z
    ]]></literal>
    <justification jstring="[hyper(119,a,6114,a(flip),b,965,a(flip))].">
      <j1 rule="hyper" parents="119 6114 965"/>
    </justification>
  </clause>

  <clause id="6416">
    <literal><![CDATA[
      (x * K(y \ x,z)) * (y \ 1) = T(x * (y \ 1),z)
    ]]></literal>
    <justification jstring="[para(6114(a,1),1039(a,1,1))].">
      <j1 rule="para" parents="6114 1039"/>
    </justification>
  </clause>

  <clause id="6417">
    <literal><![CDATA[
      (x \ y) * K((x \ 1) \ (x \ y),z) != u
    ]]></literal>
    <literal><![CDATA[
      x \ T(y,z) = u
    ]]></literal>
    <justification jstring="[para(6114(a,1),1050(a,1))].">
      <j1 rule="para" parents="6114 1050"/>
    </justification>
  </clause>

  <clause id="6418">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ y,z) = T(y * K(x \ y,z),y)
    ]]></literal>
    <justification jstring="[para(6114(a,1),1960(a,2,1))].">
      <j1 rule="para" parents="6114 1960"/>
    </justification>
  </clause>

  <clause id="6419">
    <literal><![CDATA[
      (x * T(x \ y,z)) \ y != u
    ]]></literal>
    <literal><![CDATA[
      K(z,x \ y) = u
    ]]></literal>
    <justification jstring="[para(6114(a,2),6345(a,1,1))].">
      <j1 rule="para" parents="6114 6345"/>
    </justification>
  </clause>

  <clause id="6420">
    <literal><![CDATA[
      R(x,y,K(y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(515,a,6115,a)].">
      <j1 rule="hyper" parents="515 6115"/>
    </justification>
  </clause>

  <clause id="6425">
    <literal><![CDATA[
      K((x \ y) \ 1,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(6138(a,2),4985(a,1))].">
      <j1 rule="para" parents="6138 4985"/>
    </justification>
  </clause>

  <clause id="6427">
    <literal><![CDATA[
      T(x,(y \ z) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(6171(a,2),4865(a,1))].">
      <j1 rule="para" parents="6171 4865"/>
    </justification>
  </clause>

  <clause id="6428">
    <literal><![CDATA[
      T(x,K(y,(z / x) \ 1)) = T(x,K(y,z \ x))
    ]]></literal>
    <justification jstring="[para(5351(a,2),6181(a,1,2))].">
      <j1 rule="para" parents="5351 6181"/>
    </justification>
  </clause>

  <clause id="6429">
    <literal><![CDATA[
      (x \ 1) * (((y * x) \ y) \ y) = R(y,x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(119,a,6205,a(flip),b,556,a)].">
      <j1 rule="hyper" parents="119 6205 556"/>
    </justification>
  </clause>

  <clause id="6430">
    <literal><![CDATA[
      T(x * (1 / y),y) = ((x * (1 / y)) \ x) \ x
    ]]></literal>
    <justification jstring="[para(75(a,1),6205(a,1,2))].">
      <j1 rule="para" parents="75 6205"/>
    </justification>
  </clause>

  <clause id="6431">
    <literal><![CDATA[
      x / T(x * (1 / y),y) = (x * (1 / y)) \ x
    ]]></literal>
    <justification jstring="[para(75(a,1),6208(a,1,2,2))].">
      <j1 rule="para" parents="75 6208"/>
    </justification>
  </clause>

  <clause id="6432">
    <literal><![CDATA[
      T(x,y \ (y / z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z \ 1) = u
    ]]></literal>
    <justification jstring="[para(6213(a,2),4454(a,1))].">
      <j1 rule="para" parents="6213 4454"/>
    </justification>
  </clause>

  <clause id="6434">
    <literal><![CDATA[
      R(T(x,y * K(x,z)),y,K(x,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(6233(a,1),1096(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6233 1096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6435">
    <literal><![CDATA[
      (x * K(y,z)) / y != u
    ]]></literal>
    <literal><![CDATA[
      (x / y) * K(y,z) = u
    ]]></literal>
    <justification jstring="[para(6234(a,1),330(a,1,2)),flip(b)].">
      <j1 rule="para" parents="6234 330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6437">
    <literal><![CDATA[
      (x * y) \ (T(x,z) * y) = K(T(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(123,a,6236,a)].">
      <j1 rule="hyper" parents="123 6236"/>
    </justification>
  </clause>

  <clause id="6441">
    <literal><![CDATA[
      x / (y * K(z,y)) = (x / y) * K(y,z)
    ]]></literal>
    <justification jstring="[para(6248(a,1),324(a,1,2))].">
      <j1 rule="para" parents="6248 324"/>
    </justification>
  </clause>

  <clause id="6442">
    <literal><![CDATA[
      T(K(x,y),z * y) * K(y,x) = K(K(x,y),y * z)
    ]]></literal>
    <justification jstring="[para(6255(a,2),4974(a,1,1))].">
      <j1 rule="para" parents="6255 4974"/>
    </justification>
  </clause>

  <clause id="6443">
    <literal><![CDATA[
      K(((x \ 1) * y) \ y,z) = T(K(x,z),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,5548,a(flip),b,6273,a),flip(a)].">
      <j1 rule="hyper" parents="58 5548 6273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6444">
    <literal><![CDATA[
      K(x \ y,z) \ K(K(x \ y,z),y) = ((K(y / x,z) * y) / y) \ 1
    ]]></literal>
    <justification jstring="[para(6290(a,2),4905(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6290 4905"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6446">
    <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),6324(a,1,2))].">
      <j1 rule="para" parents="90 6324"/>
    </justification>
  </clause>

  <clause id="6448">
    <literal><![CDATA[
      ((x * y) * z) / (y * z) = R(x,T(y,z),T(z,y))
    ]]></literal>
    <justification jstring="[hyper(117,a,6333,a(flip),b,4271,a)].">
      <j1 rule="hyper" parents="117 6333 4271"/>
    </justification>
  </clause>

  <clause id="6449">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * y) * z) = a(x,T(y,z),T(z,y))
    ]]></literal>
    <justification jstring="[hyper(116,a,6333,a(flip),b,4274,a)].">
      <j1 rule="hyper" parents="116 6333 4274"/>
    </justification>
  </clause>

  <clause id="6450">
    <literal><![CDATA[
      T(x,K(y,z)) != K(y,z) \ u
    ]]></literal>
    <literal><![CDATA[
      u * K(z,y) = x
    ]]></literal>
    <justification jstring="[para(6334(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="6334 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6451">
    <literal><![CDATA[
      T(x * K(y,z),K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) * x = u
    ]]></literal>
    <justification jstring="[para(6334(a,2),5163(a,1))].">
      <j1 rule="para" parents="6334 5163"/>
    </justification>
  </clause>

  <clause id="6452">
    <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(6337(a,1),109(a,2,1,1))].">
      <j1 rule="para" parents="6337 109"/>
    </justification>
  </clause>

  <clause id="6453">
    <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(6337(a,1),237(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6337 237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6454">
    <literal><![CDATA[
      (K(x,y) \ z) * K(x,y) = T(z,K(x,y))
    ]]></literal>
    <justification jstring="[para(5130(a,2),6340(a,1,1))].">
      <j1 rule="para" parents="5130 6340"/>
    </justification>
  </clause>

  <clause id="6455">
    <literal><![CDATA[
      T(T(x,y) * z,K(x,y)) = (x * z) * K(x,y)
    ]]></literal>
    <justification jstring="[para(4819(a,1),6340(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4819 6340"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6456">
    <literal><![CDATA[
      (K(x,y) * z) \ z = T(K(y,x),z)
    ]]></literal>
    <justification jstring="[para(6350(a,1),4277(a,1,1))].">
      <j1 rule="para" parents="6350 4277"/>
    </justification>
  </clause>

  <clause id="6457">
    <literal><![CDATA[
      T(K(x * y,x),y) = K(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(5417,a,6384,a)].">
      <j1 rule="hyper" parents="5417 6384"/>
    </justification>
  </clause>

  <clause id="6458">
    <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(6384(a,2),4955(a,1,1))].">
      <j1 rule="para" parents="6384 4955"/>
    </justification>
  </clause>

  <clause id="6459">
    <literal><![CDATA[
      K(x,K(y,y * x)) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,6457,a(flip),b,5624,a),flip(a)].">
      <j1 rule="hyper" parents="115 6457 5624"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6460">
    <literal><![CDATA[
      T(x,K(y,y * x)) = x
    ]]></literal>
    <justification jstring="[hyper(51,a,6459,a)].">
      <j1 rule="hyper" parents="51 6459"/>
    </justification>
  </clause>

  <clause id="6461">
    <literal><![CDATA[
      T(x \ y,K(x,y)) = x \ y
    ]]></literal>
    <justification jstring="[para(5(a,1),6460(a,1,2,2))].">
      <j1 rule="para" parents="5 6460"/>
    </justification>
  </clause>

  <clause id="6462">
    <literal><![CDATA[
      K(x,y) * (x \ y) = (x \ y) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,6461,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 6461 17"/>
    </justification>
  </clause>

  <clause id="6464">
    <literal><![CDATA[
      (x \ T(x * y,z)) \ y = K(z,(x \ 1) \ y)
    ]]></literal>
    <justification jstring="[para(939(a,1),6387(a,1,1))].">
      <j1 rule="para" parents="939 6387"/>
    </justification>
  </clause>

  <clause id="6465">
    <literal><![CDATA[
      (((x \ (y / z)) * x) * z) \ y = K(x,(x * z) \ y)
    ]]></literal>
    <justification jstring="[para(1105(a,1),6387(a,1,1))].">
      <j1 rule="para" parents="1105 6387"/>
    </justification>
  </clause>

  <clause id="6466">
    <literal><![CDATA[
      (x * (y * T(y \ (x \ z),u))) \ z = K(u,(x * y) \ z)
    ]]></literal>
    <justification jstring="[para(924(a,1),6387(a,1,1))].">
      <j1 rule="para" parents="924 6387"/>
    </justification>
  </clause>

  <clause id="6467">
    <literal><![CDATA[
      ((x * T(x \ y,z)) * u) \ (y * u) = K(z,(x * u) \ (y * u))
    ]]></literal>
    <justification jstring="[para(1486(a,1),6387(a,1,1))].">
      <j1 rule="para" parents="1486 6387"/>
    </justification>
  </clause>

  <clause id="6468">
    <literal><![CDATA[
      T(x * T(x \ y,z),u) \ T(y,u) = K(z,T(x,u) \ T(y,u))
    ]]></literal>
    <justification jstring="[para(1963(a,1),6387(a,1,1))].">
      <j1 rule="para" parents="1963 6387"/>
    </justification>
  </clause>

  <clause id="6469">
    <literal><![CDATA[
      x / ((x * y) / x) = K(y,x) * (x / y)
    ]]></literal>
    <justification jstring="[hyper(320,a,6375,a,b,6397,a),flip(a)].">
      <j1 rule="hyper" parents="320 6375 6397"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6470">
    <literal><![CDATA[
      (x / (y \ z)) * K(y \ z,y) = x / (z / y)
    ]]></literal>
    <justification jstring="[para(5(a,1),6397(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 6397"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6471">
    <literal><![CDATA[
      (x * y) / ((z * y) / z) = x * K(y,z)
    ]]></literal>
    <justification jstring="[para(6(a,1),6397(a,2,1))].">
      <j1 rule="para" parents="6 6397"/>
    </justification>
  </clause>

  <clause id="6472">
    <literal><![CDATA[
      x / (y / (y / z)) = (x / z) * K(z,y / z)
    ]]></literal>
    <justification jstring="[para(7(a,1),6397(a,1,2,1))].">
      <j1 rule="para" parents="7 6397"/>
    </justification>
  </clause>

  <clause id="6473">
    <literal><![CDATA[
      x / (y / (y / z)) = (x / z) * K(z,z \ y)
    ]]></literal>
    <justification jstring="[para(4343(a,1),6397(a,1,2))].">
      <j1 rule="para" parents="4343 6397"/>
    </justification>
  </clause>

  <clause id="6474">
    <literal><![CDATA[
      K(x,((y / z) * K(z,u)) \ 1) = K(x,((u * z) / u) / y)
    ]]></literal>
    <justification jstring="[para(6397(a,1),5351(a,1,2,1))].">
      <j1 rule="para" parents="6397 5351"/>
    </justification>
  </clause>

  <clause id="6475">
    <literal><![CDATA[
      (x * (y / z)) * K(z \ y,z) = x * (z \ y)
    ]]></literal>
    <justification jstring="[para(5(a,1),6405(a,1,1,2,1))].">
      <j1 rule="para" parents="5 6405"/>
    </justification>
  </clause>

  <clause id="6476">
    <literal><![CDATA[
      (x * (y / (y / z))) * K(z,z \ y) = x * z
    ]]></literal>
    <justification jstring="[para(4343(a,1),6405(a,1,1,2))].">
      <j1 rule="para" parents="4343 6405"/>
    </justification>
  </clause>

  <clause id="6477">
    <literal><![CDATA[
      (x / (y / z)) * (z \ y) = x * K(z \ y,z)
    ]]></literal>
    <justification jstring="[para(4776(a,1),6407(a,1,1,2))].">
      <j1 rule="para" parents="4776 6407"/>
    </justification>
  </clause>

  <clause id="6482">
    <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),6166(a,1,2,1))].">
      <j1 rule="para" parents="92 6166"/>
    </justification>
  </clause>

  <clause id="6483">
    <literal><![CDATA[
      K(x,1 / (y \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(3558(a,2),6166(a,1))].">
      <j1 rule="para" parents="3558 6166"/>
    </justification>
  </clause>

  <clause id="6484">
    <literal><![CDATA[
      K(x,(K(y,z) * u) \ 1) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u \ K(z,y)) = w
    ]]></literal>
    <justification jstring="[para(5130(a,1),6166(a,1,2,1))].">
      <j1 rule="para" parents="5130 6166"/>
    </justification>
  </clause>

  <clause id="6485">
    <literal><![CDATA[
      T(K(x,y / z),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(5745(a,2),6166(a,1))].">
      <j1 rule="para" parents="5745 6166"/>
    </justification>
  </clause>

  <clause id="6486">
    <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(636(a,1),6199(a,1,1))].">
      <j1 rule="para" parents="636 6199"/>
    </justification>
  </clause>

  <clause id="6487">
    <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(6325(a,1),6199(a,1,1))].">
      <j1 rule="para" parents="6325 6199"/>
    </justification>
  </clause>

  <clause id="6489">
    <literal><![CDATA[
      K(x,(y * z) \ y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ 1) = u
    ]]></literal>
    <justification jstring="[para(6(a,1),6204(a,1,2,2))].">
      <j1 rule="para" parents="6 6204"/>
    </justification>
  </clause>

  <clause id="6490">
    <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(441(a,1),6204(a,1,2,2))].">
      <j1 rule="para" parents="441 6204"/>
    </justification>
  </clause>

  <clause id="6491">
    <literal><![CDATA[
      (x * ((y * z) / y)) * y != u
    ]]></literal>
    <literal><![CDATA[
      (x * z) * T(y,z) = u
    ]]></literal>
    <justification jstring="[para(6097(a,1),6227(a,1,1))].">
      <j1 rule="para" parents="6097 6227"/>
    </justification>
  </clause>

  <clause id="6492">
    <literal><![CDATA[
      T(x,x \ T(x * y,y \ 1)) = T(x,L(y \ 1,y,x) \ 1)
    ]]></literal>
    <justification jstring="[para(6300(a,1),4180(a,1,2,2))].">
      <j1 rule="para" parents="6300 4180"/>
    </justification>
  </clause>

  <clause id="6493">
    <literal><![CDATA[
      K(1 / (x \ y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(5(a,1),6304(a,1,1,2,1))].">
      <j1 rule="para" parents="5 6304"/>
    </justification>
  </clause>

  <clause id="6495">
    <literal><![CDATA[
      K(L(x,x \ 1,y),z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(72(a,1),6305(a,2,1))].">
      <j1 rule="para" parents="72 6305"/>
    </justification>
  </clause>

  <clause id="6497">
    <literal><![CDATA[
      K(x,L(y,y \ 1,z)) = 1 / K(y,x)
    ]]></literal>
    <justification jstring="[para(6495(a,1),4971(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6495 4971"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6498">
    <literal><![CDATA[
      K(x,L(y,y \ 1,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,4971,a(flip),b,6497,a),flip(a)].">
      <j1 rule="hyper" parents="320 4971 6497"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6499">
    <literal><![CDATA[
      K(x,L(y,y \ 1,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(6497(a,2),4978(a,1))].">
      <j1 rule="para" parents="6497 4978"/>
    </justification>
  </clause>

  <clause id="6500">
    <literal><![CDATA[
      K(x,L(1 / y,y,z)) = K(x,1 / y)
    ]]></literal>
    <justification jstring="[para(75(a,1),6498(a,1,2,2))].">
      <j1 rule="para" parents="75 6498"/>
    </justification>
  </clause>

  <clause id="6501">
    <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),6367(a,1,1))].">
      <j1 rule="para" parents="187 6367"/>
    </justification>
  </clause>

  <clause id="6502">
    <literal><![CDATA[
      x / T(x * (y / x),y \ x) = L((y / x) \ 1,y / x,x)
    ]]></literal>
    <justification jstring="[para(4649(a,1),6377(a,1,2))].">
      <j1 rule="para" parents="4649 6377"/>
    </justification>
  </clause>

  <clause id="6503">
    <literal><![CDATA[
      K((K(x,y) * z) \ 1,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(z \ K(y,x),u) = w
    ]]></literal>
    <justification jstring="[para(5130(a,1),6425(a,1,1,1))].">
      <j1 rule="para" parents="5130 6425"/>
    </justification>
  </clause>

  <clause id="6504">
    <literal><![CDATA[
      T(K(x / y,z),x) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(5540(a,2),6425(a,1))].">
      <j1 rule="para" parents="5540 6425"/>
    </justification>
  </clause>

  <clause id="6505">
    <literal><![CDATA[
      x \ (y * (z * T(z \ (y \ x),u))) != w
    ]]></literal>
    <literal><![CDATA[
      K((y * z) \ x,u) = w
    ]]></literal>
    <justification jstring="[para(5532(a,2),6425(a,1))].">
      <j1 rule="para" parents="5532 6425"/>
    </justification>
  </clause>

  <clause id="6506">
    <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),6427(a,1,2,1))].">
      <j1 rule="para" parents="17 6427"/>
    </justification>
  </clause>

  <clause id="6507">
    <literal><![CDATA[
      T(x,(y * z) \ y) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z \ 1) = u
    ]]></literal>
    <justification jstring="[para(6(a,1),6432(a,1,2,2))].">
      <j1 rule="para" parents="6 6432"/>
    </justification>
  </clause>

  <clause id="6508">
    <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(3353(a,1),6485(a,1))].">
      <j1 rule="para" parents="3353 6485"/>
    </justification>
  </clause>

  <clause id="6509">
    <literal><![CDATA[
      K(x / y,x) != z
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,x) = z
    ]]></literal>
    <justification jstring="[para(2888(a,1),6504(a,1))].">
      <j1 rule="para" parents="2888 6504"/>
    </justification>
  </clause>

  <clause id="6510">
    <literal><![CDATA[
      (x * (y \ z)) / K(y \ z,y) = x * (z / y)
    ]]></literal>
    <justification jstring="[hyper(6396,a,6101,a)].">
      <j1 rule="hyper" parents="6396 6101"/>
    </justification>
  </clause>

  <clause id="6512">
    <literal><![CDATA[
      (x * ((y / z) / x)) * z = y * K(x,(x * z) \ y)
    ]]></literal>
    <justification jstring="[hyper(320,a,2299,a(flip),b,6145,a)].">
      <j1 rule="hyper" parents="320 2299 6145"/>
    </justification>
  </clause>

  <clause id="6513">
    <literal><![CDATA[
      T(x * y,K(y,z)) = y * T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,5114,a(flip),b,6150,a),flip(a)].">
      <j1 rule="hyper" parents="58 5114 6150"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6514">
    <literal><![CDATA[
      (x * y) * K(y,T(x,z)) = T(y * x,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,6116,a,b,6513,a)].">
      <j1 rule="hyper" parents="320 6116 6513"/>
    </justification>
  </clause>

  <clause id="6515">
    <literal><![CDATA[
      x * T(y / x,T(x,z)) = T(y,K(x,z))
    ]]></literal>
    <justification jstring="[para(7(a,1),6513(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7 6513"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6516">
    <literal><![CDATA[
      T(x / y,T(y,z)) = y \ T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(123,a,6515,a),flip(a)].">
      <j1 rule="hyper" parents="123 6515"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6517">
    <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(6516(a,2),4609(a,1))].">
      <j1 rule="para" parents="6516 4609"/>
    </justification>
  </clause>

  <clause id="6518">
    <literal><![CDATA[
      ((x * T(y,z)) * z) / (T(y,z) * z) = R(x,y,z * K(y,z))
    ]]></literal>
    <justification jstring="[para(6161(a,1),5188(a,1,1))].">
      <j1 rule="para" parents="6161 5188"/>
    </justification>
  </clause>

  <clause id="6521">
    <literal><![CDATA[
      x * (K(y,x) * K(y,x)) = (T(y,x) * x) / y
    ]]></literal>
    <justification jstring="[hyper(5469,a,6223,a)].">
      <j1 rule="hyper" parents="5469 6223"/>
    </justification>
  </clause>

  <clause id="6522">
    <literal><![CDATA[
      (K(x,y) * K(y,z)) * T(y,x) = T(y,z)
    ]]></literal>
    <justification jstring="[hyper(6388,a,6231,a(flip))].">
      <j1 rule="hyper" parents="6388 6231"/>
    </justification>
  </clause>

  <clause id="6523">
    <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,6243,a(flip),b,101,a)].">
      <j1 rule="hyper" parents="117 6243 101"/>
    </justification>
  </clause>

  <clause id="6524">
    <literal><![CDATA[
      ((x \ y) * z) * K(x,T(x \ y,z)) = (y / x) * z
    ]]></literal>
    <justification jstring="[hyper(320,a,5459,a(flip),b,6256,a),flip(a)].">
      <j1 rule="hyper" parents="320 5459 6256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6527">
    <literal><![CDATA[
      K(T(K(x,y) * z,u) \ 1,w) = T(K(z \ K(y,x),w),u)
    ]]></literal>
    <justification jstring="[para(6277(a,1),5544(a,2,1))].">
      <j1 rule="para" parents="6277 5544"/>
    </justification>
  </clause>

  <clause id="6528">
    <literal><![CDATA[
      T(x,y) / (z \ x) = z * K(((z \ x) \ 1) \ z,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,4577,a(flip),b,6281,a)].">
      <j1 rule="hyper" parents="58 4577 6281"/>
    </justification>
  </clause>

  <clause id="6529">
    <literal><![CDATA[
      K((x \ 1) \ y,x) = K(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(29,a,6384,a(flip),b,6281,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="29 6384 6281"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6530">
    <literal><![CDATA[
      (x * K((y \ 1) \ x,z)) * y = T(x * y,z)
    ]]></literal>
    <justification jstring="[para(6281(a,1),4596(a,1,1))].">
      <j1 rule="para" parents="6281 4596"/>
    </justification>
  </clause>

  <clause id="6531">
    <literal><![CDATA[
      T(x * K((y \ 1) \ x,z),y) = y \ T(x * y,z)
    ]]></literal>
    <justification jstring="[para(6281(a,1),4602(a,1,1))].">
      <j1 rule="para" parents="6281 4602"/>
    </justification>
  </clause>

  <clause id="6532">
    <literal><![CDATA[
      K((x \ 1) * y,x \ 1) = K(x \ y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(5966,a,6529,a),flip(a)].">
      <j1 rule="hyper" parents="5966 6529"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6533">
    <literal><![CDATA[
      T(x,y) / ((y \ x) \ x) = T(y,x) \ x
    ]]></literal>
    <justification jstring="[hyper(30,a,4682,a(flip),b,6378,a),flip(a)].">
      <j1 rule="hyper" parents="30 4682 6378"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6534">
    <literal><![CDATA[
      (T(x,y) \ y) * ((x \ y) \ y) = T(y,x)
    ]]></literal>
    <justification jstring="[hyper(133,a,6533,a)].">
      <j1 rule="hyper" parents="133 6533"/>
    </justification>
  </clause>

  <clause id="6536">
    <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,3348,a,b,6406,a),flip(a)].">
      <j1 rule="hyper" parents="320 3348 6406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6540">
    <literal><![CDATA[
      (x * K(y,z / (z / u))) * K(u,u \ z) = (x / T(z / (z / u),y)) * u
    ]]></literal>
    <justification jstring="[para(6325(a,1),6476(a,1,1))].">
      <j1 rule="para" parents="6325 6476"/>
    </justification>
  </clause>

  <clause id="6541">
    <literal><![CDATA[
      T(x * y,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      y * T(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(6514(a,1),6199(a,1))].">
      <j1 rule="para" parents="6514 6199"/>
    </justification>
  </clause>

  <clause id="6542">
    <literal><![CDATA[
      K(((x \ y) \ 1) * z,y \ x) = K((x \ y) \ z,(x \ y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(6166,a,6532,a)].">
      <j1 rule="hyper" parents="6166 6532"/>
    </justification>
  </clause>

  <clause id="6543">
    <literal><![CDATA[
      K(x * (y \ 1),y \ 1) = K(y \ x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,5266,a,b,6532,a)].">
      <j1 rule="hyper" parents="58 5266 6532"/>
    </justification>
  </clause>

  <clause id="6544">
    <literal><![CDATA[
      T(K(x \ y,x \ 1) / x,y) = R(1 / x,y,x \ 1)
    ]]></literal>
    <justification jstring="[para(6543(a,1),5972(a,1,1,1))].">
      <j1 rule="para" parents="6543 5972"/>
    </justification>
  </clause>

  <clause id="6545">
    <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(6119(a,1),4820(a,1,2))].">
      <j1 rule="para" parents="6119 4820"/>
    </justification>
  </clause>

  <clause id="6546">
    <literal><![CDATA[
      L(T(K(x,y \ z),u),y \ z,w) = T(K(x,(z \ y) \ 1),u)
    ]]></literal>
    <justification jstring="[para(6121(a,1),20(a,2,1))].">
      <j1 rule="para" parents="6121 20"/>
    </justification>
  </clause>

  <clause id="6547">
    <literal><![CDATA[
      x \ (y \ ((z \ (y * x)) * z)) != u
    ]]></literal>
    <literal><![CDATA[
      K((y \ z) \ x,z) = u
    ]]></literal>
    <justification jstring="[para(965(a,1),6165(a,1,2))].">
      <j1 rule="para" parents="965 6165"/>
    </justification>
  </clause>

  <clause id="6548">
    <literal><![CDATA[
      L(x * y,K(y * x,z),u) = x * y
    ]]></literal>
    <justification jstring="[para(4(a,1),6251(a,2,1))].">
      <j1 rule="para" parents="4 6251"/>
    </justification>
  </clause>

  <clause id="6549">
    <literal><![CDATA[
      (x * K(y * z,u)) * (z * y) = x * (K(y * z,u) * (z * y))
    ]]></literal>
    <justification jstring="[hyper(119,a,6548,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="119 6548 13"/>
    </justification>
  </clause>

  <clause id="6550">
    <literal><![CDATA[
      T(T(x,y) * z,K(x,y)) != u
    ]]></literal>
    <literal><![CDATA[
      (x * z) * K(x,y) = u
    ]]></literal>
    <justification jstring="[para(4781(a,1),6395(a,1,1))].">
      <j1 rule="para" parents="4781 6395"/>
    </justification>
  </clause>

  <clause id="6551">
    <literal><![CDATA[
      T(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      (K(z,y) * x) * K(y,z) = u
    ]]></literal>
    <justification jstring="[para(5133(a,1),6395(a,1,1))].">
      <j1 rule="para" parents="5133 6395"/>
    </justification>
  </clause>

  <clause id="6553">
    <literal><![CDATA[
      R(x,T(y,z),T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(6448(a,1),518(a,1))].">
      <j1 rule="para" parents="6448 518"/>
    </justification>
  </clause>

  <clause id="6554">
    <literal><![CDATA[
      K(x,(y * z) \ T(y,u)) = K(x,z \ K(y,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,6140,a(flip),b,6142,a),flip(a)].">
      <j1 rule="hyper" parents="58 6140 6142"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6555">
    <literal><![CDATA[
      T(x,(y * z) \ T(y,u)) = T(x,z \ K(y,u))
    ]]></literal>
    <justification jstring="[hyper(118,a,6554,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 6554 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6556">
    <literal><![CDATA[
      K((x * y) \ T(x,z),u) = (u \ 1) / (u \ K(u,y \ K(x,z)))
    ]]></literal>
    <justification jstring="[para(6554(a,1),5138(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6554 5138"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6557">
    <literal><![CDATA[
      K(x,(y * z) \ z) = K(x,y \ K(z,y))
    ]]></literal>
    <justification jstring="[para(5598(a,1),6554(a,1,2))].">
      <j1 rule="para" parents="5598 6554"/>
    </justification>
  </clause>

  <clause id="6558">
    <literal><![CDATA[
      T(x,(y \ z) \ K(y,u)) = T(x,z \ T(y,u))
    ]]></literal>
    <justification jstring="[para(5(a,1),6555(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 6555"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6559">
    <literal><![CDATA[
      L(K(x,y \ z),z,z \ 1) = K(x,((1 / z) * y) \ 1)
    ]]></literal>
    <justification jstring="[para(2815(a,1),6144(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2815 6144"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6560">
    <literal><![CDATA[
      K(x * y,z) * (y * x) = K(y,x) * T(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,4622,a,b,6160,a)].">
      <j1 rule="hyper" parents="320 4622 6160"/>
    </justification>
  </clause>

  <clause id="6561">
    <literal><![CDATA[
      T(L(x \ 1,x,y) \ 1,z) = ((y * x) \ y) \ K(x,z)
    ]]></literal>
    <justification jstring="[para(217(a,2),6264(a,1,1,1))].">
      <j1 rule="para" parents="217 6264"/>
    </justification>
  </clause>

  <clause id="6565">
    <literal><![CDATA[
      x \ (y \ ((z \ (y * x)) * z)) = K((z / y) \ x,z)
    ]]></literal>
    <justification jstring="[para(4661(a,1),6269(a,1,2))].">
      <j1 rule="para" parents="4661 6269"/>
    </justification>
  </clause>

  <clause id="6566">
    <literal><![CDATA[
      K((x / (y \ 1)) \ z,x) = K((x * y) \ z,x)
    ]]></literal>
    <justification jstring="[hyper(6425,a,6270,a),flip(a)].">
      <j1 rule="hyper" parents="6425 6270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6567">
    <literal><![CDATA[
      (x \ T(y,z)) * K(z,(x \ 1) \ (x \ y)) = x \ y
    ]]></literal>
    <justification jstring="[hyper(6344,a,6283,a)].">
      <j1 rule="hyper" parents="6344 6283"/>
    </justification>
  </clause>

  <clause id="6568">
    <literal><![CDATA[
      K((x * y) \ z,y) = K((y * x) \ z,y)
    ]]></literal>
    <justification jstring="[hyper(29,a,6284,a,b,6285,a),flip(a)].">
      <j1 rule="hyper" parents="29 6284 6285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6569">
    <literal><![CDATA[
      1 / K((x * y) \ z,x) = K(x,(y * x) \ z)
    ]]></literal>
    <justification jstring="[para(6568(a,1),4971(a,1,2))].">
      <j1 rule="para" parents="6568 4971"/>
    </justification>
  </clause>

  <clause id="6570">
    <literal><![CDATA[
      K(x,(y * x) \ z) = K(x,(x * y) \ z)
    ]]></literal>
    <justification jstring="[hyper(4978,a,6569,a),flip(a)].">
      <j1 rule="hyper" parents="4978 6569"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6571">
    <literal><![CDATA[
      R(x,K(y,z),T(z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(515,a,6310,a)].">
      <j1 rule="hyper" parents="515 6310"/>
    </justification>
  </clause>

  <clause id="6572">
    <literal><![CDATA[
      R(x,K(y,z),T(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(6571(a,1),46(a,2))].">
      <j1 rule="para" parents="6571 46"/>
    </justification>
  </clause>

  <clause id="6573">
    <literal><![CDATA[
      x * (y \ R(y,x,y)) = T(y * x,y) / y
    ]]></literal>
    <justification jstring="[para(5293(a,1),6391(a,1,2))].">
      <j1 rule="para" parents="5293 6391"/>
    </justification>
  </clause>

  <clause id="6574">
    <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(6573(a,1),215(a,2,2))].">
      <j1 rule="para" parents="6573 215"/>
    </justification>
  </clause>

  <clause id="6575">
    <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(6416(a,2),770(a,1))].">
      <j1 rule="para" parents="6416 770"/>
    </justification>
  </clause>

  <clause id="6576">
    <literal><![CDATA[
      K(K(x,y),y * z) = K(z * y,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(5655,a,6442,a),flip(a)].">
      <j1 rule="hyper" parents="5655 6442"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6577">
    <literal><![CDATA[
      K(x * y,K(y,z)) = K(y * x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(5654,a,6576,a),flip(a)].">
      <j1 rule="hyper" parents="5654 6576"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6578">
    <literal><![CDATA[
      T(x,y) / ((1 / z) \ x) = (1 / z) * K((((1 / z) \ x) \ 1) \ (z \ 1),y)
    ]]></literal>
    <justification jstring="[para(3985(a,1),6528(a,2,2))].">
      <j1 rule="para" parents="3985 6528"/>
    </justification>
  </clause>

  <clause id="6579">
    <literal><![CDATA[
      T(x * K(x * y,y \ 1),y) = y \ T(x * y,y \ 1)
    ]]></literal>
    <justification jstring="[para(5862(a,1),6531(a,1,1,2))].">
      <j1 rule="para" parents="5862 6531"/>
    </justification>
  </clause>

  <clause id="6580">
    <literal><![CDATA[
      K((x / y) \ z,x) = K((y \ x) \ z,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,6411,a(flip),b,6565,a),flip(a)].">
      <j1 rule="hyper" parents="58 6411 6565"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6581">
    <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,6567,a),flip(a)].">
      <j1 rule="hyper" parents="354 6567"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6582">
    <literal><![CDATA[
      L(K(x,y \ z),z,u) = K(x,(u * y) \ (u * z))
    ]]></literal>
    <justification jstring="[hyper(58,a,6144,a(flip),b,6132,a)].">
      <j1 rule="hyper" parents="58 6144 6132"/>
    </justification>
  </clause>

  <clause id="6583">
    <literal><![CDATA[
      K(x,(y * z) \ (y * x)) = K(x,z \ x)
    ]]></literal>
    <justification jstring="[hyper(6118,a,6582,a),flip(a)].">
      <j1 rule="hyper" parents="6118 6582"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6584">
    <literal><![CDATA[
      L(K(x,(y \ z) \ u),u,y) = K(x,z \ (y * u))
    ]]></literal>
    <justification jstring="[para(5(a,1),6582(a,2,2,1))].">
      <j1 rule="para" parents="5 6582"/>
    </justification>
  </clause>

  <clause id="6585">
    <literal><![CDATA[
      L(K(x,y \ (z \ u)),z \ u,z) = K(x,(z * y) \ u)
    ]]></literal>
    <justification jstring="[para(5(a,1),6582(a,2,2,2))].">
      <j1 rule="para" parents="5 6582"/>
    </justification>
  </clause>

  <clause id="6586">
    <literal><![CDATA[
      K(x,(y * (z / u)) \ (y * z)) = L(K(x,u),z,y)
    ]]></literal>
    <justification jstring="[para(75(a,1),6582(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="75 6582"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6587">
    <literal><![CDATA[
      L(K(x,y \ z),z,u) = K(x,L(y \ z,y,u))
    ]]></literal>
    <justification jstring="[para(92(a,2),6582(a,2,2))].">
      <j1 rule="para" parents="92 6582"/>
    </justification>
  </clause>

  <clause id="6588">
    <literal><![CDATA[
      K(x,(y * z) \ (y * x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ x) = u
    ]]></literal>
    <justification jstring="[para(6582(a,1),6118(a,1))].">
      <j1 rule="para" parents="6582 6118"/>
    </justification>
  </clause>

  <clause id="6589">
    <literal><![CDATA[
      K(x,(y \ z) \ x) = K(x,z \ (y * x))
    ]]></literal>
    <justification jstring="[para(5(a,1),6583(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 6583"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6590">
    <literal><![CDATA[
      K(x \ y,(x * z) \ y) = K(x \ y,z \ (x \ y))
    ]]></literal>
    <justification jstring="[para(5(a,1),6583(a,1,2,2))].">
      <j1 rule="para" parents="5 6583"/>
    </justification>
  </clause>

  <clause id="6591">
    <literal><![CDATA[
      K(x,L(y \ x,y,z)) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[para(92(a,2),6583(a,1,2))].">
      <j1 rule="para" parents="92 6583"/>
    </justification>
  </clause>

  <clause id="6592">
    <literal><![CDATA[
      K(x,(K(y,z) * u) \ x) = K(x,u \ (K(z,y) * x))
    ]]></literal>
    <justification jstring="[para(5133(a,1),6583(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5133 6583"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6593">
    <literal><![CDATA[
      T(x,L(y \ x,y,z)) = T(x,y \ x)
    ]]></literal>
    <justification jstring="[hyper(118,a,6591,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 6591 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6594">
    <literal><![CDATA[
      T(x,(y \ z) \ x) = T(x,z \ (y * x))
    ]]></literal>
    <justification jstring="[para(490(a,1),6593(a,1,2)),flip(a)].">
      <j1 rule="para" parents="490 6593"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6595">
    <literal><![CDATA[
      K(x,((y * K(z,y)) \ u) \ x) = K(x,u \ (y * (K(z,y) * x)))
    ]]></literal>
    <justification jstring="[para(5452(a,1),6589(a,2,2,2))].">
      <j1 rule="para" parents="5452 6589"/>
    </justification>
  </clause>

  <clause id="6596">
    <literal><![CDATA[
      K(x,T((y \ z) \ 1,z) \ x) = K(x,y \ ((((y \ z) \ 1) \ y) * x))
    ]]></literal>
    <justification jstring="[para(5846(a,2),6589(a,1,2,1))].">
      <j1 rule="para" parents="5846 6589"/>
    </justification>
  </clause>

  <clause id="6597">
    <literal><![CDATA[
      K(x,L(y \ z,y,K(z,u))) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(4214,a,6587,a),flip(a)].">
      <j1 rule="hyper" parents="4214 6587"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6598">
    <literal><![CDATA[
      K(x,L(y \ z,y,u)) = K(x,(u * y) \ (u * z))
    ]]></literal>
    <justification jstring="[hyper(58,a,6582,a(flip),b,6587,a),flip(a)].">
      <j1 rule="hyper" parents="58 6582 6587"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6599">
    <literal><![CDATA[
      K(x,(K(y,z) * u) \ T(y,z)) = K(x,u \ y)
    ]]></literal>
    <justification jstring="[para(4850(a,1),6597(a,1,2))].">
      <j1 rule="para" parents="4850 6597"/>
    </justification>
  </clause>

  <clause id="6600">
    <literal><![CDATA[
      K(x,T(y,z) \ z) = K(x,y \ T(z,y))
    ]]></literal>
    <justification jstring="[para(4811(a,1),6599(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4811 6599"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6601">
    <literal><![CDATA[
      T(x,T(y,z) \ z) = T(x,y \ T(z,y))
    ]]></literal>
    <justification jstring="[hyper(118,a,6600,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 6600 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6602">
    <literal><![CDATA[
      (x * y) * K(z,u \ (x * y)) = x * (y * K(z,(x \ u) \ y))
    ]]></literal>
    <justification jstring="[hyper(119,a,6584,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="119 6584 13"/>
    </justification>
  </clause>

  <clause id="6603">
    <literal><![CDATA[
      L(T(K(x,(y \ z) \ u),w),u,y) = T(K(x,z \ (y * u)),w)
    ]]></literal>
    <justification jstring="[para(6584(a,1),20(a,2,1))].">
      <j1 rule="para" parents="6584 20"/>
    </justification>
  </clause>

  <clause id="6604">
    <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(6584(a,1),5468(a,1))].">
      <j1 rule="para" parents="6584 5468"/>
    </justification>
  </clause>

  <clause id="6605">
    <literal><![CDATA[
      K(x,y \ (z * x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,(z \ y) \ x) = u
    ]]></literal>
    <justification jstring="[para(6584(a,1),6118(a,1))].">
      <j1 rule="para" parents="6584 6118"/>
    </justification>
  </clause>

  <clause id="6606">
    <literal><![CDATA[
      K(x,(y * ((y \ z) / u)) \ z) = L(K(x,u),y \ z,y)
    ]]></literal>
    <justification jstring="[para(5(a,1),6586(a,1,2,2))].">
      <j1 rule="para" parents="5 6586"/>
    </justification>
  </clause>

  <clause id="6607">
    <literal><![CDATA[
      K(x,L(y,z / y,u)) = L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(94(a,2),6586(a,1,2))].">
      <j1 rule="para" parents="94 6586"/>
    </justification>
  </clause>

  <clause id="6608">
    <literal><![CDATA[
      K(x,L(y,z / y,u)) = L(K(y,x),z,u) \ 1
    ]]></literal>
    <justification jstring="[hyper(320,a,5750,a,b,6607,a),flip(a)].">
      <j1 rule="hyper" parents="320 5750 6607"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6609">
    <literal><![CDATA[
      L(K(x,y),z * y,u) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(6(a,1),6607(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6 6607"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6610">
    <literal><![CDATA[
      K(x,L(y,z,u)) * K(y,x) = a(u,z * y,K(y,x))
    ]]></literal>
    <justification jstring="[para(6609(a,1),5890(a,1,1))].">
      <j1 rule="para" parents="6609 5890"/>
    </justification>
  </clause>

  <clause id="6611">
    <literal><![CDATA[
      K(x,y) * K(y,L(x,z,u)) = a(u,z * x,K(x,y))
    ]]></literal>
    <justification jstring="[para(6609(a,1),5892(a,1,2))].">
      <j1 rule="para" parents="6609 5892"/>
    </justification>
  </clause>

  <clause id="6612">
    <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(6609(a,1),5900(a,1,1))].">
      <j1 rule="para" parents="6609 5900"/>
    </justification>
  </clause>

  <clause id="6613">
    <literal><![CDATA[
      K(L(x,y / x,z),u) = L(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[hyper(4976,a,6608,a)].">
      <j1 rule="hyper" parents="4976 6608"/>
    </justification>
  </clause>

  <clause id="6614">
    <literal><![CDATA[
      K(x,L(y,z / y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(K(x,y),z,u) = w
    ]]></literal>
    <justification jstring="[para(6608(a,2),5753(a,1))].">
      <j1 rule="para" parents="6608 5753"/>
    </justification>
  </clause>

  <clause id="6615">
    <literal><![CDATA[
      L(K(x,y),z * x,u) = K(L(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(6(a,1),6613(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6 6613"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6616">
    <literal><![CDATA[
      L(K(x \ y,z),y,u) = K(L(x \ y,x,u),z)
    ]]></literal>
    <justification jstring="[para(72(a,1),6613(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="72 6613"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6617">
    <literal><![CDATA[
      L(K(x,y),z * T(x,u),w) = K(L(x,z * K(x,u),w),y)
    ]]></literal>
    <justification jstring="[para(6193(a,1),6613(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6193 6613"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6618">
    <literal><![CDATA[
      K(L(x,y,z),y * x) = K(x,y * x)
    ]]></literal>
    <justification jstring="[hyper(6122,a,6615,a),flip(a)].">
      <j1 rule="hyper" parents="6122 6615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6619">
    <literal><![CDATA[
      (x * (y * z)) \ (x * (z * y)) = K(L(z,y,x),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,304,a,b,6615,a)].">
      <j1 rule="hyper" parents="58 304 6615"/>
    </justification>
  </clause>

  <clause id="6620">
    <literal><![CDATA[
      K(x,y) * K(L(y,z,u),x) = a(u,z * y,K(x,y))
    ]]></literal>
    <justification jstring="[para(6615(a,1),5892(a,1,2))].">
      <j1 rule="para" parents="6615 5892"/>
    </justification>
  </clause>

  <clause id="6621">
    <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(6615(a,1),5899(a,1,2))].">
      <j1 rule="para" parents="6615 5899"/>
    </justification>
  </clause>

  <clause id="6622">
    <literal><![CDATA[
      K(L(x,y,z),y * x) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(320,a,5385,a(flip),b,6618,a),flip(a)].">
      <j1 rule="hyper" parents="320 5385 6618"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6623">
    <literal><![CDATA[
      L(K(x \ y,z),y,u) = K((u * x) \ (u * y),z)
    ]]></literal>
    <justification jstring="[para(92(a,1),6616(a,2,1))].">
      <j1 rule="para" parents="92 6616"/>
    </justification>
  </clause>

  <clause id="6624">
    <literal><![CDATA[
      L(K(x \ (y \ z),u),y \ z,y) = K((y * x) \ z,u)
    ]]></literal>
    <justification jstring="[para(298(a,1),6616(a,2,1))].">
      <j1 rule="para" parents="298 6616"/>
    </justification>
  </clause>

  <clause id="6625">
    <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),6616(a,2,1))].">
      <j1 rule="para" parents="450 6616"/>
    </justification>
  </clause>

  <clause id="6626">
    <literal><![CDATA[
      L(K((x \ y) \ z,u),z,x) = K(y \ (x * z),u)
    ]]></literal>
    <justification jstring="[para(490(a,1),6616(a,2,1))].">
      <j1 rule="para" parents="490 6616"/>
    </justification>
  </clause>

  <clause id="6627">
    <literal><![CDATA[
      L(K(L(x,y,z) \ x,u),x,z * y) = K(a(z,y,x),u)
    ]]></literal>
    <justification jstring="[para(1929(a,2),6616(a,2,1))].">
      <j1 rule="para" parents="1929 6616"/>
    </justification>
  </clause>

  <clause id="6628">
    <literal><![CDATA[
      L(K(x \ y,z),y,x \ 1) = K((1 / x) * y,z)
    ]]></literal>
    <justification jstring="[para(2815(a,1),6616(a,2,1))].">
      <j1 rule="para" parents="2815 6616"/>
    </justification>
  </clause>

  <clause id="6629">
    <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(5164(a,1),6616(a,2,1))].">
      <j1 rule="para" parents="5164 6616"/>
    </justification>
  </clause>

  <clause id="6630">
    <literal><![CDATA[
      T(x,L(y \ z,y,u)) = T(x,(u * y) \ (u * z))
    ]]></literal>
    <justification jstring="[hyper(118,a,6598,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 6598 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6631">
    <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(6429(a,1),6598(a,2,2,1))].">
      <j1 rule="para" parents="6429 6598"/>
    </justification>
  </clause>

  <clause id="6632">
    <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),6614(a,1,2))].">
      <j1 rule="para" parents="94 6614"/>
    </justification>
  </clause>

  <clause id="6633">
    <literal><![CDATA[
      (x * (y * z)) * K(z,L(y,z,x)) = x * (z * y)
    ]]></literal>
    <justification jstring="[hyper(34,a,6338,a,b,6619,a)].">
      <j1 rule="hyper" parents="34 6338 6619"/>
    </justification>
  </clause>

  <clause id="6634">
    <literal><![CDATA[
      (x * (y * z)) / K(L(y,z,x),z) != u
    ]]></literal>
    <literal><![CDATA[
      x * (z * y) = u
    ]]></literal>
    <justification jstring="[para(6619(a,1),330(a,1,2)),flip(b)].">
      <j1 rule="para" parents="6619 330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6635">
    <literal><![CDATA[
      L(K(x \ y,z),y,y \ 1) = K(((y \ 1) * x) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,4001,a(flip),b,6623,a),flip(a)].">
      <j1 rule="hyper" parents="320 4001 6623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6636">
    <literal><![CDATA[
      L(K(x * y,x),y,z) = K((z * (x \ 1)) \ (z * y),x)
    ]]></literal>
    <justification jstring="[para(6529(a,1),6623(a,1,1))].">
      <j1 rule="para" parents="6529 6623"/>
    </justification>
  </clause>

  <clause id="6637">
    <literal><![CDATA[
      K((x \ y) \ z,z) = K(y \ (x * z),z)
    ]]></literal>
    <justification jstring="[hyper(6122,a,6626,a)].">
      <j1 rule="hyper" parents="6122 6626"/>
    </justification>
  </clause>

  <clause id="6638">
    <literal><![CDATA[
      K((x \ y) \ z,u \ (x * z)) = K(y \ (x * z),(x \ u) \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,6584,a(flip),b,6626,a)].">
      <j1 rule="hyper" parents="58 6584 6626"/>
    </justification>
  </clause>

  <clause id="6639">
    <literal><![CDATA[
      K(x \ (y * z),z) != u
    ]]></literal>
    <literal><![CDATA[
      K((y \ x) \ z,z) = u
    ]]></literal>
    <justification jstring="[para(6626(a,1),6122(a,1))].">
      <j1 rule="para" parents="6626 6122"/>
    </justification>
  </clause>

  <clause id="6640">
    <literal><![CDATA[
      L(K(x \ y,z),y,x \ 1) = K((x \ 1) * y,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,3981,a(flip),b,6628,a),flip(a)].">
      <j1 rule="hyper" parents="320 3981 6628"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6642">
    <literal><![CDATA[
      L(x,y,z \ 1) != K((z \ 1) * y,u)
    ]]></literal>
    <literal><![CDATA[
      K(z \ y,u) = x
    ]]></literal>
    <justification jstring="[para(6640(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="6640 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6643">
    <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,6620,a(flip),b,5458,a),flip(a)].">
      <j1 rule="hyper" parents="119 6620 5458"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6644">
    <literal><![CDATA[
      K(x,L(L(y \ 1,y,z),z * y,u)) = K(x,1 / L(y,z,u))
    ]]></literal>
    <justification jstring="[para(424(a,2),6167(a,1,2))].">
      <j1 rule="para" parents="424 6167"/>
    </justification>
  </clause>

  <clause id="6645">
    <literal><![CDATA[
      x / (K(y,z) * T(z,u)) = (x / T(z,u)) * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(6572,a,6354,a),flip(a)].">
      <j1 rule="hyper" parents="6572 6354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6646">
    <literal><![CDATA[
      (x / T(y,y * z)) * K(y,z) = x / L(y,z,y)
    ]]></literal>
    <justification jstring="[para(5090(a,1),6645(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5090 6645"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6647">
    <literal><![CDATA[
      (x / T(y,z)) * K(y,y * z) = x / R(y,z,y)
    ]]></literal>
    <justification jstring="[para(5093(a,1),6645(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5093 6645"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6648">
    <literal><![CDATA[
      (x / T(y,z)) * T(y,y * z) = (x / R(y,z,y)) * y
    ]]></literal>
    <justification jstring="[para(6647(a,1),6196(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6647 6196"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6649">
    <literal><![CDATA[
      a(x,T(y,z),T(z,y)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(691,a,6449,a),flip(a)].">
      <j1 rule="hyper" parents="691 6449"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6650">
    <literal><![CDATA[
      a(x,T(y,z),T(z,y)) != 1
    ]]></literal>
    <literal><![CDATA[
      (x * y) * z = x * (y * z)
    ]]></literal>
    <justification jstring="[para(6649(a,2),977(a,1))].">
      <j1 rule="para" parents="6649 977"/>
    </justification>
  </clause>

  <clause id="6651">
    <literal><![CDATA[
      L(K(x,y \ z),z,z \ 1) = K(x,((z \ 1) * y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,5326,a(flip),b,6559,a),flip(a)].">
      <j1 rule="hyper" parents="320 5326 6559"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6652">
    <literal><![CDATA[
      T(L(x \ 1,x,y) \ 1,x * L(x \ 1,z,u)) = ((y * x) \ y) \ 1
    ]]></literal>
    <justification jstring="[para(1757(a,1),6561(a,2,2))].">
      <j1 rule="para" parents="1757 6561"/>
    </justification>
  </clause>

  <clause id="6653">
    <literal><![CDATA[
      L(K(x,K(y,z) * (u \ w)),u \ w,u) = K(x,(u * K(z,y)) \ w)
    ]]></literal>
    <justification jstring="[para(5130(a,1),6585(a,1,1,2))].">
      <j1 rule="para" parents="5130 6585"/>
    </justification>
  </clause>

  <clause id="6654">
    <literal><![CDATA[
      K((x * y) \ 1,x) = K(y \ (x \ 1),x)
    ]]></literal>
    <justification jstring="[hyper(58,a,3160,a(flip),b,6624,a),flip(a)].">
      <j1 rule="hyper" parents="58 3160 6624"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6655">
    <literal><![CDATA[
      x * ((x \ y) * K(z \ (x \ y),u)) = y * K((x * z) \ y,u)
    ]]></literal>
    <justification jstring="[hyper(119,a,6624,a(flip),b,91,a),flip(a)].">
      <j1 rule="hyper" parents="119 6624 91"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6656">
    <literal><![CDATA[
      L(K(x * (y \ z),x),y \ z,y) = K((y * (x \ 1)) \ z,x)
    ]]></literal>
    <justification jstring="[para(6529(a,1),6624(a,1,1))].">
      <j1 rule="para" parents="6529 6624"/>
    </justification>
  </clause>

  <clause id="6657">
    <literal><![CDATA[
      L(K((x \ y) \ (z \ u),y),z \ u,z) = K((z * (y / x)) \ u,y)
    ]]></literal>
    <justification jstring="[para(6580(a,1),6624(a,1,1))].">
      <j1 rule="para" parents="6580 6624"/>
    </justification>
  </clause>

  <clause id="6658">
    <literal><![CDATA[
      ((x \ (1 / y)) * x) * y = K(y \ (x \ 1),x)
    ]]></literal>
    <justification jstring="[hyper(5062,a,6654,a)].">
      <j1 rule="hyper" parents="5062 6654"/>
    </justification>
  </clause>

  <clause id="6659">
    <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(6627(a,1),1934(a,1,1))].">
      <j1 rule="para" parents="6627 1934"/>
    </justification>
  </clause>

  <clause id="6660">
    <literal><![CDATA[
      (x * K(y,z)) * K(z,z * y) = (x / R(z,y,z)) * z
    ]]></literal>
    <justification jstring="[hyper(58,a,6382,a(flip),b,6648,a)].">
      <j1 rule="hyper" parents="58 6382 6648"/>
    </justification>
  </clause>

  <clause id="6661">
    <literal><![CDATA[
      (1 / x) \ K(y,((x \ 1) * z) \ 1) = x * K(y,z \ x)
    ]]></literal>
    <justification jstring="[hyper(116,a,6651,a(flip),b,2820,a)].">
      <j1 rule="hyper" parents="116 6651 2820"/>
    </justification>
  </clause>

  <clause id="6662">
    <literal><![CDATA[
      K(x,((y \ 1) * (y / z)) \ 1) = L(K(x,z),y,y \ 1)
    ]]></literal>
    <justification jstring="[para(75(a,1),6651(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="75 6651"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6663">
    <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(2421(a,2),6133(a,1,2))].">
      <j1 rule="para" parents="2421 6133"/>
    </justification>
  </clause>

  <clause id="6664">
    <literal><![CDATA[
      K(x,(T(y,z) * u) \ y) = K(x,u \ K(z,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,6139,a(flip),b,6134,a),flip(a)].">
      <j1 rule="hyper" parents="58 6139 6134"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6665">
    <literal><![CDATA[
      K(x,(T(y,z) \ u) \ K(z,y)) = K(x,u \ y)
    ]]></literal>
    <justification jstring="[para(5(a,1),6664(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 6664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6666">
    <literal><![CDATA[
      R(x,K(y,z),L(z,u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(515,a,6311,a)].">
      <j1 rule="hyper" parents="515 6311"/>
    </justification>
  </clause>

  <clause id="6667">
    <literal><![CDATA[
      (x * L(K(y,z),u,w)) \ x = L(K(z,y),u,w)
    ]]></literal>
    <justification jstring="[para(5687(a,1),6360(a,1,1,2))].">
      <j1 rule="para" parents="5687 6360"/>
    </justification>
  </clause>

  <clause id="6668">
    <literal><![CDATA[
      x / L(K(y,z),u,w) = x * L(K(z,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(197,a,6667,a)].">
      <j1 rule="hyper" parents="197 6667"/>
    </justification>
  </clause>

  <clause id="6669">
    <literal><![CDATA[
      (x * (y * K(z,u))) * L(K(u,z),y,x) = x * y
    ]]></literal>
    <justification jstring="[hyper(137,a,6667,a),flip(a)].">
      <j1 rule="hyper" parents="137 6667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6670">
    <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(6667(a,1),330(a,1,2)),flip(b)].">
      <j1 rule="para" parents="6667 330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6671">
    <literal><![CDATA[
      (x * (y * K(z,u))) \ (x * y) = L(K(u,z),y,x)
    ]]></literal>
    <justification jstring="[para(90(a,1),6667(a,1,1))].">
      <j1 rule="para" parents="90 6667"/>
    </justification>
  </clause>

  <clause id="6672">
    <literal><![CDATA[
      (x * ((x \ y) * K(z,u))) \ y = L(K(u,z),x \ y,x)
    ]]></literal>
    <justification jstring="[para(448(a,1),6667(a,1,1))].">
      <j1 rule="para" parents="448 6667"/>
    </justification>
  </clause>

  <clause id="6673">
    <literal><![CDATA[
      (x * (y * K(z,u))) * w != x * y
    ]]></literal>
    <literal><![CDATA[
      L(K(u,z),y,x) = w
    ]]></literal>
    <justification jstring="[para(6669(a,1),38(a,1)),flip(a)].">
      <j1 rule="para" parents="6669 38"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6674">
    <literal><![CDATA[
      (x * (y \ T(y * z,y))) \ (x * z) = L(K(y,y * z),z,x)
    ]]></literal>
    <justification jstring="[para(6384(a,2),6671(a,1,1,2))].">
      <j1 rule="para" parents="6384 6671"/>
    </justification>
  </clause>

  <clause id="6675">
    <literal><![CDATA[
      x \ T(x * K(y \ x,z),x) = K(T(y,x) \ x,z)
    ]]></literal>
    <justification jstring="[hyper(116,a,6418,a(flip),b,6114,a(flip))].">
      <j1 rule="hyper" parents="116 6418 6114"/>
    </justification>
  </clause>

  <clause id="6676">
    <literal><![CDATA[
      K(T(x / y,x) \ x,z) = x \ T(x * K(y,z),x)
    ]]></literal>
    <justification jstring="[para(75(a,1),6675(a,1,2,1,2,1)),flip(a)].">
      <j1 rule="para" parents="75 6675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6677">
    <literal><![CDATA[
      K(T(x / y,x) \ x,z) = K(y,T(x / z,x) \ x)
    ]]></literal>
    <justification jstring="[hyper(320,a,5996,a,b,6676,a),flip(a)].">
      <j1 rule="hyper" parents="320 5996 6676"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6678">
    <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,6446,a),flip(a)].">
      <j1 rule="hyper" parents="320 20 6446"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6679">
    <literal><![CDATA[
      (x * (y \ ((z \ (y * (x \ u))) * z))) \ u = K(z,(x * (y \ z)) \ u)
    ]]></literal>
    <justification jstring="[para(965(a,1),6466(a,1,1,2))].">
      <j1 rule="para" parents="965 6466"/>
    </justification>
  </clause>

  <clause id="6680">
    <literal><![CDATA[
      (x * (y * (z * T(z \ (y \ (x \ u)),w)))) \ u = K(w,(x * (y * z)) \ u)
    ]]></literal>
    <justification jstring="[para(924(a,1),6466(a,1,1,2))].">
      <j1 rule="para" parents="924 6466"/>
    </justification>
  </clause>

  <clause id="6681">
    <literal><![CDATA[
      (x * (((y \ ((x \ z) * u)) * y) / u)) \ z = K(y,(x * (y / u)) \ z)
    ]]></literal>
    <justification jstring="[para(1583(a,1),6466(a,1,1,2))].">
      <j1 rule="para" parents="1583 6466"/>
    </justification>
  </clause>

  <clause id="6682">
    <literal><![CDATA[
      T(K(x \ K(x,y),z),y) = K(x \ 1,z)
    ]]></literal>
    <justification jstring="[para(4879(a,1),6527(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4879 6527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6683">
    <literal><![CDATA[
      K(x \ K(x,y),z) * y = y * K(x \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(119,a,6682,a(flip),b,17,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 6682 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6684">
    <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),6632(a,1,2,1,2))].">
      <j1 rule="para" parents="72 6632"/>
    </justification>
  </clause>

  <clause id="6685">
    <literal><![CDATA[
      (x * (y * z)) * K(z,L(y,z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      x * (z * y) = u
    ]]></literal>
    <justification jstring="[para(6335(a,1),6634(a,1))].">
      <j1 rule="para" parents="6335 6634"/>
    </justification>
  </clause>

  <clause id="6686">
    <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(4816(a,1),6678(a,2,1))].">
      <j1 rule="para" parents="4816 6678"/>
    </justification>
  </clause>

  <clause id="6687">
    <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),6129(a,1,2))].">
      <j1 rule="para" parents="502 6129"/>
    </justification>
  </clause>

  <clause id="6688">
    <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(6238(a,2),4906(a,1))].">
      <j1 rule="para" parents="6238 4906"/>
    </justification>
  </clause>

  <clause id="6689">
    <literal><![CDATA[
      T(x,x \ T(x * y,y \ 1)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,6212,a(flip),b,6492,a),flip(a)].">
      <j1 rule="hyper" parents="320 6212 6492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6691">
    <literal><![CDATA[
      T(x / y,(x / y) \ T(x,y \ 1)) = T(x / y,y)
    ]]></literal>
    <justification jstring="[para(7(a,1),6689(a,1,2,2,1))].">
      <j1 rule="para" parents="7 6689"/>
    </justification>
  </clause>

  <clause id="6692">
    <literal><![CDATA[
      T(x / y,(x / y) \ T(x,y \ 1)) = y \ x
    ]]></literal>
    <justification jstring="[hyper(320,a,107,a(flip),b,6691,a),flip(a)].">
      <j1 rule="hyper" parents="320 107 6691"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6693">
    <literal><![CDATA[
      T(x,y \ 1) / (y \ x) = (x / y) \ T(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(6692(a,1),265(a,1,2))].">
      <j1 rule="para" parents="6692 265"/>
    </justification>
  </clause>

  <clause id="6694">
    <literal><![CDATA[
      T(x,(y \ 1) \ 1) / ((y \ 1) \ x) = (x / (y \ 1)) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(2959(a,1),6693(a,2,2))].">
      <j1 rule="para" parents="2959 6693"/>
    </justification>
  </clause>

  <clause id="6695">
    <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),6502(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="75 6502"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6696">
    <literal><![CDATA[
      R(x,y,z * K(y,z)) = R(x,T(y,z),z)
    ]]></literal>
    <justification jstring="[hyper(518,a,6518,a),flip(a)].">
      <j1 rule="hyper" parents="518 6518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6697">
    <literal><![CDATA[
      K((x / y) \ z,x) != u
    ]]></literal>
    <literal><![CDATA[
      K((y \ x) \ z,x) = u
    ]]></literal>
    <justification jstring="[para(6565(a,1),6547(a,1))].">
      <j1 rule="para" parents="6565 6547"/>
    </justification>
  </clause>

  <clause id="6698">
    <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,3570,a,b,6644,a)].">
      <j1 rule="hyper" parents="58 3570 6644"/>
    </justification>
  </clause>

  <clause id="6699">
    <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(6674(a,1),5076(a,1,1,2))].">
      <j1 rule="para" parents="6674 5076"/>
    </justification>
  </clause>

  <clause id="6700">
    <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,6687,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 6687 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6701">
    <literal><![CDATA[
      K(x * (1 / (y / z)),z \ y) = K(x / (y / z),z \ y)
    ]]></literal>
    <justification jstring="[hyper(6485,a,6182,a),flip(a)].">
      <j1 rule="hyper" parents="6485 6182"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6702">
    <literal><![CDATA[
      x / (K(y / (z / u),u \ z) * x) = K(u \ z,y * (1 / (z / u)))
    ]]></literal>
    <justification jstring="[para(6701(a,1),5142(a,1,2,1))].">
      <j1 rule="para" parents="6701 5142"/>
    </justification>
  </clause>

  <clause id="6703">
    <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(4749(a,1),6355(a,1,1,1))].">
      <j1 rule="para" parents="4749 6355"/>
    </justification>
  </clause>

  <clause id="6704">
    <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(6452(a,1),44(a,1))].">
      <j1 rule="para" parents="6452 44"/>
    </justification>
  </clause>

  <clause id="6705">
    <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(6452(a,1),5632(a,1))].">
      <j1 rule="para" parents="6452 5632"/>
    </justification>
  </clause>

  <clause id="6706">
    <literal><![CDATA[
      (((x / y) * T(y,z)) * u) \ (x * u) = K(z,((x / y) * u) \ (x * u))
    ]]></literal>
    <justification jstring="[para(75(a,1),6467(a,1,1,1,2,1))].">
      <j1 rule="para" parents="75 6467"/>
    </justification>
  </clause>

  <clause id="6707">
    <literal><![CDATA[
      K(x,T(y \ z,u) \ T(z,u)) = T(K(y,x) * z,u) \ T(z,u)
    ]]></literal>
    <justification jstring="[para(5100(a,1),6468(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5100 6468"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6708">
    <literal><![CDATA[
      L(K(x,y \ z),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(u * y) \ (u * z)) = w
    ]]></literal>
    <justification jstring="[para(6144(a,1),6482(a,1))].">
      <j1 rule="para" parents="6144 6482"/>
    </justification>
  </clause>

  <clause id="6709">
    <literal><![CDATA[
      K(x,L(y \ z,y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(u * y) \ (u * z)) = w
    ]]></literal>
    <justification jstring="[para(6587(a,1),6708(a,1))].">
      <j1 rule="para" parents="6587 6708"/>
    </justification>
  </clause>

  <clause id="6710">
    <literal><![CDATA[
      K(((x \ y) \ 1) * z,y \ x) = K((x \ y) \ z,y \ x)
    ]]></literal>
    <justification jstring="[hyper(320,a,6108,a(flip),b,6542,a),flip(a)].">
      <j1 rule="hyper" parents="320 6108 6542"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6711">
    <literal><![CDATA[
      (x * K(y * z,u)) * (z * y) = x * (K(z,y) * T(y * z,u))
    ]]></literal>
    <justification jstring="[para(6560(a,1),6549(a,2,2))].">
      <j1 rule="para" parents="6560 6549"/>
    </justification>
  </clause>

  <clause id="6712">
    <literal><![CDATA[
      K((x * y) \ T(x,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(y \ K(x,z),u) = w
    ]]></literal>
    <justification jstring="[para(6556(a,2),5241(a,1))].">
      <j1 rule="para" parents="6556 5241"/>
    </justification>
  </clause>

  <clause id="6713">
    <literal><![CDATA[
      K(x,(K(y,z) * (y \ u)) \ x) = K(x,u \ (y * (K(z,y) * x)))
    ]]></literal>
    <justification jstring="[para(5398(a,1),6595(a,1,2,1))].">
      <j1 rule="para" parents="5398 6595"/>
    </justification>
  </clause>

  <clause id="6714">
    <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(6602(a,1),38(a,1)),flip(a)].">
      <j1 rule="para" parents="6602 38"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6715">
    <literal><![CDATA[
      K((x \ 1) \ y,z \ (x * y)) = K(x * y,(x \ z) \ y)
    ]]></literal>
    <justification jstring="[para(60(a,1),6638(a,2,1))].">
      <j1 rule="para" parents="60 6638"/>
    </justification>
  </clause>

  <clause id="6716">
    <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(1310(a,1),6638(a,2,1))].">
      <j1 rule="para" parents="1310 6638"/>
    </justification>
  </clause>

  <clause id="6717">
    <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(6655(a,2),6345(a,1,1))].">
      <j1 rule="para" parents="6655 6345"/>
    </justification>
  </clause>

  <clause id="6718">
    <literal><![CDATA[
      T(x,y) / ((y \ 1) \ x) = (x / (y \ 1)) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(2959(a,1),6694(a,1,1))].">
      <j1 rule="para" parents="2959 6694"/>
    </justification>
  </clause>

  <clause id="6719">
    <literal><![CDATA[
      ((x / y) / (y \ 1)) \ T(x / y,y) = (y \ x) / ((y \ 1) \ (x / y))
    ]]></literal>
    <justification jstring="[para(107(a,1),6718(a,1,1)),flip(a)].">
      <j1 rule="para" parents="107 6718"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6720">
    <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,6707,a,b,xx)].">
      <j1 rule="hyper" parents="119 6707"/>
    </justification>
  </clause>

  <clause id="6721">
    <literal><![CDATA[
      (K(x,y) * K(x * y,z)) * (y * x) = T(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,5133,a(flip),b,6711,a),flip(a)].">
      <j1 rule="hyper" parents="320 5133 6711"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6722">
    <literal><![CDATA[
      (x * y) \ T(y * x,z) = K(y,x) * K(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(30,a,5701,a,b,6721,a)].">
      <j1 rule="hyper" parents="30 5701 6721"/>
    </justification>
  </clause>

  <clause id="6723">
    <literal><![CDATA[
      ((x * y) * T(z,y)) / (y * T(z,y)) = R(x,y * K(z,y),z)
    ]]></literal>
    <justification jstring="[para(6196(a,1),6523(a,1,2))].">
      <j1 rule="para" parents="6196 6523"/>
    </justification>
  </clause>

  <clause id="6724">
    <literal><![CDATA[
      R(x,y * K(z,y),z) = R(x,y,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(518,a,6723,a),flip(a)].">
      <j1 rule="hyper" parents="518 6723"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6725">
    <literal><![CDATA[
      R(x,y \ z,T(y,y \ z)) = R(x,z / y,y)
    ]]></literal>
    <justification jstring="[para(4776(a,1),6724(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4776 6724"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6726">
    <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(5913(a,2),6653(a,2,2,1))].">
      <j1 rule="para" parents="5913 6653"/>
    </justification>
  </clause>

  <clause id="6727">
    <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(6683(a,2),6653(a,2,2,1))].">
      <j1 rule="para" parents="6683 6653"/>
    </justification>
  </clause>

  <clause id="6728">
    <literal><![CDATA[
      K((x * (y / z)) \ u,y) = K((x * (z \ y)) \ u,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,6624,a(flip),b,6657,a),flip(a)].">
      <j1 rule="hyper" parents="58 6624 6657"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6729">
    <literal><![CDATA[
      K((x * (y / x)) \ z,y) = K(y \ z,y)
    ]]></literal>
    <justification jstring="[para(5(a,1),6728(a,2,1,1))].">
      <j1 rule="para" parents="5 6728"/>
    </justification>
  </clause>

  <clause id="6730">
    <literal><![CDATA[
      K(((x \ y) * x) \ z,y) = K(y \ z,y)
    ]]></literal>
    <justification jstring="[para(72(a,1),6729(a,1,1,1,2))].">
      <j1 rule="para" parents="72 6729"/>
    </justification>
  </clause>

  <clause id="6731">
    <literal><![CDATA[
      T(x,((y \ x) * y) \ z) = (u * K(x \ z,x)) \ (u * x)
    ]]></literal>
    <justification jstring="[para(6730(a,1),6315(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6730 6315"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6732">
    <literal><![CDATA[
      T(x,((y \ x) * y) \ z) = T(x,x \ z)
    ]]></literal>
    <justification jstring="[hyper(320,a,6315,a(flip),b,6731,a),flip(a)].">
      <j1 rule="hyper" parents="320 6315 6731"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6733">
    <literal><![CDATA[
      T(x,x \ T(y,y \ x)) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(5597(a,1),6732(a,1,2))].">
      <j1 rule="para" parents="5597 6732"/>
    </justification>
  </clause>

  <clause id="6734">
    <literal><![CDATA[
      T(x,x \ y) / T(y,y \ x) = y \ T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(6733(a,1),265(a,1,2))].">
      <j1 rule="para" parents="6733 265"/>
    </justification>
  </clause>

  <clause id="6735">
    <literal><![CDATA[
      T(x,x \ y) / ((y \ x) \ x) = y \ T(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(675,a,6734,a)].">
      <j1 rule="hyper" parents="675 6734"/>
    </justification>
  </clause>

  <clause id="6736">
    <literal><![CDATA[
      x \ T(y,y \ x) = y / ((y \ ((x \ y) \ y)) * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,6179,a(flip),b,6735,a),flip(a)].">
      <j1 rule="hyper" parents="58 6179 6735"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6737">
    <literal><![CDATA[
      (x * (1 / T(y,z))) * T(y,z) = R(x,1 / T(y,z),y)
    ]]></literal>
    <justification jstring="[hyper(4954,a,6349,a),flip(a)].">
      <j1 rule="hyper" parents="4954 6349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6738">
    <literal><![CDATA[
      R(x,1 / T(y,z),y) / y = (x * (1 / T(y,z))) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(117,a,6737,a(flip),b,6196,a)].">
      <j1 rule="hyper" parents="117 6737 6196"/>
    </justification>
  </clause>

  <clause id="6739">
    <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(6737(a,1),2612(a,1))].">
      <j1 rule="para" parents="6737 2612"/>
    </justification>
  </clause>

  <clause id="6740">
    <literal><![CDATA[
      R(x,T(y,z) \ 1,y) / y = (x * (1 / T(y,z))) * K(y,z)
    ]]></literal>
    <justification jstring="[para(4033(a,1),6738(a,1,1))].">
      <j1 rule="para" parents="4033 6738"/>
    </justification>
  </clause>

  <clause id="6741">
    <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(4033(a,1),6739(a,1))].">
      <j1 rule="para" parents="4033 6739"/>
    </justification>
  </clause>

  <clause id="6742">
    <literal><![CDATA[
      (x * y) \ (y * (K(x,y) * (x * z))) = L(L(z,x,y),y * x,K(x,y))
    ]]></literal>
    <justification jstring="[para(5256(a,1),5006(a,1,2))].">
      <j1 rule="para" parents="5256 5006"/>
    </justification>
  </clause>

  <clause id="6743">
    <literal><![CDATA[
      R(K(x,y),x * z,u) = K(R(x,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(5121,a,5978,a)].">
      <j1 rule="hyper" parents="5121 5978"/>
    </justification>
  </clause>

  <clause id="6744">
    <literal><![CDATA[
      K(R(x,y,z),x \ 1) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,3718,a(flip),b,6743,a),flip(a)].">
      <j1 rule="hyper" parents="58 3718 6743"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6745">
    <literal><![CDATA[
      K(R(x,x \ y,z),u) = R(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(5(a,1),6743(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5 6743"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6746">
    <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(6743(a,1),26(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6743 26"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6747">
    <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(5102(a,1),6743(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5102 6743"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6748">
    <literal><![CDATA[
      R(x,y,z) * (1 / R(x,y,z)) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,5970,a,b,6744,a)].">
      <j1 rule="hyper" parents="58 5970 6744"/>
    </justification>
  </clause>

  <clause id="6749">
    <literal><![CDATA[
      R(x,y,z) \ K(x,x \ 1) = 1 / R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(116,a,6744,a(flip),b,5970,a)].">
      <j1 rule="hyper" parents="116 6744 5970"/>
    </justification>
  </clause>

  <clause id="6750">
    <literal><![CDATA[
      K(R(x,x \ 1,y),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,379,a(flip),b,6745,a),flip(a)].">
      <j1 rule="hyper" parents="320 379 6745"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6751">
    <literal><![CDATA[
      K(R(x,x \ y,z),u) * (y * z) = (K(x,u) * y) * z
    ]]></literal>
    <justification jstring="[para(6745(a,2),101(a,1,1))].">
      <j1 rule="para" parents="6745 101"/>
    </justification>
  </clause>

  <clause id="6752">
    <literal><![CDATA[
      K((x * y) / ((z \ x) * y),u) = R(K(z,u),x,y)
    ]]></literal>
    <justification jstring="[para(98(a,1),6745(a,1,1))].">
      <j1 rule="para" parents="98 6745"/>
    </justification>
  </clause>

  <clause id="6753">
    <literal><![CDATA[
      K(x,R(y,y \ z,u)) = (w * R(K(y,x),z,u)) \ w
    ]]></literal>
    <justification jstring="[para(6745(a,1),6338(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6745 6338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6754">
    <literal><![CDATA[
      K(R(x,x \ 1,y),L(z,x,x \ 1)) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,5804,a(flip),b,6750,a),flip(a)].">
      <j1 rule="hyper" parents="320 5804 6750"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6757">
    <literal><![CDATA[
      (1 / x) * (R(x,y,z) \ x) = 1 / R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(29,a,3722,a,b,6748,a)].">
      <j1 rule="hyper" parents="29 3722 6748"/>
    </justification>
  </clause>

  <clause id="6758">
    <literal><![CDATA[
      (R(x,y,z) \ 1) * ((x \ 1) \ 1) = (1 / R(x,y,z)) * x
    ]]></literal>
    <justification jstring="[para(6749(a,1),3400(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6749 3400"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6759">
    <literal><![CDATA[
      (1 / x) \ (1 / R(x,y,z)) = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(123,a,6757,a)].">
      <j1 rule="hyper" parents="123 6757"/>
    </justification>
  </clause>

  <clause id="6760">
    <literal><![CDATA[
      (x \ R(x,y,z)) \ 1 = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(58,a,6018,a(flip),b,6759,a)].">
      <j1 rule="hyper" parents="58 6018 6759"/>
    </justification>
  </clause>

  <clause id="6761">
    <literal><![CDATA[
      (x \ 1) * (R(x,y,z) \ x) = R(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(119,a,6759,a(flip),b,6017,a(flip))].">
      <j1 rule="hyper" parents="119 6759 6017"/>
    </justification>
  </clause>

  <clause id="6762">
    <literal><![CDATA[
      K(x,(R(y,z,u) \ y) \ x) = K(x,x * (y \ R(y,z,u)))
    ]]></literal>
    <justification jstring="[para(6760(a,1),5422(a,1,2,1))].">
      <j1 rule="para" parents="6760 5422"/>
    </justification>
  </clause>

  <clause id="6763">
    <literal><![CDATA[
      R(K(x / y,z),x,u) = K((x * u) / (y * u),z)
    ]]></literal>
    <justification jstring="[para(75(a,1),6752(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="75 6752"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6764">
    <literal><![CDATA[
      R(K(x / (y / z),u),x,z) = K((x * z) / y,u)
    ]]></literal>
    <justification jstring="[para(7(a,1),6763(a,2,1,2))].">
      <j1 rule="para" parents="7 6763"/>
    </justification>
  </clause>

  <clause id="6765">
    <literal><![CDATA[
      K((x * y) / z,x) = K(x / (z / y),x)
    ]]></literal>
    <justification jstring="[hyper(58,a,5472,a(flip),b,6764,a),flip(a)].">
      <j1 rule="hyper" parents="58 5472 6764"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6766">
    <literal><![CDATA[
      K((x * y) / z,x) = K((z / y) \ x,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,6287,a(flip),b,6765,a),flip(a)].">
      <j1 rule="hyper" parents="320 6287 6765"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6767">
    <literal><![CDATA[
      K((x * y) / z,x) != u
    ]]></literal>
    <literal><![CDATA[
      K((z / y) \ x,x) = u
    ]]></literal>
    <justification jstring="[para(6765(a,2),6509(a,1))].">
      <j1 rule="para" parents="6765 6509"/>
    </justification>
  </clause>

  <clause id="6768">
    <literal><![CDATA[
      (K(x,y) * T(x,z)) * u = K(x,y) * (T(x,z) * u)
    ]]></literal>
    <justification jstring="[para(4089(a,1),6751(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4089 6751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6769">
    <literal><![CDATA[
      L(x,T(y,z),K(y,u)) = x
    ]]></literal>
    <justification jstring="[hyper(479,a,6768,a)].">
      <j1 rule="hyper" parents="479 6768"/>
    </justification>
  </clause>

  <clause id="6770">
    <literal><![CDATA[
      (K(x,y) * T(x,z)) \ 1 = T(x,z) \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,4979,a(flip),b,6769,a)].">
      <j1 rule="hyper" parents="58 4979 6769"/>
    </justification>
  </clause>

  <clause id="6771">
    <literal><![CDATA[
      (K(x,y) * T(x,z)) \ 1 = T(x,y) \ K(z,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,5658,a,b,6770,a),flip(a)].">
      <j1 rule="hyper" parents="320 5658 6770"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6772">
    <literal><![CDATA[
      (1 / R(x,y,z)) * x = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(3709,a,6758,a),flip(a)].">
      <j1 rule="hyper" parents="3709 6758"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6773">
    <literal><![CDATA[
      x / R(x,y,z) = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(1887,a,6772,a)].">
      <j1 rule="hyper" parents="1887 6772"/>
    </justification>
  </clause>

  <clause id="6774">
    <literal><![CDATA[
      T(1 / R(x,y,z),x) = R(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(239,a,6772,a,b,1316,a)].">
      <j1 rule="hyper" parents="239 6772 1316"/>
    </justification>
  </clause>

  <clause id="6775">
    <literal><![CDATA[
      (R(x,y,z) \ x) \ x = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(188,a,6773,a)].">
      <j1 rule="hyper" parents="188 6773"/>
    </justification>
  </clause>

  <clause id="6776">
    <literal><![CDATA[
      (R(x,y,z) \ x) * R(x,y,z) = x
    ]]></literal>
    <justification jstring="[hyper(133,a,6773,a)].">
      <j1 rule="hyper" parents="133 6773"/>
    </justification>
  </clause>

  <clause id="6777">
    <literal><![CDATA[
      (x / R(x,y,z)) * u != w
    ]]></literal>
    <literal><![CDATA[
      (R(x,y,z) \ x) * u = w
    ]]></literal>
    <justification jstring="[para(6775(a,1),348(a,1,1,2))].">
      <j1 rule="para" parents="6775 348"/>
    </justification>
  </clause>

  <clause id="6778">
    <literal><![CDATA[
      T(x,y) / R(x,z,u) = R(x,z,u) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(6776(a,1),4578(a,1,1,1))].">
      <j1 rule="para" parents="6776 4578"/>
    </justification>
  </clause>

  <clause id="6779">
    <literal><![CDATA[
      (R(x,y,z) \ T(x,u)) \ T(x,u) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(188,a,6778,a)].">
      <j1 rule="hyper" parents="188 6778"/>
    </justification>
  </clause>

  <clause id="6780">
    <literal><![CDATA[
      K(x,(y / R(y,z,u)) \ x) = K(x,x * (y \ R(y,z,u)))
    ]]></literal>
    <justification jstring="[para(6773(a,2),6762(a,1,2,1))].">
      <j1 rule="para" parents="6773 6762"/>
    </justification>
  </clause>

  <clause id="6781">
    <literal><![CDATA[
      T(x,y) * K(x * y,(y * x) \ x) = (x * y) * (x / (y * x))
    ]]></literal>
    <justification jstring="[para(5598(a,1),5216(a,1,2,2))].">
      <j1 rule="para" parents="5598 5216"/>
    </justification>
  </clause>

  <clause id="6782">
    <literal><![CDATA[
      K((T(x,y) \ T(z,y)) \ 1,x) = K((x \ z) \ 1,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,5588,a(flip),b,5534,a),flip(a)].">
      <j1 rule="hyper" parents="58 5588 5534"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6783">
    <literal><![CDATA[
      K((T(x,y) \ T(z,y)) \ 1,x) = K(z \ x,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(320,a,6259,a(flip),b,6782,a),flip(a)].">
      <j1 rule="hyper" parents="320 6259 6782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6784">
    <literal><![CDATA[
      K(T(x,y) \ T(z,y),z) = K(x \ z,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(6425,a,6783,a)].">
      <j1 rule="hyper" parents="6425 6783"/>
    </justification>
  </clause>

  <clause id="6785">
    <literal><![CDATA[
      K(x,T(y,z) \ T(x,z)) = 1 / K(y \ x,T(x,z))
    ]]></literal>
    <justification jstring="[para(6784(a,1),4971(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6784 4971"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6786">
    <literal><![CDATA[
      K(x,T(y,z) \ T(x,z)) = K(T(x,z),y \ x)
    ]]></literal>
    <justification jstring="[hyper(320,a,4971,a(flip),b,6785,a),flip(a)].">
      <j1 rule="hyper" parents="320 4971 6785"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6787">
    <literal><![CDATA[
      (x * T(x \ y,z)) / K((x / y) \ 1,z) = T(y,K(z,x \ y))
    ]]></literal>
    <justification jstring="[hyper(320,a,6428,a(flip),b,5645,a),flip(a)].">
      <j1 rule="hyper" parents="320 6428 5645"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6788">
    <literal><![CDATA[
      (x * K((x \ y) \ 1,z)) / K((y / x) \ 1,z) = T(x,K(z,y \ x))
    ]]></literal>
    <justification jstring="[para(5054(a,1),6787(a,1,1))].">
      <j1 rule="para" parents="5054 6787"/>
    </justification>
  </clause>

  <clause id="6789">
    <literal><![CDATA[
      (1 / (1 / ((x * y) / x))) \ K(x,y) = (y \ 1) * K(y,1 / y)
    ]]></literal>
    <justification jstring="[para(4758(a,1),5732(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4758 5732"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6790">
    <literal><![CDATA[
      (1 / (1 / ((x * y) / x))) \ K(x,y) = 1 / y
    ]]></literal>
    <justification jstring="[hyper(320,a,4826,a(flip),b,6789,a),flip(a)].">
      <j1 rule="hyper" parents="320 4826 6789"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6792">
    <literal><![CDATA[
      (x * (y \ 1)) * K(z,(y \ 1) \ 1) = (x * K(z,y)) * (y \ 1)
    ]]></literal>
    <justification jstring="[para(5883(a,1),5882(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5883 5882"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6793">
    <literal><![CDATA[
      (x * K(y,z)) * (z \ 1) = (x * (z \ 1)) * K(y,z)
    ]]></literal>
    <justification jstring="[para(3554(a,1),6792(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3554 6792"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6794">
    <literal><![CDATA[
      R(x / T(y,z),y,y \ 1) = (x * (y \ 1)) * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(6381,a,6793,a)].">
      <j1 rule="hyper" parents="6381 6793"/>
    </justification>
  </clause>

  <clause id="6795">
    <literal><![CDATA[
      ((x * T(y,z)) * (y \ 1)) * K(z,y) = R(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[para(6(a,1),6794(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6 6794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6796">
    <literal><![CDATA[
      L(T(K(x,y),z),u,w) \ v5 = L(T(K(y,x),z),u,w) * v5
    ]]></literal>
    <justification jstring="[para(5680(a,1),5901(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5680 5901"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6797">
    <literal><![CDATA[
      L(T(K(x,y),z),z,z \ 1) * u = ((1 / z) * (K(y,x) * z)) \ u
    ]]></literal>
    <justification jstring="[para(2821(a,1),6796(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2821 6796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6798">
    <literal><![CDATA[
      ((1 / x) * (K(y,z) * x)) \ u = ((1 / x) * (K(z,y) * x)) * u
    ]]></literal>
    <justification jstring="[para(2821(a,1),6797(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2821 6797"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6799">
    <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(5068(a,2),5952(a,2,1))].">
      <j1 rule="para" parents="5068 5952"/>
    </justification>
  </clause>

  <clause id="6800">
    <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,5961,a),flip(a)].">
      <j1 rule="hyper" parents="320 24 5961"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6801">
    <literal><![CDATA[
      x / (T(x,y) \ ((x \ 1) \ 1)) = (1 / (1 / x)) / K(y,x)
    ]]></literal>
    <justification jstring="[para(4796(a,2),5976(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4796 5976"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6802">
    <literal><![CDATA[
      x / (T(x,y) \ ((x \ 1) \ 1)) = T(1 / (1 / x),y)
    ]]></literal>
    <justification jstring="[hyper(320,a,4868,a(flip),b,6801,a),flip(a)].">
      <j1 rule="hyper" parents="320 4868 6801"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6803">
    <literal><![CDATA[
      x / (x * (1 / T(x,y))) = T(1 / (1 / x),y)
    ]]></literal>
    <justification jstring="[para(3438(a,1),6802(a,1,2))].">
      <j1 rule="para" parents="3438 6802"/>
    </justification>
  </clause>

  <clause id="6804">
    <literal><![CDATA[
      T(1 / (1 / x),y) \ x = x * (1 / T(x,y))
    ]]></literal>
    <justification jstring="[hyper(188,a,6803,a)].">
      <j1 rule="hyper" parents="188 6803"/>
    </justification>
  </clause>

  <clause id="6805">
    <literal><![CDATA[
      ((x \ y) / (x \ 1)) \ T(x \ y,x) = (x \ y) / ((x \ 1) \ (y / x))
    ]]></literal>
    <justification jstring="[hyper(58,a,6718,a(flip),b,5991,a)].">
      <j1 rule="hyper" parents="58 6718 5991"/>
    </justification>
  </clause>

  <clause id="6806">
    <literal><![CDATA[
      L(T(1 / x,y),y,K(x,z)) = T(1 / x,K(x,z) * y)
    ]]></literal>
    <justification jstring="[hyper(773,a,6007,a)].">
      <j1 rule="hyper" parents="773 6007"/>
    </justification>
  </clause>

  <clause id="6807">
    <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(6806(a,1),5695(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6806 5695"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6808">
    <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,5547,a(flip),b,6807,a),flip(a)].">
      <j1 rule="hyper" parents="320 5547 6807"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6809">
    <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(6808(a,1),695(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6808 695"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6810">
    <literal><![CDATA[
      ((K(x,y) / z) * (z * K(y,x))) \ (K(x,y) / z) = 1 / (z * K(y,x))
    ]]></literal>
    <justification jstring="[para(6335(a,1),6357(a,2,2))].">
      <j1 rule="para" parents="6335 6357"/>
    </justification>
  </clause>

  <clause id="6811">
    <literal><![CDATA[
      K(x \ y,z) \ K(K(x \ y,z),y) = K(y / x,z) \ 1
    ]]></literal>
    <justification jstring="[para(6(a,1),6444(a,2,1))].">
      <j1 rule="para" parents="6 6444"/>
    </justification>
  </clause>

  <clause id="6812">
    <literal><![CDATA[
      K(x \ y,z) \ K(K(x \ y,z),y) = K(z,y / x)
    ]]></literal>
    <justification jstring="[hyper(320,a,4969,a(flip),b,6811,a),flip(a)].">
      <j1 rule="hyper" parents="320 4969 6811"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6814">
    <literal><![CDATA[
      K(x \ y,z) \ K(y,K(z,x \ y)) = K(z,y / x)
    ]]></literal>
    <justification jstring="[para(5621(a,1),6812(a,1,2))].">
      <j1 rule="para" parents="5621 6812"/>
    </justification>
  </clause>

  <clause id="6815">
    <literal><![CDATA[
      (x * (y \ ((z \ (y * (x \ u))) * z))) \ u = K(z,(x * (z / y)) \ u)
    ]]></literal>
    <justification jstring="[para(4661(a,1),6681(a,1,1,2))].">
      <j1 rule="para" parents="4661 6681"/>
    </justification>
  </clause>

  <clause id="6816">
    <literal><![CDATA[
      K(x \ y,z * (1 / (y / x))) = K(x \ y,z / (y / x))
    ]]></literal>
    <justification jstring="[hyper(5150,a,6702,a),flip(a)].">
      <j1 rule="hyper" parents="5150 6702"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6817">
    <literal><![CDATA[
      K(x,((y / z) * u) \ (y * u)) = ((y * K(z,x)) * u) \ (y * u)
    ]]></literal>
    <justification jstring="[para(6151(a,1),6706(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6151 6706"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6818">
    <literal><![CDATA[
      ((x * K(y,z)) * u) * K(z,((x / y) * u) \ (x * u)) = x * u
    ]]></literal>
    <justification jstring="[hyper(119,a,6817,a,b,xx)].">
      <j1 rule="hyper" parents="119 6817"/>
    </justification>
  </clause>

  <clause id="6819">
    <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(6249(a,1),6817(a,2,1))].">
      <j1 rule="para" parents="6249 6817"/>
    </justification>
  </clause>

  <clause id="6820">
    <literal><![CDATA[
      K(((x / y) * z) \ (x * z),u) = (x * z) \ ((x * K(y,u)) * z)
    ]]></literal>
    <justification jstring="[para(6818(a,1),6338(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6818 6338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6821">
    <literal><![CDATA[
      ((x * K(y,z)) * K(y,u)) * K(z,y) = x * K(y,u)
    ]]></literal>
    <justification jstring="[para(6234(a,1),6818(a,1,2,2))].">
      <j1 rule="para" parents="6234 6818"/>
    </justification>
  </clause>

  <clause id="6822">
    <literal><![CDATA[
      (x * K(y,z)) * K(u,y) = (x * K(u,y)) * K(y,z)
    ]]></literal>
    <justification jstring="[para(6329(a,1),6821(a,1,1,1))].">
      <j1 rule="para" parents="6329 6821"/>
    </justification>
  </clause>

  <clause id="6823">
    <literal><![CDATA[
      ((x * K(y,z)) * K(z,u)) / z = (x * K(z,u)) / T(z,y)
    ]]></literal>
    <justification jstring="[hyper(117,a,6822,a(flip),b,6325,a)].">
      <j1 rule="hyper" parents="117 6822 6325"/>
    </justification>
  </clause>

  <clause id="6824">
    <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(6822(a,2),6352(a,1,1)),flip(b)].">
      <j1 rule="para" parents="6822 6352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6825">
    <literal><![CDATA[
      ((x * K(y,z)) / z) * K(z,u) = (x * K(z,u)) / T(z,y)
    ]]></literal>
    <justification jstring="[hyper(6435,a,6823,a)].">
      <j1 rule="hyper" parents="6435 6823"/>
    </justification>
  </clause>

  <clause id="6826">
    <literal><![CDATA[
      (x * K(y,z)) / T(y,u) = (x / T(y,u)) * K(y,z)
    ]]></literal>
    <justification jstring="[para(6342(a,1),6825(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6342 6825"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6827">
    <literal><![CDATA[
      ((x / T(y,z)) * K(y,u)) \ (x * K(y,u)) = T(y,z)
    ]]></literal>
    <justification jstring="[hyper(188,a,6826,a)].">
      <j1 rule="hyper" parents="188 6826"/>
    </justification>
  </clause>

  <clause id="6828">
    <literal><![CDATA[
      (1 / T(x,y)) * K(x,z) = K(x,z) / T(x,y)
    ]]></literal>
    <justification jstring="[para(2(a,1),6826(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2 6826"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6829">
    <literal><![CDATA[
      ((x \ y) * K(x,z)) \ (y * K(x,z)) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(265(a,1),6827(a,1,1,1))].">
      <j1 rule="para" parents="265 6827"/>
    </justification>
  </clause>

  <clause id="6830">
    <literal><![CDATA[
      (x \ y) / ((x \ 1) \ (y / x)) = ((y / x) / (x \ 1)) \ (x \ y)
    ]]></literal>
    <justification jstring="[para(107(a,1),6719(a,1,2)),flip(a)].">
      <j1 rule="para" parents="107 6719"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6831">
    <literal><![CDATA[
      L(L(x,y,z),z * y,K(y,z)) = (y * z) \ (z * (T(y,z) * x))
    ]]></literal>
    <justification jstring="[para(4781(a,1),6742(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4781 6742"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6832">
    <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,6831,a),flip(a)].">
      <j1 rule="hyper" parents="320 231 6831"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6833">
    <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(6831(a,2),832(a,1))].">
      <j1 rule="para" parents="6831 832"/>
    </justification>
  </clause>

  <clause id="6834">
    <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(5172(a,1),6788(a,1,1))].">
      <j1 rule="para" parents="5172 6788"/>
    </justification>
  </clause>

  <clause id="6835">
    <literal><![CDATA[
      ((x \ y) / (x \ 1)) \ T(x \ y,x) = ((y / x) / (x \ 1)) \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(320,a,6830,a(flip),b,6805,a),flip(a)].">
      <j1 rule="hyper" parents="320 6830 6805"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6836">
    <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,6810,a)].">
      <j1 rule="hyper" parents="134 6810"/>
    </justification>
  </clause>

  <clause id="6837">
    <literal><![CDATA[
      K(x,(y * (x / z)) \ u) = K(x,(y * (z \ x)) \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,6679,a(flip),b,6815,a),flip(a)].">
      <j1 rule="hyper" parents="58 6679 6815"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6838">
    <literal><![CDATA[
      K(x,(y * (x / y)) \ z) = K(x,x \ z)
    ]]></literal>
    <justification jstring="[para(5(a,1),6837(a,2,2,1))].">
      <j1 rule="para" parents="5 6837"/>
    </justification>
  </clause>

  <clause id="6839">
    <literal><![CDATA[
      K(x,(y * ((z \ x) \ x)) \ u) = K(x,(y * z) \ u)
    ]]></literal>
    <justification jstring="[para(72(a,1),6837(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="72 6837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6840">
    <literal><![CDATA[
      K(x,((y / T(z,z \ x)) * z) \ u) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[para(369(a,1),6839(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="369 6839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6841">
    <literal><![CDATA[
      K(x,(y * K(z \ x,z)) \ u) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[para(6325(a,1),6840(a,1,2,1))].">
      <j1 rule="para" parents="6325 6840"/>
    </justification>
  </clause>

  <clause id="6842">
    <literal><![CDATA[
      K(x,((y \ x) \ x) \ z) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(4802(a,1),6841(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4802 6841"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6843">
    <literal><![CDATA[
      a(K(x,y) / z,z,K(x,y)) * (1 / (z * K(y,x))) = K(x,y) / z
    ]]></literal>
    <justification jstring="[para(5897(a,1),6836(a,1,1))].">
      <j1 rule="para" parents="5897 6836"/>
    </justification>
  </clause>

  <clause id="6844">
    <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(4559(a,1),4285(a,1,1))].">
      <j1 rule="para" parents="4559 4285"/>
    </justification>
  </clause>

  <clause id="6845">
    <literal><![CDATA[
      L(R(x,y,x),y,R(x,y,x)) != z
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(4510(a,1),4672(a,1))].">
      <j1 rule="para" parents="4510 4672"/>
    </justification>
  </clause>

  <clause id="6846">
    <literal><![CDATA[
      T(x * K(y * L(x,z,u),x),y) = R(x,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[para(4939(a,1),785(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4939 785"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6847">
    <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(5382,a,6846,a)].">
      <j1 rule="hyper" parents="5382 6846"/>
    </justification>
  </clause>

  <clause id="6848">
    <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(4941(a,1),984(a,1,1,1))].">
      <j1 rule="para" parents="4941 984"/>
    </justification>
  </clause>

  <clause id="6849">
    <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(939(a,1),5064(a,1,2))].">
      <j1 rule="para" parents="939 5064"/>
    </justification>
  </clause>

  <clause id="6850">
    <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(5517(a,1),5516(a,1,1,1))].">
      <j1 rule="para" parents="5517 5516"/>
    </justification>
  </clause>

  <clause id="6851">
    <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(5620(a,1),39(a,1))].">
      <j1 rule="para" parents="5620 39"/>
    </justification>
  </clause>

  <clause id="6852">
    <literal><![CDATA[
      K(x,y * (((1 / z) * u) * w)) = K(x,y * (((z \ 1) * u) * w))
    ]]></literal>
    <justification jstring="[para(2859(a,1),5992(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="2859 5992"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6853">
    <literal><![CDATA[
      K(x,y * ((((K(z,u) / z) \ 1) * u) * w)) = K(x,y * ((u * (1 / (1 / z))) * w))
    ]]></literal>
    <justification jstring="[para(5520(a,1),6852(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5520 6852"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6854">
    <literal><![CDATA[
      K(x,y \ z) * K((z \ y) \ x,x) = x \ R(x,(z \ y) \ 1,x)
    ]]></literal>
    <justification jstring="[para(5363(a,1),6143(a,1,2))].">
      <j1 rule="para" parents="5363 6143"/>
    </justification>
  </clause>

  <clause id="6855">
    <literal><![CDATA[
      K(x,y \ z) * K(y \ (z * x),x) = x \ R(x,(z \ y) \ 1,x)
    ]]></literal>
    <justification jstring="[para(6637(a,1),6854(a,1,2))].">
      <j1 rule="para" parents="6637 6854"/>
    </justification>
  </clause>

  <clause id="6856">
    <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(6409(a,2),6505(a,1))].">
      <j1 rule="para" parents="6409 6505"/>
    </justification>
  </clause>

  <clause id="6857">
    <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(6529(a,1),6856(a,1,1))].">
      <j1 rule="para" parents="6529 6856"/>
    </justification>
  </clause>

  <clause id="6858">
    <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(1240(a,1),6486(a,1,1))].">
      <j1 rule="para" parents="1240 6486"/>
    </justification>
  </clause>

  <clause id="6859">
    <literal><![CDATA[
      L(((x / y) / x) \ 1,(x / y) / x,x) = x / (y \ T(x,y \ 1))
    ]]></literal>
    <justification jstring="[para(3906(a,1),6695(a,2,2))].">
      <j1 rule="para" parents="3906 6695"/>
    </justification>
  </clause>

  <clause id="6860">
    <literal><![CDATA[
      x / (y \ T(x,y \ 1)) = (T(x,y \ 1) / y) \ x
    ]]></literal>
    <justification jstring="[hyper(58,a,3918,a(flip),b,6859,a),flip(a)].">
      <j1 rule="hyper" parents="58 3918 6859"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6861">
    <literal><![CDATA[
      (T(x,(y \ 1) \ 1) / (y \ 1)) \ x = x / ((y \ 1) \ T(x,y))
    ]]></literal>
    <justification jstring="[para(2959(a,1),6860(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2959 6860"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6862">
    <literal><![CDATA[
      x / ((y \ 1) \ T(x,y)) = (T(x,y) / (y \ 1)) \ x
    ]]></literal>
    <justification jstring="[para(2959(a,1),6861(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="2959 6861"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6863">
    <literal><![CDATA[
      ((T(x,y) / (y \ 1)) \ x) \ x = (y \ 1) \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(188,a,6862,a)].">
      <j1 rule="hyper" parents="188 6862"/>
    </justification>
  </clause>

  <clause id="6864">
    <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(6672(a,1),6717(a,1))].">
      <j1 rule="para" parents="6672 6717"/>
    </justification>
  </clause>

  <clause id="6865">
    <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),6864(a,1,1,2))].">
      <j1 rule="para" parents="75 6864"/>
    </justification>
  </clause>

  <clause id="6866">
    <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(5130(a,1),6864(a,1,1,2))].">
      <j1 rule="para" parents="5130 6864"/>
    </justification>
  </clause>

  <clause id="6867">
    <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),4639(a,2,1,2,1,2))].">
      <j1 rule="para" parents="258 4639"/>
    </justification>
  </clause>

  <clause id="6868">
    <literal><![CDATA[
      K(x \ (y * z),(x \ (y * z)) \ 1) = K(x \ (y * z),z \ (y \ x))
    ]]></literal>
    <justification jstring="[hyper(1835,a,4772,a)].">
      <j1 rule="hyper" parents="1835 4772"/>
    </justification>
  </clause>

  <clause id="6869">
    <literal><![CDATA[
      K(x \ (y * z),(y * z) \ x) = K(x \ (y * z),z \ (y \ x))
    ]]></literal>
    <justification jstring="[hyper(6166,a,6868,a)].">
      <j1 rule="hyper" parents="6166 6868"/>
    </justification>
  </clause>

  <clause id="6870">
    <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,4864,a(flip),b,4818,a),flip(a)].">
      <j1 rule="hyper" parents="116 4864 4818"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6871">
    <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(4781(a,1),5122(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4781 5122"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6872">
    <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,6871,a),flip(a)].">
      <j1 rule="hyper" parents="320 13 6871"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6873">
    <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(6871(a,2),482(a,1))].">
      <j1 rule="para" parents="6871 482"/>
    </justification>
  </clause>

  <clause id="6874">
    <literal><![CDATA[
      L(L(x,y * z,K(y,u)),z,y) = L(x,z,T(y,u))
    ]]></literal>
    <justification jstring="[hyper(978,a,6872,a)].">
      <j1 rule="hyper" parents="978 6872"/>
    </justification>
  </clause>

  <clause id="6875">
    <literal><![CDATA[
      x * (K(x \ 1,x) * K(y,y \ (1 / (x \ 1)))) = y * ((1 / (1 / x)) / y)
    ]]></literal>
    <justification jstring="[para(5329(a,1),5215(a,1,2,2))].">
      <j1 rule="para" parents="5329 5215"/>
    </justification>
  </clause>

  <clause id="6876">
    <literal><![CDATA[
      K(x,x \ y) * K(z,y / (y / x)) = T(y / (y / x),z) \ x
    ]]></literal>
    <justification jstring="[para(4968(a,1),5456(a,1,1))].">
      <j1 rule="para" parents="4968 5456"/>
    </justification>
  </clause>

  <clause id="6877">
    <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(3115(a,1),5659(a,1,3))].">
      <j1 rule="para" parents="3115 5659"/>
    </justification>
  </clause>

  <clause id="6878">
    <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(5879(a,1),5729(a,1,2,2,2))].">
      <j1 rule="para" parents="5879 5729"/>
    </justification>
  </clause>

  <clause id="6879">
    <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(5641(a,1),5825(a,1,2))].">
      <j1 rule="para" parents="5641 5825"/>
    </justification>
  </clause>

  <clause id="6880">
    <literal><![CDATA[
      (1 / x) * K(((1 / x) \ y) \ 1,z) = K((y * x) \ 1,z) / x
    ]]></literal>
    <justification jstring="[para(75(a,1),6023(a,1,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="75 6023"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6882">
    <literal><![CDATA[
      (1 / x) * K(y \ (1 / x),z) = K((y * x) \ 1,z) / x
    ]]></literal>
    <justification jstring="[para(6259(a,1),6880(a,1,2))].">
      <j1 rule="para" parents="6259 6880"/>
    </justification>
  </clause>

  <clause id="6883">
    <literal><![CDATA[
      K((x * y) \ 1,x * y) = K(x \ (1 / y),x * y)
    ]]></literal>
    <justification jstring="[hyper(29,a,3658,a,b,6882,a)].">
      <j1 rule="hyper" parents="29 3658 6882"/>
    </justification>
  </clause>

  <clause id="6884">
    <literal><![CDATA[
      (1 / x) * K(y \ (x \ 1),z) = K((y * x) \ 1,z) / x
    ]]></literal>
    <justification jstring="[para(3985(a,1),6882(a,1,2))].">
      <j1 rule="para" parents="3985 6882"/>
    </justification>
  </clause>

  <clause id="6885">
    <literal><![CDATA[
      K((x * (y \ 1)) \ 1,x * (y \ 1)) = K(x \ y,x * (y \ 1))
    ]]></literal>
    <justification jstring="[para(72(a,1),6883(a,2,1,2))].">
      <j1 rule="para" parents="72 6883"/>
    </justification>
  </clause>

  <clause id="6886">
    <literal><![CDATA[
      (x * K((y / x) \ 1,y / x)) * (x \ 1) = K(y \ x,y * (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(58,a,4077,a,b,6885,a)].">
      <j1 rule="hyper" parents="58 4077 6885"/>
    </justification>
  </clause>

  <clause id="6887">
    <literal><![CDATA[
      (x * K(y \ x,x \ y)) * (x \ 1) = K(y \ x,y * (x \ 1))
    ]]></literal>
    <justification jstring="[para(2939(a,1),6886(a,1,1,2))].">
      <j1 rule="para" parents="2939 6886"/>
    </justification>
  </clause>

  <clause id="6888">
    <literal><![CDATA[
      K(x \ y,x * (y \ 1)) = K(x \ y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(3811,a,6887,a),flip(a)].">
      <j1 rule="hyper" parents="3811 6887"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6889">
    <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),6888(a,1,2,2))].">
      <j1 rule="para" parents="106 6888"/>
    </justification>
  </clause>

  <clause id="6890">
    <literal><![CDATA[
      K(x \ (y \ 1),(y \ 1) \ x) = K(x \ (1 / y),x * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,5423,a(flip),b,6889,a),flip(a)].">
      <j1 rule="hyper" parents="58 5423 6889"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6891">
    <literal><![CDATA[
      K(x \ (1 / y),x * y) = K(x \ (y \ 1),y * x)
    ]]></literal>
    <justification jstring="[hyper(58,a,5799,a(flip),b,6890,a),flip(a)].">
      <j1 rule="hyper" parents="58 5799 6890"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6892">
    <literal><![CDATA[
      K((x * y) \ 1,x * y) = K(x \ (y \ 1),y * x)
    ]]></literal>
    <justification jstring="[hyper(58,a,6883,a,b,6891,a)].">
      <j1 rule="hyper" parents="58 6883 6891"/>
    </justification>
  </clause>

  <clause id="6893">
    <literal><![CDATA[
      (T(x * y,z) / y) * (x \ 1) = (1 / y) * (x \ T(x * y,z))
    ]]></literal>
    <justification jstring="[para(1001(a,1),6024(a,1,1))].">
      <j1 rule="para" parents="1001 6024"/>
    </justification>
  </clause>

  <clause id="6894">
    <literal><![CDATA[
      (1 / x) * ((x \ y) \ T((x \ y) * x,x)) = (x \ T(y,x)) * ((x \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(1380(a,1),6893(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1380 6893"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6896">
    <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(6116(a,1),6158(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6116 6158"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6897">
    <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,6896,a),flip(a)].">
      <j1 rule="hyper" parents="320 15 6896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6898">
    <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(6896(a,2),518(a,1))].">
      <j1 rule="para" parents="6896 518"/>
    </justification>
  </clause>

  <clause id="6899">
    <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,6897,a)].">
      <j1 rule="hyper" parents="58 26 6897"/>
    </justification>
  </clause>

  <clause id="6900">
    <literal><![CDATA[
      T(x,y) / ((1 / z) \ x) = (1 / z) * K((((z \ 1) \ x) \ 1) \ (z \ 1),y)
    ]]></literal>
    <justification jstring="[para(4005(a,1),6578(a,2,2))].">
      <j1 rule="para" parents="4005 6578"/>
    </justification>
  </clause>

  <clause id="6901">
    <literal><![CDATA[
      (x * (y * ((z \ (y \ (x \ u))) * z))) \ u = K(z,(x * (y * z)) \ u)
    ]]></literal>
    <justification jstring="[para(105(a,1),6680(a,1,1,2,2))].">
      <j1 rule="para" parents="105 6680"/>
    </justification>
  </clause>

  <clause id="6902">
    <literal><![CDATA[
      ((x * y) * ((z \ ((x * y) \ u)) * z)) \ u = K(z,(x * (y * z)) \ u)
    ]]></literal>
    <justification jstring="[para(3544(a,2),6901(a,1,1))].">
      <j1 rule="para" parents="3544 6901"/>
    </justification>
  </clause>

  <clause id="6903">
    <literal><![CDATA[
      (x * T(y,L(z,y,x))) \ (x * (y * (z * K(y,z)))) = L(z,y,x)
    ]]></literal>
    <justification jstring="[para(4884(a,1),6686(a,1,1,2))].">
      <j1 rule="para" parents="4884 6686"/>
    </justification>
  </clause>

  <clause id="6904">
    <literal><![CDATA[
      (x * T(y,L(z,y,x))) \ (x * (T(y,z) * z)) = L(z,y,x)
    ]]></literal>
    <justification jstring="[para(4829(a,1),6903(a,1,2,2))].">
      <j1 rule="para" parents="4829 6903"/>
    </justification>
  </clause>

  <clause id="6905">
    <literal><![CDATA[
      x * (K(x \ 1,x) * K(y,y \ x)) = y * ((1 / (1 / x)) / y)
    ]]></literal>
    <justification jstring="[para(72(a,1),6875(a,1,2,2,2,2))].">
      <j1 rule="para" parents="72 6875"/>
    </justification>
  </clause>

  <clause id="6907">
    <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,4611,a,b,6905,a)].">
      <j1 rule="hyper" parents="320 4611 6905"/>
    </justification>
  </clause>

  <clause id="6908">
    <literal><![CDATA[
      (x \ T(y,x)) * ((x \ y) \ 1) = (1 / x) * ((y * x) / y)
    ]]></literal>
    <justification jstring="[para(4630(a,1),6894(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4630 6894"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6909">
    <literal><![CDATA[
      K(x,y) = (y \ T(x,y)) * ((y \ x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,4889,a,b,6908,a)].">
      <j1 rule="hyper" parents="320 4889 6908"/>
    </justification>
  </clause>

  <clause id="6910">
    <literal><![CDATA[
      (x \ T(x * y,x)) * (y \ 1) = K(x * y,x)
    ]]></literal>
    <justification jstring="[para(4(a,1),6909(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="4 6909"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6911">
    <literal><![CDATA[
      (x \ T(x * K(y,z),x)) * (K(z,y) * 1) = K(x * K(y,z),x)
    ]]></literal>
    <justification jstring="[para(5130(a,1),6910(a,1,2))].">
      <j1 rule="para" parents="5130 6910"/>
    </justification>
  </clause>

  <clause id="6912">
    <literal><![CDATA[
      K(x,T(y / z,y) \ y) * (K(z,x) * 1) = K(y * K(x,z),y)
    ]]></literal>
    <justification jstring="[para(5996(a,2),6911(a,1,1))].">
      <j1 rule="para" parents="5996 6911"/>
    </justification>
  </clause>

  <clause id="6913">
    <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),6912(a,1,2))].">
      <j1 rule="para" parents="3 6912"/>
    </justification>
  </clause>

  <clause id="6914">
    <literal><![CDATA[
      T(x,y) / ((1 / z) \ x) = K(((((z \ 1) \ x) \ 1) * z) \ 1,y) / z
    ]]></literal>
    <justification jstring="[hyper(320,a,6884,a(flip),b,6900,a),flip(a)].">
      <j1 rule="hyper" parents="320 6884 6900"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6915">
    <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(6283(a,1),4151(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6283 4151"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6916">
    <literal><![CDATA[
      R((x \ (1 / y)) * x,y,z) * (y * z) = (y * z) * ((x \ ((y * z) \ z)) * x)
    ]]></literal>
    <justification jstring="[para(3845(a,2),4645(a,1,1))].">
      <j1 rule="para" parents="3845 4645"/>
    </justification>
  </clause>

  <clause id="6917">
    <literal><![CDATA[
      K(x \ 1,x) * K(y,y \ x) = (x \ 1) * (y * (x / y))
    ]]></literal>
    <justification jstring="[hyper(4674,a,6907,a),flip(a)].">
      <j1 rule="hyper" parents="4674 6907"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6918">
    <literal><![CDATA[
      (1 / x) * (y * (x / y)) = K(y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(2849,a,6917,a)].">
      <j1 rule="hyper" parents="2849 6917"/>
    </justification>
  </clause>

  <clause id="6919">
    <literal><![CDATA[
      x \ K(y,y \ (x \ 1)) = y * ((x \ 1) / y)
    ]]></literal>
    <justification jstring="[hyper(116,a,6918,a(flip),b,183,a(flip))].">
      <j1 rule="hyper" parents="116 6918 183"/>
    </justification>
  </clause>

  <clause id="6920">
    <literal><![CDATA[
      K(x,R(y,z,u) \ 1) * (z * u) = (K(x,y \ 1) * z) * u
    ]]></literal>
    <justification jstring="[para(5303(a,1),5305(a,2,1))].">
      <j1 rule="para" parents="5303 5305"/>
    </justification>
  </clause>

  <clause id="6921">
    <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,6920,a)].">
      <j1 rule="hyper" parents="30 101 6920"/>
    </justification>
  </clause>

  <clause id="6922">
    <literal><![CDATA[
      K(x,R(y,x,z) \ 1) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(30,a,4207,a(flip),b,6920,a),flip(a)].">
      <j1 rule="hyper" parents="30 4207 6920"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6923">
    <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),6922(a,1,2,1))].">
      <j1 rule="para" parents="26 6922"/>
    </justification>
  </clause>

  <clause id="6925">
    <literal><![CDATA[
      K(x,R(y \ 1,z,u) \ 1) = R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(3554(a,1),6921(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3554 6921"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6926">
    <literal><![CDATA[
      K(x,R(y / z,u,w) \ 1) = R(K(x,z / y),u,w)
    ]]></literal>
    <justification jstring="[para(5351(a,1),6921(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5351 6921"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6927">
    <literal><![CDATA[
      K(x,R(y \ z,u,w) \ 1) = R(K(x,z \ y),u,w)
    ]]></literal>
    <justification jstring="[para(6108(a,1),6921(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6108 6921"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6928">
    <literal><![CDATA[
      T(x,R(y \ 1,z,u) \ 1) = x * R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(119,a,6925,a(flip),b,4729,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 6925 4729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6929">
    <literal><![CDATA[
      R(K(x,y),z,u) \ w = R(K(y,x),z,u) * w
    ]]></literal>
    <justification jstring="[para(6925(a,1),5711(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6925 5711"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6930">
    <literal><![CDATA[
      R(K(x,y),z,u) \ 1 = R(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(3208,a,6929,a)].">
      <j1 rule="hyper" parents="3208 6929"/>
    </justification>
  </clause>

  <clause id="6931">
    <literal><![CDATA[
      (x * y) / ((K(z,u) * x) * y) = R(K(u,z),x,y)
    ]]></literal>
    <justification jstring="[hyper(618,a,6929,a)].">
      <j1 rule="hyper" parents="618 6929"/>
    </justification>
  </clause>

  <clause id="6932">
    <literal><![CDATA[
      x / (R(K(y,z),u,w) * x) = R(K(z,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(575,a,6929,a)].">
      <j1 rule="hyper" parents="575 6929"/>
    </justification>
  </clause>

  <clause id="6933">
    <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,6929,a),flip(a)].">
      <j1 rule="hyper" parents="320 101 6929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6934">
    <literal><![CDATA[
      R(K(x,y),y / x,z) * ((y / T(x,y)) * z) = (y / x) * z
    ]]></literal>
    <justification jstring="[hyper(58,a,5275,a(flip),b,6929,a),flip(a)].">
      <j1 rule="hyper" parents="58 5275 6929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6935">
    <literal><![CDATA[
      R(K(x,y),z,u) \ 1 != w
    ]]></literal>
    <literal><![CDATA[
      R(K(y,x),z,u) = w
    ]]></literal>
    <justification jstring="[para(6929(a,2),127(a,1)),flip(b)].">
      <j1 rule="para" parents="6929 127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6936">
    <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(6929(a,1),330(a,1,2)),flip(b)].">
      <j1 rule="para" parents="6929 330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6937">
    <literal><![CDATA[
      R(K(x,y),z,(K(y,x) * z) \ 1) = z * ((K(y,x) * z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(896,a,6930,a),flip(a)].">
      <j1 rule="hyper" parents="896 6930"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6938">
    <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(6930(a,1),5674(a,1,1,2,2))].">
      <j1 rule="para" parents="6930 5674"/>
    </justification>
  </clause>

  <clause id="6939">
    <literal><![CDATA[
      ((x \ 1) * y) / ((x \ K(x,z)) * y) = R(K(z,x),x \ 1,y)
    ]]></literal>
    <justification jstring="[para(3206(a,1),6931(a,1,2,1))].">
      <j1 rule="para" parents="3206 6931"/>
    </justification>
  </clause>

  <clause id="6940">
    <literal><![CDATA[
      R(K(x,y / z),y,u) = K(x,(y * u) / (z * u))
    ]]></literal>
    <justification jstring="[hyper(5496,a,6926,a),flip(a)].">
      <j1 rule="hyper" parents="5496 6926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6941">
    <literal><![CDATA[
      R(K(x,y / z),y,y \ 1) = K(x,(z * (y \ 1)) \ 1)
    ]]></literal>
    <justification jstring="[para(523(a,1),6926(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="523 6926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6942">
    <literal><![CDATA[
      R(K(x,y / z),y,z \ 1) = K(x,y * (z \ 1))
    ]]></literal>
    <justification jstring="[para(504(a,1),6926(a,1,2)),flip(a)].">
      <j1 rule="para" parents="504 6926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6943">
    <literal><![CDATA[
      R(K(x,y / z),y,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * u) / (z * u)) = w
    ]]></literal>
    <justification jstring="[para(6926(a,1),5496(a,1))].">
      <j1 rule="para" parents="6926 5496"/>
    </justification>
  </clause>

  <clause id="6944">
    <literal><![CDATA[
      R(K(x,(y / z) / u),y / z,z) = K(x,y / (u * z))
    ]]></literal>
    <justification jstring="[para(7(a,1),6940(a,2,2,1))].">
      <j1 rule="para" parents="7 6940"/>
    </justification>
  </clause>

  <clause id="6945">
    <literal><![CDATA[
      R(K(x,y / (z / u)),y,u) = K(x,(y * u) / z)
    ]]></literal>
    <justification jstring="[para(7(a,1),6940(a,2,2,2))].">
      <j1 rule="para" parents="7 6940"/>
    </justification>
  </clause>

  <clause id="6946">
    <literal><![CDATA[
      K(x,(y * z) / ((u \ y) * z)) = R(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(72(a,1),6940(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="72 6940"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6947">
    <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(6773(a,1),6940(a,1,1,2))].">
      <j1 rule="para" parents="6773 6940"/>
    </justification>
  </clause>

  <clause id="6948">
    <literal><![CDATA[
      R(K(x,(y / z) \ x),x,z) = K(x,(x * z) / y)
    ]]></literal>
    <justification jstring="[para(5197(a,1),6945(a,1,1))].">
      <j1 rule="para" parents="5197 6945"/>
    </justification>
  </clause>

  <clause id="6949">
    <literal><![CDATA[
      K(x,R(y,y \ z,u)) = R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(98(a,2),6946(a,1,2))].">
      <j1 rule="para" parents="98 6946"/>
    </justification>
  </clause>

  <clause id="6950">
    <literal><![CDATA[
      R(K(x,y),T(y,z),u) = K(x,y)
    ]]></literal>
    <justification jstring="[para(4085(a,1),6946(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4085 6946"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6951">
    <literal><![CDATA[
      (K(x,y) * T(y,z)) * u = K(x,y) * (T(y,z) * u)
    ]]></literal>
    <justification jstring="[para(6950(a,1),101(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6950 101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6952">
    <literal><![CDATA[
      K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      R(K(x,y),y,u) = z
    ]]></literal>
    <justification jstring="[para(6950(a,1),6553(a,1))].">
      <j1 rule="para" parents="6950 6553"/>
    </justification>
  </clause>

  <clause id="6953">
    <literal><![CDATA[
      (x * R(K(y,z),u,w)) \ x = R(K(z,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(58,a,6753,a(flip),b,6949,a)].">
      <j1 rule="hyper" parents="58 6753 6949"/>
    </justification>
  </clause>

  <clause id="6954">
    <literal><![CDATA[
      (x * R(K(y,z),u,w)) * R(K(z,y),u,w) = x
    ]]></literal>
    <justification jstring="[hyper(119,a,6949,a(flip),b,6753,a(flip))].">
      <j1 rule="hyper" parents="119 6949 6753"/>
    </justification>
  </clause>

  <clause id="6955">
    <literal><![CDATA[
      R(K(x,y),y * z,u) = K(x,R(y,z,u))
    ]]></literal>
    <justification jstring="[para(4(a,1),6949(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 6949"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6956">
    <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),6949(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="184 6949"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6957">
    <literal><![CDATA[
      R(K(x,y),K(z,y) * u,w) = K(x,R(y,T(y,z) \ u,w))
    ]]></literal>
    <justification jstring="[para(5106(a,1),6949(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5106 6949"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6958">
    <literal><![CDATA[
      K(x * y,R(x,y,z)) = K(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(4219,a,6955,a),flip(a)].">
      <j1 rule="hyper" parents="4219 6955"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6959">
    <literal><![CDATA[
      K(R(x,y * z,u) \ 1,y) = K(x \ 1,R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,5703,a(flip),b,6955,a)].">
      <j1 rule="hyper" parents="58 5703 6955"/>
    </justification>
  </clause>

  <clause id="6960">
    <literal><![CDATA[
      R(T(K(x,y),z),y * u,w) = T(K(x,R(y,u,w)),z)
    ]]></literal>
    <justification jstring="[para(6955(a,1),22(a,2,1))].">
      <j1 rule="para" parents="6955 22"/>
    </justification>
  </clause>

  <clause id="6961">
    <literal><![CDATA[
      K(x,R(y,z,u)) * ((y * z) * u) = (y * (K(x,y) * z)) * u
    ]]></literal>
    <justification jstring="[para(6955(a,1),5419(a,1,1))].">
      <j1 rule="para" parents="6955 5419"/>
    </justification>
  </clause>

  <clause id="6962">
    <literal><![CDATA[
      K(x,(x * y) / z) = K(x,(z / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(4219,a,6948,a),flip(a)].">
      <j1 rule="hyper" parents="4219 6948"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6963">
    <literal><![CDATA[
      R(K(x,(y / z) \ x),x,z) = K(x,(y / (x * z)) \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,5351,a,b,6948,a),flip(a)].">
      <j1 rule="hyper" parents="320 5351 6948"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6964">
    <literal><![CDATA[
      K(x,(x * y) / z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,(z / y) \ x) = u
    ]]></literal>
    <justification jstring="[para(6948(a,1),4219(a,1))].">
      <j1 rule="para" parents="6948 4219"/>
    </justification>
  </clause>

  <clause id="6966">
    <literal><![CDATA[
      K(x,(L(y,z,u) / y) \ x) = K(x,(x / L(y,z,u)) * y)
    ]]></literal>
    <justification jstring="[para(1641(a,1),6962(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1641 6962"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6967">
    <literal><![CDATA[
      L(x,T(y,z),K(u,y)) = x
    ]]></literal>
    <justification jstring="[hyper(479,a,6951,a)].">
      <j1 rule="hyper" parents="479 6951"/>
    </justification>
  </clause>

  <clause id="6968">
    <literal><![CDATA[
      (K(x,y) * T(y,z)) \ u = T(y,z) \ (K(y,x) * u)
    ]]></literal>
    <justification jstring="[hyper(5768,a,6967,a),flip(a)].">
      <j1 rule="hyper" parents="5768 6967"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6969">
    <literal><![CDATA[
      L(x,T(y,z),K(u,y)) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(6967(a,1),45(a,2))].">
      <j1 rule="para" parents="6967 45"/>
    </justification>
  </clause>

  <clause id="6970">
    <literal><![CDATA[
      T(x,y) \ (K(x,z) * u) = K(x,z) * (T(x,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,5771,a(flip),b,6968,a),flip(a)].">
      <j1 rule="hyper" parents="58 5771 6968"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6971">
    <literal><![CDATA[
      T(x,x * y) * (L(x,y,x) \ z) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(119,a,5772,a(flip),b,6970,a)].">
      <j1 rule="hyper" parents="119 5772 6970"/>
    </justification>
  </clause>

  <clause id="6974">
    <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),6923(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="534 6923"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6975">
    <literal><![CDATA[
      K(x,((y \ z) * (z \ 1)) \ 1) = R(K(x,y),z,z \ 1)
    ]]></literal>
    <justification jstring="[para(72(a,1),6941(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="72 6941"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6976">
    <literal><![CDATA[
      R(K(x,y \ x),x,z) = K(x,((y * z) / (x * z)) \ 1)
    ]]></literal>
    <justification jstring="[para(6(a,1),6963(a,1,1,2,1))].">
      <j1 rule="para" parents="6 6963"/>
    </justification>
  </clause>

  <clause id="6977">
    <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),6976(a,2,2,1,2))].">
      <j1 rule="para" parents="7 6976"/>
    </justification>
  </clause>

  <clause id="6978">
    <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),6943(a,1,1,2))].">
      <j1 rule="para" parents="72 6943"/>
    </justification>
  </clause>

  <clause id="6979">
    <literal><![CDATA[
      K(x,(y \ L(y,z,u)) \ x) = K(x,(x / L(y,z,u)) * y)
    ]]></literal>
    <justification jstring="[para(3520(a,1),6966(a,1,2,1))].">
      <j1 rule="para" parents="3520 6966"/>
    </justification>
  </clause>

  <clause id="6980">
    <literal><![CDATA[
      K(x,L(y,z,u) \ (y * x)) = K(x,(x / L(y,z,u)) * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,6589,a(flip),b,6979,a)].">
      <j1 rule="hyper" parents="58 6589 6979"/>
    </justification>
  </clause>

  <clause id="6981">
    <literal><![CDATA[
      K(x,(x / L(y,z,u)) * y) = K(x,y * (L(y,z,u) \ x))
    ]]></literal>
    <justification jstring="[para(1412(a,1),6980(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1412 6980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6982">
    <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,6932,a,b,6937,a)].">
      <j1 rule="hyper" parents="58 6932 6937"/>
    </justification>
  </clause>

  <clause id="6983">
    <literal><![CDATA[
      ((x * (K(y,x) * z)) * u) / ((x * z) * u) = K(y,R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(131,a,6961,a)].">
      <j1 rule="hyper" parents="131 6961"/>
    </justification>
  </clause>

  <clause id="6984">
    <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(6983(a,1),251(a,1,1)),flip(b)].">
      <j1 rule="para" parents="6983 251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6985">
    <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(6958(a,1),6956(a,1,1))].">
      <j1 rule="para" parents="6958 6956"/>
    </justification>
  </clause>

  <clause id="6986">
    <literal><![CDATA[
      K((x / y) \ 1,z \ (y / x)) = K(y / x,((z * x) / y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,5430,a(flip),b,6977,a)].">
      <j1 rule="hyper" parents="58 5430 6977"/>
    </justification>
  </clause>

  <clause id="6987">
    <literal><![CDATA[
      K((x / y) \ 1,z \ (y / x)) = K(y / x,y / (z * x))
    ]]></literal>
    <justification jstring="[hyper(320,a,5351,a(flip),b,6986,a),flip(a)].">
      <j1 rule="hyper" parents="320 5351 6986"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6989">
    <literal><![CDATA[
      K(x / y,x / (z * y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x / y,z \ (x / y)) = u
    ]]></literal>
    <justification jstring="[para(6987(a,1),5668(a,1))].">
      <j1 rule="para" parents="6987 5668"/>
    </justification>
  </clause>

  <clause id="6990">
    <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,6743,a(flip),b,6985,a),flip(a)].">
      <j1 rule="hyper" parents="58 6743 6985"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6991">
    <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(6990(a,1),5142(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6990 5142"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6992">
    <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(6991(a,2),5150(a,1))].">
      <j1 rule="para" parents="6991 5150"/>
    </justification>
  </clause>

  <clause id="6993">
    <literal><![CDATA[
      ((1 / R(x,y,z)) * x) * (x \ 1) = T(1 / R(x,y,z),x)
    ]]></literal>
    <justification jstring="[hyper(5024,a,5805,a),flip(a)].">
      <j1 rule="hyper" parents="5024 5805"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6994">
    <literal><![CDATA[
      (x / R(x,y,z)) * (x \ 1) = T(1 / R(x,y,z),x)
    ]]></literal>
    <justification jstring="[para(1876(a,1),6993(a,1,1))].">
      <j1 rule="para" parents="1876 6993"/>
    </justification>
  </clause>

  <clause id="6995">
    <literal><![CDATA[
      (x / R(x,y,z)) * (x \ 1) = R(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(320,a,6774,a(flip),b,6994,a),flip(a)].">
      <j1 rule="hyper" parents="320 6774 6994"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6996">
    <literal><![CDATA[
      (R(x,y,z) \ x) * (x \ 1) = R(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(6777,a,6995,a)].">
      <j1 rule="hyper" parents="6777 6995"/>
    </justification>
  </clause>

  <clause id="6997">
    <literal><![CDATA[
      T(R(x,y,z) \ x,x \ 1) = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(239,a,6996,a,b,6761,a)].">
      <j1 rule="hyper" parents="239 6996 6761"/>
    </justification>
  </clause>

  <clause id="6998">
    <literal><![CDATA[
      K(R(x,y,z) \ x,x \ 1) = 1
    ]]></literal>
    <justification jstring="[hyper(50,a,6997,a)].">
      <j1 rule="hyper" parents="50 6997"/>
    </justification>
  </clause>

  <clause id="6999">
    <literal><![CDATA[
      T(1 / x,R(x,y,z) \ x) = 1 / x
    ]]></literal>
    <justification jstring="[para(6998(a,1),4882(a,1,1,1))].">
      <j1 rule="para" parents="6998 4882"/>
    </justification>
  </clause>

  <clause id="7000">
    <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(6999(a,1),2115(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6999 2115"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7001">
    <literal><![CDATA[
      L(x \ y,T(x,x \ z),x \ z) = z \ ((z / x) * y)
    ]]></literal>
    <justification jstring="[para(223(a,1),5939(a,1,1)),flip(a)].">
      <j1 rule="para" parents="223 5939"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7002">
    <literal><![CDATA[
      L(x \ y,(x \ z) \ z,x \ z) = z \ ((z / x) * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,1614,a(flip),b,7001,a)].">
      <j1 rule="hyper" parents="58 1614 7001"/>
    </justification>
  </clause>

  <clause id="7003">
    <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(6366(a,2),6392(a,2,2))].">
      <j1 rule="para" parents="6366 6392"/>
    </justification>
  </clause>

  <clause id="7004">
    <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),6848(a,2,1,1))].">
      <j1 rule="para" parents="4 6848"/>
    </justification>
  </clause>

  <clause id="7005">
    <literal><![CDATA[
      (x * y) * ((z \ ((x * y) \ y)) * z) = (((z \ (1 / x)) * z) * x) * y
    ]]></literal>
    <justification jstring="[hyper(283,a,6916,a),flip(a)].">
      <j1 rule="hyper" parents="283 6916"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7006">
    <literal><![CDATA[
      (x * y) * ((z \ ((x * y) \ y)) * z) = K(x \ (z \ 1),z) * y
    ]]></literal>
    <justification jstring="[para(6658(a,1),7005(a,2,1))].">
      <j1 rule="para" parents="6658 7005"/>
    </justification>
  </clause>

  <clause id="7007">
    <literal><![CDATA[
      K(x,y / (x / ((z * y) \ 1))) = y / (K(z \ (x \ 1),x) * y)
    ]]></literal>
    <justification jstring="[para(7006(a,1),5733(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7006 5733"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7008">
    <literal><![CDATA[
      K(x,y / (x / ((z * y) \ 1))) = K(x,z \ (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(320,a,5142,a(flip),b,7007,a),flip(a)].">
      <j1 rule="hyper" parents="320 5142 7007"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7009">
    <literal><![CDATA[
      K(x,y / (x * (z * y))) = K(x,z \ (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(5962,a,7008,a)].">
      <j1 rule="hyper" parents="5962 7008"/>
    </justification>
  </clause>

  <clause id="7011">
    <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,5351,a(flip),b,6974,a),flip(a)].">
      <j1 rule="hyper" parents="320 5351 6974"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7012">
    <literal><![CDATA[
      R(K(x,x / y),x * z,u) = K(x,((x * z) * u) / ((y * z) * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,6926,a(flip),b,7011,a)].">
      <j1 rule="hyper" parents="58 6926 7011"/>
    </justification>
  </clause>

  <clause id="7013">
    <literal><![CDATA[
      R(K(x,y \ x),x * z,u) = K(x,((x * z) * u) / ((y * z) * u))
    ]]></literal>
    <justification jstring="[para(5197(a,1),7012(a,1,1))].">
      <j1 rule="para" parents="5197 7012"/>
    </justification>
  </clause>

  <clause id="7014">
    <literal><![CDATA[
      K(x,((x * y) * z) / ((u * y) * z)) = K(R(x,y,z),u \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,6743,a(flip),b,7013,a),flip(a)].">
      <j1 rule="hyper" parents="58 6743 7013"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7015">
    <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),7014(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="5 7014"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7016">
    <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(5450(a,1),7014(a,1,2,1))].">
      <j1 rule="para" parents="5450 7014"/>
    </justification>
  </clause>

  <clause id="7017">
    <literal><![CDATA[
      K(x,(y * z) / ((u * (x \ y)) * z)) = R(K(x,u \ x),y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,6745,a(flip),b,7015,a),flip(a)].">
      <j1 rule="hyper" parents="58 6745 7015"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7018">
    <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,4465,a(flip),b,7003,a),flip(a)].">
      <j1 rule="hyper" parents="320 4465 7003"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7019">
    <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),4152(a,1,2,2,1,1,2))].">
      <j1 rule="para" parents="17 4152"/>
    </justification>
  </clause>

  <clause id="7020">
    <literal><![CDATA[
      x * (x * T(T(x,y) \ ((y * x) / x),z)) = (x * T(x \ y,z)) * x
    ]]></literal>
    <justification jstring="[para(4233(a,1),7019(a,1,2,2,1,1))].">
      <j1 rule="para" parents="4233 7019"/>
    </justification>
  </clause>

  <clause id="7021">
    <literal><![CDATA[
      x * (x * T(T(x,y) \ y,z)) = (x * T(x \ y,z)) * x
    ]]></literal>
    <justification jstring="[para(6(a,1),7020(a,1,2,2,1,2))].">
      <j1 rule="para" parents="6 7020"/>
    </justification>
  </clause>

  <clause id="7022">
    <literal><![CDATA[
      (x \ (y * (T(z,x) \ z))) * x = ((x \ y) * x) * (T(z,x) \ z)
    ]]></literal>
    <justification jstring="[para(225(a,1),4621(a,1,1)),flip(a)].">
      <j1 rule="para" parents="225 4621"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7024">
    <literal><![CDATA[
      ((x \ y) * x) * (T(z,x) \ z) = (x \ (y * K(x,z))) * x
    ]]></literal>
    <justification jstring="[para(4730(a,2),7022(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4730 7022"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7025">
    <literal><![CDATA[
      (x \ (y * K(x,z))) * x = ((x \ y) * x) * K(x,z)
    ]]></literal>
    <justification jstring="[para(4730(a,2),7024(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4730 7024"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7027">
    <literal><![CDATA[
      x \ (y * K(x,z)) = (x \ y) * K(x,z)
    ]]></literal>
    <justification jstring="[hyper(30,a,6230,a,b,7025,a),flip(a)].">
      <j1 rule="hyper" parents="30 6230 7025"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7028">
    <literal><![CDATA[
      x * ((x \ y) * K(x,z)) = y * K(x,z)
    ]]></literal>
    <justification jstring="[hyper(134,a,7027,a)].">
      <j1 rule="hyper" parents="134 7027"/>
    </justification>
  </clause>

  <clause id="7029">
    <literal><![CDATA[
      T(x,y) \ (z * K(x,y)) = T(x \ z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(239,a,7027,a(flip),b,5081,a),flip(a)].">
      <j1 rule="hyper" parents="239 7027 5081"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7031">
    <literal><![CDATA[
      (x * y) * K(x,z) = x * (y * K(x,z))
    ]]></literal>
    <justification jstring="[para(4(a,1),7028(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4 7028"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7032">
    <literal><![CDATA[
      K(x,(x \ y) \ z) = K(x,y \ (x * z))
    ]]></literal>
    <justification jstring="[hyper(6714,a,7031,a),flip(a)].">
      <j1 rule="hyper" parents="6714 7031"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7033">
    <literal><![CDATA[
      R(x,y,K(x,z)) = x
    ]]></literal>
    <justification jstring="[hyper(4038,a,7031,a)].">
      <j1 rule="hyper" parents="4038 7031"/>
    </justification>
  </clause>

  <clause id="7034">
    <literal><![CDATA[
      L(K(x,y),z,x) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(4028,a,7031,a)].">
      <j1 rule="hyper" parents="4028 7031"/>
    </justification>
  </clause>

  <clause id="7035">
    <literal><![CDATA[
      T(x,y) * T(z,K(x,y)) = (x * z) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,5078,a,b,7031,a)].">
      <j1 rule="hyper" parents="320 5078 7031"/>
    </justification>
  </clause>

  <clause id="7036">
    <literal><![CDATA[
      T(T(x,y) * z,K(x,y)) = x * (z * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,6455,a,b,7031,a)].">
      <j1 rule="hyper" parents="58 6455 7031"/>
    </justification>
  </clause>

  <clause id="7037">
    <literal><![CDATA[
      a(x,y,K(x,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,7031,a(flip),b,80,a),flip(a)].">
      <j1 rule="hyper" parents="115 7031 80"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7038">
    <literal><![CDATA[
      (x * (y * K(x,z))) * x = (x * y) * T(x,z)
    ]]></literal>
    <justification jstring="[para(7031(a,1),6196(a,1,1))].">
      <j1 rule="para" parents="7031 6196"/>
    </justification>
  </clause>

  <clause id="7039">
    <literal><![CDATA[
      (x * (y * K(x,z))) / x = ((x * y) / x) * K(x,z)
    ]]></literal>
    <justification jstring="[para(7031(a,1),6224(a,1,1))].">
      <j1 rule="para" parents="7031 6224"/>
    </justification>
  </clause>

  <clause id="7040">
    <literal><![CDATA[
      R(T(x,y),z,K(x,u)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(7033(a,1),22(a,2,1))].">
      <j1 rule="para" parents="7033 22"/>
    </justification>
  </clause>

  <clause id="7041">
    <literal><![CDATA[
      (T(x,y) * z) * K(x,u) = T(x,y) * (z * K(x,u))
    ]]></literal>
    <justification jstring="[para(7033(a,1),512(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7033 512"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7042">
    <literal><![CDATA[
      (L(x,y,z) * u) * K(x,w) = L(x,y,z) * (u * K(x,w))
    ]]></literal>
    <justification jstring="[para(7033(a,1),513(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7033 513"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7043">
    <literal><![CDATA[
      (R(x,y,z) * u) * K(x,w) = R(x,y,z) * (u * K(x,w))
    ]]></literal>
    <justification jstring="[para(7033(a,1),514(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7033 514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7044">
    <literal><![CDATA[
      x \ (y * T(x,z)) = T(y,x) * K(x,z)
    ]]></literal>
    <justification jstring="[para(7033(a,1),6156(a,1,1))].">
      <j1 rule="para" parents="7033 6156"/>
    </justification>
  </clause>

  <clause id="7045">
    <literal><![CDATA[
      (K(x,y) * z) * K(x,u) = K(x,y) * (z * K(x,u))
    ]]></literal>
    <justification jstring="[para(7033(a,1),6751(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7033 6751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7046">
    <literal><![CDATA[
      R(x,y,T(x,z)) = R(x,y,x)
    ]]></literal>
    <justification jstring="[para(7033(a,1),6899(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7033 6899"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7047">
    <literal><![CDATA[
      R(K(x,y),z,K(y,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(7033(a,1),6949(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7033 6949"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7048">
    <literal><![CDATA[
      L(K(x,y),z,y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(5893,a,7037,a)].">
      <j1 rule="hyper" parents="5893 7037"/>
    </justification>
  </clause>

  <clause id="7049">
    <literal><![CDATA[
      K(x,(x * y) \ z) = K(x,y \ (x \ z))
    ]]></literal>
    <justification jstring="[hyper(6864,a,7034,a)].">
      <j1 rule="hyper" parents="6864 7034"/>
    </justification>
  </clause>

  <clause id="7050">
    <literal><![CDATA[
      L(K(x,y),z,x) = u \ (u * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(320,a,4,a,b,7034,a),flip(a)].">
      <j1 rule="hyper" parents="320 4 7034"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7051">
    <literal><![CDATA[
      K(L(x,y,x),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,6615,a(flip),b,7034,a)].">
      <j1 rule="hyper" parents="58 6615 7034"/>
    </justification>
  </clause>

  <clause id="7052">
    <literal><![CDATA[
      K(x,L(y,z,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,6609,a(flip),b,7034,a)].">
      <j1 rule="hyper" parents="58 6609 7034"/>
    </justification>
  </clause>

  <clause id="7053">
    <literal><![CDATA[
      (1 / x) \ K(x \ 1,y) = x * K(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(116,a,7034,a(flip),b,2820,a)].">
      <j1 rule="hyper" parents="116 7034 2820"/>
    </justification>
  </clause>

  <clause id="7054">
    <literal><![CDATA[
      a(x,y,K(z,x)) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,7034,a(flip),b,5896,a),flip(a)].">
      <j1 rule="hyper" parents="115 7034 5896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7055">
    <literal><![CDATA[
      (x * y) * K(z,x) = x * (y * K(z,x))
    ]]></literal>
    <justification jstring="[hyper(977,a,7054,a)].">
      <j1 rule="hyper" parents="977 7054"/>
    </justification>
  </clause>

  <clause id="7056">
    <literal><![CDATA[
      K((x * y) \ z,x) = K(y \ (x \ z),x)
    ]]></literal>
    <justification jstring="[hyper(6856,a,7048,a)].">
      <j1 rule="hyper" parents="6856 7048"/>
    </justification>
  </clause>

  <clause id="7057">
    <literal><![CDATA[
      K((x \ y) \ z,x) = K(y \ (x * z),x)
    ]]></literal>
    <justification jstring="[hyper(58,a,6626,a(flip),b,7048,a),flip(a)].">
      <j1 rule="hyper" parents="58 6626 7048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7058">
    <literal><![CDATA[
      K(L(x,y,z),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,6615,a(flip),b,7048,a)].">
      <j1 rule="hyper" parents="58 6615 7048"/>
    </justification>
  </clause>

  <clause id="7059">
    <literal><![CDATA[
      K(x,L(y,z,y)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,6609,a(flip),b,7048,a)].">
      <j1 rule="hyper" parents="58 6609 7048"/>
    </justification>
  </clause>

  <clause id="7061">
    <literal><![CDATA[
      x \ (y * K(z,x)) = (x \ y) * K(z,x)
    ]]></literal>
    <justification jstring="[para(7048(a,1),474(a,1,2,2))].">
      <j1 rule="para" parents="7048 474"/>
    </justification>
  </clause>

  <clause id="7063">
    <literal><![CDATA[
      L(x,y,x) * K(x,z) = L(T(x,z),y,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,7051,a(flip),b,4764,a)].">
      <j1 rule="hyper" parents="119 7051 4764"/>
    </justification>
  </clause>

  <clause id="7064">
    <literal><![CDATA[
      K(T(x / (x / y),x),z) = K(y,z)
    ]]></literal>
    <justification jstring="[para(4401(a,2),7051(a,1,1))].">
      <j1 rule="para" parents="4401 7051"/>
    </justification>
  </clause>

  <clause id="7065">
    <literal><![CDATA[
      K(R(x,y,x),z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(4673(a,1),7051(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4673 7051"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7066">
    <literal><![CDATA[
      T(x,L(y,z,y)) = x / K(y,x)
    ]]></literal>
    <justification jstring="[para(7051(a,1),4805(a,2,2))].">
      <j1 rule="para" parents="7051 4805"/>
    </justification>
  </clause>

  <clause id="7067">
    <literal><![CDATA[
      K(x,y) * L(x,z,x) = L(T(x,y),z,x)
    ]]></literal>
    <justification jstring="[para(7051(a,1),4844(a,1,1))].">
      <j1 rule="para" parents="7051 4844"/>
    </justification>
  </clause>

  <clause id="7068">
    <literal><![CDATA[
      T(x,L(y,z,x)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(118,a,7052,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 7052 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7069">
    <literal><![CDATA[
      K(x,L(L(y,z,x),u,w)) = K(x,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(25(a,1),7052(a,1,2))].">
      <j1 rule="para" parents="25 7052"/>
    </justification>
  </clause>

  <clause id="7070">
    <literal><![CDATA[
      K(x,T((x \ y) \ z,u)) = K(x,T(y \ (x * z),u))
    ]]></literal>
    <justification jstring="[para(757(a,1),7052(a,1,2)),flip(a)].">
      <j1 rule="para" parents="757 7052"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7071">
    <literal><![CDATA[
      K(x,(y * (x / y)) \ (x * z)) = K(x,K(y \ x,y) * z)
    ]]></literal>
    <justification jstring="[para(5767(a,1),7052(a,1,2))].">
      <j1 rule="para" parents="5767 7052"/>
    </justification>
  </clause>

  <clause id="7072">
    <literal><![CDATA[
      K(L(x,y,z),L(u,w,x)) = L(K(x,u),y * x,z)
    ]]></literal>
    <justification jstring="[para(7052(a,1),6615(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7052 6615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7073">
    <literal><![CDATA[
      K(L(L(x,y,z),u,w),z) = K(L(x,u,w),z)
    ]]></literal>
    <justification jstring="[para(25(a,1),7058(a,1,1))].">
      <j1 rule="para" parents="25 7058"/>
    </justification>
  </clause>

  <clause id="7074">
    <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(7058(a,1),5524(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="7058 5524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7075">
    <literal><![CDATA[
      K((x * (y / x)) \ (y * z),y) = K(K(x \ y,x) * z,y)
    ]]></literal>
    <justification jstring="[para(5767(a,1),7058(a,1,1))].">
      <j1 rule="para" parents="5767 7058"/>
    </justification>
  </clause>

  <clause id="7076">
    <literal><![CDATA[
      T(x,L(y,z,y)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(118,a,7059,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 7059 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7077">
    <literal><![CDATA[
      K(x,T(y / z,y)) = K(x,z \ y)
    ]]></literal>
    <justification jstring="[para(4404(a,1),7059(a,1,2))].">
      <j1 rule="para" parents="4404 7059"/>
    </justification>
  </clause>

  <clause id="7078">
    <literal><![CDATA[
      K(x,R(y,z,y)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(4673(a,1),7059(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4673 7059"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7079">
    <literal><![CDATA[
      R(K(x,y),z,x) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,6745,a(flip),b,7065,a)].">
      <j1 rule="hyper" parents="58 6745 7065"/>
    </justification>
  </clause>

  <clause id="7080">
    <literal><![CDATA[
      R(x,y,x) * K(x,z) = R(T(x,z),y,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,7065,a(flip),b,4765,a)].">
      <j1 rule="hyper" parents="119 7065 4765"/>
    </justification>
  </clause>

  <clause id="7081">
    <literal><![CDATA[
      K((x \ y) \ T(y,x),z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(4335(a,1),7065(a,1,1))].">
      <j1 rule="para" parents="4335 7065"/>
    </justification>
  </clause>

  <clause id="7082">
    <literal><![CDATA[
      K(T(x,x * y),z) = K(T(x,y),z)
    ]]></literal>
    <justification jstring="[para(4385(a,1),7065(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4385 7065"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7083">
    <literal><![CDATA[
      K(T(x,x \ y),z) = K(T(x,y),z)
    ]]></literal>
    <justification jstring="[para(4440(a,1),7065(a,1,1))].">
      <j1 rule="para" parents="4440 7065"/>
    </justification>
  </clause>

  <clause id="7084">
    <literal><![CDATA[
      K(x,R(y,z,y)) = 1 / K(y,x)
    ]]></literal>
    <justification jstring="[para(7065(a,1),4971(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7065 4971"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7085">
    <literal><![CDATA[
      K(x,y) * (R(x,z,x) * u) = R(T(x,y),z,x) * u
    ]]></literal>
    <justification jstring="[para(7065(a,1),5118(a,1,1))].">
      <j1 rule="para" parents="7065 5118"/>
    </justification>
  </clause>

  <clause id="7086">
    <literal><![CDATA[
      (K(x,y) * z) * x = K(x,y) * (z * x)
    ]]></literal>
    <justification jstring="[para(7065(a,1),6751(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7065 6751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7087">
    <literal><![CDATA[
      T(x,(x * y) \ z) = T(x,y \ (x \ z))
    ]]></literal>
    <justification jstring="[para(298(a,1),7068(a,1,2))].">
      <j1 rule="para" parents="298 7068"/>
    </justification>
  </clause>

  <clause id="7088">
    <literal><![CDATA[
      T(x / L(y,z,y),y) = L(y,z,y) \ x
    ]]></literal>
    <justification jstring="[hyper(420,a,7076,a),flip(a)].">
      <j1 rule="hyper" parents="420 7076"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7091">
    <literal><![CDATA[
      L(x,y,x) * T(z,x) = z * L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,7076,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 7076 17"/>
    </justification>
  </clause>

  <clause id="7092">
    <literal><![CDATA[
      T(x,T(y / z,y)) = T(x,z \ y)
    ]]></literal>
    <justification jstring="[para(4404(a,1),7076(a,1,2))].">
      <j1 rule="para" parents="4404 7076"/>
    </justification>
  </clause>

  <clause id="7093">
    <literal><![CDATA[
      T(x,R(y,z,y)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(4673(a,1),7076(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4673 7076"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7094">
    <literal><![CDATA[
      R(K(x,y),z,y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,6949,a(flip),b,7078,a)].">
      <j1 rule="hyper" parents="58 6949 7078"/>
    </justification>
  </clause>

  <clause id="7095">
    <literal><![CDATA[
      R(x * K(y,x),z,x) = R(x,z,x) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,7078,a(flip),b,5524,a),flip(a)].">
      <j1 rule="hyper" parents="119 7078 5524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7096">
    <literal><![CDATA[
      K(x,T(y,y * z)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(4385(a,1),7078(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4385 7078"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7097">
    <literal><![CDATA[
      K(x,T(y,y \ z)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(4440(a,1),7078(a,1,2))].">
      <j1 rule="para" parents="4440 7078"/>
    </justification>
  </clause>

  <clause id="7098">
    <literal><![CDATA[
      K(x,R(y,z,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,6955,a(flip),b,7079,a)].">
      <j1 rule="hyper" parents="58 6955 7079"/>
    </justification>
  </clause>

  <clause id="7099">
    <literal><![CDATA[
      K(x,(y * x) / z) = K(x,y / (z / x))
    ]]></literal>
    <justification jstring="[hyper(58,a,6945,a(flip),b,7079,a)].">
      <j1 rule="hyper" parents="58 6945 7079"/>
    </justification>
  </clause>

  <clause id="7100">
    <literal><![CDATA[
      K(x,(y / x) / z) = K(x,y / (z * x))
    ]]></literal>
    <justification jstring="[hyper(58,a,6944,a(flip),b,7079,a),flip(a)].">
      <j1 rule="hyper" parents="58 6944 7079"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7101">
    <literal><![CDATA[
      R(x,y,z) != K(z,u)
    ]]></literal>
    <literal><![CDATA[
      K(z,u) = x
    ]]></literal>
    <justification jstring="[para(7079(a,1),46(a,1)),flip(a)].">
      <j1 rule="para" parents="7079 46"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7103">
    <literal><![CDATA[
      (x * (K(y,x) * z)) * y = K(y,x) * ((x * z) * y)
    ]]></literal>
    <justification jstring="[para(7079(a,1),5419(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7079 5419"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7104">
    <literal><![CDATA[
      T(x / y,R(y,z,y)) = y \ x
    ]]></literal>
    <justification jstring="[hyper(458,a,7093,a)].">
      <j1 rule="hyper" parents="458 7093"/>
    </justification>
  </clause>

  <clause id="7105">
    <literal><![CDATA[
      T(x / R(y,z,y),y) = R(y,z,y) \ x
    ]]></literal>
    <justification jstring="[hyper(420,a,7093,a),flip(a)].">
      <j1 rule="hyper" parents="420 7093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7106">
    <literal><![CDATA[
      R(x,y,x) * T(z,x) = z * R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,7093,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 7093 17"/>
    </justification>
  </clause>

  <clause id="7107">
    <literal><![CDATA[
      T(x,(y \ z) \ T(z,y)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(4335(a,1),7093(a,1,2))].">
      <j1 rule="para" parents="4335 7093"/>
    </justification>
  </clause>

  <clause id="7108">
    <literal><![CDATA[
      T(x,T(y,y \ z)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(4440(a,1),7093(a,1,2))].">
      <j1 rule="para" parents="4440 7093"/>
    </justification>
  </clause>

  <clause id="7109">
    <literal><![CDATA[
      (K(x,y) * z) * y = K(x,y) * (z * y)
    ]]></literal>
    <justification jstring="[para(7094(a,1),101(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7094 101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7110">
    <literal><![CDATA[
      T(x,R(y,z,x)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(118,a,7098,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 7098 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7112">
    <literal><![CDATA[
      T(x,(y * x) / z) = T(x,y / (z / x))
    ]]></literal>
    <justification jstring="[para(525(a,1),7110(a,1,2))].">
      <j1 rule="para" parents="525 7110"/>
    </justification>
  </clause>

  <clause id="7118">
    <literal><![CDATA[
      R(x / y,z,x / y) = R(x / y,z,y \ x)
    ]]></literal>
    <justification jstring="[para(107(a,1),7046(a,1,3)),flip(a)].">
      <j1 rule="para" parents="107 7046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7122">
    <literal><![CDATA[
      T(x,y * K(x,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,6434,a(flip),b,7040,a),flip(a)].">
      <j1 rule="hyper" parents="58 6434 7040"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7123">
    <literal><![CDATA[
      R(T(x,y),z,T(x,u)) = R(T(x,y),z,x)
    ]]></literal>
    <justification jstring="[para(7040(a,1),6899(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7040 6899"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7126">
    <literal><![CDATA[
      K(x,y * K(x,z)) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(116,a,7122,a(flip),b,4755,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="116 7122 4755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7129">
    <literal><![CDATA[
      T(x,y * L(K(x,z),u,w)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(5677(a,1),7122(a,1,2,2))].">
      <j1 rule="para" parents="5677 7122"/>
    </justification>
  </clause>

  <clause id="7132">
    <literal><![CDATA[
      T(x,y * K(z,x)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(6329(a,1),7122(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6329 7122"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7133">
    <literal><![CDATA[
      T(x,y / (z / x)) = T(x,y / (x \ z))
    ]]></literal>
    <justification jstring="[para(6398(a,1),7122(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6398 7122"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7135">
    <literal><![CDATA[
      T(x,y * (z * x)) = T(x,y * (x * z))
    ]]></literal>
    <justification jstring="[para(6633(a,1),7122(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6633 7122"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7136">
    <literal><![CDATA[
      (K(x,y) * z) * K(y,u) = K(x,y) * (z * K(y,u))
    ]]></literal>
    <justification jstring="[para(7047(a,1),101(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7047 101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7137">
    <literal><![CDATA[
      T(x,L(y,z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = u
    ]]></literal>
    <justification jstring="[para(7066(a,2),4809(a,1))].">
      <j1 rule="para" parents="7066 4809"/>
    </justification>
  </clause>

  <clause id="7138">
    <literal><![CDATA[
      K(x,R(y,z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(7084(a,2),4978(a,1))].">
      <j1 rule="para" parents="7084 4978"/>
    </justification>
  </clause>

  <clause id="7139">
    <literal><![CDATA[
      R(x,y,x) * (x \ z) = (z / x) * R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,7104,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 7104 17"/>
    </justification>
  </clause>

  <clause id="7140">
    <literal><![CDATA[
      K((x \ y) \ y,z) = K(T(x,y),z)
    ]]></literal>
    <justification jstring="[para(190(a,1),7064(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="190 7064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7141">
    <literal><![CDATA[
      K(x,(y \ z) \ z) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(72(a,1),7077(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="72 7077"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7142">
    <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),7077(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="471 7077"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7143">
    <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),7077(a,1,2))].">
      <j1 rule="para" parents="526 7077"/>
    </justification>
  </clause>

  <clause id="7144">
    <literal><![CDATA[
      K(T(x,y * x),z) = K(T(x,y),z)
    ]]></literal>
    <justification jstring="[para(4307(a,2),7082(a,1,1))].">
      <j1 rule="para" parents="4307 7082"/>
    </justification>
  </clause>

  <clause id="7145">
    <literal><![CDATA[
      K(T(x,y),z) = T(K(x,z),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,6297,a(flip),b,7083,a),flip(a)].">
      <j1 rule="hyper" parents="58 6297 7083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7146">
    <literal><![CDATA[
      K(T(x,y),y / z) = K(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(320,a,6126,a(flip),b,7145,a),flip(a)].">
      <j1 rule="hyper" parents="320 6126 7145"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7147">
    <literal><![CDATA[
      K(T(x,K(y,z)),y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,2000,a(flip),b,7145,a),flip(a)].">
      <j1 rule="hyper" parents="320 2000 7145"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7148">
    <literal><![CDATA[
      (K(x,y) * z) * K(T(y,z),x) = z
    ]]></literal>
    <justification jstring="[hyper(119,a,7145,a,b,6456,a)].">
      <j1 rule="hyper" parents="119 7145 6456"/>
    </justification>
  </clause>

  <clause id="7149">
    <literal><![CDATA[
      x * K(T(y,x),z) = K(z,y) \ x
    ]]></literal>
    <justification jstring="[hyper(119,a,7145,a,b,5132,a)].">
      <j1 rule="hyper" parents="119 7145 5132"/>
    </justification>
  </clause>

  <clause id="7150">
    <literal><![CDATA[
      x * K(T(y,x),z) = K(y,z) * x
    ]]></literal>
    <justification jstring="[hyper(119,a,7145,a,b,17,a(flip))].">
      <j1 rule="hyper" parents="119 7145 17"/>
    </justification>
  </clause>

  <clause id="7151">
    <literal><![CDATA[
      T(K(x,y),z) * T(x,z) = T(T(x,z),y)
    ]]></literal>
    <justification jstring="[para(7145(a,1),4770(a,2,1)),flip(a)].">
      <j1 rule="para" parents="7145 4770"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7152">
    <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,7147,a(flip),b,5285,a(flip))].">
      <j1 rule="hyper" parents="119 7147 5285"/>
    </justification>
  </clause>

  <clause id="7153">
    <literal><![CDATA[
      T(x,(y \ z) \ z) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(72(a,1),7092(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="72 7092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7154">
    <literal><![CDATA[
      T(x,y \ T(x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(x,z) / y) = u
    ]]></literal>
    <justification jstring="[para(7092(a,1),5192(a,1))].">
      <j1 rule="para" parents="7092 5192"/>
    </justification>
  </clause>

  <clause id="7155">
    <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(1408(a,1),7096(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="1408 7096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7156">
    <literal><![CDATA[
      K(x,T(y,z \ 1)) = K(x,T(y,z \ y))
    ]]></literal>
    <justification jstring="[para(1687(a,1),7096(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1687 7096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7157">
    <literal><![CDATA[
      K(x,T(y,z * y)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(4307(a,2),7096(a,1,2))].">
      <j1 rule="para" parents="4307 7096"/>
    </justification>
  </clause>

  <clause id="7158">
    <literal><![CDATA[
      K(x,T(y,z)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(58,a,6216,a(flip),b,7097,a),flip(a)].">
      <j1 rule="hyper" parents="58 6216 7097"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7159">
    <literal><![CDATA[
      K(x,T(y * z,y \ 1)) = K(x,T(y * z,z))
    ]]></literal>
    <justification jstring="[para(4183(a,1),7097(a,1,2))].">
      <j1 rule="para" parents="4183 7097"/>
    </justification>
  </clause>

  <clause id="7160">
    <literal><![CDATA[
      K(T(x,y),z) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(320,a,7145,a,b,7158,a)].">
      <j1 rule="hyper" parents="320 7145 7158"/>
    </justification>
  </clause>

  <clause id="7161">
    <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,6960,a,b,7158,a)].">
      <j1 rule="hyper" parents="320 6960 7158"/>
    </justification>
  </clause>

  <clause id="7162">
    <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,6603,a,b,7158,a)].">
      <j1 rule="hyper" parents="320 6603 7158"/>
    </justification>
  </clause>

  <clause id="7163">
    <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,6546,a,b,7158,a)].">
      <j1 rule="hyper" parents="320 6546 7158"/>
    </justification>
  </clause>

  <clause id="7164">
    <literal><![CDATA[
      (K(x,y) * z) \ z = K(y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,6456,a,b,7158,a)].">
      <j1 rule="hyper" parents="320 6456 7158"/>
    </justification>
  </clause>

  <clause id="7165">
    <literal><![CDATA[
      K((x \ y) \ y,z) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(320,a,6292,a,b,7158,a)].">
      <j1 rule="hyper" parents="320 6292 7158"/>
    </justification>
  </clause>

  <clause id="7166">
    <literal><![CDATA[
      K(x,K(y,z)) * K(z,y) = K(z,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(320,a,5625,a,b,7158,a)].">
      <j1 rule="hyper" parents="320 5625 7158"/>
    </justification>
  </clause>

  <clause id="7167">
    <literal><![CDATA[
      K(x,y) * K(z,K(y,x)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,5624,a,b,7158,a)].">
      <j1 rule="hyper" parents="320 5624 7158"/>
    </justification>
  </clause>

  <clause id="7168">
    <literal><![CDATA[
      K(T(x,y) \ 1,z) = K(x \ 1,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(320,a,5544,a,b,7158,a)].">
      <j1 rule="hyper" parents="320 5544 7158"/>
    </justification>
  </clause>

  <clause id="7169">
    <literal><![CDATA[
      K(x,T(y \ 1,z)) = K(x,T(y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,5506,a,b,7158,a),flip(a)].">
      <j1 rule="hyper" parents="320 5506 7158"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7170">
    <literal><![CDATA[
      x \ (K(y,z) \ x) = K(z,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(320,a,5132,a,b,7158,a)].">
      <j1 rule="hyper" parents="320 5132 7158"/>
    </justification>
  </clause>

  <clause id="7171">
    <literal><![CDATA[
      K(x / y,T(z,x)) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,6268,a(flip),b,7158,a),flip(a)].">
      <j1 rule="hyper" parents="320 6268 7158"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7172">
    <literal><![CDATA[
      K(x,T(y,K(x,z))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,5636,a(flip),b,7158,a),flip(a)].">
      <j1 rule="hyper" parents="320 5636 7158"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7173">
    <literal><![CDATA[
      K(x,T(y,R(x,z,u))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,3353,a(flip),b,7158,a),flip(a)].">
      <j1 rule="hyper" parents="320 3353 7158"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7174">
    <literal><![CDATA[
      K(x,T(y,L(x,z,u))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,3352,a(flip),b,7158,a),flip(a)].">
      <j1 rule="hyper" parents="320 3352 7158"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7175">
    <literal><![CDATA[
      K(x,T(y,T(T(x,z),u))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,3344,a(flip),b,7158,a),flip(a)].">
      <j1 rule="hyper" parents="320 3344 7158"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7176">
    <literal><![CDATA[
      (K(x,y) * z) * K(y,T(x,z)) = z
    ]]></literal>
    <justification jstring="[hyper(119,a,7158,a,b,6456,a)].">
      <j1 rule="hyper" parents="119 7158 6456"/>
    </justification>
  </clause>

  <clause id="7177">
    <literal><![CDATA[
      x * K(y,T(z,x)) = K(z,y) \ x
    ]]></literal>
    <justification jstring="[hyper(119,a,7158,a,b,5132,a)].">
      <j1 rule="hyper" parents="119 7158 5132"/>
    </justification>
  </clause>

  <clause id="7178">
    <literal><![CDATA[
      x * K(y,T(z,u)) = x * T(K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(119,a,7158,a,b,4,a)].">
      <j1 rule="hyper" parents="119 7158 4"/>
    </justification>
  </clause>

  <clause id="7179">
    <literal><![CDATA[
      x * K(y,T(z,x)) = K(y,z) * x
    ]]></literal>
    <justification jstring="[hyper(119,a,7158,a,b,17,a(flip))].">
      <j1 rule="hyper" parents="119 7158 17"/>
    </justification>
  </clause>

  <clause id="7180">
    <literal><![CDATA[
      x * T(K(x,y),z) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(119,a,7158,a(flip),b,4729,a(flip))].">
      <j1 rule="hyper" parents="119 7158 4729"/>
    </justification>
  </clause>

  <clause id="7181">
    <literal><![CDATA[
      K(x,T(T(y,z),u)) = T(K(x,T(y,u)),z)
    ]]></literal>
    <justification jstring="[para(18(a,1),7158(a,1,2))].">
      <j1 rule="para" parents="18 7158"/>
    </justification>
  </clause>

  <clause id="7182">
    <literal><![CDATA[
      L(K(x,T(y,z)),u,w) = T(L(K(x,y),u,w),z)
    ]]></literal>
    <justification jstring="[para(7158(a,2),20(a,1,1))].">
      <j1 rule="para" parents="7158 20"/>
    </justification>
  </clause>

  <clause id="7183">
    <literal><![CDATA[
      T(x,y) != K(z,T(u,y))
    ]]></literal>
    <literal><![CDATA[
      K(z,u) = x
    ]]></literal>
    <justification jstring="[para(7158(a,2),44(a,1)),flip(a)].">
      <j1 rule="para" parents="7158 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7184">
    <literal><![CDATA[
      x * K(y,T(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) * x = u
    ]]></literal>
    <justification jstring="[para(7158(a,2),284(a,1,2))].">
      <j1 rule="para" parents="7158 284"/>
    </justification>
  </clause>

  <clause id="7185">
    <literal><![CDATA[
      x * (y * K(z,T(u,x * y))) = L(K(z,u),y,x) * (x * y)
    ]]></literal>
    <justification jstring="[para(7158(a,2),632(a,1,2,2))].">
      <j1 rule="para" parents="7158 632"/>
    </justification>
  </clause>

  <clause id="7186">
    <literal><![CDATA[
      x * T(K(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7158(a,1),4766(a,1,2))].">
      <j1 rule="para" parents="7158 4766"/>
    </justification>
  </clause>

  <clause id="7187">
    <literal><![CDATA[
      K(x,y) * (K(z,u) * x) = T(x,y) * K(z,T(u,x))
    ]]></literal>
    <justification jstring="[para(7158(a,2),5089(a,2,2))].">
      <j1 rule="para" parents="7158 5089"/>
    </justification>
  </clause>

  <clause id="7188">
    <literal><![CDATA[
      K(x,y) * K(y,T(x,z)) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[para(7158(a,2),5619(a,1,2))].">
      <j1 rule="para" parents="7158 5619"/>
    </justification>
  </clause>

  <clause id="7189">
    <literal><![CDATA[
      K(x,T(y,K(z,u))) * K(u,z) = K(u,z) * K(x,y)
    ]]></literal>
    <justification jstring="[para(7158(a,2),5631(a,1,1))].">
      <j1 rule="para" parents="7158 5631"/>
    </justification>
  </clause>

  <clause id="7190">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(z,y) * u) = K(z,T(y,x)) * u
    ]]></literal>
    <justification jstring="[para(7158(a,2),5627(a,2,1))].">
      <j1 rule="para" parents="7158 5627"/>
    </justification>
  </clause>

  <clause id="7191">
    <literal><![CDATA[
      T(K(x,y),y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(7158(a,1),5780(a,1))].">
      <j1 rule="para" parents="7158 5780"/>
    </justification>
  </clause>

  <clause id="7192">
    <literal><![CDATA[
      x * (K(x,T(y,z)) * (z * K(x,y))) = T(x,y) * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(7158(a,2),5079(a,1,2,1))].">
      <j1 rule="para" parents="7158 5079"/>
    </justification>
  </clause>

  <clause id="7193">
    <literal><![CDATA[
      K(x,T((y \ 1) * ((z \ y) * z),u)) = K(x,K(z \ y,T(z,u)))
    ]]></literal>
    <justification jstring="[para(7158(a,2),5742(a,2,2))].">
      <j1 rule="para" parents="7158 5742"/>
    </justification>
  </clause>

  <clause id="7194">
    <literal><![CDATA[
      K(x,T(y / z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(7158(a,2),6485(a,1))].">
      <j1 rule="para" parents="7158 6485"/>
    </justification>
  </clause>

  <clause id="7195">
    <literal><![CDATA[
      K(x / y,T(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(7158(a,2),6504(a,1))].">
      <j1 rule="para" parents="7158 6504"/>
    </justification>
  </clause>

  <clause id="7196">
    <literal><![CDATA[
      K(x,T(L(y,z / y,u),w)) = T(L(K(x,y),z,u),w)
    ]]></literal>
    <justification jstring="[para(6607(a,1),7158(a,2,1))].">
      <j1 rule="para" parents="6607 7158"/>
    </justification>
  </clause>

  <clause id="7197">
    <literal><![CDATA[
      K(x,T(y,z)) \ 1 = K(y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(5166,a,7160,a)].">
      <j1 rule="hyper" parents="5166 7160"/>
    </justification>
  </clause>

  <clause id="7198">
    <literal><![CDATA[
      K(T(T(x,y),z),u) = K(x,T(T(u,z),y))
    ]]></literal>
    <justification jstring="[hyper(320,a,7160,a(flip),b,7160,a),flip(a)].">
      <j1 rule="hyper" parents="320 7160 7160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7199">
    <literal><![CDATA[
      x * K(T(y,z),u) = x * K(y,T(u,z))
    ]]></literal>
    <justification jstring="[hyper(119,a,7160,a,b,4,a)].">
      <j1 rule="hyper" parents="119 7160 4"/>
    </justification>
  </clause>

  <clause id="7200">
    <literal><![CDATA[
      x * K(T(x,y),z) = T(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(119,a,7160,a,b,4729,a(flip))].">
      <j1 rule="hyper" parents="119 7160 4729"/>
    </justification>
  </clause>

  <clause id="7201">
    <literal><![CDATA[
      K(x,T(y,z) \ T(x,z)) = K(x,T(y \ x,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,6786,a,b,7160,a)].">
      <j1 rule="hyper" parents="58 6786 7160"/>
    </justification>
  </clause>

  <clause id="7202">
    <literal><![CDATA[
      (x * y) \ (T(x,z) * y) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,6437,a,b,7160,a)].">
      <j1 rule="hyper" parents="58 6437 7160"/>
    </justification>
  </clause>

  <clause id="7203">
    <literal><![CDATA[
      (x * K(y,T(z,u))) \ x = K(z,T(y,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,6338,a,b,7160,a)].">
      <j1 rule="hyper" parents="58 6338 7160"/>
    </justification>
  </clause>

  <clause id="7204">
    <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,5589,a,b,7160,a)].">
      <j1 rule="hyper" parents="58 5589 7160"/>
    </justification>
  </clause>

  <clause id="7205">
    <literal><![CDATA[
      K(x,T(y,x * z)) = K(T(x,z),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,7082,a(flip),b,7160,a),flip(a)].">
      <j1 rule="hyper" parents="58 7082 7160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7206">
    <literal><![CDATA[
      K(x,T(y,x \ z)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(58,a,6297,a(flip),b,7160,a),flip(a)].">
      <j1 rule="hyper" parents="58 6297 7160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7207">
    <literal><![CDATA[
      K(((x \ 1) \ y) \ y,z) = K(1 / x,T(z,y * x))
    ]]></literal>
    <justification jstring="[hyper(58,a,5847,a(flip),b,7160,a)].">
      <j1 rule="hyper" parents="58 5847 7160"/>
    </justification>
  </clause>

  <clause id="7208">
    <literal><![CDATA[
      (x / y) * K(z,T(y,u)) = x / T(y,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(119,a,7160,a(flip),b,6364,a)].">
      <j1 rule="hyper" parents="119 7160 6364"/>
    </justification>
  </clause>

  <clause id="7209">
    <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,7160,a(flip),b,5285,a(flip))].">
      <j1 rule="hyper" parents="119 7160 5285"/>
    </justification>
  </clause>

  <clause id="7210">
    <literal><![CDATA[
      T(x,T(y,z)) \ 1 = x \ K(y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(116,a,7160,a(flip),b,4796,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="116 7160 4796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7211">
    <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),7160(a,1,1))].">
      <j1 rule="para" parents="20 7160"/>
    </justification>
  </clause>

  <clause id="7212">
    <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),7160(a,1,1))].">
      <j1 rule="para" parents="22 7160"/>
    </justification>
  </clause>

  <clause id="7213">
    <literal><![CDATA[
      K(x / y,T(z,y)) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[para(107(a,1),7160(a,1,1)),flip(a)].">
      <j1 rule="para" parents="107 7160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7214">
    <literal><![CDATA[
      K(T(x,y),z / y) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(107(a,1),7160(a,2,2))].">
      <j1 rule="para" parents="107 7160"/>
    </justification>
  </clause>

  <clause id="7215">
    <literal><![CDATA[
      K((x * y) / x,T(z,x)) = K(y,z)
    ]]></literal>
    <justification jstring="[para(224(a,1),7160(a,1,1)),flip(a)].">
      <j1 rule="para" parents="224 7160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7216">
    <literal><![CDATA[
      K(x,T(y,R(T(x,z),u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[para(212(a,1),7160(a,1,1)),flip(a)].">
      <j1 rule="para" parents="212 7160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7217">
    <literal><![CDATA[
      K(T(x,y),L(y,z,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(176(a,1),7160(a,2,2))].">
      <j1 rule="para" parents="176 7160"/>
    </justification>
  </clause>

  <clause id="7218">
    <literal><![CDATA[
      K(T(x,(1 / y) \ z),z * y) = K(x,z * y)
    ]]></literal>
    <justification jstring="[para(1058(a,1),7160(a,2,2))].">
      <j1 rule="para" parents="1058 7160"/>
    </justification>
  </clause>

  <clause id="7219">
    <literal><![CDATA[
      K(x \ T(x * y,z),T(u,x)) = K(x \ T(y * x,z),u)
    ]]></literal>
    <justification jstring="[para(4602(a,1),7160(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4602 7160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7220">
    <literal><![CDATA[
      K(x,T(y,z)) * T(x,z) = T(T(x,z),y)
    ]]></literal>
    <justification jstring="[para(7160(a,1),4770(a,2,1)),flip(a)].">
      <j1 rule="para" parents="7160 4770"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7221">
    <literal><![CDATA[
      x / K(y,T(x,z)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(7160(a,1),4805(a,2,2)),flip(a)].">
      <j1 rule="para" parents="7160 4805"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7222">
    <literal><![CDATA[
      K(x,T(y,K(z,z \ x))) = K(x,y)
    ]]></literal>
    <justification jstring="[para(5014(a,1),7160(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5014 7160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7223">
    <literal><![CDATA[
      1 / K(x,T(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,T(x,z)) = u
    ]]></literal>
    <justification jstring="[para(7160(a,1),4978(a,1,2))].">
      <j1 rule="para" parents="7160 4978"/>
    </justification>
  </clause>

  <clause id="7224">
    <literal><![CDATA[
      K(x,T(y,z)) \ u = K(y,T(x,z)) * u
    ]]></literal>
    <justification jstring="[para(7160(a,1),5130(a,1,1))].">
      <j1 rule="para" parents="7160 5130"/>
    </justification>
  </clause>

  <clause id="7225">
    <literal><![CDATA[
      (x * y) / (K(z,T(x,u)) * y) = T(x,T(z,u))
    ]]></literal>
    <justification jstring="[para(7160(a,1),5253(a,1,2,1))].">
      <j1 rule="para" parents="7160 5253"/>
    </justification>
  </clause>

  <clause id="7226">
    <literal><![CDATA[
      K(x,T(y,z)) \ u != w
    ]]></literal>
    <literal><![CDATA[
      K(y,T(x,z)) * u = w
    ]]></literal>
    <justification jstring="[para(7160(a,1),5163(a,1,1))].">
      <j1 rule="para" parents="7160 5163"/>
    </justification>
  </clause>

  <clause id="7227">
    <literal><![CDATA[
      K(x,T(y,z)) * T(x,z) = T(T(x,y),z)
    ]]></literal>
    <justification jstring="[para(7160(a,1),4842(a,1,1))].">
      <j1 rule="para" parents="7160 4842"/>
    </justification>
  </clause>

  <clause id="7228">
    <literal><![CDATA[
      K(x,T(y,z)) \ (y * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(y,T(x,z)) * u = w
    ]]></literal>
    <justification jstring="[para(7160(a,1),5135(a,1,1))].">
      <j1 rule="para" parents="7160 5135"/>
    </justification>
  </clause>

  <clause id="7229">
    <literal><![CDATA[
      a(x,y,K(z,T(y,u))) = 1
    ]]></literal>
    <justification jstring="[para(7160(a,1),6099(a,1,3))].">
      <j1 rule="para" parents="7160 6099"/>
    </justification>
  </clause>

  <clause id="7230">
    <literal><![CDATA[
      x / K(y,T(z,u)) = x * K(z,T(y,u))
    ]]></literal>
    <justification jstring="[para(7160(a,1),6335(a,1,2))].">
      <j1 rule="para" parents="7160 6335"/>
    </justification>
  </clause>

  <clause id="7231">
    <literal><![CDATA[
      x * K(y,T(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      w * K(z,T(y,u)) = x
    ]]></literal>
    <justification jstring="[para(7160(a,1),6344(a,1,2))].">
      <j1 rule="para" parents="7160 6344"/>
    </justification>
  </clause>

  <clause id="7232">
    <literal><![CDATA[
      x / K(y,T(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      x * K(z,T(y,u)) = w
    ]]></literal>
    <justification jstring="[para(7160(a,1),6346(a,1,2))].">
      <j1 rule="para" parents="7160 6346"/>
    </justification>
  </clause>

  <clause id="7233">
    <literal><![CDATA[
      (x * K(T(y,z),u)) * K(u,w) = (x * K(u,w)) * K(y,T(u,z))
    ]]></literal>
    <justification jstring="[para(7160(a,1),6822(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7160 6822"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7234">
    <literal><![CDATA[
      L(K(x,T(y,z)),y,u) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(47,a,7229,a)].">
      <j1 rule="hyper" parents="47 7229"/>
    </justification>
  </clause>

  <clause id="7235">
    <literal><![CDATA[
      K(x,K(T(y,K(x,z)),u)) = K(x,K(y,u))
    ]]></literal>
    <justification jstring="[para(7145(a,2),7172(a,1,2))].">
      <j1 rule="para" parents="7145 7172"/>
    </justification>
  </clause>

  <clause id="7236">
    <literal><![CDATA[
      K(x,y / R(x,z,u)) = K(x,R(x,z,u) \ y)
    ]]></literal>
    <justification jstring="[para(107(a,1),7173(a,1,2)),flip(a)].">
      <j1 rule="para" parents="107 7173"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7237">
    <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(7174(a,1),5586(a,1,2))].">
      <j1 rule="para" parents="7174 5586"/>
    </justification>
  </clause>

  <clause id="7238">
    <literal><![CDATA[
      K(x,y * K(x,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,4729,a,b,7126,a),flip(a)].">
      <j1 rule="hyper" parents="320 4729 7126"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7239">
    <literal><![CDATA[
      T(x,K(y,x * K(y,z))) = x
    ]]></literal>
    <justification jstring="[para(7126(a,2),2904(a,1,2))].">
      <j1 rule="para" parents="7126 2904"/>
    </justification>
  </clause>

  <clause id="7240">
    <literal><![CDATA[
      K(x,y * K(x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(7126(a,2),4838(a,1))].">
      <j1 rule="para" parents="7126 4838"/>
    </justification>
  </clause>

  <clause id="7241">
    <literal><![CDATA[
      K(x,y * L(K(x,z),u,w)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(5677(a,1),7238(a,1,2,2))].">
      <j1 rule="para" parents="5677 7238"/>
    </justification>
  </clause>

  <clause id="7242">
    <literal><![CDATA[
      K(x,y * T(x,z)) = K(x,y * x)
    ]]></literal>
    <justification jstring="[para(6116(a,1),7238(a,1,2))].">
      <j1 rule="para" parents="6116 7238"/>
    </justification>
  </clause>

  <clause id="7243">
    <literal><![CDATA[
      K(x,y * K(z,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(6329(a,1),7238(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6329 7238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7244">
    <literal><![CDATA[
      K(x,y / K(z,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(6335(a,2),7238(a,1,2))].">
      <j1 rule="para" parents="6335 7238"/>
    </justification>
  </clause>

  <clause id="7245">
    <literal><![CDATA[
      K(x,y / T(z,x)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(6322(a,1),7238(a,1,2))].">
      <j1 rule="para" parents="6322 7238"/>
    </justification>
  </clause>

  <clause id="7246">
    <literal><![CDATA[
      K(x,y / (z / x)) = K(x,y / (x \ z))
    ]]></literal>
    <justification jstring="[para(6398(a,1),7238(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6398 7238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7247">
    <literal><![CDATA[
      K(x \ y,z / (y / x)) = K(x \ y,z / (x \ y))
    ]]></literal>
    <justification jstring="[para(6470(a,1),7238(a,1,2))].">
      <j1 rule="para" parents="6470 7238"/>
    </justification>
  </clause>

  <clause id="7248">
    <literal><![CDATA[
      K(x,T(K(y,x) * z,u)) = K(x,T(z,u))
    ]]></literal>
    <justification jstring="[para(6720(a,1),7238(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6720 7238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7249">
    <literal><![CDATA[
      x \ R(x,y * K(x,z),x) = K(x,y) * K(y * T(x,z),x)
    ]]></literal>
    <justification jstring="[para(7238(a,1),6242(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7238 6242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7250">
    <literal><![CDATA[
      K(x,K(y,x * K(y,z))) = 1
    ]]></literal>
    <justification jstring="[hyper(50,a,7239,a)].">
      <j1 rule="hyper" parents="50 7239"/>
    </justification>
  </clause>

  <clause id="7251">
    <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),7243(a,1,2))].">
      <j1 rule="para" parents="368 7243"/>
    </justification>
  </clause>

  <clause id="7252">
    <literal><![CDATA[
      K(x * K(y,z),z) = 1 / K(z,x)
    ]]></literal>
    <justification jstring="[para(7243(a,1),4971(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7243 4971"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7253">
    <literal><![CDATA[
      R(K(x,y),y * K(z,x),u) = K(x,y * K(z,x))
    ]]></literal>
    <justification jstring="[para(7243(a,1),5472(a,1,1))].">
      <j1 rule="para" parents="7243 5472"/>
    </justification>
  </clause>

  <clause id="7255">
    <literal><![CDATA[
      K(x,y \ K(z,x)) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(5347,a,7244,a),flip(a)].">
      <j1 rule="hyper" parents="5347 7244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7256">
    <literal><![CDATA[
      T(x,T(y / z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(4404(a,1),7137(a,1,2))].">
      <j1 rule="para" parents="4404 7137"/>
    </justification>
  </clause>

  <clause id="7257">
    <literal><![CDATA[
      K(x,T(y,y \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(4440(a,1),7138(a,1,2))].">
      <j1 rule="para" parents="4440 7138"/>
    </justification>
  </clause>

  <clause id="7258">
    <literal><![CDATA[
      K(T(R(x,x \ y,y \ z),z),u) = K(((x \ y) * (y \ z)) \ z,u)
    ]]></literal>
    <justification jstring="[para(700(a,1),7140(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="700 7140"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7259">
    <literal><![CDATA[
      K(T(x * K(y,z),x),u) = K(K(y,z) * x,u)
    ]]></literal>
    <justification jstring="[para(6361(a,1),7140(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6361 7140"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7260">
    <literal><![CDATA[
      K((x * (y \ z)) \ (x * z),u) = L(K(T(y,z),u),z,x)
    ]]></literal>
    <justification jstring="[para(7140(a,1),6623(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7140 6623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7261">
    <literal><![CDATA[
      K(x,(y * (z \ u)) \ (y * u)) = L(K(x,T(z,u)),u,y)
    ]]></literal>
    <justification jstring="[para(7141(a,1),6582(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7141 6582"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7262">
    <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(7141(a,1),6708(a,1,1))].">
      <j1 rule="para" parents="7141 6708"/>
    </justification>
  </clause>

  <clause id="7263">
    <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),7146(a,1,1))].">
      <j1 rule="para" parents="212 7146"/>
    </justification>
  </clause>

  <clause id="7264">
    <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),7146(a,1,1))].">
      <j1 rule="para" parents="213 7146"/>
    </justification>
  </clause>

  <clause id="7265">
    <literal><![CDATA[
      T(x,K(x,y) * z) = T(x,z)
    ]]></literal>
    <justification jstring="[para(7148(a,1),7132(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7148 7132"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7266">
    <literal><![CDATA[
      K(x,K(x,y) * z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(7148(a,1),7243(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7148 7243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7267">
    <literal><![CDATA[
      T(x,K(x,y) * L(K(z,x),u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(320,a,2933,a(flip),b,7265,a),flip(a)].">
      <j1 rule="hyper" parents="320 2933 7265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7268">
    <literal><![CDATA[
      K(x,K(x,y) * z) = x \ T(x,z)
    ]]></literal>
    <justification jstring="[hyper(116,a,7265,a(flip),b,4755,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="116 7265 4755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7269">
    <literal><![CDATA[
      T(T(x,y),K(x,z) * u) = T(T(x,u),y)
    ]]></literal>
    <justification jstring="[para(7265(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7265 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7270">
    <literal><![CDATA[
      T(x,K(y,x) * z) = T(x,z)
    ]]></literal>
    <justification jstring="[para(5133(a,1),7265(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5133 7265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7272">
    <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(7265(a,1),5202(a,1,1))].">
      <j1 rule="para" parents="7265 5202"/>
    </justification>
  </clause>

  <clause id="7273">
    <literal><![CDATA[
      T(x,y * (K(z,x) * u)) = T(x,y * u)
    ]]></literal>
    <justification jstring="[para(6038(a,1),7265(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6038 7265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7274">
    <literal><![CDATA[
      K(x,T(y,K(x,z) * u)) = K(T(x,u),y)
    ]]></literal>
    <justification jstring="[para(7265(a,1),7160(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7265 7160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7275">
    <literal><![CDATA[
      K(x,T(x,y) * z) = K(x,x * z)
    ]]></literal>
    <justification jstring="[para(4781(a,1),7266(a,1,2))].">
      <j1 rule="para" parents="4781 7266"/>
    </justification>
  </clause>

  <clause id="7276">
    <literal><![CDATA[
      K(x,K(y,x) \ z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(5130(a,2),7266(a,1,2))].">
      <j1 rule="para" parents="5130 7266"/>
    </justification>
  </clause>

  <clause id="7277">
    <literal><![CDATA[
      K(x,K(y,x) * z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(5133(a,1),7266(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5133 7266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7278">
    <literal><![CDATA[
      K(x,T(x,y) \ z) = K(x,x \ z)
    ]]></literal>
    <justification jstring="[para(5081(a,1),7266(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5081 7266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7279">
    <literal><![CDATA[
      K(x,y * (K(z,x) * u)) = K(x,y * u)
    ]]></literal>
    <justification jstring="[para(6038(a,1),7266(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6038 7266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7280">
    <literal><![CDATA[
      K(x,R(K(x,y),z,u) * w) = K(x,w)
    ]]></literal>
    <justification jstring="[para(6925(a,1),7266(a,1,2,1))].">
      <j1 rule="para" parents="6925 7266"/>
    </justification>
  </clause>

  <clause id="7281">
    <literal><![CDATA[
      T(x,K(y,x) * z) = L(T(x,z),u,K(w \ 1,w))
    ]]></literal>
    <justification jstring="[hyper(320,a,3663,a,b,7270,a),flip(a)].">
      <j1 rule="hyper" parents="320 3663 7270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7283">
    <literal><![CDATA[
      K(x,R(K(y,x),z,u) * w) = K(x,w)
    ]]></literal>
    <justification jstring="[para(5706(a,1),7277(a,1,2,1))].">
      <j1 rule="para" parents="5706 7277"/>
    </justification>
  </clause>

  <clause id="7284">
    <literal><![CDATA[
      K(x,(K(y,x) * z) * u) = K(x,z * u)
    ]]></literal>
    <justification jstring="[para(6751(a,1),7277(a,1,2))].">
      <j1 rule="para" parents="6751 7277"/>
    </justification>
  </clause>

  <clause id="7285">
    <literal><![CDATA[
      x / K(y,T(z,x)) = K(z,y) * x
    ]]></literal>
    <justification jstring="[hyper(6396,a,7150,a)].">
      <j1 rule="hyper" parents="6396 7150"/>
    </justification>
  </clause>

  <clause id="7286">
    <literal><![CDATA[
      K(T(x,L(y,z,u)),y \ 1) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(2293,a,7150,a)].">
      <j1 rule="hyper" parents="2293 7150"/>
    </justification>
  </clause>

  <clause id="7287">
    <literal><![CDATA[
      K(x / y,z) * y = y * K(y \ x,z)
    ]]></literal>
    <justification jstring="[para(107(a,1),7150(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="107 7150"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7288">
    <literal><![CDATA[
      K((x * y) / x,z) * x = x * K(y,z)
    ]]></literal>
    <justification jstring="[para(224(a,1),7150(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="224 7150"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7289">
    <literal><![CDATA[
      (x * (K(y,z) * u)) \ (x * u) = L(K(z,T(y,u)),u,x)
    ]]></literal>
    <justification jstring="[para(7150(a,1),6671(a,1,1,2))].">
      <j1 rule="para" parents="7150 6671"/>
    </justification>
  </clause>

  <clause id="7290">
    <literal><![CDATA[
      T(x / ((y \ z) \ z),T(y,z)) = ((y \ z) \ z) \ x
    ]]></literal>
    <justification jstring="[hyper(420,a,7153,a),flip(a)].">
      <j1 rule="hyper" parents="420 7153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7291">
    <literal><![CDATA[
      K(x,y) * (z * K(y,T(x,z))) = z
    ]]></literal>
    <justification jstring="[para(7170(a,1),68(a,1,2,2))].">
      <j1 rule="para" parents="7170 68"/>
    </justification>
  </clause>

  <clause id="7293">
    <literal><![CDATA[
      L(x,y / z,K(z \ y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      w = x
    ]]></literal>
    <justification jstring="[para(7171(a,1),4213(a,1,3))].">
      <j1 rule="para" parents="7171 4213"/>
    </justification>
  </clause>

  <clause id="7297">
    <literal><![CDATA[
      T(x,T(y,T(T(x,z),u))) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(118,a,7175,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 7175 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7298">
    <literal><![CDATA[
      (x \ y) * K(z,T(x,x \ y)) = T(x,z) \ y
    ]]></literal>
    <justification jstring="[hyper(320,a,5087,a(flip),b,7177,a),flip(a)].">
      <j1 rule="hyper" parents="320 5087 7177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7299">
    <literal><![CDATA[
      K(x / y,z) \ y = y * K(z,y \ x)
    ]]></literal>
    <justification jstring="[para(107(a,1),7177(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="107 7177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7300">
    <literal><![CDATA[
      (x * y) / T(T(x,y),z) = K(z,x) * y
    ]]></literal>
    <justification jstring="[hyper(6501,a,7179,a)].">
      <j1 rule="hyper" parents="6501 7179"/>
    </justification>
  </clause>

  <clause id="7301">
    <literal><![CDATA[
      x * (y * K(z,T(u,y))) = x * (K(z,u) * y)
    ]]></literal>
    <justification jstring="[hyper(119,a,7179,a,b,4,a)].">
      <j1 rule="hyper" parents="119 7179 4"/>
    </justification>
  </clause>

  <clause id="7302">
    <literal><![CDATA[
      K(x \ y,T(z,y \ x)) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(29,a,5647,a(flip),b,7179,a),flip(a)].">
      <j1 rule="hyper" parents="29 5647 7179"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7303">
    <literal><![CDATA[
      K(x,T((y / z) \ 1,z)) = K(x,(z \ y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(29,a,5611,a(flip),b,7179,a),flip(a)].">
      <j1 rule="hyper" parents="29 5611 7179"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7304">
    <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),7179(a,1,2,2))].">
      <j1 rule="para" parents="20 7179"/>
    </justification>
  </clause>

  <clause id="7305">
    <literal><![CDATA[
      K(x,y) * z != z * u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7179(a,1),38(a,1))].">
      <j1 rule="para" parents="7179 38"/>
    </justification>
  </clause>

  <clause id="7306">
    <literal><![CDATA[
      K(x,y / z) * z = z * K(x,z \ y)
    ]]></literal>
    <justification jstring="[para(107(a,1),7179(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="107 7179"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7307">
    <literal><![CDATA[
      x * K(y,K(z,T(u,x))) = K(y,K(z,u)) * x
    ]]></literal>
    <justification jstring="[para(7158(a,2),7179(a,1,2,2))].">
      <j1 rule="para" parents="7158 7179"/>
    </justification>
  </clause>

  <clause id="7308">
    <literal><![CDATA[
      T(x,T(y \ 1,z)) = T(x,T(y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(5512,a,7180,a),flip(a)].">
      <j1 rule="hyper" parents="5512 7180"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7309">
    <literal><![CDATA[
      T(x,T(y,z)) != x * u
    ]]></literal>
    <literal><![CDATA[
      T(K(x,y),z) = u
    ]]></literal>
    <justification jstring="[para(7180(a,1),38(a,1))].">
      <j1 rule="para" parents="7180 38"/>
    </justification>
  </clause>

  <clause id="7310">
    <literal><![CDATA[
      K(x,T(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(T(x,z),y) = u
    ]]></literal>
    <justification jstring="[para(7197(a,1),4985(a,1))].">
      <j1 rule="para" parents="7197 4985"/>
    </justification>
  </clause>

  <clause id="7311">
    <literal><![CDATA[
      T(T(x,y),z) * K(y,x) = T(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(5560,a,7200,a)].">
      <j1 rule="hyper" parents="5560 7200"/>
    </justification>
  </clause>

  <clause id="7312">
    <literal><![CDATA[
      T(x,T(y,z)) != x * u
    ]]></literal>
    <literal><![CDATA[
      K(T(x,z),y) = u
    ]]></literal>
    <justification jstring="[para(7200(a,1),38(a,1))].">
      <j1 rule="para" parents="7200 38"/>
    </justification>
  </clause>

  <clause id="7313">
    <literal><![CDATA[
      K(x,T(y,x * z)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,7160,a(flip),b,7205,a),flip(a)].">
      <j1 rule="hyper" parents="320 7160 7205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7314">
    <literal><![CDATA[
      K(x,T(y,x \ z)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,7158,a,b,7206,a),flip(a)].">
      <j1 rule="hyper" parents="320 7158 7206"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7315">
    <literal><![CDATA[
      K(x / (y \ z),z \ y) = K((y \ z) \ x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(5783,a,7213,a)].">
      <j1 rule="hyper" parents="5783 7213"/>
    </justification>
  </clause>

  <clause id="7316">
    <literal><![CDATA[
      K(x \ (y \ x),z) = K(y \ 1,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(58,a,5434,a(flip),b,7213,a),flip(a)].">
      <j1 rule="hyper" parents="58 5434 7213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7317">
    <literal><![CDATA[
      K(x \ y,z) * (y / x) = T(y / x,T(z,x))
    ]]></literal>
    <justification jstring="[para(7213(a,1),4770(a,2,1)),flip(a)].">
      <j1 rule="para" parents="7213 4770"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7318">
    <literal><![CDATA[
      K(x \ y,z) * (y / x) != u
    ]]></literal>
    <literal><![CDATA[
      T(y / x,T(z,x)) = u
    ]]></literal>
    <justification jstring="[para(7213(a,1),4771(a,1,1))].">
      <j1 rule="para" parents="7213 4771"/>
    </justification>
  </clause>

  <clause id="7319">
    <literal><![CDATA[
      K((x * y) / x,T(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) = u
    ]]></literal>
    <justification jstring="[para(7213(a,2),6299(a,1))].">
      <j1 rule="para" parents="7213 6299"/>
    </justification>
  </clause>

  <clause id="7320">
    <literal><![CDATA[
      K(T(x,y),z \ 1) = K(x,y \ (z \ y))
    ]]></literal>
    <justification jstring="[hyper(5347,a,7214,a)].">
      <j1 rule="hyper" parents="5347 7214"/>
    </justification>
  </clause>

  <clause id="7321">
    <literal><![CDATA[
      (x / (y / z)) * K(u,z \ y) = x / T(y / z,T(u,z))
    ]]></literal>
    <justification jstring="[hyper(119,a,7214,a(flip),b,6364,a)].">
      <j1 rule="hyper" parents="119 7214 6364"/>
    </justification>
  </clause>

  <clause id="7323">
    <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),7214(a,1,1))].">
      <j1 rule="para" parents="212 7214"/>
    </justification>
  </clause>

  <clause id="7324">
    <literal><![CDATA[
      a(x,T(y,z),K(u,y)) = 1
    ]]></literal>
    <justification jstring="[para(7215(a,1),6099(a,1,3))].">
      <j1 rule="para" parents="7215 6099"/>
    </justification>
  </clause>

  <clause id="7325">
    <literal><![CDATA[
      R(x,K(y,z),L(T(z,u),w,v5)) = x
    ]]></literal>
    <justification jstring="[para(7215(a,1),6666(a,1,2))].">
      <j1 rule="para" parents="7215 6666"/>
    </justification>
  </clause>

  <clause id="7326">
    <literal><![CDATA[
      (x * T(y,z)) * K(u,y) = x * (T(y,z) * K(u,y))
    ]]></literal>
    <justification jstring="[hyper(977,a,7324,a)].">
      <j1 rule="hyper" parents="977 7324"/>
    </justification>
  </clause>

  <clause id="7327">
    <literal><![CDATA[
      L(K(x,y),T(y,z),u) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(47,a,7324,a)].">
      <j1 rule="hyper" parents="47 7324"/>
    </justification>
  </clause>

  <clause id="7328">
    <literal><![CDATA[
      (x * T(y,z)) \ (x * R(y,z,y)) = K(y * z,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,5294,a,b,7327,a)].">
      <j1 rule="hyper" parents="58 5294 7327"/>
    </justification>
  </clause>

  <clause id="7330">
    <literal><![CDATA[
      K(x,K(y \ x,y) * z) = K(x,z * K(y \ x,y))
    ]]></literal>
    <justification jstring="[para(6337(a,1),7222(a,1,2))].">
      <j1 rule="para" parents="6337 7222"/>
    </justification>
  </clause>

  <clause id="7331">
    <literal><![CDATA[
      K(x,y * T(x,z)) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(320,a,5385,a(flip),b,7242,a),flip(a)].">
      <j1 rule="hyper" parents="320 5385 7242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7332">
    <literal><![CDATA[
      K(x,y / T(z / T(u,z),x)) = K(x,y / (T(z,u) / u))
    ]]></literal>
    <justification jstring="[para(4391(a,1),7245(a,1,2,2))].">
      <j1 rule="para" parents="4391 7245"/>
    </justification>
  </clause>

  <clause id="7333">
    <literal><![CDATA[
      K(x * K(y,z),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,4971,a(flip),b,7252,a),flip(a)].">
      <j1 rule="hyper" parents="320 4971 7252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7334">
    <literal><![CDATA[
      K(x * K(y,z),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) = u
    ]]></literal>
    <justification jstring="[para(7252(a,2),4978(a,1))].">
      <j1 rule="para" parents="7252 4978"/>
    </justification>
  </clause>

  <clause id="7335">
    <literal><![CDATA[
      K(x * T(y,z),z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(1433(a,1),7333(a,1,1))].">
      <j1 rule="para" parents="1433 7333"/>
    </justification>
  </clause>

  <clause id="7336">
    <literal><![CDATA[
      K(x \ T(y,z),z) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[para(1430(a,1),7333(a,1,1))].">
      <j1 rule="para" parents="1430 7333"/>
    </justification>
  </clause>

  <clause id="7337">
    <literal><![CDATA[
      R(K(x,y),x * K(z,y),u) = K(x * K(z,y),y)
    ]]></literal>
    <justification jstring="[para(7333(a,1),4204(a,1,1))].">
      <j1 rule="para" parents="7333 4204"/>
    </justification>
  </clause>

  <clause id="7338">
    <literal><![CDATA[
      K(x * L(K(y,z),u,w),z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(4823(a,1),7333(a,1,1,2))].">
      <j1 rule="para" parents="4823 7333"/>
    </justification>
  </clause>

  <clause id="7340">
    <literal><![CDATA[
      K(x * K(y,z),y) = K(x,y)
    ]]></literal>
    <justification jstring="[para(6329(a,1),7333(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6329 7333"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7341">
    <literal><![CDATA[
      K(x * T(y,z),y) = K(x * y,y)
    ]]></literal>
    <justification jstring="[para(6331(a,1),7333(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6331 7333"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7342">
    <literal><![CDATA[
      K(x * K(y,T(z,u)),z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(7160(a,1),7333(a,1,1,2))].">
      <j1 rule="para" parents="7160 7333"/>
    </justification>
  </clause>

  <clause id="7343">
    <literal><![CDATA[
      K(K(x,y) * z,x) = K(z,x)
    ]]></literal>
    <justification jstring="[para(7148(a,1),7333(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7148 7333"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7344">
    <literal><![CDATA[
      K(K(x,y) \ z,x) = K(z,x)
    ]]></literal>
    <justification jstring="[para(7149(a,1),7333(a,1,1))].">
      <j1 rule="para" parents="7149 7333"/>
    </justification>
  </clause>

  <clause id="7345">
    <literal><![CDATA[
      K(K(x,y) * z,y) = K(z,y)
    ]]></literal>
    <justification jstring="[para(7150(a,1),7333(a,1,1))].">
      <j1 rule="para" parents="7150 7333"/>
    </justification>
  </clause>

  <clause id="7346">
    <literal><![CDATA[
      K(x * K(y,z),T(z,u)) = K(x,T(z,u))
    ]]></literal>
    <justification jstring="[para(7215(a,1),7333(a,1,1,2))].">
      <j1 rule="para" parents="7215 7333"/>
    </justification>
  </clause>

  <clause id="7347">
    <literal><![CDATA[
      K(x * L(K(y,z),u,w),y) = K(x,y)
    ]]></literal>
    <justification jstring="[para(5677(a,1),7340(a,1,1,2))].">
      <j1 rule="para" parents="5677 7340"/>
    </justification>
  </clause>

  <clause id="7349">
    <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(7340(a,1),5526(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7340 5526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7352">
    <literal><![CDATA[
      K(T(x,y) * z,x) = K(x * z,x)
    ]]></literal>
    <justification jstring="[para(4781(a,1),7343(a,1,1))].">
      <j1 rule="para" parents="4781 7343"/>
    </justification>
  </clause>

  <clause id="7353">
    <literal><![CDATA[
      K(T(x,y) \ z,x) = K(x \ z,x)
    ]]></literal>
    <justification jstring="[para(5081(a,1),7343(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5081 7343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7354">
    <literal><![CDATA[
      K(x * (K(y,z) * u),z) = K(x * u,z)
    ]]></literal>
    <justification jstring="[para(6038(a,1),7343(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6038 7343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7355">
    <literal><![CDATA[
      L(K(x,y),K(y,z) * x,u) = K(K(y,z) * x,y)
    ]]></literal>
    <justification jstring="[para(7343(a,1),6102(a,1,1))].">
      <j1 rule="para" parents="7343 6102"/>
    </justification>
  </clause>

  <clause id="7356">
    <literal><![CDATA[
      K(R(K(x,y),z,u) * w,x) = K(w,x)
    ]]></literal>
    <justification jstring="[para(6925(a,1),7343(a,1,1,1))].">
      <j1 rule="para" parents="6925 7343"/>
    </justification>
  </clause>

  <clause id="7357">
    <literal><![CDATA[
      K(K(x,y) * z,x) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,x) = u
    ]]></literal>
    <justification jstring="[para(7344(a,1),6299(a,1))].">
      <j1 rule="para" parents="7344 6299"/>
    </justification>
  </clause>

  <clause id="7360">
    <literal><![CDATA[
      K(x,K(x,y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) = u
    ]]></literal>
    <justification jstring="[para(7268(a,2),4838(a,1))].">
      <j1 rule="para" parents="7268 4838"/>
    </justification>
  </clause>

  <clause id="7362">
    <literal><![CDATA[
      T(x * K(y,x),T(z,T(x,u))) = T(x * K(y,x),z)
    ]]></literal>
    <justification jstring="[para(4816(a,1),7297(a,1,2,2,1))].">
      <j1 rule="para" parents="4816 7297"/>
    </justification>
  </clause>

  <clause id="7363">
    <literal><![CDATA[
      T(x,T(y,x * z)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(118,a,7313,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 7313 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7364">
    <literal><![CDATA[
      K(x,T(y / (x * z),z)) = K(x,(x * z) \ y)
    ]]></literal>
    <justification jstring="[para(107(a,1),7313(a,1,2)),flip(a)].">
      <j1 rule="para" parents="107 7313"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7365">
    <literal><![CDATA[
      T(x,T(y,x \ z)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(118,a,7314,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 7314 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7366">
    <literal><![CDATA[
      T(x,T(y,x \ z)) = x * K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(119,a,7314,a(flip),b,4729,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 7314 4729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7367">
    <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),7314(a,1,2))].">
      <j1 rule="para" parents="22 7314"/>
    </justification>
  </clause>

  <clause id="7368">
    <literal><![CDATA[
      K(x * y,T(z,y \ 1)) = K(x * y,T(z,x))
    ]]></literal>
    <justification jstring="[para(6174(a,1),7314(a,1,2))].">
      <j1 rule="para" parents="6174 7314"/>
    </justification>
  </clause>

  <clause id="7369">
    <literal><![CDATA[
      R(K(x,T(y,z)),x * u,w) = K(R(x,u,w),T(y,x \ z))
    ]]></literal>
    <justification jstring="[para(7314(a,1),6743(a,1,1))].">
      <j1 rule="para" parents="7314 6743"/>
    </justification>
  </clause>

  <clause id="7370">
    <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(7325(a,1),542(a,1,1))].">
      <j1 rule="para" parents="7325 542"/>
    </justification>
  </clause>

  <clause id="7371">
    <literal><![CDATA[
      T(x,y * T(x,z)) = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(118,a,7331,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 7331 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7372">
    <literal><![CDATA[
      K((1 / ((x * y) \ x)) * z,y) = K(z * (1 / ((x * y) \ x)),y)
    ]]></literal>
    <justification jstring="[para(6210(a,1),7335(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6210 7335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7373">
    <literal><![CDATA[
      K(x \ (y \ (z * y)),y) = K(x \ z,y)
    ]]></literal>
    <justification jstring="[para(17(a,1),7336(a,1,1,2))].">
      <j1 rule="para" parents="17 7336"/>
    </justification>
  </clause>

  <clause id="7374">
    <literal><![CDATA[
      K(x * T(y,z),y) = K(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,5266,a(flip),b,7341,a),flip(a)].">
      <j1 rule="hyper" parents="320 5266 7341"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7375">
    <literal><![CDATA[
      K(T(x,y) * z,x) = K(z * T(x,y),x)
    ]]></literal>
    <justification jstring="[para(84(a,1),7342(a,1,1)),flip(a)].">
      <j1 rule="para" parents="84 7342"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7376">
    <literal><![CDATA[
      K(T(x,T(y,z)) * u,y) = K(x * u,y)
    ]]></literal>
    <justification jstring="[para(5539(a,1),7342(a,1,1))].">
      <j1 rule="para" parents="5539 7342"/>
    </justification>
  </clause>

  <clause id="7377">
    <literal><![CDATA[
      x * K(T(y,z) \ x,y) = (y \ x) * y
    ]]></literal>
    <justification jstring="[hyper(119,a,7353,a,b,85,a)].">
      <j1 rule="hyper" parents="119 7353 85"/>
    </justification>
  </clause>

  <clause id="7378">
    <literal><![CDATA[
      K(x / T(y,z),y) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,5567,a,b,7353,a)].">
      <j1 rule="hyper" parents="58 5567 7353"/>
    </justification>
  </clause>

  <clause id="7379">
    <literal><![CDATA[
      T(x / y,T(z,y)) = T(x / y,T(z,x))
    ]]></literal>
    <justification jstring="[para(7(a,1),7363(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7 7363"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7380">
    <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(7365(a,1),4764(a,1,2,1))].">
      <j1 rule="para" parents="7365 4764"/>
    </justification>
  </clause>

  <clause id="7381">
    <literal><![CDATA[
      T(x * y,T(z,y \ 1)) = T(x * y,T(z,x))
    ]]></literal>
    <justification jstring="[para(6174(a,1),7365(a,1,2))].">
      <j1 rule="para" parents="6174 7365"/>
    </justification>
  </clause>

  <clause id="7383">
    <literal><![CDATA[
      T(x,x * (y / T(x,z))) = T(x,y)
    ]]></literal>
    <justification jstring="[para(7(a,1),7371(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7 7371"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7386">
    <literal><![CDATA[
      K(x * (y / T(x,z)),x) = K(y,x)
    ]]></literal>
    <justification jstring="[para(7(a,1),7374(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7 7374"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7388">
    <literal><![CDATA[
      (x / T(y,z)) * K(y \ x,y) = T(x / T(y,z),y)
    ]]></literal>
    <justification jstring="[hyper(119,a,7378,a(flip),b,4729,a(flip))].">
      <j1 rule="hyper" parents="119 7378 4729"/>
    </justification>
  </clause>

  <clause id="7389">
    <literal><![CDATA[
      L(K(x,y),z,x) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(7050(a,2),287(a,1)),flip(b)].">
      <j1 rule="para" parents="7050 287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7391">
    <literal><![CDATA[
      K(x,(x * y) \ (x * z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(6582(a,1),7389(a,1))].">
      <j1 rule="para" parents="6582 7389"/>
    </justification>
  </clause>

  <clause id="7392">
    <literal><![CDATA[
      K(L(x,y,x),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) = u
    ]]></literal>
    <justification jstring="[para(6615(a,1),7389(a,1))].">
      <j1 rule="para" parents="6615 7389"/>
    </justification>
  </clause>

  <clause id="7393">
    <literal><![CDATA[
      K(x,(x * y) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ (x \ z)) = u
    ]]></literal>
    <justification jstring="[para(6585(a,1),7389(a,1))].">
      <j1 rule="para" parents="6585 7389"/>
    </justification>
  </clause>

  <clause id="7394">
    <literal><![CDATA[
      K(T(x / (x / y),x),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) = u
    ]]></literal>
    <justification jstring="[para(4401(a,2),7392(a,1,1))].">
      <j1 rule="para" parents="4401 7392"/>
    </justification>
  </clause>

  <clause id="7395">
    <literal><![CDATA[
      K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(R(x,u,x),y) = z
    ]]></literal>
    <justification jstring="[para(4673(a,1),7392(a,1,1))].">
      <j1 rule="para" parents="4673 7392"/>
    </justification>
  </clause>

  <clause id="7396">
    <literal><![CDATA[
      T(x,y * (z * K(x,u))) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(90(a,1),7129(a,1,2))].">
      <j1 rule="para" parents="90 7129"/>
    </justification>
  </clause>

  <clause id="7397">
    <literal><![CDATA[
      T(x,y * K(L(x,z,u),w)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(6615(a,1),7129(a,1,2,2))].">
      <j1 rule="para" parents="6615 7129"/>
    </justification>
  </clause>

  <clause id="7398">
    <literal><![CDATA[
      T(K(x,y),(z * y) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(6174(a,2),7191(a,1))].">
      <j1 rule="para" parents="6174 7191"/>
    </justification>
  </clause>

  <clause id="7399">
    <literal><![CDATA[
      K((x \ y) \ z,T(z,u)) = K(y \ (x * z),T(z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,6626,a(flip),b,7234,a),flip(a)].">
      <j1 rule="hyper" parents="58 6626 7234"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7400">
    <literal><![CDATA[
      K(x,y / T(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y / z) = u
    ]]></literal>
    <justification jstring="[para(6322(a,1),7240(a,1,2))].">
      <j1 rule="para" parents="6322 7240"/>
    </justification>
  </clause>

  <clause id="7401">
    <literal><![CDATA[
      K(x,y / (x \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (z / x)) = u
    ]]></literal>
    <justification jstring="[para(6398(a,1),7240(a,1,2))].">
      <j1 rule="para" parents="6398 7240"/>
    </justification>
  </clause>

  <clause id="7402">
    <literal><![CDATA[
      K(x,y * (x * z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z * x)) = u
    ]]></literal>
    <justification jstring="[para(6633(a,1),7240(a,1,2))].">
      <j1 rule="para" parents="6633 7240"/>
    </justification>
  </clause>

  <clause id="7403">
    <literal><![CDATA[
      K(x,y * (z * K(x,u))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(90(a,1),7241(a,1,2))].">
      <j1 rule="para" parents="90 7241"/>
    </justification>
  </clause>

  <clause id="7404">
    <literal><![CDATA[
      K(x,y * (z * K(u,x))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(6669(a,1),7241(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6669 7241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7405">
    <literal><![CDATA[
      T(x,a(y,z,K(x,u))) = x
    ]]></literal>
    <justification jstring="[para(5892(a,1),7267(a,1,2))].">
      <j1 rule="para" parents="5892 7267"/>
    </justification>
  </clause>

  <clause id="7406">
    <literal><![CDATA[
      K(x,y) * a(z,u,K(y,w)) = a(z,u,K(y,w)) * K(x,y)
    ]]></literal>
    <justification jstring="[para(7405(a,1),7179(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7405 7179"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7407">
    <literal><![CDATA[
      K(x,(K(x,y) * z) * u) = K(x,z * u)
    ]]></literal>
    <justification jstring="[para(101(a,1),7280(a,1,2))].">
      <j1 rule="para" parents="101 7280"/>
    </justification>
  </clause>

  <clause id="7408">
    <literal><![CDATA[
      K(x,K(R(x,y,z),u) * w) = K(x,w)
    ]]></literal>
    <justification jstring="[para(6743(a,1),7280(a,1,2,1))].">
      <j1 rule="para" parents="6743 7280"/>
    </justification>
  </clause>

  <clause id="7409">
    <literal><![CDATA[
      K(x,K(y,R(x,z,u)) * w) = K(x,w)
    ]]></literal>
    <justification jstring="[para(6955(a,1),7283(a,1,2,1))].">
      <j1 rule="para" parents="6955 7283"/>
    </justification>
  </clause>

  <clause id="7410">
    <literal><![CDATA[
      T(K(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(T(x,z),y) = u
    ]]></literal>
    <justification jstring="[para(7158(a,1),7310(a,1))].">
      <j1 rule="para" parents="7158 7310"/>
    </justification>
  </clause>

  <clause id="7411">
    <literal><![CDATA[
      K(x \ T(y,z),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,z) = u
    ]]></literal>
    <justification jstring="[para(1430(a,1),7334(a,1,1))].">
      <j1 rule="para" parents="1430 7334"/>
    </justification>
  </clause>

  <clause id="7412">
    <literal><![CDATA[
      K(K(x,y) \ z,x) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,x) = u
    ]]></literal>
    <justification jstring="[para(7149(a,1),7334(a,1,1))].">
      <j1 rule="para" parents="7149 7334"/>
    </justification>
  </clause>

  <clause id="7413">
    <literal><![CDATA[
      K(x * (y * K(z,u)),u) = K(x * y,u)
    ]]></literal>
    <justification jstring="[para(90(a,1),7338(a,1,1))].">
      <j1 rule="para" parents="90 7338"/>
    </justification>
  </clause>

  <clause id="7414">
    <literal><![CDATA[
      K(x * K(y,L(z,u,w)),z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(6609(a,1),7338(a,1,1,2))].">
      <j1 rule="para" parents="6609 7338"/>
    </justification>
  </clause>

  <clause id="7415">
    <literal><![CDATA[
      K(x * (y * K(z,u)),z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(6669(a,1),7338(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6669 7338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7416">
    <literal><![CDATA[
      K(x * K(L(y,z,u),w),y) = K(x,y)
    ]]></literal>
    <justification jstring="[para(6615(a,1),7347(a,1,1,2))].">
      <j1 rule="para" parents="6615 7347"/>
    </justification>
  </clause>

  <clause id="7417">
    <literal><![CDATA[
      K((K(x,y) * z) * u,x) = K(z * u,x)
    ]]></literal>
    <justification jstring="[para(101(a,1),7356(a,1,1))].">
      <j1 rule="para" parents="101 7356"/>
    </justification>
  </clause>

  <clause id="7418">
    <literal><![CDATA[
      K(K(R(x,y,z),u) * w,x) = K(w,x)
    ]]></literal>
    <justification jstring="[para(6743(a,1),7356(a,1,1,1))].">
      <j1 rule="para" parents="6743 7356"/>
    </justification>
  </clause>

  <clause id="7419">
    <literal><![CDATA[
      K(x * y,x) != z
    ]]></literal>
    <literal><![CDATA[
      K(y * x,x) = z
    ]]></literal>
    <justification jstring="[para(4813(a,1),7357(a,1,1))].">
      <j1 rule="para" parents="4813 7357"/>
    </justification>
  </clause>

  <clause id="7420">
    <literal><![CDATA[
      K(T(x,y) \ z,y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ z,y) = u
    ]]></literal>
    <justification jstring="[para(5131(a,1),7357(a,1,1))].">
      <j1 rule="para" parents="5131 7357"/>
    </justification>
  </clause>

  <clause id="7421">
    <literal><![CDATA[
      K(x,T(y,x) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(5131(a,1),7360(a,1,2))].">
      <j1 rule="para" parents="5131 7360"/>
    </justification>
  </clause>

  <clause id="7422">
    <literal><![CDATA[
      K(x,(x \ y) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,(y / x) \ z) = u
    ]]></literal>
    <justification jstring="[para(5414(a,1),7360(a,1,2))].">
      <j1 rule="para" parents="5414 7360"/>
    </justification>
  </clause>

  <clause id="7423">
    <literal><![CDATA[
      T(x,L(x,y,z) * (z * y)) = T(x,z * (y * x))
    ]]></literal>
    <justification jstring="[para(483(a,1),7397(a,1,2))].">
      <j1 rule="para" parents="483 7397"/>
    </justification>
  </clause>

  <clause id="7424">
    <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(7397(a,1),4806(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7397 4806"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7425">
    <literal><![CDATA[
      K(x,R(x,y,z) * u) = K(x,u * R(x,y,z))
    ]]></literal>
    <justification jstring="[para(4813(a,1),7408(a,1,2))].">
      <j1 rule="para" parents="4813 7408"/>
    </justification>
  </clause>

  <clause id="7426">
    <literal><![CDATA[
      K(x,T(R(x,y,z),u) \ w) = K(x,R(x,y,z) \ w)
    ]]></literal>
    <justification jstring="[para(5081(a,1),7408(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5081 7408"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7427">
    <literal><![CDATA[
      K(x,(y / R(x,z,u)) \ w) = K(x,(R(x,z,u) \ y) \ w)
    ]]></literal>
    <justification jstring="[para(5414(a,1),7408(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5414 7408"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7428">
    <literal><![CDATA[
      K(x,R(T(x,y),z,u) * w) = K(x,R(x,z,u) * w)
    ]]></literal>
    <justification jstring="[para(5118(a,1),7408(a,1,2))].">
      <j1 rule="para" parents="5118 7408"/>
    </justification>
  </clause>

  <clause id="7429">
    <literal><![CDATA[
      K((x \ y) \ z,x \ y) != u
    ]]></literal>
    <literal><![CDATA[
      K((y / x) \ z,x \ y) = u
    ]]></literal>
    <justification jstring="[para(5590(a,1),7412(a,1,1))].">
      <j1 rule="para" parents="5590 7412"/>
    </justification>
  </clause>

  <clause id="7430">
    <literal><![CDATA[
      K(L(x,y,z) * u,x) = K(u * L(x,y,z),x)
    ]]></literal>
    <justification jstring="[para(84(a,1),7414(a,1,1)),flip(a)].">
      <j1 rule="para" parents="84 7414"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7431">
    <literal><![CDATA[
      K((L(x,y,z) \ u) * L(x,y,z),x) = K(u,x)
    ]]></literal>
    <justification jstring="[para(302(a,1),7414(a,1,1))].">
      <j1 rule="para" parents="302 7414"/>
    </justification>
  </clause>

  <clause id="7432">
    <literal><![CDATA[
      K(K(L(x,y,z),u) * w,x) = K(w,x)
    ]]></literal>
    <justification jstring="[para(7148(a,1),7414(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7148 7414"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7433">
    <literal><![CDATA[
      K(R(x,y,z) * u,x) = K(u * R(x,y,z),x)
    ]]></literal>
    <justification jstring="[para(4813(a,1),7418(a,1,1))].">
      <j1 rule="para" parents="4813 7418"/>
    </justification>
  </clause>

  <clause id="7434">
    <literal><![CDATA[
      K(T(x,R(y,z,u)) * w,y) = K(x * w,y)
    ]]></literal>
    <justification jstring="[para(4819(a,1),7418(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4819 7418"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7435">
    <literal><![CDATA[
      K((x \ 1) \ y,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x * y,y) = z
    ]]></literal>
    <justification jstring="[para(5362(a,2),7419(a,1))].">
      <j1 rule="para" parents="5362 7419"/>
    </justification>
  </clause>

  <clause id="7436">
    <literal><![CDATA[
      K(x,(x \ y) \ (x \ z)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(5(a,1),7032(a,2,2,2))].">
      <j1 rule="para" parents="5 7032"/>
    </justification>
  </clause>

  <clause id="7437">
    <literal><![CDATA[
      T(x * K(y,z),y) = T(x,y) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(6239,a,7044,a)].">
      <j1 rule="hyper" parents="6239 7044"/>
    </justification>
  </clause>

  <clause id="7438">
    <literal><![CDATA[
      T(T(x,y),K(y,z)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(239,a,7044,a(flip),b,5083,a)].">
      <j1 rule="hyper" parents="239 7044 5083"/>
    </justification>
  </clause>

  <clause id="7439">
    <literal><![CDATA[
      T(K(x,y) * z,T(x,y)) = T(z * K(x,y),x)
    ]]></literal>
    <justification jstring="[hyper(6705,a,7438,a),flip(a)].">
      <j1 rule="hyper" parents="6705 7438"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7440">
    <literal><![CDATA[
      T(T(x,K(y,z)),y) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(434,a,7438,a)].">
      <j1 rule="hyper" parents="434 7438"/>
    </justification>
  </clause>

  <clause id="7441">
    <literal><![CDATA[
      T(T(x,y),K(y,z)) = x * T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(320,a,7180,a,b,7438,a),flip(a)].">
      <j1 rule="hyper" parents="320 7180 7438"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7442">
    <literal><![CDATA[
      T(T(T(x,y),z),K(y,u)) = T(T(x,T(y,u)),z)
    ]]></literal>
    <justification jstring="[para(7438(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7438 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7443">
    <literal><![CDATA[
      T(x / y,T(y,z)) = T(y \ x,K(y,z))
    ]]></literal>
    <justification jstring="[para(107(a,1),7438(a,1,1)),flip(a)].">
      <j1 rule="para" parents="107 7438"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7444">
    <literal><![CDATA[
      T((x * y) / x,T(x,z)) = T(y,K(x,z))
    ]]></literal>
    <justification jstring="[para(224(a,1),7438(a,1,1)),flip(a)].">
      <j1 rule="para" parents="224 7438"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7445">
    <literal><![CDATA[
      T(x / y,T(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(y \ x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7440(a,1),678(a,1))].">
      <j1 rule="para" parents="7440 678"/>
    </justification>
  </clause>

  <clause id="7446">
    <literal><![CDATA[
      L(x,T(y,K(x,z)),x) = L(x,T(y,T(x,z)),x)
    ]]></literal>
    <justification jstring="[para(7440(a,1),4465(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7440 4465"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7447">
    <literal><![CDATA[
      T(T(x,K(y,z)),T(z,y)) = T(x,z)
    ]]></literal>
    <justification jstring="[para(5630(a,1),7440(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5630 7440"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7448">
    <literal><![CDATA[
      T(K(x,y),T(z,y)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(5637(a,1),7440(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5637 7440"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7449">
    <literal><![CDATA[
      T(x * K(y,z),T(z,y)) = T(K(y,z) * x,z)
    ]]></literal>
    <justification jstring="[para(6337(a,1),7440(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6337 7440"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7450">
    <literal><![CDATA[
      T(K(x,y \ z),T(y,z)) = T(K(x,y \ z),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,7108,a(flip),b,7448,a)].">
      <j1 rule="hyper" parents="58 7108 7448"/>
    </justification>
  </clause>

  <clause id="7451">
    <literal><![CDATA[
      K(x,(y * x) \ z) = K(x,y \ (x \ z))
    ]]></literal>
    <justification jstring="[hyper(58,a,6570,a,b,7049,a)].">
      <j1 rule="hyper" parents="58 6570 7049"/>
    </justification>
  </clause>

  <clause id="7452">
    <literal><![CDATA[
      (((x \ (y / z)) * x) * z) \ y = K(x,z \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(58,a,6465,a,b,7049,a)].">
      <j1 rule="hyper" parents="58 6465 7049"/>
    </justification>
  </clause>

  <clause id="7453">
    <literal><![CDATA[
      (x * ((y / z) / x)) * z = y * K(x,z \ (x \ y))
    ]]></literal>
    <justification jstring="[para(7049(a,1),6512(a,2,2))].">
      <j1 rule="para" parents="7049 6512"/>
    </justification>
  </clause>

  <clause id="7454">
    <literal><![CDATA[
      R(x,y,K(z,x)) = x
    ]]></literal>
    <justification jstring="[hyper(4038,a,7055,a)].">
      <j1 rule="hyper" parents="4038 7055"/>
    </justification>
  </clause>

  <clause id="7455">
    <literal><![CDATA[
      (x * (y * K(z,x))) / x = (x * y) / T(x,z)
    ]]></literal>
    <justification jstring="[hyper(117,a,7055,a(flip),b,6325,a)].">
      <j1 rule="hyper" parents="117 7055 6325"/>
    </justification>
  </clause>

  <clause id="7457">
    <literal><![CDATA[
      R(x,y,K(z,T(x,u))) = x
    ]]></literal>
    <justification jstring="[hyper(140,a,7454,a(flip))].">
      <j1 rule="hyper" parents="140 7454"/>
    </justification>
  </clause>

  <clause id="7459">
    <literal><![CDATA[
      R(R(x,y,z),u,K(w,x)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[para(7454(a,1),26(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7454 26"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7461">
    <literal><![CDATA[
      (L(x,y,z) * u) * K(w,x) = L(x,y,z) * (u * K(w,x))
    ]]></literal>
    <justification jstring="[para(7454(a,1),513(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7454 513"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7462">
    <literal><![CDATA[
      R(x,y,T(K(z,x),u)) = x
    ]]></literal>
    <justification jstring="[para(1533(a,1),7454(a,1,3))].">
      <j1 rule="para" parents="1533 7454"/>
    </justification>
  </clause>

  <clause id="7463">
    <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(7457(a,1),513(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7457 513"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7464">
    <literal><![CDATA[
      (K(x,y) * z) * K(u,T(x,w)) = K(x,y) * (z * K(u,T(x,w)))
    ]]></literal>
    <justification jstring="[para(7457(a,1),6751(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7457 6751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7465">
    <literal><![CDATA[
      x \ (y * T(K(z,x),u)) = (x \ y) * T(K(z,x),u)
    ]]></literal>
    <justification jstring="[para(7462(a,1),505(a,1,1))].">
      <j1 rule="para" parents="7462 505"/>
    </justification>
  </clause>

  <clause id="7466">
    <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(7459(a,1),857(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7459 857"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7467">
    <literal><![CDATA[
      K((x * y) \ z,y) = K(x \ (y \ z),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,6568,a,b,7056,a)].">
      <j1 rule="hyper" parents="58 6568 7056"/>
    </justification>
  </clause>

  <clause id="7468">
    <literal><![CDATA[
      K((x / (y \ 1)) \ z,x) = K(y \ (x \ z),x)
    ]]></literal>
    <justification jstring="[hyper(58,a,6566,a,b,7056,a)].">
      <j1 rule="hyper" parents="58 6566 7056"/>
    </justification>
  </clause>

  <clause id="7469">
    <literal><![CDATA[
      K((x \ y) \ (x \ z),x) = K(y \ z,x)
    ]]></literal>
    <justification jstring="[para(5(a,1),7056(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5 7056"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7470">
    <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(1407(a,1),7056(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="1407 7056"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7471">
    <literal><![CDATA[
      x * K(y \ (z \ x),z) = y * ((z \ (y \ x)) * z)
    ]]></literal>
    <justification jstring="[para(7056(a,1),6284(a,1,2))].">
      <j1 rule="para" parents="7056 6284"/>
    </justification>
  </clause>

  <clause id="7472">
    <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(7057(a,1),5522(a,1,1,1,2))].">
      <j1 rule="para" parents="7057 5522"/>
    </justification>
  </clause>

  <clause id="7473">
    <literal><![CDATA[
      T(x / T(y,z),y) = (y \ x) * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(6379,a,7061,a)].">
      <j1 rule="hyper" parents="6379 7061"/>
    </justification>
  </clause>

  <clause id="7474">
    <literal><![CDATA[
      K(x,y) * (L(y,z,y) \ u) = L(T(y,x),z,y) \ u
    ]]></literal>
    <justification jstring="[para(7063(a,1),5770(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7063 5770"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7475">
    <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(6928(a,1),7063(a,2,1))].">
      <j1 rule="para" parents="6928 7063"/>
    </justification>
  </clause>

  <clause id="7476">
    <literal><![CDATA[
      T(x,y) \ L(T(x,y),z,x) = x \ L(x,z,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,7067,a(flip),b,4779,a)].">
      <j1 rule="hyper" parents="116 7067 4779"/>
    </justification>
  </clause>

  <clause id="7477">
    <literal><![CDATA[
      R(x,y,x) \ T(x,z) = x \ L(T(x,z),y,x)
    ]]></literal>
    <justification jstring="[para(7067(a,1),6016(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7067 6016"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7478">
    <literal><![CDATA[
      K(x,y) * R(x,z,x) = R(T(x,y),z,x)
    ]]></literal>
    <justification jstring="[hyper(3354,a,7080,a)].">
      <j1 rule="hyper" parents="3354 7080"/>
    </justification>
  </clause>

  <clause id="7479">
    <literal><![CDATA[
      T(x,y) \ R(T(x,y),z,x) = x \ R(x,z,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,7080,a(flip),b,5101,a)].">
      <j1 rule="hyper" parents="116 7080 5101"/>
    </justification>
  </clause>

  <clause id="7480">
    <literal><![CDATA[
      L(x,y,K(x,z)) = x
    ]]></literal>
    <justification jstring="[hyper(4028,a,7086,a)].">
      <j1 rule="hyper" parents="4028 7086"/>
    </justification>
  </clause>

  <clause id="7481">
    <literal><![CDATA[
      (K(x,y) * z) * x = T(x,y) * T(z,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,5089,a(flip),b,7086,a),flip(a)].">
      <j1 rule="hyper" parents="320 5089 7086"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7483">
    <literal><![CDATA[
      T(K(x \ y,x) * z,x \ y) = (y / x) \ (z * (x \ y))
    ]]></literal>
    <justification jstring="[hyper(239,a,7086,a,b,5372,a)].">
      <j1 rule="hyper" parents="239 7086 5372"/>
    </justification>
  </clause>

  <clause id="7484">
    <literal><![CDATA[
      (K(x,y) * (z * x)) \ (K(x,y) * z) = L(x \ 1,x,K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(7086(a,1),217(a,2,1)),flip(a)].">
      <j1 rule="para" parents="7086 217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7485">
    <literal><![CDATA[
      L(T(x,y),z,K(x,u)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(7480(a,1),20(a,2,1))].">
      <j1 rule="para" parents="7480 20"/>
    </justification>
  </clause>

  <clause id="7486">
    <literal><![CDATA[
      (K(x,y) * z) * R(x,u,w) = K(x,y) * (z * R(x,u,w))
    ]]></literal>
    <justification jstring="[para(7480(a,1),447(a,1,2,1))].">
      <j1 rule="para" parents="7480 447"/>
    </justification>
  </clause>

  <clause id="7489">
    <literal><![CDATA[
      L(K(x,y),z,K(y,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(7480(a,1),6607(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7480 6607"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7490">
    <literal><![CDATA[
      L(K(x,y),z,K(x,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(7480(a,1),6613(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7480 6613"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7491">
    <literal><![CDATA[
      L(x,y,T(x,z)) = L(x,y,x)
    ]]></literal>
    <justification jstring="[para(7480(a,1),6874(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7480 6874"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7495">
    <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,7491,a)].">
      <j1 rule="hyper" parents="320 247 7491"/>
    </justification>
  </clause>

  <clause id="7496">
    <literal><![CDATA[
      L(x / y,z,x / y) = L(x / y,z,y \ x)
    ]]></literal>
    <justification jstring="[para(107(a,1),7491(a,1,3)),flip(a)].">
      <j1 rule="para" parents="107 7491"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7499">
    <literal><![CDATA[
      K(x,L(y,z,T(y,u))) = K(x,y)
    ]]></literal>
    <justification jstring="[para(7491(a,2),7059(a,1,2))].">
      <j1 rule="para" parents="7491 7059"/>
    </justification>
  </clause>

  <clause id="7500">
    <literal><![CDATA[
      L(L(T(x,y),z,u),w,K(x,v5)) = L(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(7485(a,1),25(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7485 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7503">
    <literal><![CDATA[
      L(T(x,y),z,T(x,u)) = L(T(x,y),z,x)
    ]]></literal>
    <justification jstring="[para(7485(a,1),6874(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7485 6874"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7505">
    <literal><![CDATA[
      K((K(x,y) * z) \ u,y) = K(z \ (K(y,x) * u),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,6629,a(flip),b,7489,a),flip(a)].">
      <j1 rule="hyper" parents="58 6629 7489"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7506">
    <literal><![CDATA[
      K(x,L(y,z,K(y,u))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,6609,a(flip),b,7489,a)].">
      <j1 rule="hyper" parents="58 6609 7489"/>
    </justification>
  </clause>

  <clause id="7507">
    <literal><![CDATA[
      K(x,L(y,z,K(x,u))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,6609,a(flip),b,7490,a)].">
      <j1 rule="hyper" parents="58 6609 7490"/>
    </justification>
  </clause>

  <clause id="7508">
    <literal><![CDATA[
      L(K(x,y),z,T(y,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(6614,a,7499,a)].">
      <j1 rule="hyper" parents="6614 7499"/>
    </justification>
  </clause>

  <clause id="7509">
    <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),7507(a,1,2))].">
      <j1 rule="para" parents="25 7507"/>
    </justification>
  </clause>

  <clause id="7510">
    <literal><![CDATA[
      K(x,(K(y,x) * z) \ u) = K(x,z \ (K(x,y) * u))
    ]]></literal>
    <justification jstring="[para(5164(a,1),7507(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5164 7507"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7511">
    <literal><![CDATA[
      K((T(x,y) * z) \ u,x) = K(z \ (T(x,y) \ u),x)
    ]]></literal>
    <justification jstring="[hyper(6856,a,7508,a)].">
      <j1 rule="hyper" parents="6856 7508"/>
    </justification>
  </clause>

  <clause id="7512">
    <literal><![CDATA[
      T(x,(x \ y) \ (x \ z)) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[para(5(a,1),7087(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 7087"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7513">
    <literal><![CDATA[
      (x / L(y,z,y)) * y = y * (L(y,z,y) \ x)
    ]]></literal>
    <justification jstring="[hyper(119,a,7088,a(flip),b,17,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 7088 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7514">
    <literal><![CDATA[
      L(x,y,x) * (x \ z) = (z / x) * L(x,y,x)
    ]]></literal>
    <justification jstring="[para(107(a,1),7091(a,1,2))].">
      <j1 rule="para" parents="107 7091"/>
    </justification>
  </clause>

  <clause id="7516">
    <literal><![CDATA[
      K(x * (y / R(z,u,z)),z) = K(x * (R(z,u,z) \ y),z)
    ]]></literal>
    <justification jstring="[para(7105(a,1),7335(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7105 7335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7518">
    <literal><![CDATA[
      L(x,y,K(z,x)) = x
    ]]></literal>
    <justification jstring="[hyper(4028,a,7109,a)].">
      <j1 rule="hyper" parents="4028 7109"/>
    </justification>
  </clause>

  <clause id="7520">
    <literal><![CDATA[
      T(K(x,y) * z,y) = K(x,y) * T(z,y)
    ]]></literal>
    <justification jstring="[hyper(239,a,7109,a,b,5411,a)].">
      <j1 rule="hyper" parents="239 7109 5411"/>
    </justification>
  </clause>

  <clause id="7521">
    <literal><![CDATA[
      T(K(x,y) * z,y) = T(y,x) \ (z * y)
    ]]></literal>
    <justification jstring="[hyper(239,a,7109,a,b,4818,a)].">
      <j1 rule="hyper" parents="239 7109 4818"/>
    </justification>
  </clause>

  <clause id="7522">
    <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(7109(a,1),5091(a,1,2,2))].">
      <j1 rule="para" parents="7109 5091"/>
    </justification>
  </clause>

  <clause id="7524">
    <literal><![CDATA[
      L(R(x,y,z),u,K(w,x)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[para(7518(a,1),24(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7518 24"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7525">
    <literal><![CDATA[
      (K(x,y) * z) * T(y,u) = K(x,y) * (z * T(y,u))
    ]]></literal>
    <justification jstring="[para(7518(a,1),449(a,1,2,1))].">
      <j1 rule="para" parents="7518 449"/>
    </justification>
  </clause>

  <clause id="7526">
    <literal><![CDATA[
      L(K(x,y),z,K(u,y)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(7518(a,1),6607(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7518 6607"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7527">
    <literal><![CDATA[
      K(L(x,y,K(z,u)),u) = K(x,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,6615,a(flip),b,7526,a)].">
      <j1 rule="hyper" parents="58 6615 7526"/>
    </justification>
  </clause>

  <clause id="7528">
    <literal><![CDATA[
      T(x,L(y,z,K(u,x))) = (K(y,x) / x) \ 1
    ]]></literal>
    <justification jstring="[para(7527(a,1),4991(a,2,1,1))].">
      <j1 rule="para" parents="7527 4991"/>
    </justification>
  </clause>

  <clause id="7529">
    <literal><![CDATA[
      R(T(x,y),x \ y,T(x,z)) = (x \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(320,a,4375,a(flip),b,7123,a),flip(a)].">
      <j1 rule="hyper" parents="320 4375 7123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7531">
    <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(7123(a,1),1326(a,1,1))].">
      <j1 rule="para" parents="7123 1326"/>
    </justification>
  </clause>

  <clause id="7532">
    <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(4816(a,1),7123(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4816 7123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7533">
    <literal><![CDATA[
      T(x,(y * x) / z) = T(x,y / (x \ z))
    ]]></literal>
    <justification jstring="[hyper(58,a,7112,a,b,7133,a)].">
      <j1 rule="hyper" parents="58 7112 7133"/>
    </justification>
  </clause>

  <clause id="7534">
    <literal><![CDATA[
      K(x,T(y,(z \ u) \ y)) = K(x,T(y,u \ z))
    ]]></literal>
    <justification jstring="[para(6125(a,1),7156(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6125 7156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7535">
    <literal><![CDATA[
      K(x \ 1,T(y,L(x,z,u))) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(173(a,1),7168(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="173 7168"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7536">
    <literal><![CDATA[
      K(x,T(T(y,z),u)) = T(T(K(x,y),u),z)
    ]]></literal>
    <justification jstring="[para(7158(a,1),7181(a,2,1))].">
      <j1 rule="para" parents="7158 7181"/>
    </justification>
  </clause>

  <clause id="7537">
    <literal><![CDATA[
      K(x * y,K(x,z)) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(6257,a,7188,a)].">
      <j1 rule="hyper" parents="6257 7188"/>
    </justification>
  </clause>

  <clause id="7538">
    <literal><![CDATA[
      K(x,K(y,z)) * T(z,y) = T(z,T(y,x))
    ]]></literal>
    <justification jstring="[para(7188(a,1),6522(a,1,1))].">
      <j1 rule="para" parents="7188 6522"/>
    </justification>
  </clause>

  <clause id="7539">
    <literal><![CDATA[
      K(x * y,K(y,z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,6577,a,b,7537,a)].">
      <j1 rule="hyper" parents="58 6577 7537"/>
    </justification>
  </clause>

  <clause id="7540">
    <literal><![CDATA[
      K(x \ y,K(x,z)) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[para(5(a,1),7537(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5 7537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7541">
    <literal><![CDATA[
      K(x * y,K(x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,K(x,z)) = u
    ]]></literal>
    <justification jstring="[para(7540(a,1),6299(a,1))].">
      <j1 rule="para" parents="7540 6299"/>
    </justification>
  </clause>

  <clause id="7542">
    <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,5589,a,b,7198,a)].">
      <j1 rule="hyper" parents="58 5589 7198"/>
    </justification>
  </clause>

  <clause id="7543">
    <literal><![CDATA[
      K(T(T(x,y),z),u) = K(x,T(T(u,y),z))
    ]]></literal>
    <justification jstring="[para(18(a,1),7198(a,1,1))].">
      <j1 rule="para" parents="18 7198"/>
    </justification>
  </clause>

  <clause id="7544">
    <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(7210(a,1),2027(a,1,2))].">
      <j1 rule="para" parents="7210 2027"/>
    </justification>
  </clause>

  <clause id="7545">
    <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),7217(a,1,1))].">
      <j1 rule="para" parents="22 7217"/>
    </justification>
  </clause>

  <clause id="7546">
    <literal><![CDATA[
      K(x,y) * T(x,T(z,y)) = T(T(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(5407,a,7220,a)].">
      <j1 rule="hyper" parents="5407 7220"/>
    </justification>
  </clause>

  <clause id="7547">
    <literal><![CDATA[
      K(x,y) \ T(T(x,y),z) = T(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(116,a,7220,a(flip),b,5405,a)].">
      <j1 rule="hyper" parents="116 7220 5405"/>
    </justification>
  </clause>

  <clause id="7548">
    <literal><![CDATA[
      K(x,K(y,z)) * T(x,y) = T(T(x,y),K(y,z))
    ]]></literal>
    <justification jstring="[para(3327(a,1),7220(a,1,1,2))].">
      <j1 rule="para" parents="3327 7220"/>
    </justification>
  </clause>

  <clause id="7549">
    <literal><![CDATA[
      K(x,y) * T(T(y,z),x) = T(y,T(z,x))
    ]]></literal>
    <justification jstring="[para(7227(a,1),5454(a,1,2))].">
      <j1 rule="para" parents="7227 5454"/>
    </justification>
  </clause>

  <clause id="7550">
    <literal><![CDATA[
      K(x,(y * x) / z) = K(x,y / (x \ z))
    ]]></literal>
    <justification jstring="[hyper(58,a,7099,a,b,7246,a)].">
      <j1 rule="hyper" parents="58 7099 7246"/>
    </justification>
  </clause>

  <clause id="7551">
    <literal><![CDATA[
      K(x,T(K(x,y) * z,u)) = K(x,T(z,u))
    ]]></literal>
    <justification jstring="[para(5133(a,1),7248(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5133 7248"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7552">
    <literal><![CDATA[
      T(T(x,y),K(x,z) * u) = T(T(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(320,a,18,a,b,7269,a),flip(a)].">
      <j1 rule="hyper" parents="320 18 7269"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7553">
    <literal><![CDATA[
      T(x,y * (K(x,z) * u)) = T(x,y * u)
    ]]></literal>
    <justification jstring="[para(5133(a,1),7273(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5133 7273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7554">
    <literal><![CDATA[
      K(x,T(y,K(x,z) * u)) = K(x,T(y,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,7160,a(flip),b,7274,a),flip(a)].">
      <j1 rule="hyper" parents="320 7160 7274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7555">
    <literal><![CDATA[
      K(x,y * (K(x,z) * u)) = K(x,y * u)
    ]]></literal>
    <justification jstring="[para(5133(a,1),7279(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5133 7279"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7556">
    <literal><![CDATA[
      K(x,(y * x) * z) = K(x,(x * y) * z)
    ]]></literal>
    <justification jstring="[para(4813(a,1),7284(a,1,2,1))].">
      <j1 rule="para" parents="4813 7284"/>
    </justification>
  </clause>

  <clause id="7557">
    <literal><![CDATA[
      K(x,(T(y,x) * z) * u) = K(x,(y * z) * u)
    ]]></literal>
    <justification jstring="[para(4781(a,1),7284(a,1,2,1))].">
      <j1 rule="para" parents="4781 7284"/>
    </justification>
  </clause>

  <clause id="7558">
    <literal><![CDATA[
      K(x,(y \ T(z,x)) * u) = K(x,(y \ z) * u)
    ]]></literal>
    <justification jstring="[para(5553(a,1),7284(a,1,2,1))].">
      <j1 rule="para" parents="5553 7284"/>
    </justification>
  </clause>

  <clause id="7559">
    <literal><![CDATA[
      K(x,(T(y,x) / z) * u) = K(x,(y / z) * u)
    ]]></literal>
    <justification jstring="[para(5738(a,1),7284(a,1,2,1))].">
      <j1 rule="para" parents="5738 7284"/>
    </justification>
  </clause>

  <clause id="7560">
    <literal><![CDATA[
      K(x,y * K(z,R(x,u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[para(7288(a,1),7409(a,1,2))].">
      <j1 rule="para" parents="7288 7409"/>
    </justification>
  </clause>

  <clause id="7561">
    <literal><![CDATA[
      K(x,y / (z / R(x,u,w))) = K(x,y / (R(x,u,w) \ z))
    ]]></literal>
    <justification jstring="[para(6221(a,1),7560(a,1,2))].">
      <j1 rule="para" parents="6221 7560"/>
    </justification>
  </clause>

  <clause id="7562">
    <literal><![CDATA[
      x \ (T(y / x,z) \ y) = K(z,x \ y)
    ]]></literal>
    <justification jstring="[hyper(5965,a,7299,a)].">
      <j1 rule="hyper" parents="5965 7299"/>
    </justification>
  </clause>

  <clause id="7563">
    <literal><![CDATA[
      T(x / y,z) \ x = y * K(z,y \ x)
    ]]></literal>
    <justification jstring="[hyper(5477,a,7299,a)].">
      <j1 rule="hyper" parents="5477 7299"/>
    </justification>
  </clause>

  <clause id="7564">
    <literal><![CDATA[
      (x * L(y,z,y)) / T(T(x,y),u) = K(u,x) * L(y,z,y)
    ]]></literal>
    <justification jstring="[para(7076(a,1),7300(a,1,2,1))].">
      <j1 rule="para" parents="7076 7300"/>
    </justification>
  </clause>

  <clause id="7565">
    <literal><![CDATA[
      K(x,(y / z) \ 1) * y = y * K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(5351(a,2),7306(a,1,1))].">
      <j1 rule="para" parents="5351 7306"/>
    </justification>
  </clause>

  <clause id="7566">
    <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(6431(a,1),7306(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6431 7306"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7567">
    <literal><![CDATA[
      T(T(x,y),z) * K(z,x) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(18(a,1),7311(a,1,1))].">
      <j1 rule="para" parents="18 7311"/>
    </justification>
  </clause>

  <clause id="7568">
    <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),7316(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="367 7316"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7569">
    <literal><![CDATA[
      K(x,T(y \ 1,z)) = K(x,z \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(58,a,7160,a(flip),b,7320,a)].">
      <j1 rule="hyper" parents="58 7160 7320"/>
    </justification>
  </clause>

  <clause id="7570">
    <literal><![CDATA[
      K(x * T(y,z),T(z,u)) = K(x * y,T(z,u))
    ]]></literal>
    <justification jstring="[para(1433(a,1),7346(a,1,1))].">
      <j1 rule="para" parents="1433 7346"/>
    </justification>
  </clause>

  <clause id="7571">
    <literal><![CDATA[
      K(x * T(y,z),T(y,u)) = K(x * y,T(y,u))
    ]]></literal>
    <justification jstring="[para(6331(a,1),7346(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6331 7346"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7572">
    <literal><![CDATA[
      K(x * (K(y,z) * u),y) = K(x * u,y)
    ]]></literal>
    <justification jstring="[para(5133(a,1),7354(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5133 7354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7573">
    <literal><![CDATA[
      K(x * (T(y,z) * u),y) = K(x * (y * u),y)
    ]]></literal>
    <justification jstring="[para(4819(a,1),7354(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4819 7354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7574">
    <literal><![CDATA[
      K(x * (y / (z * y)),z \ 1) = K(x * ((z * y) \ y),z \ 1)
    ]]></literal>
    <justification jstring="[para(5354(a,1),7354(a,1,1,2))].">
      <j1 rule="para" parents="5354 7354"/>
    </justification>
  </clause>

  <clause id="7575">
    <literal><![CDATA[
      K(x * (y \ T(z,u)),u) = K(x * (y \ z),u)
    ]]></literal>
    <justification jstring="[para(5553(a,1),7354(a,1,1,2))].">
      <j1 rule="para" parents="5553 7354"/>
    </justification>
  </clause>

  <clause id="7576">
    <literal><![CDATA[
      T(x,T(y,x \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7366(a,2),4766(a,1))].">
      <j1 rule="para" parents="7366 4766"/>
    </justification>
  </clause>

  <clause id="7577">
    <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(7376(a,1),5378(a,1,1,2))].">
      <j1 rule="para" parents="7376 5378"/>
    </justification>
  </clause>

  <clause id="7578">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ z,x) = (x \ z) * x
    ]]></literal>
    <justification jstring="[hyper(6195,a,7377,a)].">
      <j1 rule="hyper" parents="6195 7377"/>
    </justification>
  </clause>

  <clause id="7579">
    <literal><![CDATA[
      K(x,y * (z * L(K(x,u),w,v5))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(5677(a,1),7403(a,1,2,2,2))].">
      <j1 rule="para" parents="5677 7403"/>
    </justification>
  </clause>

  <clause id="7580">
    <literal><![CDATA[
      K(x,y * (z * L(K(u,x),w,v5))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(4823(a,1),7404(a,1,2,2,2))].">
      <j1 rule="para" parents="4823 7404"/>
    </justification>
  </clause>

  <clause id="7581">
    <literal><![CDATA[
      K(x,T(y * (z * K(u,x)),w)) = T(K(x,y * z),w)
    ]]></literal>
    <justification jstring="[para(7404(a,1),7158(a,2,1))].">
      <j1 rule="para" parents="7404 7158"/>
    </justification>
  </clause>

  <clause id="7582">
    <literal><![CDATA[
      K(x * (y / T(z,u)),u) = K(x * (y / z),u)
    ]]></literal>
    <justification jstring="[para(6188(a,1),7413(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6188 7413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7583">
    <literal><![CDATA[
      K(x * (y / R(z,u,z)),z) = K(x * (y / T(z,u)),z)
    ]]></literal>
    <justification jstring="[para(6647(a,1),7415(a,1,1,2))].">
      <j1 rule="para" parents="6647 7415"/>
    </justification>
  </clause>

  <clause id="7584">
    <literal><![CDATA[
      K(x,y) * T(K(x,y) \ z,y) = T(z,y)
    ]]></literal>
    <justification jstring="[hyper(6034,a,7437,a)].">
      <j1 rule="hyper" parents="6034 7437"/>
    </justification>
  </clause>

  <clause id="7585">
    <literal><![CDATA[
      (T(x,y) / y) * T(y,z) = T(x * K(y,z),y)
    ]]></literal>
    <justification jstring="[hyper(320,a,6151,a,b,7437,a)].">
      <j1 rule="hyper" parents="320 6151 7437"/>
    </justification>
  </clause>

  <clause id="7587">
    <literal><![CDATA[
      x \ T(x * K(y,z),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * K(y,z) = u
    ]]></literal>
    <justification jstring="[para(7437(a,2),5096(a,1,2))].">
      <j1 rule="para" parents="7437 5096"/>
    </justification>
  </clause>

  <clause id="7588">
    <literal><![CDATA[
      K(x,T(x * K(y,z),y)) = K(x,x * K(y,z))
    ]]></literal>
    <justification jstring="[para(7437(a,2),7275(a,1,2))].">
      <j1 rule="para" parents="7437 7275"/>
    </justification>
  </clause>

  <clause id="7589">
    <literal><![CDATA[
      T(T(x,1 / y),K(1 / y,z)) = x * K(x,1 / T(y,z))
    ]]></literal>
    <justification jstring="[para(5514(a,2),7441(a,2,2))].">
      <j1 rule="para" parents="5514 7441"/>
    </justification>
  </clause>

  <clause id="7590">
    <literal><![CDATA[
      T(x \ y,K(x,z)) = x \ T(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,6516,a(flip),b,7443,a),flip(a)].">
      <j1 rule="hyper" parents="58 6516 7443"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7591">
    <literal><![CDATA[
      T(x * y,K(y,z)) / y = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(6517,a,7444,a)].">
      <j1 rule="hyper" parents="6517 7444"/>
    </justification>
  </clause>

  <clause id="7592">
    <literal><![CDATA[
      T(x * y,K(x,z)) = x * T(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(119,a,7444,a(flip),b,6516,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 7444 6516"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7593">
    <literal><![CDATA[
      x * (y * ((x \ 1) / y)) = K(y,x \ (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(5304,a,7451,a)].">
      <j1 rule="hyper" parents="5304 7451"/>
    </justification>
  </clause>

  <clause id="7594">
    <literal><![CDATA[
      K(x,L(x \ y,x,z)) = K(x,z \ (x \ (z * y)))
    ]]></literal>
    <justification jstring="[hyper(58,a,6598,a,b,7451,a)].">
      <j1 rule="hyper" parents="58 6598 7451"/>
    </justification>
  </clause>

  <clause id="7595">
    <literal><![CDATA[
      K(x,y \ (x \ (y * (z * x)))) = K(x,L(T(z,x),x,y))
    ]]></literal>
    <justification jstring="[para(232(a,1),7451(a,1,2)),flip(a)].">
      <j1 rule="para" parents="232 7451"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7596">
    <literal><![CDATA[
      L(K(x,y \ (x \ z)),u * x,w) = K(L(x,u,w),(y * x) \ z)
    ]]></literal>
    <justification jstring="[para(7451(a,1),6615(a,1,1))].">
      <j1 rule="para" parents="7451 6615"/>
    </justification>
  </clause>

  <clause id="7597">
    <literal><![CDATA[
      K(x,y \ (x \ (y * z))) != u
    ]]></literal>
    <literal><![CDATA[
      L(K(x,x \ z),z,y) = u
    ]]></literal>
    <justification jstring="[para(7451(a,1),6684(a,1))].">
      <j1 rule="para" parents="7451 6684"/>
    </justification>
  </clause>

  <clause id="7598">
    <literal><![CDATA[
      K((x * y) \ (z * y),y) = K(x \ z,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,7373,a(flip),b,7467,a),flip(a)].">
      <j1 rule="hyper" parents="320 7373 7467"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7599">
    <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(7467(a,1),5522(a,1,1,1,2))].">
      <j1 rule="para" parents="7467 5522"/>
    </justification>
  </clause>

  <clause id="7600">
    <literal><![CDATA[
      K((x \ y) \ z,x) = K(y \ (z * x),x)
    ]]></literal>
    <justification jstring="[hyper(58,a,7373,a(flip),b,7469,a)].">
      <j1 rule="hyper" parents="58 7373 7469"/>
    </justification>
  </clause>

  <clause id="7601">
    <literal><![CDATA[
      T(x / T(y,z),y) * y = (y \ x) * (y * K(z,y))
    ]]></literal>
    <justification jstring="[para(7473(a,2),6090(a,1,1))].">
      <j1 rule="para" parents="7473 6090"/>
    </justification>
  </clause>

  <clause id="7602">
    <literal><![CDATA[
      K(x,y) * R(T(y,x),z,y) = R(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(5147,a,7478,a)].">
      <j1 rule="hyper" parents="5147 7478"/>
    </justification>
  </clause>

  <clause id="7603">
    <literal><![CDATA[
      K(x,y) * (x \ R(x,z,x)) = x \ R(T(x,y),z,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,7478,a(flip),b,5102,a),flip(a)].">
      <j1 rule="hyper" parents="116 7478 5102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7604">
    <literal><![CDATA[
      T(K(x,y) * z,x) = K(x,y) * T(z,x)
    ]]></literal>
    <justification jstring="[hyper(239,a,7481,a,b,4778,a)].">
      <j1 rule="hyper" parents="239 7481 4778"/>
    </justification>
  </clause>

  <clause id="7605">
    <literal><![CDATA[
      (T(x,y) * (x \ z)) * x = T(x,y) * T(z,x)
    ]]></literal>
    <justification jstring="[para(4779(a,2),7481(a,1,1))].">
      <j1 rule="para" parents="4779 7481"/>
    </justification>
  </clause>

  <clause id="7607">
    <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(7503(a,1),4568(a,1))].">
      <j1 rule="para" parents="7503 4568"/>
    </justification>
  </clause>

  <clause id="7608">
    <literal><![CDATA[
      K(x,L(T(y,z),u,y)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(7503(a,1),7059(a,1,2))].">
      <j1 rule="para" parents="7503 7059"/>
    </justification>
  </clause>

  <clause id="7609">
    <literal><![CDATA[
      L(K(x,T(y,z)),u,y) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(6614,a,7608,a)].">
      <j1 rule="hyper" parents="6614 7608"/>
    </justification>
  </clause>

  <clause id="7610">
    <literal><![CDATA[
      K((x * y) \ z,T(x,u)) = K(y \ (x \ z),T(x,u))
    ]]></literal>
    <justification jstring="[hyper(6856,a,7609,a)].">
      <j1 rule="hyper" parents="6856 7609"/>
    </justification>
  </clause>

  <clause id="7611">
    <literal><![CDATA[
      K((x \ 1) * y,T(x \ 1,z)) = K(x \ y,T(x \ 1,z))
    ]]></literal>
    <justification jstring="[hyper(6642,a,7609,a),flip(a)].">
      <j1 rule="hyper" parents="6642 7609"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7612">
    <literal><![CDATA[
      K((x \ y) \ z,T(x,u)) = K(y \ (x * z),T(x,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,6626,a(flip),b,7609,a),flip(a)].">
      <j1 rule="hyper" parents="58 6626 7609"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7613">
    <literal><![CDATA[
      K(x,y) * T(K(x,y) \ z,x) = T(z,x)
    ]]></literal>
    <justification jstring="[hyper(6048,a,7520,a)].">
      <j1 rule="hyper" parents="6048 7520"/>
    </justification>
  </clause>

  <clause id="7614">
    <literal><![CDATA[
      T(K(x,y \ z) * y,y \ z) = T(y \ z,x) \ z
    ]]></literal>
    <justification jstring="[hyper(320,a,5230,a(flip),b,7520,a),flip(a)].">
      <j1 rule="hyper" parents="320 5230 7520"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7616">
    <literal><![CDATA[
      K(x,y) * T(K(x * y,x),y) = T(x \ R(x,y,x),y)
    ]]></literal>
    <justification jstring="[para(5293(a,1),7520(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5293 7520"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7617">
    <literal><![CDATA[
      T(K(x,y) * (z / y),y) = T(y,x) \ z
    ]]></literal>
    <justification jstring="[para(7(a,1),7521(a,2,2))].">
      <j1 rule="para" parents="7 7521"/>
    </justification>
  </clause>

  <clause id="7618">
    <literal><![CDATA[
      T(K(x,y) * (z * (1 / y)),y) = T(y,x) \ R(z,y \ 1,y)
    ]]></literal>
    <justification jstring="[para(2605(a,1),7521(a,2,2))].">
      <j1 rule="para" parents="2605 7521"/>
    </justification>
  </clause>

  <clause id="7619">
    <literal><![CDATA[
      K(x,T(y,T(z,x))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(7538(a,1),7266(a,1,2))].">
      <j1 rule="para" parents="7538 7266"/>
    </justification>
  </clause>

  <clause id="7620">
    <literal><![CDATA[
      K(T(x,T(y,z)),z) = K(T(x,y),z)
    ]]></literal>
    <justification jstring="[para(7538(a,1),7343(a,1,1))].">
      <j1 rule="para" parents="7538 7343"/>
    </justification>
  </clause>

  <clause id="7621">
    <literal><![CDATA[
      K(x,T(y,T(z,R(x,u,w)))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(7538(a,1),7408(a,1,2))].">
      <j1 rule="para" parents="7538 7408"/>
    </justification>
  </clause>

  <clause id="7622">
    <literal><![CDATA[
      K(x,T(y,x / z)) = K(x,T(y,z \ x))
    ]]></literal>
    <justification jstring="[para(7092(a,1),7619(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7092 7619"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7623">
    <literal><![CDATA[
      K(x,y) * T(x,K(z,T(u,y))) = T(T(x,y),K(z,u))
    ]]></literal>
    <justification jstring="[para(7158(a,2),7546(a,1,2,2))].">
      <j1 rule="para" parents="7158 7546"/>
    </justification>
  </clause>

  <clause id="7624">
    <literal><![CDATA[
      K(x,y / z) * T(z \ y,x) = T(y / z,T(z,x))
    ]]></literal>
    <justification jstring="[para(107(a,1),7549(a,1,2,1))].">
      <j1 rule="para" parents="107 7549"/>
    </justification>
  </clause>

  <clause id="7625">
    <literal><![CDATA[
      T(T(x,y),T(x,z) \ u) = T(T(x,y),x \ u)
    ]]></literal>
    <justification jstring="[para(5081(a,1),7552(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5081 7552"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7626">
    <literal><![CDATA[
      K(x,T(y,K(z,x) * u)) = K(x,T(y,u))
    ]]></literal>
    <justification jstring="[para(5133(a,1),7554(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5133 7554"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7627">
    <literal><![CDATA[
      K(x,y * (z * (K(u,x) * w))) = K(x,y * (z * w))
    ]]></literal>
    <justification jstring="[para(6038(a,1),7555(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6038 7555"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7628">
    <literal><![CDATA[
      x / T(y \ x,z) = T(x / y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(33,a,6373,a,b,7562,a)].">
      <j1 rule="hyper" parents="33 6373 7562"/>
    </justification>
  </clause>

  <clause id="7629">
    <literal><![CDATA[
      x / (y * K(z,y \ x)) = T(x / y,z)
    ]]></literal>
    <justification jstring="[hyper(197,a,7563,a)].">
      <j1 rule="hyper" parents="197 7563"/>
    </justification>
  </clause>

  <clause id="7630">
    <literal><![CDATA[
      (T(x / y,z) \ x) \ x = T(y \ x,z)
    ]]></literal>
    <justification jstring="[para(7563(a,2),6321(a,1,1))].">
      <j1 rule="para" parents="7563 6321"/>
    </justification>
  </clause>

  <clause id="7631">
    <literal><![CDATA[
      T(T(x,y) * K(z,x),z) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,7437,a,b,7567,a)].">
      <j1 rule="hyper" parents="58 7437 7567"/>
    </justification>
  </clause>

  <clause id="7632">
    <literal><![CDATA[
      x \ (T(y,z) * T(x,y)) = T(y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(58,a,7044,a,b,7567,a)].">
      <j1 rule="hyper" parents="58 7044 7567"/>
    </justification>
  </clause>

  <clause id="7633">
    <literal><![CDATA[
      T(x,T(y \ 1,z)) = T(x,z \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(118,a,7569,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 7569 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7634">
    <literal><![CDATA[
      K(x,T(y,z) \ 1) = K(x,z \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(58,a,7169,a(flip),b,7569,a)].">
      <j1 rule="hyper" parents="58 7169 7569"/>
    </justification>
  </clause>

  <clause id="7635">
    <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(7572(a,1),5523(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="7572 5523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7636">
    <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(7572(a,1),5524(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="7572 5524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7637">
    <literal><![CDATA[
      T(x * K(y,z),z) = T(x,z) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(741,a,7584,a),flip(a)].">
      <j1 rule="hyper" parents="741 7584"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7638">
    <literal><![CDATA[
      K(x,(y * K(z,x)) \ u) = (y * T(y \ u,x)) \ u
    ]]></literal>
    <justification jstring="[para(7584(a,1),6466(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7584 6466"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7639">
    <literal><![CDATA[
      x \ T(L(y,x \ 1,x),K(x,z)) = T((x \ 1) * y,K(x,z))
    ]]></literal>
    <justification jstring="[para(437(a,1),7590(a,1,1)),flip(a)].">
      <j1 rule="para" parents="437 7590"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7640">
    <literal><![CDATA[
      T(x * y,K(y,z)) = T(x,K(y,z)) * y
    ]]></literal>
    <justification jstring="[hyper(133,a,7591,a),flip(a)].">
      <j1 rule="hyper" parents="133 7591"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7641">
    <literal><![CDATA[
      K(x \ ((y \ z) * y),y) = K(x \ z,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,7469,a(flip),b,7600,a),flip(a)].">
      <j1 rule="hyper" parents="58 7469 7600"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7642">
    <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(7602(a,1),5178(a,1,2))].">
      <j1 rule="para" parents="7602 5178"/>
    </justification>
  </clause>

  <clause id="7643">
    <literal><![CDATA[
      T(K(x,y) * T(y,z),x) = T(y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(320,a,7549,a(flip),b,7604,a),flip(a)].">
      <j1 rule="hyper" parents="320 7549 7604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7644">
    <literal><![CDATA[
      T(K(x,y) * z,x) / z = K(x,y) * K(z,x)
    ]]></literal>
    <justification jstring="[hyper(117,a,7604,a,b,6196,a)].">
      <j1 rule="hyper" parents="117 7604 6196"/>
    </justification>
  </clause>

  <clause id="7645">
    <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),7604(a,2,2))].">
      <j1 rule="para" parents="20 7604"/>
    </justification>
  </clause>

  <clause id="7647">
    <literal><![CDATA[
      (x \ K(y,z)) * T((x \ K(y,z)) \ u,y) = x \ T(x * u,y)
    ]]></literal>
    <justification jstring="[hyper(116,a,7613,a(flip),b,1094,a),flip(a)].">
      <j1 rule="hyper" parents="116 7613 1094"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7648">
    <literal><![CDATA[
      K(x,y) * (z * T(z \ (K(x,y) \ u),x)) = T(u / z,x) * z
    ]]></literal>
    <justification jstring="[para(7613(a,1),1576(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7613 1576"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7649">
    <literal><![CDATA[
      (x / y) * K(x,T(z,y \ x)) = K(x,z) * (x / y)
    ]]></literal>
    <justification jstring="[para(7622(a,1),7179(a,1,2))].">
      <j1 rule="para" parents="7622 7179"/>
    </justification>
  </clause>

  <clause id="7650">
    <literal><![CDATA[
      K(x,T(y,K(z,x) * u)) = T(K(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(320,a,7158,a(flip),b,7626,a),flip(a)].">
      <j1 rule="hyper" parents="320 7158 7626"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7651">
    <literal><![CDATA[
      K(x,T(y,z * K(u,x))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(7288(a,1),7626(a,1,2,2))].">
      <j1 rule="para" parents="7288 7626"/>
    </justification>
  </clause>

  <clause id="7652">
    <literal><![CDATA[
      x / T((y \ x) \ x,z) = T(y,z) \ x
    ]]></literal>
    <justification jstring="[para(72(a,1),7628(a,2,1,1))].">
      <j1 rule="para" parents="72 7628"/>
    </justification>
  </clause>

  <clause id="7653">
    <literal><![CDATA[
      T(x / (x / y),z) \ x = x / T(y,z)
    ]]></literal>
    <justification jstring="[para(75(a,1),7628(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="75 7628"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7654">
    <literal><![CDATA[
      (x * y) / (x * K(z,y)) = T((x * y) / x,z)
    ]]></literal>
    <justification jstring="[para(4(a,1),7629(a,1,2,2,2))].">
      <j1 rule="para" parents="4 7629"/>
    </justification>
  </clause>

  <clause id="7655">
    <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(7629(a,1),4397(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7629 4397"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7656">
    <literal><![CDATA[
      x / ((x * y) * K(z,y \ 1)) = T(x / (x * y),z)
    ]]></literal>
    <justification jstring="[para(6127(a,1),7629(a,1,2,2))].">
      <j1 rule="para" parents="6127 7629"/>
    </justification>
  </clause>

  <clause id="7657">
    <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(6431(a,1),7629(a,2,1))].">
      <j1 rule="para" parents="6431 7629"/>
    </justification>
  </clause>

  <clause id="7658">
    <literal><![CDATA[
      T((x \ y) \ y,z) = (T(x,z) \ y) \ y
    ]]></literal>
    <justification jstring="[para(72(a,1),7630(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="72 7630"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7659">
    <literal><![CDATA[
      ((x \ T(y,x)) \ y) \ y = T(T(x,y) \ y,x)
    ]]></literal>
    <justification jstring="[para(4244(a,1),7630(a,1,1,1))].">
      <j1 rule="para" parents="4244 7630"/>
    </justification>
  </clause>

  <clause id="7660">
    <literal><![CDATA[
      K(x,T(T(y / z,u),y)) = K(x,T(z \ y,u))
    ]]></literal>
    <justification jstring="[para(7630(a,1),7141(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7630 7141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7661">
    <literal><![CDATA[
      T(x * K(y,x),T(z,y)) = T(x,z) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(5205,a,7631,a)].">
      <j1 rule="hyper" parents="5205 7631"/>
    </justification>
  </clause>

  <clause id="7662">
    <literal><![CDATA[
      x \ (K(y,z) * (x * y)) = T(y,T(z,x))
    ]]></literal>
    <justification jstring="[para(5089(a,2),7632(a,1,2))].">
      <j1 rule="para" parents="5089 7632"/>
    </justification>
  </clause>

  <clause id="7663">
    <literal><![CDATA[
      T(x,T(y,z) \ 1) = T(x,z \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(58,a,7308,a(flip),b,7633,a)].">
      <j1 rule="hyper" parents="58 7308 7633"/>
    </justification>
  </clause>

  <clause id="7664">
    <literal><![CDATA[
      T(x,T((y / z) \ 1,y)) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[para(75(a,1),7633(a,2,2,2))].">
      <j1 rule="para" parents="75 7633"/>
    </justification>
  </clause>

  <clause id="7665">
    <literal><![CDATA[
      K(x,y \ K(z,y)) = K(x,z \ (y \ z))
    ]]></literal>
    <justification jstring="[para(4804(a,1),7634(a,1,2))].">
      <j1 rule="para" parents="4804 7634"/>
    </justification>
  </clause>

  <clause id="7666">
    <literal><![CDATA[
      T(K(x,y) * T(y,z),x) = y * K(T(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(320,a,7200,a,b,7643,a),flip(a)].">
      <j1 rule="hyper" parents="320 7200 7643"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7667">
    <literal><![CDATA[
      T(K(x,y),K(z,x) * u) = T(K(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(58,a,7158,a(flip),b,7650,a)].">
      <j1 rule="hyper" parents="58 7158 7650"/>
    </justification>
  </clause>

  <clause id="7668">
    <literal><![CDATA[
      K(x,T(y,z * L(K(u,x),w,v5))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(4823(a,1),7651(a,1,2,2,2))].">
      <j1 rule="para" parents="4823 7651"/>
    </justification>
  </clause>

  <clause id="7669">
    <literal><![CDATA[
      K(x,T(y,z * K(x,u))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(6329(a,1),7651(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6329 7651"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7670">
    <literal><![CDATA[
      x / T(T(y,y \ x),z) = T(y,z) \ x
    ]]></literal>
    <justification jstring="[para(106(a,2),7652(a,1,2,1))].">
      <j1 rule="para" parents="106 7652"/>
    </justification>
  </clause>

  <clause id="7671">
    <literal><![CDATA[
      T(x,y) / T(R(x,z,u),w) = T(R(x,z,u),w) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(6779(a,1),7652(a,1,2,1))].">
      <j1 rule="para" parents="6779 7652"/>
    </justification>
  </clause>

  <clause id="7672">
    <literal><![CDATA[
      x / (x / T(y,z)) = T(x / (x / y),z)
    ]]></literal>
    <justification jstring="[hyper(197,a,7653,a)].">
      <j1 rule="hyper" parents="197 7653"/>
    </justification>
  </clause>

  <clause id="7673">
    <literal><![CDATA[
      T(1 / (1 / x),y) \ K(z,x) = K(z,x) / T(x,y)
    ]]></literal>
    <justification jstring="[para(5446(a,1),7653(a,1,1,1))].">
      <j1 rule="para" parents="5446 7653"/>
    </justification>
  </clause>

  <clause id="7674">
    <literal><![CDATA[
      T(T(x,y),x \ z) = (T(x,y) \ z) \ z
    ]]></literal>
    <justification jstring="[hyper(603,a,7658,a)].">
      <j1 rule="hyper" parents="603 7658"/>
    </justification>
  </clause>

  <clause id="7678">
    <literal><![CDATA[
      K(x,y) * (z * x) = z * T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(134,a,7662,a),flip(a)].">
      <j1 rule="hyper" parents="134 7662"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7679">
    <literal><![CDATA[
      T(x,(y * z) \ z) = T(x,z \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(6506,a,7663,a)].">
      <j1 rule="hyper" parents="6506 7663"/>
    </justification>
  </clause>

  <clause id="7680">
    <literal><![CDATA[
      K(T(x,(y / z) \ 1),y) = K(T(x,y \ z),y)
    ]]></literal>
    <justification jstring="[para(7664(a,1),7620(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7664 7620"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7681">
    <literal><![CDATA[
      K(x,(y * z) \ z) = K(x,z \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(58,a,6557,a,b,7665,a)].">
      <j1 rule="hyper" parents="58 6557 7665"/>
    </justification>
  </clause>

  <clause id="7682">
    <literal><![CDATA[
      T(K(x,y),R(K(z,x),u,w) * v5) = T(K(x,y),v5)
    ]]></literal>
    <justification jstring="[para(5706(a,1),7667(a,1,2,1))].">
      <j1 rule="para" parents="5706 7667"/>
    </justification>
  </clause>

  <clause id="7683">
    <literal><![CDATA[
      T(K(x,y),z * K(u,x)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(7288(a,1),7667(a,1,2))].">
      <j1 rule="para" parents="7288 7667"/>
    </justification>
  </clause>

  <clause id="7684">
    <literal><![CDATA[
      K(x,T(y,z * (u * x))) = K(x,T(y,z * (x * u)))
    ]]></literal>
    <justification jstring="[para(6633(a,1),7669(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6633 7669"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7685">
    <literal><![CDATA[
      K(x,T(y,(z * K(u,x)) * w)) = K(x,T(y,z * w))
    ]]></literal>
    <justification jstring="[para(6818(a,1),7669(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6818 7669"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7689">
    <literal><![CDATA[
      T(x,T(T(y,z),y \ u)) = T(x,T(T(y,z),u))
    ]]></literal>
    <justification jstring="[para(7674(a,2),7153(a,1,2))].">
      <j1 rule="para" parents="7674 7153"/>
    </justification>
  </clause>

  <clause id="7690">
    <literal><![CDATA[
      T(K(x,y),z * x) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(239,a,7678,a,b,6116,a)].">
      <j1 rule="hyper" parents="239 7678 6116"/>
    </justification>
  </clause>

  <clause id="7691">
    <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(7678(a,1),92(a,2,1))].">
      <j1 rule="para" parents="7678 92"/>
    </justification>
  </clause>

  <clause id="7692">
    <literal><![CDATA[
      T(K(x,y),z * x) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(320,a,7158,a(flip),b,7690,a),flip(a)].">
      <j1 rule="hyper" parents="320 7158 7690"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7693">
    <literal><![CDATA[
      K(x,T(y,z * x)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,7158,a,b,7690,a)].">
      <j1 rule="hyper" parents="58 7158 7690"/>
    </justification>
  </clause>

  <clause id="7694">
    <literal><![CDATA[
      K(L(x,y,x),T(z,u)) = K(x,T(z,u * x))
    ]]></literal>
    <justification jstring="[hyper(320,a,7051,a,b,7693,a)].">
      <j1 rule="hyper" parents="320 7051 7693"/>
    </justification>
  </clause>

  <clause id="7695">
    <literal><![CDATA[
      K(x,T(y,z / x)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(7(a,1),7693(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7 7693"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7696">
    <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),7693(a,1,2,2))].">
      <j1 rule="para" parents="80 7693"/>
    </justification>
  </clause>

  <clause id="7697">
    <literal><![CDATA[
      T(x,T(y,z / x)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(118,a,7695,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 7695 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7698">
    <literal><![CDATA[
      K(x,T(y,z \ 1)) = K(x,T(y,z \ x))
    ]]></literal>
    <justification jstring="[para(4453(a,1),7695(a,1,2))].">
      <j1 rule="para" parents="4453 7695"/>
    </justification>
  </clause>

  <clause id="7699">
    <literal><![CDATA[
      T(x \ y,T(z,y)) = T(x \ y,T(z,x))
    ]]></literal>
    <justification jstring="[para(72(a,1),7697(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="72 7697"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7700">
    <literal><![CDATA[
      K(x,T(y \ 1,z)) = K(x,(y * z) \ z)
    ]]></literal>
    <justification jstring="[hyper(320,a,7569,a,b,7681,a)].">
      <j1 rule="hyper" parents="320 7569 7681"/>
    </justification>
  </clause>

  <clause id="7701">
    <literal><![CDATA[
      T(K(x,y),z * L(K(u,x),w,v5)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(4823(a,1),7683(a,1,2,2))].">
      <j1 rule="para" parents="4823 7683"/>
    </justification>
  </clause>

  <clause id="7702">
    <literal><![CDATA[
      K(x,T(y \ x,T(z,y))) = K(x,T(y \ x,z))
    ]]></literal>
    <justification jstring="[para(7699(a,1),7619(a,1,2))].">
      <j1 rule="para" parents="7699 7619"/>
    </justification>
  </clause>

  <clause id="7703">
    <literal><![CDATA[
      T(T(x,y),K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7441(a,2),7186(a,1))].">
      <j1 rule="para" parents="7441 7186"/>
    </justification>
  </clause>

  <clause id="7704">
    <literal><![CDATA[
      K(T(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z,y)) = u
    ]]></literal>
    <justification jstring="[para(4971(a,1),7223(a,1))].">
      <j1 rule="para" parents="4971 7223"/>
    </justification>
  </clause>

  <clause id="7705">
    <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(6785(a,2),7223(a,1))].">
      <j1 rule="para" parents="6785 7223"/>
    </justification>
  </clause>

  <clause id="7706">
    <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),7704(a,1,1))].">
      <j1 rule="para" parents="20 7704"/>
    </justification>
  </clause>

  <clause id="7707">
    <literal><![CDATA[
      (x * y) \ (T(x,z) * y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z,y)) = u
    ]]></literal>
    <justification jstring="[para(6437(a,2),7704(a,1))].">
      <j1 rule="para" parents="6437 7704"/>
    </justification>
  </clause>

  <clause id="7708">
    <literal><![CDATA[
      T(K(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7145(a,1),7704(a,1))].">
      <j1 rule="para" parents="7145 7704"/>
    </justification>
  </clause>

  <clause id="7709">
    <literal><![CDATA[
      K((x \ y) \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z,y)) = u
    ]]></literal>
    <justification jstring="[para(7140(a,2),7704(a,1))].">
      <j1 rule="para" parents="7140 7704"/>
    </justification>
  </clause>

  <clause id="7710">
    <literal><![CDATA[
      K(x,T(y,x * z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7205(a,2),7704(a,1))].">
      <j1 rule="para" parents="7205 7704"/>
    </justification>
  </clause>

  <clause id="7711">
    <literal><![CDATA[
      K(x,y \ (z \ y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z \ 1,y)) = u
    ]]></literal>
    <justification jstring="[para(7320(a,1),7704(a,1))].">
      <j1 rule="para" parents="7320 7704"/>
    </justification>
  </clause>

  <clause id="7712">
    <literal><![CDATA[
      K(T(x,y) \ 1,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ 1,T(z,y)) = u
    ]]></literal>
    <justification jstring="[para(5544(a,2),7708(a,1))].">
      <j1 rule="para" parents="5544 7708"/>
    </justification>
  </clause>

  <clause id="7713">
    <literal><![CDATA[
      K(1 / T(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(1 / x,T(z,y)) = u
    ]]></literal>
    <justification jstring="[para(5549(a,2),7708(a,1))].">
      <j1 rule="para" parents="5549 7708"/>
    </justification>
  </clause>

  <clause id="7714">
    <literal><![CDATA[
      K(x,T(y,x \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7206(a,2),7708(a,1))].">
      <j1 rule="para" parents="7206 7708"/>
    </justification>
  </clause>

  <clause id="7715">
    <literal><![CDATA[
      T(K(x,y),z * x) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7692(a,2),7708(a,1))].">
      <j1 rule="para" parents="7692 7708"/>
    </justification>
  </clause>

  <clause id="7716">
    <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(6317(a,1),7256(a,1,2,1))].">
      <j1 rule="para" parents="6317 7256"/>
    </justification>
  </clause>

  <clause id="7718">
    <literal><![CDATA[
      K(x / y,T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(5(a,1),7319(a,1,1,1))].">
      <j1 rule="para" parents="5 7319"/>
    </justification>
  </clause>

  <clause id="7719">
    <literal><![CDATA[
      K(x \ (y \ (z * y)),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ z,y) = u
    ]]></literal>
    <justification jstring="[para(17(a,1),7411(a,1,1,2))].">
      <j1 rule="para" parents="17 7411"/>
    </justification>
  </clause>

  <clause id="7720">
    <literal><![CDATA[
      T(x,L(y,z,K(u,x))) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,4991,a,b,7528,a),flip(a)].">
      <j1 rule="hyper" parents="320 4991 7528"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7721">
    <literal><![CDATA[
      T(x,(K(y,x) * z) \ (K(y,x) * u)) = T(x,z \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,6630,a(flip),b,7720,a)].">
      <j1 rule="hyper" parents="58 6630 7720"/>
    </justification>
  </clause>

  <clause id="7722">
    <literal><![CDATA[
      T(x * y,T(z,y \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x * y,T(z,x)) = u
    ]]></literal>
    <justification jstring="[para(6174(a,1),7576(a,1,2))].">
      <j1 rule="para" parents="6174 7576"/>
    </justification>
  </clause>

  <clause id="7723">
    <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),7621(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="107 7621"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7724">
    <literal><![CDATA[
      K(x,T(y,z * x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7694(a,1),7392(a,1))].">
      <j1 rule="para" parents="7694 7392"/>
    </justification>
  </clause>

  <clause id="7725">
    <literal><![CDATA[
      T(K(x,y),x * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7158(a,1),7710(a,1))].">
      <j1 rule="para" parents="7158 7710"/>
    </justification>
  </clause>

  <clause id="7726">
    <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(4576(a,1),7718(a,1,1))].">
      <j1 rule="para" parents="4576 7718"/>
    </justification>
  </clause>

  <clause id="7727">
    <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(4927(a,2),7718(a,1,1))].">
      <j1 rule="para" parents="4927 7718"/>
    </justification>
  </clause>

  <clause id="7728">
    <literal><![CDATA[
      T(x \ (y / z),K(x,z)) = T(x,z) \ (y / T(z,x))
    ]]></literal>
    <justification jstring="[para(6322(a,1),7029(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6322 7029"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7729">
    <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,7035,a),flip(a)].">
      <j1 rule="hyper" parents="320 147 7035"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7730">
    <literal><![CDATA[
      (x * (y * T(x,z))) \ ((x * y) * T(x,z)) = a(x,y * K(x,z),x)
    ]]></literal>
    <justification jstring="[para(7038(a,1),6237(a,1,2))].">
      <j1 rule="para" parents="7038 6237"/>
    </justification>
  </clause>

  <clause id="7731">
    <literal><![CDATA[
      K(x,y * (((z * (u \ 1)) / z) \ 1)) = K(x,y * (u * K(u \ 1,z)))
    ]]></literal>
    <justification jstring="[para(7053(a,1),5730(a,2,2,2))].">
      <j1 rule="para" parents="7053 5730"/>
    </justification>
  </clause>

  <clause id="7732">
    <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,6402,a,b,7095,a)].">
      <j1 rule="hyper" parents="320 6402 7095"/>
    </justification>
  </clause>

  <clause id="7733">
    <literal><![CDATA[
      R(T(x / y,K(y,x)),z,x / y) = R(x / y,z,y \ x)
    ]]></literal>
    <justification jstring="[para(6374(a,2),7118(a,1,1))].">
      <j1 rule="para" parents="6374 7118"/>
    </justification>
  </clause>

  <clause id="7734">
    <literal><![CDATA[
      K(x,y) * ((z / y) * R(y,u,y)) = R(y,u,y) * (T(y,x) \ z)
    ]]></literal>
    <justification jstring="[para(7139(a,1),6047(a,1,2))].">
      <j1 rule="para" parents="7139 6047"/>
    </justification>
  </clause>

  <clause id="7735">
    <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(7182(a,2),797(a,1))].">
      <j1 rule="para" parents="7182 797"/>
    </justification>
  </clause>

  <clause id="7736">
    <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(718(a,1),7212(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="718 7212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7737">
    <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(1891(a,1),7212(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1891 7212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7738">
    <literal><![CDATA[
      K(R(T(x,K(y,z)),u,w),z) = K(R(x,u,w),z)
    ]]></literal>
    <justification jstring="[para(2890(a,1),7212(a,2,2))].">
      <j1 rule="para" parents="2890 7212"/>
    </justification>
  </clause>

  <clause id="7739">
    <literal><![CDATA[
      (x \ y) * K(z,T(x,y)) = T(x,z) \ y
    ]]></literal>
    <justification jstring="[para(7097(a,1),7298(a,1,2))].">
      <j1 rule="para" parents="7097 7298"/>
    </justification>
  </clause>

  <clause id="7740">
    <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),7739(a,1,2,2))].">
      <j1 rule="para" parents="214 7739"/>
    </justification>
  </clause>

  <clause id="7741">
    <literal><![CDATA[
      (T(x,y) \ z) \ (x \ z) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(7739(a,1),7203(a,1,1))].">
      <j1 rule="para" parents="7739 7203"/>
    </justification>
  </clause>

  <clause id="7742">
    <literal><![CDATA[
      K(x,T((y / z) \ 1,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(7303(a,2),6166(a,1))].">
      <j1 rule="para" parents="7303 6166"/>
    </justification>
  </clause>

  <clause id="7743">
    <literal><![CDATA[
      K(x \ y,z \ (x \ y)) * (y / x) = T(y / x,T((x * z) \ y,x))
    ]]></literal>
    <justification jstring="[para(6590(a,1),7317(a,1,1))].">
      <j1 rule="para" parents="6590 7317"/>
    </justification>
  </clause>

  <clause id="7744">
    <literal><![CDATA[
      K(x,T(y / (x * z),z)) = K(x,z \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(320,a,7049,a(flip),b,7364,a),flip(a)].">
      <j1 rule="hyper" parents="320 7049 7364"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7745">
    <literal><![CDATA[
      K(x * L(y,z,u),T(y,x)) = K(x * L(y,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(5785,a,7368,a),flip(a)].">
      <j1 rule="hyper" parents="5785 7368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7746">
    <literal><![CDATA[
      T(x * y,T(y,x)) != z
    ]]></literal>
    <literal><![CDATA[
      T(x * y,y) = z
    ]]></literal>
    <justification jstring="[para(7381(a,1),3030(a,1))].">
      <j1 rule="para" parents="7381 3030"/>
    </justification>
  </clause>

  <clause id="7747">
    <literal><![CDATA[
      T(T(x * K(y,z),u),T(z,y)) = T(T(K(y,z) * x,z),u)
    ]]></literal>
    <justification jstring="[para(7449(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7449 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7748">
    <literal><![CDATA[
      K(((x \ 1) \ y) \ z,y) = K(x \ (y \ z),y)
    ]]></literal>
    <justification jstring="[hyper(6697,a,7468,a)].">
      <j1 rule="hyper" parents="6697 7468"/>
    </justification>
  </clause>

  <clause id="7749">
    <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(7476(a,1),5110(a,1,2))].">
      <j1 rule="para" parents="7476 5110"/>
    </justification>
  </clause>

  <clause id="7750">
    <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(7477(a,1),7473(a,2,1))].">
      <j1 rule="para" parents="7477 7473"/>
    </justification>
  </clause>

  <clause id="7751">
    <literal><![CDATA[
      K(x,T(y,z \ (u * y))) = K(x,T(y,z \ u))
    ]]></literal>
    <justification jstring="[para(6594(a,1),7534(a,1,2))].">
      <j1 rule="para" parents="6594 7534"/>
    </justification>
  </clause>

  <clause id="7752">
    <literal><![CDATA[
      K(x,K(y,z)) * T(x,y) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,7438,a(flip),b,7548,a),flip(a)].">
      <j1 rule="hyper" parents="320 7438 7548"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7753">
    <literal><![CDATA[
      K(x,K(y,z)) = K(z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(30,a,7538,a,b,7752,a)].">
      <j1 rule="hyper" parents="30 7538 7752"/>
    </justification>
  </clause>

  <clause id="7754">
    <literal><![CDATA[
      K(x,y) * K(y,T(x,z)) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(30,a,6522,a,b,7752,a)].">
      <j1 rule="hyper" parents="30 6522 7752"/>
    </justification>
  </clause>

  <clause id="7755">
    <literal><![CDATA[
      K(K(x,y),z) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(5628,a,7753,a)].">
      <j1 rule="hyper" parents="5628 7753"/>
    </justification>
  </clause>

  <clause id="7756">
    <literal><![CDATA[
      K(x * y,K(y,z)) = K(z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(320,a,7539,a,b,7753,a)].">
      <j1 rule="hyper" parents="320 7539 7753"/>
    </justification>
  </clause>

  <clause id="7757">
    <literal><![CDATA[
      x * K(y,K(z,x)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(119,a,7753,a,b,4729,a(flip))].">
      <j1 rule="hyper" parents="119 7753 4729"/>
    </justification>
  </clause>

  <clause id="7758">
    <literal><![CDATA[
      (K(x,y) * z) * K(y,K(x,z)) = z * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,7753,a,b,11,a(flip))].">
      <j1 rule="hyper" parents="119 7753 11"/>
    </justification>
  </clause>

  <clause id="7759">
    <literal><![CDATA[
      K(x,K(y,z)) \ K(y,x) = T(K(y,x),z)
    ]]></literal>
    <justification jstring="[para(7753(a,1),4790(a,2,1)),flip(a)].">
      <j1 rule="para" parents="7753 4790"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7760">
    <literal><![CDATA[
      K(x,K(y,z)) \ K(y,x) != u
    ]]></literal>
    <literal><![CDATA[
      T(K(y,x),z) = u
    ]]></literal>
    <justification jstring="[para(7753(a,1),4865(a,1,1))].">
      <j1 rule="para" parents="7753 4865"/>
    </justification>
  </clause>

  <clause id="7761">
    <literal><![CDATA[
      K(x,K(y,z)) \ 1 = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[para(7753(a,1),5622(a,1,1))].">
      <j1 rule="para" parents="7753 5622"/>
    </justification>
  </clause>

  <clause id="7762">
    <literal><![CDATA[
      K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(K(x,y),z) = u
    ]]></literal>
    <justification jstring="[para(7753(a,1),5628(a,1))].">
      <j1 rule="para" parents="7753 5628"/>
    </justification>
  </clause>

  <clause id="7763">
    <literal><![CDATA[
      K(x,y) * K(x,K(y,z)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(7753(a,1),5624(a,1,2))].">
      <j1 rule="para" parents="7753 5624"/>
    </justification>
  </clause>

  <clause id="7764">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,y) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(7753(a,1),5625(a,1,1))].">
      <j1 rule="para" parents="7753 5625"/>
    </justification>
  </clause>

  <clause id="7765">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,y) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(7753(a,1),7166(a,1,1))].">
      <j1 rule="para" parents="7753 7166"/>
    </justification>
  </clause>

  <clause id="7766">
    <literal><![CDATA[
      K(x,y) * K(x,K(y,z)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(7753(a,1),7167(a,1,2))].">
      <j1 rule="para" parents="7753 7167"/>
    </justification>
  </clause>

  <clause id="7767">
    <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,5709,a(flip),b,7755,a),flip(a)].">
      <j1 rule="hyper" parents="320 5709 7755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7768">
    <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,6921,a,b,7755,a)].">
      <j1 rule="hyper" parents="58 6921 7755"/>
    </justification>
  </clause>

  <clause id="7769">
    <literal><![CDATA[
      (x / y) * K(z,K(u,y)) = x / T(y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(119,a,7755,a(flip),b,6364,a)].">
      <j1 rule="hyper" parents="119 7755 6364"/>
    </justification>
  </clause>

  <clause id="7770">
    <literal><![CDATA[
      (x * K(y,z)) * K(y,K(z,u)) = x * T(K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(119,a,7755,a(flip),b,6154,a)].">
      <j1 rule="hyper" parents="119 7755 6154"/>
    </justification>
  </clause>

  <clause id="7771">
    <literal><![CDATA[
      K(x,y) * K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(K(x,y),z) = u
    ]]></literal>
    <justification jstring="[para(7755(a,1),4766(a,1,2))].">
      <j1 rule="para" parents="7755 4766"/>
    </justification>
  </clause>

  <clause id="7772">
    <literal><![CDATA[
      K(x,K(y,z)) * (z \ u) = T(z,K(x,y)) \ u
    ]]></literal>
    <justification jstring="[para(7755(a,1),5131(a,1,1))].">
      <j1 rule="para" parents="7755 5131"/>
    </justification>
  </clause>

  <clause id="7773">
    <literal><![CDATA[
      K(x,K(y,z)) * (z \ u) != w
    ]]></literal>
    <literal><![CDATA[
      T(z,K(x,y)) \ u = w
    ]]></literal>
    <justification jstring="[para(7755(a,1),5180(a,1,1))].">
      <j1 rule="para" parents="7755 5180"/>
    </justification>
  </clause>

  <clause id="7774">
    <literal><![CDATA[
      K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,K(y,x)) = u
    ]]></literal>
    <justification jstring="[para(7755(a,1),5654(a,1))].">
      <j1 rule="para" parents="7755 5654"/>
    </justification>
  </clause>

  <clause id="7775">
    <literal><![CDATA[
      K(L(K(x,y),z,u) \ 1,w) = L(K(y,K(x,w)),z,u)
    ]]></literal>
    <justification jstring="[para(7755(a,1),5690(a,2,1))].">
      <j1 rule="para" parents="7755 5690"/>
    </justification>
  </clause>

  <clause id="7776">
    <literal><![CDATA[
      K(K(x,y) * z,K(x,u)) = K(K(z,x),u)
    ]]></literal>
    <justification jstring="[para(7343(a,1),7755(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7343 7755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7777">
    <literal><![CDATA[
      K(x,K(y,z * y)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,7753,a,b,7756,a)].">
      <j1 rule="hyper" parents="58 7753 7756"/>
    </justification>
  </clause>

  <clause id="7778">
    <literal><![CDATA[
      K(x,T(y,T(z,K(u,x)))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(7757(a,1),7669(a,1,2,2))].">
      <j1 rule="para" parents="7757 7669"/>
    </justification>
  </clause>

  <clause id="7779">
    <literal><![CDATA[
      K(x,K(y,z)) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(5626,a,7761,a)].">
      <j1 rule="hyper" parents="5626 7761"/>
    </justification>
  </clause>

  <clause id="7780">
    <literal><![CDATA[
      K(K(x,y),z) = K(y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(4985,a,7761,a)].">
      <j1 rule="hyper" parents="4985 7761"/>
    </justification>
  </clause>

  <clause id="7781">
    <literal><![CDATA[
      K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,K(x,z)) = u
    ]]></literal>
    <justification jstring="[para(7761(a,1),5626(a,1))].">
      <j1 rule="para" parents="7761 5626"/>
    </justification>
  </clause>

  <clause id="7782">
    <literal><![CDATA[
      K(x,K(x * y,z)) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(7541,a,7779,a),flip(a)].">
      <j1 rule="hyper" parents="7541 7779"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7783">
    <literal><![CDATA[
      K(K(x,y),z) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,7755,a,b,7779,a)].">
      <j1 rule="hyper" parents="320 7755 7779"/>
    </justification>
  </clause>

  <clause id="7784">
    <literal><![CDATA[
      K(x,K(y,z)) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(320,a,7753,a,b,7779,a),flip(a)].">
      <j1 rule="hyper" parents="320 7753 7779"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7785">
    <literal><![CDATA[
      x * K(y,K(x,z)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(119,a,7779,a,b,4729,a(flip))].">
      <j1 rule="hyper" parents="119 7779 4729"/>
    </justification>
  </clause>

  <clause id="7786">
    <literal><![CDATA[
      K(x,K(y,z)) * y = T(y,K(x,z))
    ]]></literal>
    <justification jstring="[para(7779(a,1),4770(a,2,1)),flip(a)].">
      <j1 rule="para" parents="7779 4770"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7787">
    <literal><![CDATA[
      K(x,K(y,z)) * (y * u) = T(y,K(x,z)) * u
    ]]></literal>
    <justification jstring="[para(7779(a,1),4781(a,1,1))].">
      <j1 rule="para" parents="7779 4781"/>
    </justification>
  </clause>

  <clause id="7788">
    <literal><![CDATA[
      K(x,K(y,z * y)) = K(y,K(x,y * z))
    ]]></literal>
    <justification jstring="[para(5385(a,2),7779(a,1,2))].">
      <j1 rule="para" parents="5385 7779"/>
    </justification>
  </clause>

  <clause id="7789">
    <literal><![CDATA[
      K(x,K(y,z)) * (y * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(y,K(x,z)) * u = w
    ]]></literal>
    <justification jstring="[para(7779(a,1),5041(a,1,1))].">
      <j1 rule="para" parents="7779 5041"/>
    </justification>
  </clause>

  <clause id="7790">
    <literal><![CDATA[
      K(x,y) * K(y,K(z,x)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(7779(a,1),5624(a,1,2))].">
      <j1 rule="para" parents="7779 5624"/>
    </justification>
  </clause>

  <clause id="7791">
    <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(7779(a,1),5208(a,1,2))].">
      <j1 rule="para" parents="7779 5208"/>
    </justification>
  </clause>

  <clause id="7792">
    <literal><![CDATA[
      K(x,K(y,K(x,z) * u)) = K(y,K(x,u))
    ]]></literal>
    <justification jstring="[para(7266(a,1),7779(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7266 7779"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7793">
    <literal><![CDATA[
      K(x,K(y,L(z,u,K(x,w)))) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[para(7507(a,1),7779(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7507 7779"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7794">
    <literal><![CDATA[
      x * K(y,K(z,x)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(7779(a,1),7757(a,1,2))].">
      <j1 rule="para" parents="7779 7757"/>
    </justification>
  </clause>

  <clause id="7795">
    <literal><![CDATA[
      K(K(x,y),z) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(320,a,7753,a,b,7780,a),flip(a)].">
      <j1 rule="hyper" parents="320 7753 7780"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7796">
    <literal><![CDATA[
      K(K(x,y),z) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(320,a,7753,a,b,7783,a),flip(a)].">
      <j1 rule="hyper" parents="320 7753 7783"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7797">
    <literal><![CDATA[
      K(x,K(y,z)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,7780,a(flip),b,7783,a)].">
      <j1 rule="hyper" parents="58 7780 7783"/>
    </justification>
  </clause>

  <clause id="7798">
    <literal><![CDATA[
      K(x,K(y,z)) * (z * K(y,x)) = K(y,x) * z
    ]]></literal>
    <justification jstring="[para(7783(a,1),4813(a,1,1))].">
      <j1 rule="para" parents="7783 4813"/>
    </justification>
  </clause>

  <clause id="7799">
    <literal><![CDATA[
      K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,K(x,y)) = u
    ]]></literal>
    <justification jstring="[para(7783(a,1),5654(a,1))].">
      <j1 rule="para" parents="7783 5654"/>
    </justification>
  </clause>

  <clause id="7800">
    <literal><![CDATA[
      K(x,K(R(y \ 1,z,u) \ 1,w)) = K(R(K(y,x),z,u),w)
    ]]></literal>
    <justification jstring="[para(5709(a,1),7783(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5709 7783"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7801">
    <literal><![CDATA[
      x * K(K(y,z),x) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(7783(a,2),7757(a,1,2))].">
      <j1 rule="para" parents="7783 7757"/>
    </justification>
  </clause>

  <clause id="7802">
    <literal><![CDATA[
      K(x,y) * K(y,T(x,z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,7188,a,b,7784,a)].">
      <j1 rule="hyper" parents="320 7188 7784"/>
    </justification>
  </clause>

  <clause id="7803">
    <literal><![CDATA[
      K(x,K(y,x \ z)) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(320,a,7540,a(flip),b,7784,a),flip(a)].">
      <j1 rule="hyper" parents="320 7540 7784"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7804">
    <literal><![CDATA[
      K(x,K(y,z * x)) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(320,a,7539,a(flip),b,7784,a),flip(a)].">
      <j1 rule="hyper" parents="320 7539 7784"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7805">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,K(y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(119,a,7784,a,b,7761,a)].">
      <j1 rule="hyper" parents="119 7784 7761"/>
    </justification>
  </clause>

  <clause id="7806">
    <literal><![CDATA[
      x \ T(x * y,K(z,u)) = y * K(z,K(u,(x \ 1) \ y))
    ]]></literal>
    <justification jstring="[hyper(119,a,7784,a,b,6410,a),flip(a)].">
      <j1 rule="hyper" parents="119 7784 6410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7807">
    <literal><![CDATA[
      x * T(x \ y,K(z,u)) = y * K(z,K(u,x \ y))
    ]]></literal>
    <justification jstring="[hyper(119,a,7784,a,b,6111,a),flip(a)].">
      <j1 rule="hyper" parents="119 7784 6111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7808">
    <literal><![CDATA[
      K(x,K(y,z)) * z = T(z,K(x,y))
    ]]></literal>
    <justification jstring="[para(7784(a,2),4770(a,2,1)),flip(a)].">
      <j1 rule="para" parents="7784 4770"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7809">
    <literal><![CDATA[
      K(x,K(y,z)) * (z * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(z,K(x,y)) * u = w
    ]]></literal>
    <justification jstring="[para(7784(a,2),5041(a,1,1))].">
      <j1 rule="para" parents="7784 5041"/>
    </justification>
  </clause>

  <clause id="7810">
    <literal><![CDATA[
      K(x,y) * K(x,K(z,y)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(7784(a,1),5624(a,1,2))].">
      <j1 rule="para" parents="7784 5624"/>
    </justification>
  </clause>

  <clause id="7811">
    <literal><![CDATA[
      x * L(K(y,K(z,x)),u,w) = T(x,L(K(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(7784(a,2),5754(a,1,2,1))].">
      <j1 rule="para" parents="7784 5754"/>
    </justification>
  </clause>

  <clause id="7812">
    <literal><![CDATA[
      K(x,K(y,((1 / z) / (u / z)) \ 1)) * (u / z) = T(u,K(x,y)) / z
    ]]></literal>
    <justification jstring="[para(7784(a,2),5738(a,1,1))].">
      <j1 rule="para" parents="7784 5738"/>
    </justification>
  </clause>

  <clause id="7813">
    <literal><![CDATA[
      (x * K(y,K(z,u))) / K(y,z) = x / T(K(y,z),u)
    ]]></literal>
    <justification jstring="[para(7784(a,2),6342(a,1,1,2))].">
      <j1 rule="para" parents="7784 6342"/>
    </justification>
  </clause>

  <clause id="7814">
    <literal><![CDATA[
      (x * K(y,K(z,u \ x))) / u = T(x / u,K(y,z))
    ]]></literal>
    <justification jstring="[para(7784(a,2),6279(a,1,1,2))].">
      <j1 rule="para" parents="7784 6279"/>
    </justification>
  </clause>

  <clause id="7815">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) = K(z,K(x,T(y,u)))
    ]]></literal>
    <justification jstring="[para(7160(a,1),7784(a,1,2))].">
      <j1 rule="para" parents="7160 7784"/>
    </justification>
  </clause>

  <clause id="7816">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,z) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(7784(a,1),7166(a,1,1))].">
      <j1 rule="para" parents="7784 7166"/>
    </justification>
  </clause>

  <clause id="7817">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y,x) = K(y,T(x,z))
    ]]></literal>
    <justification jstring="[para(7784(a,2),7166(a,1,1))].">
      <j1 rule="para" parents="7784 7166"/>
    </justification>
  </clause>

  <clause id="7818">
    <literal><![CDATA[
      K(x,y) * K(x,K(z,y)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(7784(a,1),7167(a,1,2))].">
      <j1 rule="para" parents="7784 7167"/>
    </justification>
  </clause>

  <clause id="7819">
    <literal><![CDATA[
      K(x,K(y,z)) / y = 1 / T(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(117,a,7795,a(flip),b,4795,a(flip))].">
      <j1 rule="hyper" parents="117 7795 4795"/>
    </justification>
  </clause>

  <clause id="7820">
    <literal><![CDATA[
      K(x,K(y,z)) * (y \ u) = T(y,K(x,z)) \ u
    ]]></literal>
    <justification jstring="[para(7795(a,1),5131(a,1,1))].">
      <j1 rule="para" parents="7795 5131"/>
    </justification>
  </clause>

  <clause id="7821">
    <literal><![CDATA[
      K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,K(z,x)) = u
    ]]></literal>
    <justification jstring="[para(7795(a,1),5654(a,1))].">
      <j1 rule="para" parents="7795 5654"/>
    </justification>
  </clause>

  <clause id="7822">
    <literal><![CDATA[
      K(x,y) \ K(K(x,y),z) = T(K(x,y),z) \ 1
    ]]></literal>
    <justification jstring="[hyper(116,a,7796,a,b,4796,a(flip))].">
      <j1 rule="hyper" parents="116 7796 4796"/>
    </justification>
  </clause>

  <clause id="7823">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(x,K(y,z)) * u) = u
    ]]></literal>
    <justification jstring="[hyper(118,a,7796,a(flip),b,5142,a),flip(a)].">
      <j1 rule="hyper" parents="118 7796 5142"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7824">
    <literal><![CDATA[
      K(x,K(y,z)) \ u = K(x,K(y,z)) * u
    ]]></literal>
    <justification jstring="[para(7796(a,1),5130(a,1,1))].">
      <j1 rule="para" parents="7796 5130"/>
    </justification>
  </clause>

  <clause id="7825">
    <literal><![CDATA[
      x * (T(x,K(y,z)) \ u) = K(x,K(y,z)) * u
    ]]></literal>
    <justification jstring="[para(7796(a,1),4818(a,2,1))].">
      <j1 rule="para" parents="7796 4818"/>
    </justification>
  </clause>

  <clause id="7826">
    <literal><![CDATA[
      K(x,K(y,z)) * (x \ u) = T(x,K(y,z)) \ u
    ]]></literal>
    <justification jstring="[para(7796(a,1),5131(a,1,1))].">
      <j1 rule="para" parents="7796 5131"/>
    </justification>
  </clause>

  <clause id="7827">
    <literal><![CDATA[
      K(x,K(y,z)) * u != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) * w = u
    ]]></literal>
    <justification jstring="[para(7796(a,1),5147(a,1,1))].">
      <j1 rule="para" parents="7796 5147"/>
    </justification>
  </clause>

  <clause id="7828">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(x,K(y,z)) * u) != w
    ]]></literal>
    <literal><![CDATA[
      u = w
    ]]></literal>
    <justification jstring="[para(7796(a,1),5149(a,1,1))].">
      <j1 rule="para" parents="7796 5149"/>
    </justification>
  </clause>

  <clause id="7829">
    <literal><![CDATA[
      K(x,K(y,z)) \ u != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) * u = w
    ]]></literal>
    <justification jstring="[para(7796(a,1),5163(a,1,1))].">
      <j1 rule="para" parents="7796 5163"/>
    </justification>
  </clause>

  <clause id="7830">
    <literal><![CDATA[
      K(x,K(y,z)) * u != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) \ u = w
    ]]></literal>
    <justification jstring="[para(7796(a,1),5167(a,1,1))].">
      <j1 rule="para" parents="7796 5167"/>
    </justification>
  </clause>

  <clause id="7831">
    <literal><![CDATA[
      K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y)) = u
    ]]></literal>
    <justification jstring="[para(7796(a,1),5654(a,1))].">
      <j1 rule="para" parents="7796 5654"/>
    </justification>
  </clause>

  <clause id="7832">
    <literal><![CDATA[
      T(x,K(y,z)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(118,a,7797,a,b,5406,a)].">
      <j1 rule="hyper" parents="118 7797 5406"/>
    </justification>
  </clause>

  <clause id="7833">
    <literal><![CDATA[
      L(K(x,K(y,z)),u,w) = K(x,L(K(z,y),u,w))
    ]]></literal>
    <justification jstring="[para(7797(a,1),5752(a,1,1))].">
      <j1 rule="para" parents="7797 5752"/>
    </justification>
  </clause>

  <clause id="7834">
    <literal><![CDATA[
      K(x,K(y,((1 / z) / (u / z)) \ 1)) = K(x,(T(u,y) / z) / (u / z))
    ]]></literal>
    <justification jstring="[para(5911(a,1),7797(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5911 7797"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7835">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) = K(x,T(K(z,y),u))
    ]]></literal>
    <justification jstring="[para(7145(a,1),7797(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7145 7797"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7836">
    <literal><![CDATA[
      K(x,y) * K(z,K(x,y)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(7797(a,1),7167(a,1,2))].">
      <j1 rule="para" parents="7797 7167"/>
    </justification>
  </clause>

  <clause id="7837">
    <literal><![CDATA[
      T(T(x,y),K(z,y)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(7703,a,7832,a),flip(a)].">
      <j1 rule="hyper" parents="7703 7832"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7838">
    <literal><![CDATA[
      T(T(x * K(y,z),u),K(y,z)) = T(K(y,z) * x,u)
    ]]></literal>
    <justification jstring="[hyper(6704,a,7832,a)].">
      <j1 rule="hyper" parents="6704 7832"/>
    </justification>
  </clause>

  <clause id="7839">
    <literal><![CDATA[
      (K(x,y) * z) * K(y,x) = T(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(6551,a,7832,a)].">
      <j1 rule="hyper" parents="6551 7832"/>
    </justification>
  </clause>

  <clause id="7840">
    <literal><![CDATA[
      T(x * y,K(z,y)) = y * T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(6541,a,7832,a),flip(a)].">
      <j1 rule="hyper" parents="6541 7832"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7841">
    <literal><![CDATA[
      T(x * K(y,z),K(y,z)) = K(y,z) * x
    ]]></literal>
    <justification jstring="[hyper(6451,a,7832,a),flip(a)].">
      <j1 rule="hyper" parents="6451 7832"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7842">
    <literal><![CDATA[
      T(K(x,y) * z,K(y,x)) = z * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(6395,a,7832,a),flip(a)].">
      <j1 rule="hyper" parents="6395 7832"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7843">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(5638,a,7832,a)].">
      <j1 rule="hyper" parents="5638 7832"/>
    </justification>
  </clause>

  <clause id="7844">
    <literal><![CDATA[
      K(x,y) * (z * K(y,x)) = T(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(5289,a,7832,a)].">
      <j1 rule="hyper" parents="5289 7832"/>
    </justification>
  </clause>

  <clause id="7845">
    <literal><![CDATA[
      T(T(x,K(y,z)),u) = T(T(x,u),K(z,y))
    ]]></literal>
    <justification jstring="[hyper(434,a,7832,a)].">
      <j1 rule="hyper" parents="434 7832"/>
    </justification>
  </clause>

  <clause id="7846">
    <literal><![CDATA[
      T(x \ y,K(z,x)) = x \ T(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,7590,a(flip),b,7832,a),flip(a)].">
      <j1 rule="hyper" parents="320 7590 7832"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7847">
    <literal><![CDATA[
      K(x,y) * T(z,K(y,x)) = z * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,7832,a,b,17,a(flip))].">
      <j1 rule="hyper" parents="119 7832 17"/>
    </justification>
  </clause>

  <clause id="7848">
    <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(7832(a,1),434(a,1,1))].">
      <j1 rule="para" parents="7832 434"/>
    </justification>
  </clause>

  <clause id="7849">
    <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(7832(a,1),434(a,1))].">
      <j1 rule="para" parents="7832 434"/>
    </justification>
  </clause>

  <clause id="7850">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(7832(a,1),5632(a,1,1))].">
      <j1 rule="para" parents="7832 5632"/>
    </justification>
  </clause>

  <clause id="7851">
    <literal><![CDATA[
      T(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(u,K(y,z)) = x
    ]]></literal>
    <justification jstring="[para(7832(a,1),5638(a,1))].">
      <j1 rule="para" parents="7832 5638"/>
    </justification>
  </clause>

  <clause id="7852">
    <literal><![CDATA[
      T(x,K(y,z)) * K(y,z) = K(y,z) * x
    ]]></literal>
    <justification jstring="[para(7832(a,1),5631(a,1,1))].">
      <j1 rule="para" parents="7832 5631"/>
    </justification>
  </clause>

  <clause id="7853">
    <literal><![CDATA[
      T(K(x,y) * z,K(y,x)) != u
    ]]></literal>
    <literal><![CDATA[
      z * K(x,y) = u
    ]]></literal>
    <justification jstring="[para(7832(a,1),6395(a,1))].">
      <j1 rule="para" parents="7832 6395"/>
    </justification>
  </clause>

  <clause id="7854">
    <literal><![CDATA[
      T(x,L(K(y,z),T(z,u),w)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[para(7327(a,2),7832(a,1,2))].">
      <j1 rule="para" parents="7327 7832"/>
    </justification>
  </clause>

  <clause id="7855">
    <literal><![CDATA[
      T(T(x,K(y,z)),z) = T(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(7832(a,1),7440(a,1,1))].">
      <j1 rule="para" parents="7832 7440"/>
    </justification>
  </clause>

  <clause id="7856">
    <literal><![CDATA[
      T(T(x,K(y,z)),T(y,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(7832(a,1),7447(a,1,1))].">
      <j1 rule="para" parents="7832 7447"/>
    </justification>
  </clause>

  <clause id="7857">
    <literal><![CDATA[
      T(x * y,K(x,z)) = x * T(y,K(z,x))
    ]]></literal>
    <justification jstring="[para(7832(a,1),7592(a,2,2))].">
      <j1 rule="para" parents="7832 7592"/>
    </justification>
  </clause>

  <clause id="7858">
    <literal><![CDATA[
      T(T(x,y),K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7832(a,1),7703(a,1))].">
      <j1 rule="para" parents="7832 7703"/>
    </justification>
  </clause>

  <clause id="7859">
    <literal><![CDATA[
      T(K(x,y) \ z,K(x,y)) = z * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(6450,a,7843,a),flip(a)].">
      <j1 rule="hyper" parents="6450 7843"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7860">
    <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(803,a,7843,a)].">
      <j1 rule="hyper" parents="803 7843"/>
    </justification>
  </clause>

  <clause id="7861">
    <literal><![CDATA[
      (K(x,y) * z) / K(x,y) = T(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(681,a,7843,a),flip(a)].">
      <j1 rule="hyper" parents="681 7843"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7862">
    <literal><![CDATA[
      T(x * (y * K(x,z)),K(x,z)) = T(x,z) * y
    ]]></literal>
    <justification jstring="[hyper(35,a,7036,a,b,7843,a),flip(a)].">
      <j1 rule="hyper" parents="35 7036 7843"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7863">
    <literal><![CDATA[
      T(K(x,y),z) * z = z * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,7843,a(flip),b,4434,a)].">
      <j1 rule="hyper" parents="119 7843 4434"/>
    </justification>
  </clause>

  <clause id="7864">
    <literal><![CDATA[
      (K(x,y) * z) / K(x,y) != u
    ]]></literal>
    <literal><![CDATA[
      T(z,K(x,y)) = u
    ]]></literal>
    <justification jstring="[para(7843(a,1),331(a,1,1,2)),flip(b)].">
      <j1 rule="para" parents="7843 331"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7865">
    <literal><![CDATA[
      (x * K(y,z)) / x = T(K(y,z),x)
    ]]></literal>
    <justification jstring="[para(7843(a,1),4433(a,1,2))].">
      <j1 rule="para" parents="7843 4433"/>
    </justification>
  </clause>

  <clause id="7866">
    <literal><![CDATA[
      T(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,K(z,y)) = u
    ]]></literal>
    <justification jstring="[para(7843(a,1),5632(a,1,1))].">
      <j1 rule="para" parents="7843 5632"/>
    </justification>
  </clause>

  <clause id="7867">
    <literal><![CDATA[
      K(x,K(y,z * y)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(320,a,7797,a,b,7777,a),flip(a)].">
      <j1 rule="hyper" parents="320 7797 7777"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7868">
    <literal><![CDATA[
      K(x,K(y,z / y)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(7(a,1),7777(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7 7777"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7869">
    <literal><![CDATA[
      K(x,K(y,y * z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(5385(a,1),7777(a,1,2))].">
      <j1 rule="para" parents="5385 7777"/>
    </justification>
  </clause>

  <clause id="7870">
    <literal><![CDATA[
      K(x,K(x * y,z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,7779,a,b,7782,a),flip(a)].">
      <j1 rule="hyper" parents="320 7779 7782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7871">
    <literal><![CDATA[
      T(x,y * T(z,K(x,u))) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(7785(a,1),7396(a,1,2,2))].">
      <j1 rule="para" parents="7785 7396"/>
    </justification>
  </clause>

  <clause id="7872">
    <literal><![CDATA[
      K(x,K(y,z)) * (y * K(z,u)) = T(y * K(z,u),K(x,z))
    ]]></literal>
    <justification jstring="[para(7340(a,1),7786(a,1,1,2))].">
      <j1 rule="para" parents="7340 7786"/>
    </justification>
  </clause>

  <clause id="7873">
    <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,5172,a(flip),b,7794,a),flip(a)].">
      <j1 rule="hyper" parents="58 5172 7794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7874">
    <literal><![CDATA[
      R(x,T(K(y,z),u),u) = R(x,K(y,z),T(u,K(y,z)))
    ]]></literal>
    <justification jstring="[para(7801(a,1),6696(a,1,3)),flip(a)].">
      <j1 rule="para" parents="7801 6696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7875">
    <literal><![CDATA[
      K(x,K(y,x \ z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,7784,a,b,7803,a),flip(a)].">
      <j1 rule="hyper" parents="320 7784 7803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7876">
    <literal><![CDATA[
      K(x,K(y,z * x)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,7784,a,b,7804,a),flip(a)].">
      <j1 rule="hyper" parents="320 7784 7804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7877">
    <literal><![CDATA[
      K(x,K(y,z * x)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(320,a,7779,a,b,7804,a),flip(a)].">
      <j1 rule="hyper" parents="320 7779 7804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7878">
    <literal><![CDATA[
      T(T(K(x,y),z),z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(167,a,5565,a,b,7805,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="167 5565 7805"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7879">
    <literal><![CDATA[
      T(K(x,T(y,z)),z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(7183,a,7878,a),flip(a)].">
      <j1 rule="hyper" parents="7183 7878"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7880">
    <literal><![CDATA[
      T(K(x \ y,z),y) = K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(6291,a,7878,a),flip(a)].">
      <j1 rule="hyper" parents="6291 7878"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7881">
    <literal><![CDATA[
      T(K(x,y \ z),z) = K(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(6146,a,7878,a),flip(a)].">
      <j1 rule="hyper" parents="6146 7878"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7882">
    <literal><![CDATA[
      T(K(1 / T(x,y),z),y) = K(1 / x,z)
    ]]></literal>
    <justification jstring="[hyper(5551,a,7878,a),flip(a)].">
      <j1 rule="hyper" parents="5551 7878"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7883">
    <literal><![CDATA[
      K(x,T(T(y,z),z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,7536,a,b,7878,a)].">
      <j1 rule="hyper" parents="58 7536 7878"/>
    </justification>
  </clause>

  <clause id="7884">
    <literal><![CDATA[
      T(x,y) != K(z,u)
    ]]></literal>
    <literal><![CDATA[
      T(K(z,u),y) = x
    ]]></literal>
    <justification jstring="[para(7878(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="7878 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7885">
    <literal><![CDATA[
      L(T(K(x,y),z),u,w) * z = z * L(K(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(7878(a,1),237(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7878 237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7886">
    <literal><![CDATA[
      R(T(K(x,y),z),u,w) * z = z * R(K(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(7878(a,1),238(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7878 238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7887">
    <literal><![CDATA[
      L(T(K(x,y),z),u,w) \ (z * L(K(x,y),u,w)) = z
    ]]></literal>
    <justification jstring="[para(7878(a,1),274(a,1,2,2,1))].">
      <j1 rule="para" parents="7878 274"/>
    </justification>
  </clause>

  <clause id="7888">
    <literal><![CDATA[
      K(T(x,y),T(z,y)) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(7410,a,7879,a)].">
      <j1 rule="hyper" parents="7410 7879"/>
    </justification>
  </clause>

  <clause id="7889">
    <literal><![CDATA[
      K(x \ y,T(z,y)) = K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(6504,a,7879,a)].">
      <j1 rule="hyper" parents="6504 7879"/>
    </justification>
  </clause>

  <clause id="7890">
    <literal><![CDATA[
      K(x,T(y \ z,z)) = K(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(6146,a,7879,a),flip(a)].">
      <j1 rule="hyper" parents="6146 7879"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7891">
    <literal><![CDATA[
      K(x,T((y \ z) \ 1,y)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(5746,a,7879,a),flip(a)].">
      <j1 rule="hyper" parents="5746 7879"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7892">
    <literal><![CDATA[
      K(T(x,y) \ 1,T(z,y)) = K(x \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(5546,a,7879,a)].">
      <j1 rule="hyper" parents="5546 7879"/>
    </justification>
  </clause>

  <clause id="7893">
    <literal><![CDATA[
      (x * K(y,z)) / x = K(y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(271,a,7879,a)].">
      <j1 rule="hyper" parents="271 7879"/>
    </justification>
  </clause>

  <clause id="7895">
    <literal><![CDATA[
      K(x \ K(x,y),z) = K(x \ 1,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,6682,a(flip),b,7879,a),flip(a)].">
      <j1 rule="hyper" parents="58 6682 7879"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7896">
    <literal><![CDATA[
      K(x,T(T(T(y,z),u),z)) = K(x,T(y,u))
    ]]></literal>
    <justification jstring="[hyper(35,a,7181,a(flip),b,7879,a),flip(a)].">
      <j1 rule="hyper" parents="35 7181 7879"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7897">
    <literal><![CDATA[
      K(x,T(y,z)) * z = z * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,7879,a(flip),b,17,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 7879 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7898">
    <literal><![CDATA[
      T(x,y) != K(z,u)
    ]]></literal>
    <literal><![CDATA[
      K(z,T(u,y)) = x
    ]]></literal>
    <justification jstring="[para(7879(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="7879 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7899">
    <literal><![CDATA[
      T(K(x,y \ z),y) = K(x,z / y)
    ]]></literal>
    <justification jstring="[para(107(a,1),7879(a,1,1,2))].">
      <j1 rule="para" parents="107 7879"/>
    </justification>
  </clause>

  <clause id="7900">
    <literal><![CDATA[
      K(x,T(y,z)) \ (z * K(x,y)) = z
    ]]></literal>
    <justification jstring="[para(7879(a,1),226(a,1,2,2))].">
      <j1 rule="para" parents="7879 226"/>
    </justification>
  </clause>

  <clause id="7901">
    <literal><![CDATA[
      x * K(y,z) != u * x
    ]]></literal>
    <literal><![CDATA[
      K(y,T(z,x)) = u
    ]]></literal>
    <justification jstring="[para(7879(a,1),241(a,1,2))].">
      <j1 rule="para" parents="7879 241"/>
    </justification>
  </clause>

  <clause id="7902">
    <literal><![CDATA[
      R(K(x,T(y,z)),u,w) * z = z * R(K(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(7879(a,1),238(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7879 238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7903">
    <literal><![CDATA[
      (K(x,T(y,z * u)) * z) * u = (z * u) * R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(7879(a,1),639(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7879 639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7904">
    <literal><![CDATA[
      (K(x,T(y,z)) * u) * (u \ z) = z * R(K(x,y),u,u \ z)
    ]]></literal>
    <justification jstring="[para(7879(a,1),727(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7879 727"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7905">
    <literal><![CDATA[
      T(K(x \ y,z),x) = K(y / x,z)
    ]]></literal>
    <justification jstring="[para(7213(a,1),7879(a,1,1))].">
      <j1 rule="para" parents="7213 7879"/>
    </justification>
  </clause>

  <clause id="7906">
    <literal><![CDATA[
      T(T(x,y),T(z,y)) = K(x,z) * T(x,y)
    ]]></literal>
    <justification jstring="[para(7879(a,1),7151(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7879 7151"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7907">
    <literal><![CDATA[
      K(x \ y,T(z,x)) = K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(7718,a,7883,a)].">
      <j1 rule="hyper" parents="7718 7883"/>
    </justification>
  </clause>

  <clause id="7908">
    <literal><![CDATA[
      K((x * y) / x,z) = K(y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(7319,a,7883,a),flip(a)].">
      <j1 rule="hyper" parents="7319 7883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7909">
    <literal><![CDATA[
      T(x,T(T(y,z),z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(118,a,7883,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 7883 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7910">
    <literal><![CDATA[
      K(R(T(x,y),z,u),T(w,y)) = K(R(x,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(58,a,7212,a,b,7883,a)].">
      <j1 rule="hyper" parents="58 7212 7883"/>
    </justification>
  </clause>

  <clause id="7911">
    <literal><![CDATA[
      K(L(T(x,y),z,u),T(w,y)) = K(L(x,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(58,a,7211,a,b,7883,a)].">
      <j1 rule="hyper" parents="58 7211 7883"/>
    </justification>
  </clause>

  <clause id="7912">
    <literal><![CDATA[
      K(L(x,y,x),z) = K(x,T(T(z,u),u * x))
    ]]></literal>
    <justification jstring="[hyper(58,a,7694,a(flip),b,7883,a),flip(a)].">
      <j1 rule="hyper" parents="58 7694 7883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7913">
    <literal><![CDATA[
      K(x,T(y \ z,y)) = K(x,z / y)
    ]]></literal>
    <justification jstring="[para(107(a,1),7883(a,1,2,1))].">
      <j1 rule="para" parents="107 7883"/>
    </justification>
  </clause>

  <clause id="7914">
    <literal><![CDATA[
      K(x,(y * z) / y) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(224(a,1),7883(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="224 7883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7915">
    <literal><![CDATA[
      K(x,T(T(T(y,z),z),u)) = K(x,T(y,u))
    ]]></literal>
    <justification jstring="[para(109(a,2),7883(a,1,2))].">
      <j1 rule="para" parents="109 7883"/>
    </justification>
  </clause>

  <clause id="7916">
    <literal><![CDATA[
      K(x,y * K(z,y)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(4816(a,1),7883(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4816 7883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7917">
    <literal><![CDATA[
      K((x * y) / x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,T(z,x)) = u
    ]]></literal>
    <justification jstring="[para(7883(a,1),7319(a,1))].">
      <j1 rule="para" parents="7883 7319"/>
    </justification>
  </clause>

  <clause id="7918">
    <literal><![CDATA[
      K(x / (x / y),z) = K(y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(7394,a,7888,a),flip(a)].">
      <j1 rule="hyper" parents="7394 7888"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7919">
    <literal><![CDATA[
      x * K(T(x,y),T(z,y)) = T(x,z)
    ]]></literal>
    <justification jstring="[hyper(119,a,7888,a,b,4729,a(flip))].">
      <j1 rule="hyper" parents="119 7888 4729"/>
    </justification>
  </clause>

  <clause id="7921">
    <literal><![CDATA[
      K(x,T(y,z)) \ z = z * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,7888,a(flip),b,7170,a),flip(a)].">
      <j1 rule="hyper" parents="119 7888 7170"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7922">
    <literal><![CDATA[
      K(T(T(x,y),z),T(u,y)) = K(T(x,z),u)
    ]]></literal>
    <justification jstring="[para(18(a,1),7888(a,1,1))].">
      <j1 rule="para" parents="18 7888"/>
    </justification>
  </clause>

  <clause id="7923">
    <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),7888(a,1,2))].">
      <j1 rule="para" parents="20 7888"/>
    </justification>
  </clause>

  <clause id="7924">
    <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),7888(a,1,2))].">
      <j1 rule="para" parents="22 7888"/>
    </justification>
  </clause>

  <clause id="7925">
    <literal><![CDATA[
      K(T(x,y),y \ z) = K(x,z / y)
    ]]></literal>
    <justification jstring="[para(107(a,1),7888(a,1,2))].">
      <j1 rule="para" parents="107 7888"/>
    </justification>
  </clause>

  <clause id="7926">
    <literal><![CDATA[
      K(x,(y * z) / y) = K(T(x,y),z)
    ]]></literal>
    <justification jstring="[para(224(a,1),7888(a,1,2)),flip(a)].">
      <j1 rule="para" parents="224 7888"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7927">
    <literal><![CDATA[
      K(T(x,y),R(T(z,y * u),y,u)) = K(x,(y * u) \ ((y * z) * u))
    ]]></literal>
    <justification jstring="[para(1096(a,1),7888(a,1,2))].">
      <j1 rule="para" parents="1096 7888"/>
    </justification>
  </clause>

  <clause id="7928">
    <literal><![CDATA[
      K(T(x,y \ z),y) = K(x,z / (z / y))
    ]]></literal>
    <justification jstring="[para(4346(a,1),7888(a,1,2))].">
      <j1 rule="para" parents="4346 7888"/>
    </justification>
  </clause>

  <clause id="7929">
    <literal><![CDATA[
      L(x,K(y,z),T(y,u)) = x
    ]]></literal>
    <justification jstring="[para(7888(a,1),4515(a,1,2))].">
      <j1 rule="para" parents="7888 4515"/>
    </justification>
  </clause>

  <clause id="7930">
    <literal><![CDATA[
      K(x * K(y,x),z) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(4816(a,1),7888(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4816 7888"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7931">
    <literal><![CDATA[
      K(x,y * K(z,y)) = K(T(x,z),y)
    ]]></literal>
    <justification jstring="[para(4816(a,1),7888(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4816 7888"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7932">
    <literal><![CDATA[
      T(x * K(T(y,z),x),z) = K(y,x) * T(x,z)
    ]]></literal>
    <justification jstring="[para(7888(a,1),5201(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7888 5201"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7933">
    <literal><![CDATA[
      T(T(x,y),T(z,y)) \ x = K(z,x) * K(y,x)
    ]]></literal>
    <justification jstring="[para(7888(a,1),5228(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7888 5228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7934">
    <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(7888(a,1),6045(a,1,1))].">
      <j1 rule="para" parents="7888 6045"/>
    </justification>
  </clause>

  <clause id="7935">
    <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(7888(a,1),6955(a,1,1))].">
      <j1 rule="para" parents="7888 6955"/>
    </justification>
  </clause>

  <clause id="7936">
    <literal><![CDATA[
      K(T(x,y),z) * y = y * K(x,z)
    ]]></literal>
    <justification jstring="[para(7888(a,1),7179(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7888 7179"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7937">
    <literal><![CDATA[
      K(x,T(y,z)) * (z * K(y,x)) = z
    ]]></literal>
    <justification jstring="[para(7888(a,1),7291(a,1,2,2))].">
      <j1 rule="para" parents="7888 7291"/>
    </justification>
  </clause>

  <clause id="7938">
    <literal><![CDATA[
      K(x / (x / y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,T(z,x)) = u
    ]]></literal>
    <justification jstring="[para(7888(a,1),7394(a,1))].">
      <j1 rule="para" parents="7888 7394"/>
    </justification>
  </clause>

  <clause id="7939">
    <literal><![CDATA[
      L(x,K(y / z,u),z \ y) = x
    ]]></literal>
    <justification jstring="[para(107(a,1),7929(a,1,3))].">
      <j1 rule="para" parents="107 7929"/>
    </justification>
  </clause>

  <clause id="7940">
    <literal><![CDATA[
      K(x,T(y,z)) * (z * x) = z * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,7909,a(flip),b,7662,a),flip(a)].">
      <j1 rule="hyper" parents="119 7909 7662"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7941">
    <literal><![CDATA[
      T(T(x,y),T(z,y)) = K(x,y) * T(x,z)
    ]]></literal>
    <justification jstring="[hyper(119,a,7909,a(flip),b,7547,a),flip(a)].">
      <j1 rule="hyper" parents="119 7909 7547"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7942">
    <literal><![CDATA[
      T(x,T(y \ z,y)) = T(x,z / y)
    ]]></literal>
    <justification jstring="[para(107(a,1),7909(a,1,2,1))].">
      <j1 rule="para" parents="107 7909"/>
    </justification>
  </clause>

  <clause id="7943">
    <literal><![CDATA[
      T(x,(y * z) / y) = T(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(224(a,1),7909(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="224 7909"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7944">
    <literal><![CDATA[
      T(x,T(T(y \ z,u),y)) = T(x,T(z / y,u))
    ]]></literal>
    <justification jstring="[para(246(a,1),7909(a,1,2,1))].">
      <j1 rule="para" parents="246 7909"/>
    </justification>
  </clause>

  <clause id="7945">
    <literal><![CDATA[
      T(x,y * K(z,y)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(4816(a,1),7909(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4816 7909"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7946">
    <literal><![CDATA[
      L(x,K(y \ 1,z),u \ (y \ u)) = x
    ]]></literal>
    <justification jstring="[para(5434(a,1),7939(a,1,2))].">
      <j1 rule="para" parents="5434 7939"/>
    </justification>
  </clause>

  <clause id="7947">
    <literal><![CDATA[
      T(x,K(y,z)) * (x \ z) = T(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(4784,a,7808,a)].">
      <j1 rule="hyper" parents="4784 7808"/>
    </justification>
  </clause>

  <clause id="7948">
    <literal><![CDATA[
      T(T(x,y / z),K(y,y / z)) = T(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(320,a,7092,a(flip),b,7837,a),flip(a)].">
      <j1 rule="hyper" parents="320 7092 7837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7949">
    <literal><![CDATA[
      T(x,K(y,z)) * z = z * T(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(119,a,7837,a(flip),b,108,a),flip(a)].">
      <j1 rule="hyper" parents="119 7837 108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7950">
    <literal><![CDATA[
      T(x,T(y,z)) * K(y,z) = K(y,z) * T(x,y)
    ]]></literal>
    <justification jstring="[para(7837(a,1),5631(a,1,1))].">
      <j1 rule="para" parents="7837 5631"/>
    </justification>
  </clause>

  <clause id="7951">
    <literal><![CDATA[
      T(T(x,y) * z,K(z,y)) = T(x,T(y,z)) * z
    ]]></literal>
    <justification jstring="[para(7837(a,1),7640(a,2,1))].">
      <j1 rule="para" parents="7837 7640"/>
    </justification>
  </clause>

  <clause id="7952">
    <literal><![CDATA[
      T(T(x,y) \ z,K(x,y)) = T(z / T(x,y),x)
    ]]></literal>
    <justification jstring="[hyper(678,a,7856,a)].">
      <j1 rule="hyper" parents="678 7856"/>
    </justification>
  </clause>

  <clause id="7953">
    <literal><![CDATA[
      T(x,K(y,z)) * T(y,z) = T(y,z) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,7856,a(flip),b,17,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 7856 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7954">
    <literal><![CDATA[
      T(x,T(y,z)) != T(u,y)
    ]]></literal>
    <literal><![CDATA[
      T(u,K(y,z)) = x
    ]]></literal>
    <justification jstring="[para(7856(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="7856 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7955">
    <literal><![CDATA[
      K(x \ y,z) * y = y * K(y / x,z)
    ]]></literal>
    <justification jstring="[para(6268(a,1),7863(a,1,1))].">
      <j1 rule="para" parents="6268 7863"/>
    </justification>
  </clause>

  <clause id="7956">
    <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(7865(a,1),4900(a,1,2,1))].">
      <j1 rule="para" parents="7865 4900"/>
    </justification>
  </clause>

  <clause id="7957">
    <literal><![CDATA[
      T(x,K(y,z * y)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(118,a,7867,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 7867 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7958">
    <literal><![CDATA[
      T(x,K(y,z / y)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(118,a,7868,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 7868 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7959">
    <literal><![CDATA[
      K(x,K(y,z \ 1)) = K(x,K(y,z \ y))
    ]]></literal>
    <justification jstring="[para(4482(a,1),7868(a,1,2))].">
      <j1 rule="para" parents="4482 7868"/>
    </justification>
  </clause>

  <clause id="7960">
    <literal><![CDATA[
      K(x,K(y,y \ z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(4912(a,1),7868(a,1,2))].">
      <j1 rule="para" parents="4912 7868"/>
    </justification>
  </clause>

  <clause id="7961">
    <literal><![CDATA[
      K(x,K(y,y * z)) = K(y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(320,a,7784,a,b,7869,a),flip(a)].">
      <j1 rule="hyper" parents="320 7784 7869"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7962">
    <literal><![CDATA[
      K(x,K(y / z,z)) = K(x,K(y / z,y))
    ]]></literal>
    <justification jstring="[para(7(a,1),7869(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7 7869"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7963">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y * z,y) = K(y * z,T(y,x))
    ]]></literal>
    <justification jstring="[para(7869(a,1),7166(a,1,1))].">
      <j1 rule="para" parents="7869 7166"/>
    </justification>
  </clause>

  <clause id="7964">
    <literal><![CDATA[
      K(x,K(y,x * z)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,7797,a,b,7870,a)].">
      <j1 rule="hyper" parents="58 7797 7870"/>
    </justification>
  </clause>

  <clause id="7965">
    <literal><![CDATA[
      K(x,K(x \ y,z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(5(a,1),7870(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 7870"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7966">
    <literal><![CDATA[
      T(x,K(y,x \ z)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(118,a,7875,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 7875 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7967">
    <literal><![CDATA[
      K(x,K(y,x * z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(4(a,1),7875(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 7875"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7968">
    <literal><![CDATA[
      T(x,K(y,z * x)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(118,a,7876,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 7876 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7969">
    <literal><![CDATA[
      K(x,K(y * x,z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,7797,a,b,7877,a)].">
      <j1 rule="hyper" parents="58 7797 7877"/>
    </justification>
  </clause>

  <clause id="7970">
    <literal><![CDATA[
      K(x / y,x / z) = K(y \ x,z \ x)
    ]]></literal>
    <justification jstring="[hyper(6485,a,7880,a),flip(a)].">
      <j1 rule="hyper" parents="6485 7880"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7971">
    <literal><![CDATA[
      K(x \ (y * z),T(y,z)) = K((y * z) / x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,6244,a(flip),b,7880,a)].">
      <j1 rule="hyper" parents="58 6244 7880"/>
    </justification>
  </clause>

  <clause id="7972">
    <literal><![CDATA[
      K(x,T(y \ (x * z),z)) = K(x,(x * z) / y)
    ]]></literal>
    <justification jstring="[hyper(7725,a,7881,a)].">
      <j1 rule="hyper" parents="7725 7881"/>
    </justification>
  </clause>

  <clause id="7973">
    <literal><![CDATA[
      K(x,T(y \ (z * x),z)) = K(x,(z * x) / y)
    ]]></literal>
    <justification jstring="[hyper(7715,a,7881,a)].">
      <j1 rule="hyper" parents="7715 7881"/>
    </justification>
  </clause>

  <clause id="7975">
    <literal><![CDATA[
      x * T(x \ y,T(z,y)) = y * K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(119,a,7889,a(flip),b,6111,a),flip(a)].">
      <j1 rule="hyper" parents="119 7889 6111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7977">
    <literal><![CDATA[
      K(x \ (K(y,z) * u),T(y,u)) = K((K(y,z) * u) / x,y)
    ]]></literal>
    <justification jstring="[para(7265(a,1),7889(a,1,2))].">
      <j1 rule="para" parents="7265 7889"/>
    </justification>
  </clause>

  <clause id="7978">
    <literal><![CDATA[
      K(x,y \ z) * (z * K(z / y,x)) = z
    ]]></literal>
    <justification jstring="[para(7889(a,1),7291(a,1,2,2))].">
      <j1 rule="para" parents="7889 7291"/>
    </justification>
  </clause>

  <clause id="7980">
    <literal><![CDATA[
      T(x,T(y \ z,z)) = T(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(118,a,7890,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 7890 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7981">
    <literal><![CDATA[
      K(x,y / (y / z)) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(75(a,1),7890(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="75 7890"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7982">
    <literal><![CDATA[
      T(K(x,T(y,z)),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(7893(a,1),292(a,1,1)),flip(b)].">
      <j1 rule="para" parents="7893 292"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7983">
    <literal><![CDATA[
      K(x,T(y,z)) * z != z * u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(7893(a,1),126(a,1,1))].">
      <j1 rule="para" parents="7893 126"/>
    </justification>
  </clause>

  <clause id="7984">
    <literal><![CDATA[
      R(T(K(x,T(y,z)),z * u),z,u) = (z * u) \ ((z * K(x,y)) * u)
    ]]></literal>
    <justification jstring="[para(7893(a,1),935(a,1,1,1))].">
      <j1 rule="para" parents="7893 935"/>
    </justification>
  </clause>

  <clause id="7985">
    <literal><![CDATA[
      (x * (y * K(z,u))) / (x * y) = L(K(z,T(u,x * y)),y,x)
    ]]></literal>
    <justification jstring="[para(7893(a,1),850(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7893 850"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7986">
    <literal><![CDATA[
      K(x,T(y \ 1,z)) = K(x,y \ K(y,z))
    ]]></literal>
    <justification jstring="[hyper(30,a,5913,a,b,7897,a),flip(a)].">
      <j1 rule="hyper" parents="30 5913 7897"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7987">
    <literal><![CDATA[
      T(x,T(y,z)) * z = x * (z * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(119,a,7897,a(flip),b,4777,a),flip(a)].">
      <j1 rule="hyper" parents="119 7897 4777"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7988">
    <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),7897(a,1,1,2))].">
      <j1 rule="para" parents="20 7897"/>
    </justification>
  </clause>

  <clause id="7989">
    <literal><![CDATA[
      K(x,y \ z) * y = y * K(x,z / y)
    ]]></literal>
    <justification jstring="[para(107(a,1),7897(a,1,1,2))].">
      <j1 rule="para" parents="107 7897"/>
    </justification>
  </clause>

  <clause id="7990">
    <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(7897(a,1),102(a,2,2))].">
      <j1 rule="para" parents="7897 102"/>
    </justification>
  </clause>

  <clause id="7991">
    <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(7897(a,1),5162(a,1,1,3)),flip(a)].">
      <j1 rule="para" parents="7897 5162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7992">
    <literal><![CDATA[
      T(K(x,y),z) * (z / y) = (z / y) * K(x,y)
    ]]></literal>
    <justification jstring="[para(6217(a,1),7897(a,1,1))].">
      <j1 rule="para" parents="6217 7897"/>
    </justification>
  </clause>

  <clause id="7993">
    <literal><![CDATA[
      K(x * K(y,z),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(7897(a,1),7357(a,1,1))].">
      <j1 rule="para" parents="7897 7357"/>
    </justification>
  </clause>

  <clause id="7994">
    <literal><![CDATA[
      K(x,(y * K(x,z)) * u) = K(x,y * u)
    ]]></literal>
    <justification jstring="[para(7897(a,1),7407(a,1,2,1))].">
      <j1 rule="para" parents="7897 7407"/>
    </justification>
  </clause>

  <clause id="7995">
    <literal><![CDATA[
      K(x,T(y * K(x,z),u)) = K(x,T(y,u))
    ]]></literal>
    <justification jstring="[para(7897(a,1),7551(a,1,2,1))].">
      <j1 rule="para" parents="7897 7551"/>
    </justification>
  </clause>

  <clause id="7997">
    <literal><![CDATA[
      x / (x * K(y,z)) = K(z,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(117,a,7900,a(flip),b,7224,a(flip))].">
      <j1 rule="hyper" parents="117 7900 7224"/>
    </justification>
  </clause>

  <clause id="7998">
    <literal><![CDATA[
      (x \ y) * K(y / x,z) = T(x \ y,T(z,x))
    ]]></literal>
    <justification jstring="[para(7905(a,1),7180(a,1,2))].">
      <j1 rule="para" parents="7905 7180"/>
    </justification>
  </clause>

  <clause id="7999">
    <literal><![CDATA[
      K(x / ((y * z) \ y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(((y * z) \ y) \ x,z) = u
    ]]></literal>
    <justification jstring="[para(7905(a,1),7398(a,1))].">
      <j1 rule="para" parents="7905 7398"/>
    </justification>
  </clause>

  <clause id="8000">
    <literal><![CDATA[
      K((x \ y) \ 1,T(z,y)) = K(x / y,z)
    ]]></literal>
    <justification jstring="[hyper(6413,a,7907,a)].">
      <j1 rule="hyper" parents="6413 7907"/>
    </justification>
  </clause>

  <clause id="8001">
    <literal><![CDATA[
      x * T(x \ y,T(z,x)) = y * K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(119,a,7907,a(flip),b,6111,a),flip(a)].">
      <j1 rule="hyper" parents="119 7907 6111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8002">
    <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),7907(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 7907"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8003">
    <literal><![CDATA[
      K(x \ y,T(z,x)) / (x \ y) = (1 / (x \ y)) * K(y / x,z)
    ]]></literal>
    <justification jstring="[para(7907(a,1),6222(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7907 6222"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8004">
    <literal><![CDATA[
      K((x * K(y,z)) \ u,T(y,x)) = K(u / (x * K(y,z)),y)
    ]]></literal>
    <justification jstring="[para(7122(a,1),7907(a,1,2))].">
      <j1 rule="para" parents="7122 7907"/>
    </justification>
  </clause>

  <clause id="8005">
    <literal><![CDATA[
      K(x \ T(x * y,y),z) = K(y,T(z,x * y))
    ]]></literal>
    <justification jstring="[para(4129(a,1),7908(a,1,1))].">
      <j1 rule="para" parents="4129 7908"/>
    </justification>
  </clause>

  <clause id="8006">
    <literal><![CDATA[
      x \ (T((y * x) / y,z) * u) = K(y,x) * (K(x,T(z,y)) * u)
    ]]></literal>
    <justification jstring="[para(7908(a,1),5416(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7908 5416"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8007">
    <literal><![CDATA[
      K(x,T(T(y,z),z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(7908(a,1),7319(a,1))].">
      <j1 rule="para" parents="7908 7319"/>
    </justification>
  </clause>

  <clause id="8008">
    <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),7913(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 7913"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8009">
    <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),7913(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="13 7913"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8010">
    <literal><![CDATA[
      K(x,T((y * z) \ (y * u),z)) = K(x,L(u / z,z,y))
    ]]></literal>
    <justification jstring="[para(861(a,1),7914(a,1,2)),flip(a)].">
      <j1 rule="para" parents="861 7914"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8011">
    <literal><![CDATA[
      K(x,L((y \ z) / u,u,y)) = K(x,T((y * u) \ z,u))
    ]]></literal>
    <justification jstring="[para(862(a,2),7914(a,1,2))].">
      <j1 rule="para" parents="862 7914"/>
    </justification>
  </clause>

  <clause id="8012">
    <literal><![CDATA[
      K(x,T(L(y,z,u),w / y)) = K(x,L(w / (w / y),z,u))
    ]]></literal>
    <justification jstring="[para(858(a,1),7914(a,1,2)),flip(a)].">
      <j1 rule="para" parents="858 7914"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8013">
    <literal><![CDATA[
      K((x * y) / ((x / z) * y),u) = R(K(z,T(u,x)),x,y)
    ]]></literal>
    <justification jstring="[para(7918(a,1),6763(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7918 6763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8014">
    <literal><![CDATA[
      K(T(x / (x / y),z),u) = K(T(y,z),T(u,x))
    ]]></literal>
    <justification jstring="[para(7672(a,1),7918(a,1,1))].">
      <j1 rule="para" parents="7672 7918"/>
    </justification>
  </clause>

  <clause id="8015">
    <literal><![CDATA[
      T(x,(y * z) / y) = x * K(T(x,y),z)
    ]]></literal>
    <justification jstring="[para(224(a,1),7919(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="224 7919"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8016">
    <literal><![CDATA[
      T(x,y \ K(z,y \ 1)) = x * K(T(x,z),y \ 1)
    ]]></literal>
    <justification jstring="[para(4880(a,1),7919(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4880 7919"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8017">
    <literal><![CDATA[
      K(T(x,y),(y * K(z,x)) \ u) = K(x,u / (y * K(z,x)))
    ]]></literal>
    <justification jstring="[para(7132(a,1),7925(a,1,1))].">
      <j1 rule="para" parents="7132 7925"/>
    </justification>
  </clause>

  <clause id="8018">
    <literal><![CDATA[
      ((x * ((y * z) / y)) / x) / ((x * z) / x) = K(T(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(58,a,4891,a,b,7926,a)].">
      <j1 rule="hyper" parents="58 4891 7926"/>
    </justification>
  </clause>

  <clause id="8019">
    <literal><![CDATA[
      K(x,T(y,L(z,u,x))) = K(x * K(z,x),y)
    ]]></literal>
    <justification jstring="[para(7058(a,1),7930(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7058 7930"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8020">
    <literal><![CDATA[
      K(x,T(y,K(L(x,z,u),w) * v5)) = K(x * K(v5,x),y)
    ]]></literal>
    <justification jstring="[para(7432(a,1),7930(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7432 7930"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8021">
    <literal><![CDATA[
      T(x,T(y,z * K(u,z))) = T(x,y * K(T(y,u),z))
    ]]></literal>
    <justification jstring="[para(7931(a,1),5191(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7931 5191"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8022">
    <literal><![CDATA[
      x / (K(T(y,z),x) * K(x * K(z,x),z)) = T(x * K(z,x),y)
    ]]></literal>
    <justification jstring="[para(7931(a,1),5418(a,1,2,1))].">
      <j1 rule="para" parents="7931 5418"/>
    </justification>
  </clause>

  <clause id="8023">
    <literal><![CDATA[
      K(x,y * K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7931(a,2),7704(a,1))].">
      <j1 rule="para" parents="7931 7704"/>
    </justification>
  </clause>

  <clause id="8024">
    <literal><![CDATA[
      K(K(x,y) * z,u) * z = z * K(z * K(x,y),u)
    ]]></literal>
    <justification jstring="[para(7259(a,1),7936(a,1,1))].">
      <j1 rule="para" parents="7259 7936"/>
    </justification>
  </clause>

  <clause id="8025">
    <literal><![CDATA[
      T(x,T(y * z,u) / y) = T(x,y \ T(z * y,u))
    ]]></literal>
    <justification jstring="[para(4602(a,1),7942(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4602 7942"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8026">
    <literal><![CDATA[
      T(x,R((y * z) / y,u,w)) = T(x,T(R(z,u,w),y))
    ]]></literal>
    <justification jstring="[para(854(a,2),7943(a,1,2))].">
      <j1 rule="para" parents="854 7943"/>
    </justification>
  </clause>

  <clause id="8027">
    <literal><![CDATA[
      T(x,T(T(y \ (z \ y),T(z,u)),y)) = T(x,(((z \ 1) \ 1) \ y) / y)
    ]]></literal>
    <justification jstring="[para(5910(a,1),7943(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5910 7943"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8028">
    <literal><![CDATA[
      L(x,y,x) \ (T(x * y,T(x,y)) \ z) = ((y * x) / y) \ ((x * y) \ z)
    ]]></literal>
    <justification jstring="[para(7943(a,1),4561(a,1,2,1))].">
      <j1 rule="para" parents="7943 4561"/>
    </justification>
  </clause>

  <clause id="8029">
    <literal><![CDATA[
      T(x,(y \ 1) \ K(z,y)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,3774,a,b,7945,a)].">
      <j1 rule="hyper" parents="58 3774 7945"/>
    </justification>
  </clause>

  <clause id="8030">
    <literal><![CDATA[
      T(x,K(y,1 / z) / z) = T(x,T(1 / z,y))
    ]]></literal>
    <justification jstring="[para(2356(a,1),7945(a,1,2))].">
      <j1 rule="para" parents="2356 7945"/>
    </justification>
  </clause>

  <clause id="8031">
    <literal><![CDATA[
      T(x,K(y,y * z)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[para(5385(a,1),7957(a,1,2))].">
      <j1 rule="para" parents="5385 7957"/>
    </justification>
  </clause>

  <clause id="8032">
    <literal><![CDATA[
      T(x,K(y,y \ z)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(4912(a,1),7958(a,1,2))].">
      <j1 rule="para" parents="4912 7958"/>
    </justification>
  </clause>

  <clause id="8033">
    <literal><![CDATA[
      K(x,K(y,z * y)) = K(y,K(x,x * z))
    ]]></literal>
    <justification jstring="[hyper(320,a,7867,a,b,7961,a)].">
      <j1 rule="hyper" parents="320 7867 7961"/>
    </justification>
  </clause>

  <clause id="8034">
    <literal><![CDATA[
      T(x,K(y,x * z)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(118,a,7964,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 7964 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8035">
    <literal><![CDATA[
      T(x,K(y,z / x)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(7(a,1),7968(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7 7968"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8036">
    <literal><![CDATA[
      T(x / y,T(z \ x,y)) = T(x / y,x / z)
    ]]></literal>
    <justification jstring="[hyper(58,a,7379,a,b,7980,a)].">
      <j1 rule="hyper" parents="58 7379 7980"/>
    </justification>
  </clause>

  <clause id="8038">
    <literal><![CDATA[
      K(x,x \ y) * K(z,T(x,y)) = T(y / (y / x),z) \ x
    ]]></literal>
    <justification jstring="[para(7981(a,1),6876(a,1,2))].">
      <j1 rule="para" parents="7981 6876"/>
    </justification>
  </clause>

  <clause id="8039">
    <literal><![CDATA[
      (x * K(y,T(z,u))) * K(z,z \ u) = (x / T(u / (u / z),y)) * z
    ]]></literal>
    <justification jstring="[para(7981(a,1),6540(a,1,1,2))].">
      <j1 rule="para" parents="7981 6540"/>
    </justification>
  </clause>

  <clause id="8040">
    <literal><![CDATA[
      K(x,y / (y / z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(T(x,y),z) = u
    ]]></literal>
    <justification jstring="[para(7981(a,2),7310(a,1))].">
      <j1 rule="para" parents="7981 7310"/>
    </justification>
  </clause>

  <clause id="8041">
    <literal><![CDATA[
      T(T(x,K(y,z)),z * y) = T(x,T(z * y,z))
    ]]></literal>
    <justification jstring="[para(8031(a,1),7855(a,1,1))].">
      <j1 rule="para" parents="8031 7855"/>
    </justification>
  </clause>

  <clause id="8042">
    <literal><![CDATA[
      T(x * K(y \ z,y),K(y,z)) = K(y \ z,y) * x
    ]]></literal>
    <justification jstring="[hyper(6451,a,8032,a),flip(a)].">
      <j1 rule="hyper" parents="6451 8032"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8043">
    <literal><![CDATA[
      T(T(x,K(y,z)),x * y) = T(x,T(x * y,z))
    ]]></literal>
    <justification jstring="[para(8034(a,1),7855(a,1,1))].">
      <j1 rule="para" parents="8034 7855"/>
    </justification>
  </clause>

  <clause id="8044">
    <literal><![CDATA[
      T(x,K(y,z / x)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(320,a,7832,a,b,8035,a),flip(a)].">
      <j1 rule="hyper" parents="320 7832 8035"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8045">
    <literal><![CDATA[
      K(K(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,K(x,y)) = u
    ]]></literal>
    <justification jstring="[para(7783(a,2),7774(a,1))].">
      <j1 rule="para" parents="7783 7774"/>
    </justification>
  </clause>

  <clause id="8046">
    <literal><![CDATA[
      K(K(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,K(z,x)) = u
    ]]></literal>
    <justification jstring="[para(7795(a,2),7774(a,1))].">
      <j1 rule="para" parents="7795 7774"/>
    </justification>
  </clause>

  <clause id="8047">
    <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(7145(a,1),7831(a,1,2))].">
      <j1 rule="para" parents="7145 7831"/>
    </justification>
  </clause>

  <clause id="8048">
    <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(7160(a,1),7831(a,1,2))].">
      <j1 rule="para" parents="7160 7831"/>
    </justification>
  </clause>

  <clause id="8049">
    <literal><![CDATA[
      K(x,K(y,z * y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y)) = u
    ]]></literal>
    <justification jstring="[para(7777(a,2),7831(a,1))].">
      <j1 rule="para" parents="7777 7831"/>
    </justification>
  </clause>

  <clause id="8050">
    <literal><![CDATA[
      T(x,K(y,z / x)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8044(a,2),7866(a,1))].">
      <j1 rule="para" parents="8044 7866"/>
    </justification>
  </clause>

  <clause id="8051">
    <literal><![CDATA[
      L(x,K(y \ 1,z),u \ (y \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(7946(a,1),45(a,2))].">
      <j1 rule="para" parents="7946 45"/>
    </justification>
  </clause>

  <clause id="8052">
    <literal><![CDATA[
      T(K(x,y \ z),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(107(a,1),7982(a,1,1,2))].">
      <j1 rule="para" parents="107 7982"/>
    </justification>
  </clause>

  <clause id="8053">
    <literal><![CDATA[
      K(x \ y,T(z,y / x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,z) = u
    ]]></literal>
    <justification jstring="[para(3346(a,1),7982(a,1))].">
      <j1 rule="para" parents="3346 7982"/>
    </justification>
  </clause>

  <clause id="8054">
    <literal><![CDATA[
      K(T(x,y) \ 1,T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ 1,z) = u
    ]]></literal>
    <justification jstring="[para(5544(a,2),7982(a,1))].">
      <j1 rule="para" parents="5544 7982"/>
    </justification>
  </clause>

  <clause id="8055">
    <literal><![CDATA[
      K(x \ y,T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y / x,z) = u
    ]]></literal>
    <justification jstring="[para(6268(a,1),7982(a,1))].">
      <j1 rule="para" parents="6268 7982"/>
    </justification>
  </clause>

  <clause id="8056">
    <literal><![CDATA[
      K(T(x,y),T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) = u
    ]]></literal>
    <justification jstring="[para(7145(a,2),7982(a,1))].">
      <j1 rule="para" parents="7145 7982"/>
    </justification>
  </clause>

  <clause id="8057">
    <literal><![CDATA[
      T(K(x \ y,z),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(y / x,z) = u
    ]]></literal>
    <justification jstring="[para(7171(a,1),7982(a,1,1))].">
      <j1 rule="para" parents="7171 7982"/>
    </justification>
  </clause>

  <clause id="8058">
    <literal><![CDATA[
      T(K(x \ y,z),x) != u
    ]]></literal>
    <literal><![CDATA[
      K(y / x,z) = u
    ]]></literal>
    <justification jstring="[para(7213(a,1),7982(a,1,1))].">
      <j1 rule="para" parents="7213 7982"/>
    </justification>
  </clause>

  <clause id="8059">
    <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(7879(a,1),7982(a,1,1,2))].">
      <j1 rule="para" parents="7879 7982"/>
    </justification>
  </clause>

  <clause id="8060">
    <literal><![CDATA[
      K(x,T(y \ z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(107(a,1),8007(a,1,2,1))].">
      <j1 rule="para" parents="107 8007"/>
    </justification>
  </clause>

  <clause id="8061">
    <literal><![CDATA[
      K(x \ y,T(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y / x,z) = u
    ]]></literal>
    <justification jstring="[para(7213(a,1),8007(a,1))].">
      <j1 rule="para" parents="7213 8007"/>
    </justification>
  </clause>

  <clause id="8062">
    <literal><![CDATA[
      K(x,T(y,K(z,z \ x))) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(7222(a,1),8007(a,1))].">
      <j1 rule="para" parents="7222 8007"/>
    </justification>
  </clause>

  <clause id="8063">
    <literal><![CDATA[
      K(x,T(y,R(T(x,z),u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(7216(a,1),8007(a,1))].">
      <j1 rule="para" parents="7216 8007"/>
    </justification>
  </clause>

  <clause id="8064">
    <literal><![CDATA[
      K(x \ y,T(z,y \ x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,z) = u
    ]]></literal>
    <justification jstring="[para(7302(a,1),8007(a,1))].">
      <j1 rule="para" parents="7302 8007"/>
    </justification>
  </clause>

  <clause id="8065">
    <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(7211(a,2),8007(a,1))].">
      <j1 rule="para" parents="7211 8007"/>
    </justification>
  </clause>

  <clause id="8066">
    <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),8056(a,1,2))].">
      <j1 rule="para" parents="18 8056"/>
    </justification>
  </clause>

  <clause id="8067">
    <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),8056(a,1,2))].">
      <j1 rule="para" parents="22 8056"/>
    </justification>
  </clause>

  <clause id="8068">
    <literal><![CDATA[
      K(T(x,y),y \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(107(a,1),8056(a,1,2))].">
      <j1 rule="para" parents="107 8056"/>
    </justification>
  </clause>

  <clause id="8069">
    <literal><![CDATA[
      K(x,T(y,z)) * K(y,x) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(2009,a,7754,a)].">
      <j1 rule="hyper" parents="2009 7754"/>
    </justification>
  </clause>

  <clause id="8070">
    <literal><![CDATA[
      K(x,K(y,z)) != 1
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(7754(a,1),4984(a,1)),flip(b)].">
      <j1 rule="para" parents="7754 4984"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8071">
    <literal><![CDATA[
      K(x,y) * K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7754(a,1),5148(a,1,2)),flip(b)].">
      <j1 rule="para" parents="7754 5148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8072">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) \ K(y,x) = T(K(y,x),T(z,y \ u))
    ]]></literal>
    <justification jstring="[para(7314(a,1),7759(a,1,1,2))].">
      <j1 rule="para" parents="7314 7759"/>
    </justification>
  </clause>

  <clause id="8073">
    <literal><![CDATA[
      T(K(x,y),K(z,y) \ u) = K(x,y) * K(x,K(y,u))
    ]]></literal>
    <justification jstring="[para(7276(a,1),7763(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7276 7763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8074">
    <literal><![CDATA[
      T(K(x,y),T(z,K(y,u))) = K(x,K(y,z)) * K(x,y)
    ]]></literal>
    <justification jstring="[para(7172(a,1),7764(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7172 7764"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8075">
    <literal><![CDATA[
      K(x,T(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * K(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7765(a,1),5640(a,1))].">
      <j1 rule="para" parents="7765 5640"/>
    </justification>
  </clause>

  <clause id="8076">
    <literal><![CDATA[
      K(x,T(y,z)) != K(x,y) * u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7765(a,1),5649(a,1))].">
      <j1 rule="para" parents="7765 5649"/>
    </justification>
  </clause>

  <clause id="8077">
    <literal><![CDATA[
      K(x,T(y,z)) \ K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = u
    ]]></literal>
    <justification jstring="[para(7765(a,1),6345(a,1,1))].">
      <j1 rule="para" parents="7765 6345"/>
    </justification>
  </clause>

  <clause id="8078">
    <literal><![CDATA[
      K(x,K(y,R(T(x,z),u,w))) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,7216,a(flip),b,7766,a),flip(a)].">
      <j1 rule="hyper" parents="115 7216 7766"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8079">
    <literal><![CDATA[
      K(K(x,y) * z,K(x,u)) = K(x,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,7780,a(flip),b,7776,a),flip(a)].">
      <j1 rule="hyper" parents="320 7780 7776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8080">
    <literal><![CDATA[
      K(K(x,y) * z,K(x,u)) = K(z,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,7755,a(flip),b,7776,a),flip(a)].">
      <j1 rule="hyper" parents="320 7755 7776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8081">
    <literal><![CDATA[
      T(K(x,y),T(z,K(u,x))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,7158,a(flip),b,7778,a)].">
      <j1 rule="hyper" parents="58 7158 7778"/>
    </justification>
  </clause>

  <clause id="8082">
    <literal><![CDATA[
      K(x,y) * K(y,K(z,T(x,u))) = T(K(x,y),T(z,u))
    ]]></literal>
    <justification jstring="[para(7160(a,1),7790(a,1,2,2))].">
      <j1 rule="para" parents="7160 7790"/>
    </justification>
  </clause>

  <clause id="8083">
    <literal><![CDATA[
      K(x,K(y,K(x,z) * u)) = K(x,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,7779,a,b,7792,a),flip(a)].">
      <j1 rule="hyper" parents="320 7779 7792"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8084">
    <literal><![CDATA[
      K(x,T(y,z)) * K(y,x) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(2009,a,7802,a)].">
      <j1 rule="hyper" parents="2009 7802"/>
    </justification>
  </clause>

  <clause id="8085">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) = K(z,K(y,T(x,u)))
    ]]></literal>
    <justification jstring="[hyper(7781,a,7815,a)].">
      <j1 rule="hyper" parents="7781 7815"/>
    </justification>
  </clause>

  <clause id="8086">
    <literal><![CDATA[
      T(x,y) * K(y,T(x,z)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(119,a,7817,a(flip),b,5410,a)].">
      <j1 rule="hyper" parents="119 7817 5410"/>
    </justification>
  </clause>

  <clause id="8087">
    <literal><![CDATA[
      K(x,T(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y)) * K(x,y) = u
    ]]></literal>
    <justification jstring="[para(7818(a,1),5640(a,1))].">
      <j1 rule="para" parents="7818 5640"/>
    </justification>
  </clause>

  <clause id="8088">
    <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(5686(a,1),7835(a,2,2,1))].">
      <j1 rule="para" parents="5686 7835"/>
    </justification>
  </clause>

  <clause id="8089">
    <literal><![CDATA[
      T(x * K(y,y \ z),K(y,z)) = K(y,y \ z) * x
    ]]></literal>
    <justification jstring="[hyper(58,a,8032,a(flip),b,7841,a)].">
      <j1 rule="hyper" parents="58 8032 7841"/>
    </justification>
  </clause>

  <clause id="8090">
    <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(7841(a,1),5634(a,1,1))].">
      <j1 rule="para" parents="7841 5634"/>
    </justification>
  </clause>

  <clause id="8091">
    <literal><![CDATA[
      T(x * T(y,z),K(y,z)) = K(y,z) * (x * y)
    ]]></literal>
    <justification jstring="[para(6116(a,1),7841(a,1,1))].">
      <j1 rule="para" parents="6116 7841"/>
    </justification>
  </clause>

  <clause id="8092">
    <literal><![CDATA[
      T(K(x,y) * z,u) * K(y,x) = K(y,x) * T(z * K(x,y),u)
    ]]></literal>
    <justification jstring="[para(7842(a,1),236(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7842 236"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8093">
    <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(7842(a,1),5158(a,1,1))].">
      <j1 rule="para" parents="7842 5158"/>
    </justification>
  </clause>

  <clause id="8094">
    <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,7844,a(flip),b,4782,a)].">
      <j1 rule="hyper" parents="119 7844 4782"/>
    </justification>
  </clause>

  <clause id="8095">
    <literal><![CDATA[
      T(x \ K(x,y),K(z,x)) = x \ K(x,y)
    ]]></literal>
    <justification jstring="[para(5636(a,1),7846(a,2,2))].">
      <j1 rule="para" parents="5636 7846"/>
    </justification>
  </clause>

  <clause id="8096">
    <literal><![CDATA[
      T(x \ y,K(z,x)) = x \ T(y,K(z,x))
    ]]></literal>
    <justification jstring="[para(7832(a,1),7846(a,2,2))].">
      <j1 rule="para" parents="7832 7846"/>
    </justification>
  </clause>

  <clause id="8097">
    <literal><![CDATA[
      T(x * K(y,z),u) / x = x \ T(K(y,z) * x,u)
    ]]></literal>
    <justification jstring="[para(7852(a,1),4582(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7852 4582"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8098">
    <literal><![CDATA[
      T(x,K(y,z)) * K(y,z * x) = K(y,z * x) * x
    ]]></literal>
    <justification jstring="[para(7968(a,1),7852(a,1,1))].">
      <j1 rule="para" parents="7968 7852"/>
    </justification>
  </clause>

  <clause id="8099">
    <literal><![CDATA[
      T(x * y,K(z,x)) = x * T(y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(7866,a,7857,a)].">
      <j1 rule="hyper" parents="7866 7857"/>
    </justification>
  </clause>

  <clause id="8100">
    <literal><![CDATA[
      K(1 / T(T(x,y),y),z) = K(1 / x,z)
    ]]></literal>
    <justification jstring="[hyper(5551,a,7882,a),flip(a)].">
      <j1 rule="hyper" parents="5551 7882"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8101">
    <literal><![CDATA[
      K(x,T(1 / (y \ z),y)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(5782,a,7891,a)].">
      <j1 rule="hyper" parents="5782 7891"/>
    </justification>
  </clause>

  <clause id="8102">
    <literal><![CDATA[
      K(x,((y \ z) * y) \ y) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(58,a,7700,a(flip),b,7891,a)].">
      <j1 rule="hyper" parents="58 7700 7891"/>
    </justification>
  </clause>

  <clause id="8103">
    <literal><![CDATA[
      K(x,T(y \ 1,z)) = K(x,z / (z * y))
    ]]></literal>
    <justification jstring="[para(4(a,1),7891(a,1,2,1,1))].">
      <j1 rule="para" parents="4 7891"/>
    </justification>
  </clause>

  <clause id="8105">
    <literal><![CDATA[
      K((x / (x / y)) \ 1,z) = K(y \ 1,T(z,y \ x))
    ]]></literal>
    <justification jstring="[para(4346(a,1),7892(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4346 7892"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8106">
    <literal><![CDATA[
      K(T(x,y) \ 1,z) = K(x \ K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(320,a,7168,a,b,7895,a)].">
      <j1 rule="hyper" parents="320 7168 7895"/>
    </justification>
  </clause>

  <clause id="8107">
    <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(7896(a,1),7982(a,1,1))].">
      <j1 rule="para" parents="7896 7982"/>
    </justification>
  </clause>

  <clause id="8108">
    <literal><![CDATA[
      K(T(x,y),T(z,y)) / T(z,y) = 1 / (K(z,x) * T(z,y))
    ]]></literal>
    <justification jstring="[para(7906(a,1),4803(a,2,2))].">
      <j1 rule="para" parents="7906 4803"/>
    </justification>
  </clause>

  <clause id="8109">
    <literal><![CDATA[
      K(T(x / (x / y),z),u) = K(T(y,z),T(u,y \ x))
    ]]></literal>
    <justification jstring="[para(4346(a,1),7922(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4346 7922"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8110">
    <literal><![CDATA[
      (x * T(y,z)) / T(x,y) = T(y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(117,a,7940,a(flip),b,5089,a(flip))].">
      <j1 rule="hyper" parents="117 7940 5089"/>
    </justification>
  </clause>

  <clause id="8111">
    <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(7940(a,1),494(a,1,2))].">
      <j1 rule="para" parents="7940 494"/>
    </justification>
  </clause>

  <clause id="8112">
    <literal><![CDATA[
      T(K(x,y),z) * ((x \ z) * x) = (x \ z) * T(x,y)
    ]]></literal>
    <justification jstring="[para(7206(a,1),7940(a,1,1))].">
      <j1 rule="para" parents="7206 7940"/>
    </justification>
  </clause>

  <clause id="8113">
    <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(7941(a,2),233(a,1,1,1))].">
      <j1 rule="para" parents="7941 233"/>
    </justification>
  </clause>

  <clause id="8114">
    <literal><![CDATA[
      T(x * y,K(z,y)) = T(x,K(z,y)) * y
    ]]></literal>
    <justification jstring="[hyper(320,a,7840,a,b,7949,a)].">
      <j1 rule="hyper" parents="320 7840 7949"/>
    </justification>
  </clause>

  <clause id="8115">
    <literal><![CDATA[
      K(x \ y,z) \ (y * K(y / x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      u = y
    ]]></literal>
    <justification jstring="[para(7955(a,1),287(a,1,2))].">
      <j1 rule="para" parents="7955 287"/>
    </justification>
  </clause>

  <clause id="8116">
    <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(7955(a,2),6384(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="7955 6384"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8117">
    <literal><![CDATA[
      K(x,K(y \ z,y)) = K(x,K(z / y,z))
    ]]></literal>
    <justification jstring="[para(4964(a,1),7962(a,1,2))].">
      <j1 rule="para" parents="4964 7962"/>
    </justification>
  </clause>

  <clause id="8118">
    <literal><![CDATA[
      K(x / y,z \ (x / y)) = K(y \ x,(z * y) \ x)
    ]]></literal>
    <justification jstring="[hyper(6989,a,7970,a)].">
      <j1 rule="hyper" parents="6989 7970"/>
    </justification>
  </clause>

  <clause id="8119">
    <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(439,a,2340,a,b,7978,a)].">
      <j1 rule="hyper" parents="439 2340 7978"/>
    </justification>
  </clause>

  <clause id="8120">
    <literal><![CDATA[
      K(x \ 1,y) * K(y,x \ K(x,z)) = K(x \ 1,K(y,z))
    ]]></literal>
    <justification jstring="[para(7986(a,1),7802(a,1,2))].">
      <j1 rule="para" parents="7986 7802"/>
    </justification>
  </clause>

  <clause id="8121">
    <literal><![CDATA[
      (x * (K(y,z) * K(x,u))) * K(z,y) = T(x,T(u,K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(6344,a,7987,a)].">
      <j1 rule="hyper" parents="6344 7987"/>
    </justification>
  </clause>

  <clause id="8122">
    <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(7987(a,1),6352(a,1,1)),flip(b)].">
      <j1 rule="para" parents="7987 6352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8123">
    <literal><![CDATA[
      K(x,(y / T(z,x)) * u) = K(x,(y / z) * u)
    ]]></literal>
    <justification jstring="[para(6322(a,1),7994(a,1,2,1))].">
      <j1 rule="para" parents="6322 7994"/>
    </justification>
  </clause>

  <clause id="8124">
    <literal><![CDATA[
      K(x,T(T(K(y,x) * z,u),w)) = K(x,T(T(z,u),w))
    ]]></literal>
    <justification jstring="[para(6720(a,1),7995(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6720 7995"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8125">
    <literal><![CDATA[
      K((x \ y) \ 1,T(z,y)) = K((y / x) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,5427,a,b,8000,a),flip(a)].">
      <j1 rule="hyper" parents="320 5427 8000"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8126">
    <literal><![CDATA[
      T(x,R((y * z) / y,u,w)) = x * K(T(x,y),R(z,u,w))
    ]]></literal>
    <justification jstring="[para(854(a,2),8015(a,1,2))].">
      <j1 rule="para" parents="854 8015"/>
    </justification>
  </clause>

  <clause id="8127">
    <literal><![CDATA[
      K(K(x,y) * z,K(y,u)) = K(z,K(y,u))
    ]]></literal>
    <justification jstring="[para(5133(a,1),8080(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5133 8080"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8128">
    <literal><![CDATA[
      R(x,K(y,z) * u,K(u,K(y,w))) = x
    ]]></literal>
    <justification jstring="[para(8080(a,1),6420(a,1,3))].">
      <j1 rule="para" parents="8080 6420"/>
    </justification>
  </clause>

  <clause id="8129">
    <literal><![CDATA[
      R(x,K(y,z),T(u,K(y,w))) = R(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(6898,a,8128,a)].">
      <j1 rule="hyper" parents="6898 8128"/>
    </justification>
  </clause>

  <clause id="8130">
    <literal><![CDATA[
      (x * (K(y,z) * u)) * K(u,K(y,z)) = x * (u * K(y,z))
    ]]></literal>
    <justification jstring="[para(8128(a,1),517(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8128 517"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8131">
    <literal><![CDATA[
      K(x,K(y,(z / x) \ u)) = K(x,K(y,(x \ z) \ u))
    ]]></literal>
    <justification jstring="[para(5414(a,1),8083(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5414 8083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8132">
    <literal><![CDATA[
      K(x,K(y \ z,T(y,u))) = K(y,K(z,T(x,u)))
    ]]></literal>
    <justification jstring="[hyper(320,a,7965,a(flip),b,8085,a),flip(a)].">
      <j1 rule="hyper" parents="320 7965 8085"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8133">
    <literal><![CDATA[
      T(x * K(y,T(x,z)),y) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,7437,a,b,8086,a)].">
      <j1 rule="hyper" parents="58 7437 8086"/>
    </justification>
  </clause>

  <clause id="8134">
    <literal><![CDATA[
      T(x \ K(x,y),T(x,z)) = T(x \ K(x,y),x)
    ]]></literal>
    <justification jstring="[para(8095(a,1),7447(a,1,1))].">
      <j1 rule="para" parents="8095 7447"/>
    </justification>
  </clause>

  <clause id="8135">
    <literal><![CDATA[
      x * T(x \ y,K(z,x)) = T(y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(119,a,8096,a,b,xx)].">
      <j1 rule="hyper" parents="119 8096"/>
    </justification>
  </clause>

  <clause id="8136">
    <literal><![CDATA[
      T(x,K(y,z)) / z = T(x / z,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(4584,a,8099,a)].">
      <j1 rule="hyper" parents="4584 8099"/>
    </justification>
  </clause>

  <clause id="8137">
    <literal><![CDATA[
      K(1 / T(x,y / x),z) = K(1 / (y / (y / x)),z)
    ]]></literal>
    <justification jstring="[para(244(a,1),8100(a,1,1,2,1))].">
      <j1 rule="para" parents="244 8100"/>
    </justification>
  </clause>

  <clause id="8138">
    <literal><![CDATA[
      K(1 / T(T(x,x * y),y),z) = K(1 / L(x,y,x),z)
    ]]></literal>
    <justification jstring="[para(712(a,1),8100(a,1,1,2,1))].">
      <j1 rule="para" parents="712 8100"/>
    </justification>
  </clause>

  <clause id="8139">
    <literal><![CDATA[
      T(x,1 / T(T(y,z),z)) = x / K(1 / y,x)
    ]]></literal>
    <justification jstring="[para(8100(a,1),4805(a,2,2))].">
      <j1 rule="para" parents="8100 4805"/>
    </justification>
  </clause>

  <clause id="8140">
    <literal><![CDATA[
      K(x,T(1 / y,z)) = K(x,z / (z * y))
    ]]></literal>
    <justification jstring="[para(4(a,1),8101(a,1,2,1,2))].">
      <j1 rule="para" parents="4 8101"/>
    </justification>
  </clause>

  <clause id="8141">
    <literal><![CDATA[
      K(x,y \ T(z,z \ y)) = K(x,z / y)
    ]]></literal>
    <justification jstring="[para(5597(a,1),8102(a,1,2))].">
      <j1 rule="para" parents="5597 8102"/>
    </justification>
  </clause>

  <clause id="8142">
    <literal><![CDATA[
      K(x,y / (y * z)) = K(x,y \ (z \ y))
    ]]></literal>
    <justification jstring="[hyper(58,a,7569,a(flip),b,8103,a),flip(a)].">
      <j1 rule="hyper" parents="58 7569 8103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8143">
    <literal><![CDATA[
      K(((x * y) / x) \ 1,z) = K(T(y,x) \ 1,z)
    ]]></literal>
    <justification jstring="[para(4905(a,2),8106(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4905 8106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8144">
    <literal><![CDATA[
      K(x,K(y / z,y)) = K(x,K(z,z \ y))
    ]]></literal>
    <justification jstring="[hyper(7831,a,8117,a),flip(a)].">
      <j1 rule="hyper" parents="7831 8117"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8145">
    <literal><![CDATA[
      T(x * K(y,x),K(y,z)) = x * K(y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(5205,a,8133,a)].">
      <j1 rule="hyper" parents="5205 8133"/>
    </justification>
  </clause>

  <clause id="8146">
    <literal><![CDATA[
      T(x * K(y,T(x,z * (u * x))),y) = T(x,K(y,z * (x * u)))
    ]]></literal>
    <justification jstring="[para(7135(a,2),8133(a,1,1,2,2))].">
      <j1 rule="para" parents="7135 8133"/>
    </justification>
  </clause>

  <clause id="8147">
    <literal><![CDATA[
      T(T(x,y) / z,K(y,z)) = T(x,T(y,z)) / z
    ]]></literal>
    <justification jstring="[para(7438(a,1),8136(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7438 8136"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8149">
    <literal><![CDATA[
      K(x,y \ T(z,z \ y)) = K(x,T(y \ z,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,7890,a,b,8141,a),flip(a)].">
      <j1 rule="hyper" parents="320 7890 8141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8150">
    <literal><![CDATA[
      K(x,(y / z) / y) = K(x,y \ (z \ y))
    ]]></literal>
    <justification jstring="[para(643(a,1),8141(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="643 8141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8151">
    <literal><![CDATA[
      T(x,y / (y * z)) = T(x,y \ (z \ y))
    ]]></literal>
    <justification jstring="[hyper(118,a,8142,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 8142 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8152">
    <literal><![CDATA[
      K(x,K(y / z,y)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(320,a,7960,a(flip),b,8144,a),flip(a)].">
      <j1 rule="hyper" parents="320 7960 8144"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8153">
    <literal><![CDATA[
      K(x,K(y / z,y)) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,7784,a(flip),b,8152,a),flip(a)].">
      <j1 rule="hyper" parents="320 7784 8152"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8154">
    <literal><![CDATA[
      K(x,K(y \ z,z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(72(a,1),8152(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="72 8152"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8155">
    <literal><![CDATA[
      K(x,K(y,y / z)) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(7831,a,8153,a)].">
      <j1 rule="hyper" parents="7831 8153"/>
    </justification>
  </clause>

  <clause id="8156">
    <literal><![CDATA[
      K(x,K(y,x / z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(7799,a,8153,a)].">
      <j1 rule="hyper" parents="7799 8153"/>
    </justification>
  </clause>

  <clause id="8157">
    <literal><![CDATA[
      K(x,K(x / y,z)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(7774,a,8153,a)].">
      <j1 rule="hyper" parents="7774 8153"/>
    </justification>
  </clause>

  <clause id="8158">
    <literal><![CDATA[
      K(x,K(y,z \ y)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(7831,a,8154,a)].">
      <j1 rule="hyper" parents="7831 8154"/>
    </justification>
  </clause>

  <clause id="8159">
    <literal><![CDATA[
      K(x,K(y \ z,z)) = K(z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(320,a,7753,a,b,8154,a),flip(a)].">
      <j1 rule="hyper" parents="320 7753 8154"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8160">
    <literal><![CDATA[
      (x / y) * K(x,K(z,y)) = T(x / y,K(x,z))
    ]]></literal>
    <justification jstring="[para(8155(a,1),7757(a,1,2))].">
      <j1 rule="para" parents="8155 7757"/>
    </justification>
  </clause>

  <clause id="8161">
    <literal><![CDATA[
      T(x,K(y,x / z)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(118,a,8156,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 8156 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8162">
    <literal><![CDATA[
      K(x,K(y,z \ x)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(72(a,1),8156(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="72 8156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8163">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x / z,y) = K(z \ x,y)
    ]]></literal>
    <justification jstring="[para(8156(a,1),6288(a,1,1))].">
      <j1 rule="para" parents="8156 6288"/>
    </justification>
  </clause>

  <clause id="8164">
    <literal><![CDATA[
      K(x,K(y,z \ x)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[para(72(a,1),8157(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="72 8157"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8165">
    <literal><![CDATA[
      K(x,K(y,z \ y)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,7797,a,b,8158,a),flip(a)].">
      <j1 rule="hyper" parents="320 7797 8158"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8166">
    <literal><![CDATA[
      K(x,K(y,z \ 1)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,7959,a,b,8158,a)].">
      <j1 rule="hyper" parents="58 7959 8158"/>
    </justification>
  </clause>

  <clause id="8167">
    <literal><![CDATA[
      K(x,K(y \ x,z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(7774,a,8159,a)].">
      <j1 rule="hyper" parents="7774 8159"/>
    </justification>
  </clause>

  <clause id="8168">
    <literal><![CDATA[
      K(x,K(y \ z,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8159(a,2),7774(a,1))].">
      <j1 rule="para" parents="8159 7774"/>
    </justification>
  </clause>

  <clause id="8169">
    <literal><![CDATA[
      K(1 / ((1 / x) / y),K(z,(y * x) / u)) = (T(y * x,K(z,u)) / x) / y
    ]]></literal>
    <justification jstring="[para(8161(a,1),5556(a,2,1,1))].">
      <j1 rule="para" parents="8161 5556"/>
    </justification>
  </clause>

  <clause id="8170">
    <literal><![CDATA[
      K(x,K(y,z \ x)) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(320,a,7784,a(flip),b,8162,a),flip(a)].">
      <j1 rule="hyper" parents="320 7784 8162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8171">
    <literal><![CDATA[
      K(x \ y,z) \ K(y,K(x,z)) = K(z,y / x)
    ]]></literal>
    <justification jstring="[para(8164(a,1),6814(a,1,2))].">
      <j1 rule="para" parents="8164 6814"/>
    </justification>
  </clause>

  <clause id="8172">
    <literal><![CDATA[
      T(x,K(y,z \ y)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(118,a,8165,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 8165 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8173">
    <literal><![CDATA[
      K(x,K(y,z \ 1)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,7959,a,b,8165,a)].">
      <j1 rule="hyper" parents="58 7959 8165"/>
    </justification>
  </clause>

  <clause id="8174">
    <literal><![CDATA[
      K(x,K(y \ 1,z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(7831,a,8166,a)].">
      <j1 rule="hyper" parents="7831 8166"/>
    </justification>
  </clause>

  <clause id="8175">
    <literal><![CDATA[
      K(x \ 1,K(y,z)) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(7799,a,8166,a)].">
      <j1 rule="hyper" parents="7799 8166"/>
    </justification>
  </clause>

  <clause id="8176">
    <literal><![CDATA[
      K(x,K(y,z \ 1)) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(320,a,7779,a,b,8166,a),flip(a)].">
      <j1 rule="hyper" parents="320 7779 8166"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8177">
    <literal><![CDATA[
      T(x,K(y,z \ 1)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(118,a,8166,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 8166 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8178">
    <literal><![CDATA[
      K(x,K(y \ 1,z)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[para(3554(a,1),8166(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3554 8166"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8179">
    <literal><![CDATA[
      K(x,K(y,z / (u * z))) = K(x,K(u,y))
    ]]></literal>
    <justification jstring="[para(5350(a,2),8166(a,1,2))].">
      <j1 rule="para" parents="5350 8166"/>
    </justification>
  </clause>

  <clause id="8180">
    <literal><![CDATA[
      K(x,K(y \ z,u)) = K(x,K(u,z \ y))
    ]]></literal>
    <justification jstring="[para(6108(a,1),8166(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6108 8166"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8181">
    <literal><![CDATA[
      K(x,K(y,z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8166(a,2),7831(a,1))].">
      <j1 rule="para" parents="8166 7831"/>
    </justification>
  </clause>

  <clause id="8182">
    <literal><![CDATA[
      K(x,K(y,z)) * (x \ y) = T(x \ y,K(y,z))
    ]]></literal>
    <justification jstring="[para(8170(a,1),7808(a,1,1))].">
      <j1 rule="para" parents="8170 7808"/>
    </justification>
  </clause>

  <clause id="8183">
    <literal><![CDATA[
      T(x,K(y \ z,z)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(7866,a,8172,a)].">
      <j1 rule="hyper" parents="7866 8172"/>
    </justification>
  </clause>

  <clause id="8184">
    <literal><![CDATA[
      K(x,K(y \ 1,z)) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(7821,a,8173,a)].">
      <j1 rule="hyper" parents="7821 8173"/>
    </justification>
  </clause>

  <clause id="8185">
    <literal><![CDATA[
      K(x \ 1,K(y,z)) = K(y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(7799,a,8173,a)].">
      <j1 rule="hyper" parents="7799 8173"/>
    </justification>
  </clause>

  <clause id="8186">
    <literal><![CDATA[
      T(x,K(y,z \ 1)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(118,a,8173,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 8173 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8187">
    <literal><![CDATA[
      K(x,K(y,1 / z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(75(a,1),8173(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="75 8173"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8188">
    <literal><![CDATA[
      K(x,K(y,z / (u * z))) = K(x,K(y,u))
    ]]></literal>
    <justification jstring="[para(5350(a,2),8173(a,1,2))].">
      <j1 rule="para" parents="5350 8173"/>
    </justification>
  </clause>

  <clause id="8189">
    <literal><![CDATA[
      K(x,K(y,z / u)) = K(x,K(y,u / z))
    ]]></literal>
    <justification jstring="[para(5351(a,1),8173(a,1,2))].">
      <j1 rule="para" parents="5351 8173"/>
    </justification>
  </clause>

  <clause id="8190">
    <literal><![CDATA[
      K(x,K(y,z \ u)) = K(x,K(y,u \ z))
    ]]></literal>
    <justification jstring="[para(6108(a,1),8173(a,1,2))].">
      <j1 rule="para" parents="6108 8173"/>
    </justification>
  </clause>

  <clause id="8191">
    <literal><![CDATA[
      K(x,y) * K(x,K(y,z)) = T(K(x,y),z \ 1)
    ]]></literal>
    <justification jstring="[para(8173(a,1),7763(a,1,2))].">
      <j1 rule="para" parents="8173 7763"/>
    </justification>
  </clause>

  <clause id="8192">
    <literal><![CDATA[
      K(x,K(y \ 1,z)) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,7779,a,b,8174,a),flip(a)].">
      <j1 rule="hyper" parents="320 7779 8174"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8193">
    <literal><![CDATA[
      (x * K(y \ 1,z)) \ K(x,K(y,z)) = (K(y \ 1,z) * x) \ 1
    ]]></literal>
    <justification jstring="[hyper(116,a,8174,a(flip),b,5568,a(flip))].">
      <j1 rule="hyper" parents="116 8174 5568"/>
    </justification>
  </clause>

  <clause id="8194">
    <literal><![CDATA[
      K(x,y * ((z \ (y \ 1)) * z)) = K(x,K(y * z,z))
    ]]></literal>
    <justification jstring="[para(5714(a,2),8174(a,1,2))].">
      <j1 rule="para" parents="5714 8174"/>
    </justification>
  </clause>

  <clause id="8195">
    <literal><![CDATA[
      K(x,K(y \ 1,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y)) = u
    ]]></literal>
    <justification jstring="[para(8174(a,2),7831(a,1))].">
      <j1 rule="para" parents="8174 7831"/>
    </justification>
  </clause>

  <clause id="8196">
    <literal><![CDATA[
      K(x \ 1,K(y,z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,7779,a,b,8175,a),flip(a)].">
      <j1 rule="hyper" parents="320 7779 8175"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8197">
    <literal><![CDATA[
      T(1 / x,K(y,z)) = K(y,K(x,z)) / x
    ]]></literal>
    <justification jstring="[hyper(117,a,8175,a(flip),b,5047,a),flip(a)].">
      <j1 rule="hyper" parents="117 8175 5047"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8198">
    <literal><![CDATA[
      K(x \ 1,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,K(z,x)) = u
    ]]></literal>
    <justification jstring="[para(8175(a,2),7831(a,1))].">
      <j1 rule="para" parents="8175 7831"/>
    </justification>
  </clause>

  <clause id="8199">
    <literal><![CDATA[
      K(1 / x,K(y,z)) = K(y,K(z,x))
    ]]></literal>
    <justification jstring="[para(75(a,1),8176(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="75 8176"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8200">
    <literal><![CDATA[
      K(x,K(y,1 / z)) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[para(3558(a,2),8176(a,1,2))].">
      <j1 rule="para" parents="3558 8176"/>
    </justification>
  </clause>

  <clause id="8201">
    <literal><![CDATA[
      T(x,K(y \ z,u)) = T(x,K(u,z \ y))
    ]]></literal>
    <justification jstring="[para(6108(a,1),8177(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6108 8177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8202">
    <literal><![CDATA[
      T(x,K(y,z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8177(a,2),7866(a,1))].">
      <j1 rule="para" parents="8177 7866"/>
    </justification>
  </clause>

  <clause id="8203">
    <literal><![CDATA[
      K(x,K(y \ 1,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8178(a,2),7831(a,1))].">
      <j1 rule="para" parents="8178 7831"/>
    </justification>
  </clause>

  <clause id="8204">
    <literal><![CDATA[
      T(x,K(y,y / z)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[para(75(a,1),8183(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="75 8183"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8205">
    <literal><![CDATA[
      K(x,K(y,(z \ 1) / (u / z))) = K(y,(T(u,x) / z) / (u / z))
    ]]></literal>
    <justification jstring="[para(5723(a,1),8184(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5723 8184"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8206">
    <literal><![CDATA[
      T(T(x,y),K(y,z)) = T(x,T(y,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(7703,a,8186,a),flip(a)].">
      <j1 rule="hyper" parents="7703 8186"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8207">
    <literal><![CDATA[
      K(x,y \ 1) * T(z,K(x,y)) = z * K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(119,a,8186,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 8186 17"/>
    </justification>
  </clause>

  <clause id="8208">
    <literal><![CDATA[
      T(x,K(y,z \ u)) = T(x,K(y,u \ z))
    ]]></literal>
    <justification jstring="[para(6108(a,1),8186(a,1,2))].">
      <j1 rule="para" parents="6108 8186"/>
    </justification>
  </clause>

  <clause id="8209">
    <literal><![CDATA[
      T(T(x,y),K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z \ 1)) = u
    ]]></literal>
    <justification jstring="[para(8186(a,1),7703(a,1))].">
      <j1 rule="para" parents="8186 7703"/>
    </justification>
  </clause>

  <clause id="8210">
    <literal><![CDATA[
      (T(x * y,K(z,u)) / y) / x = K(z,K(u,(1 / y) / x))
    ]]></literal>
    <justification jstring="[hyper(58,a,5556,a(flip),b,8199,a)].">
      <j1 rule="hyper" parents="58 5556 8199"/>
    </justification>
  </clause>

  <clause id="8211">
    <literal><![CDATA[
      K(1 / x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,K(x,z)) = u
    ]]></literal>
    <justification jstring="[para(8199(a,2),7831(a,1))].">
      <j1 rule="para" parents="8199 7831"/>
    </justification>
  </clause>

  <clause id="8212">
    <literal><![CDATA[
      K(x,K(y,1 / z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8200(a,2),7821(a,1))].">
      <j1 rule="para" parents="8200 7821"/>
    </justification>
  </clause>

  <clause id="8213">
    <literal><![CDATA[
      K(x,(y / z) / y) = K(x,y / (y * z))
    ]]></literal>
    <justification jstring="[hyper(320,a,8142,a,b,8150,a),flip(a)].">
      <j1 rule="hyper" parents="320 8142 8150"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8214">
    <literal><![CDATA[
      K(x,K(y,z / (u * z))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,u)) = w
    ]]></literal>
    <justification jstring="[para(8179(a,2),7831(a,1))].">
      <j1 rule="para" parents="8179 7831"/>
    </justification>
  </clause>

  <clause id="8215">
    <literal><![CDATA[
      K(x,K(y \ (z * u),u \ (z \ 1))) = K(x,K(z * u,(z \ y) \ u))
    ]]></literal>
    <justification jstring="[para(6715(a,1),8180(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6715 8180"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8216">
    <literal><![CDATA[
      K(x,K(y,z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,u \ z)) = w
    ]]></literal>
    <justification jstring="[para(8180(a,1),7831(a,1))].">
      <j1 rule="para" parents="8180 7831"/>
    </justification>
  </clause>

  <clause id="8217">
    <literal><![CDATA[
      K(x,K(y,z / (u * z))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(u,y)) = w
    ]]></literal>
    <justification jstring="[para(8188(a,2),7831(a,1))].">
      <j1 rule="para" parents="8188 7831"/>
    </justification>
  </clause>

  <clause id="8218">
    <literal><![CDATA[
      1 / T(x,K(y,z)) = T(1 / x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,7819,a(flip),b,8197,a)].">
      <j1 rule="hyper" parents="320 7819 8197"/>
    </justification>
  </clause>

  <clause id="8219">
    <literal><![CDATA[
      T(x,K(y,z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,u \ z)) = w
    ]]></literal>
    <justification jstring="[para(8201(a,1),7866(a,1))].">
      <j1 rule="para" parents="8201 7866"/>
    </justification>
  </clause>

  <clause id="8220">
    <literal><![CDATA[
      T(x,T(y,z \ 1)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(7703,a,8206,a),flip(a)].">
      <j1 rule="hyper" parents="7703 8206"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8221">
    <literal><![CDATA[
      T(x,T(y,z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8206(a,1),7703(a,1))].">
      <j1 rule="para" parents="8206 7703"/>
    </justification>
  </clause>

  <clause id="8222">
    <literal><![CDATA[
      T(x,T(y,z \ 1)) = x * K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,4755,a(flip),b,8220,a),flip(a)].">
      <j1 rule="hyper" parents="320 4755 8220"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8223">
    <literal><![CDATA[
      T(x * y,T(z,y)) = T(x * y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(58,a,7381,a(flip),b,8220,a),flip(a)].">
      <j1 rule="hyper" parents="58 7381 8220"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8224">
    <literal><![CDATA[
      T(x,T(y,z \ 1)) != x * u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8220(a,2),4837(a,1))].">
      <j1 rule="para" parents="8220 4837"/>
    </justification>
  </clause>

  <clause id="8226">
    <literal><![CDATA[
      T(1 / (x * K(y,z)),K(z,y)) = 1 / (K(y,z) * x)
    ]]></literal>
    <justification jstring="[para(6337(a,1),8218(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6337 8218"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8227">
    <literal><![CDATA[
      K(x,T(y,z \ 1)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(4837,a,8222,a)].">
      <j1 rule="hyper" parents="4837 8222"/>
    </justification>
  </clause>

  <clause id="8230">
    <literal><![CDATA[
      K(x,T(y,z \ x)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,7698,a(flip),b,8227,a)].">
      <j1 rule="hyper" parents="58 7698 8227"/>
    </justification>
  </clause>

  <clause id="8231">
    <literal><![CDATA[
      K(x * y,T(z,y)) = K(x * y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(58,a,7368,a(flip),b,8227,a),flip(a)].">
      <j1 rule="hyper" parents="58 7368 8227"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8232">
    <literal><![CDATA[
      K(x,T(y * z,z)) = K(x,T(y * z,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,7159,a(flip),b,8227,a)].">
      <j1 rule="hyper" parents="58 7159 8227"/>
    </justification>
  </clause>

  <clause id="8233">
    <literal><![CDATA[
      K(x,T(y,z \ y)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,7156,a(flip),b,8227,a)].">
      <j1 rule="hyper" parents="58 7156 8227"/>
    </justification>
  </clause>

  <clause id="8234">
    <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),8227(a,1,2))].">
      <j1 rule="para" parents="20 8227"/>
    </justification>
  </clause>

  <clause id="8235">
    <literal><![CDATA[
      K(x,T(y,1 / z)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(75(a,1),8227(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="75 8227"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8236">
    <literal><![CDATA[
      K(x,T(y / (z \ 1),z)) = K(x,(z \ 1) \ y)
    ]]></literal>
    <justification jstring="[para(107(a,1),8227(a,1,2)),flip(a)].">
      <j1 rule="para" parents="107 8227"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8237">
    <literal><![CDATA[
      K(x,T(y,z / u)) = K(x,T(y,u / z))
    ]]></literal>
    <justification jstring="[para(4456(a,1),8227(a,1,2))].">
      <j1 rule="para" parents="4456 8227"/>
    </justification>
  </clause>

  <clause id="8238">
    <literal><![CDATA[
      K(x,T(y,z \ u)) = K(x,T(y,u \ z))
    ]]></literal>
    <justification jstring="[para(6125(a,1),8227(a,1,2))].">
      <j1 rule="para" parents="6125 8227"/>
    </justification>
  </clause>

  <clause id="8239">
    <literal><![CDATA[
      (x \ 1) * K(y,T(z,x)) = K(y,z) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(8227(a,1),7179(a,1,2))].">
      <j1 rule="para" parents="8227 7179"/>
    </justification>
  </clause>

  <clause id="8240">
    <literal><![CDATA[
      (x \ 1) * K(y,T(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) * (x \ 1) = u
    ]]></literal>
    <justification jstring="[para(8227(a,1),7184(a,1,2))].">
      <j1 rule="para" parents="8227 7184"/>
    </justification>
  </clause>

  <clause id="8241">
    <literal><![CDATA[
      K(x,T(y,z)) * (z \ 1) = (z \ 1) * K(x,y)
    ]]></literal>
    <justification jstring="[para(8227(a,1),7897(a,1,1))].">
      <j1 rule="para" parents="8227 7897"/>
    </justification>
  </clause>

  <clause id="8242">
    <literal><![CDATA[
      (x \ y) * K(y,T(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) * (x \ y) = u
    ]]></literal>
    <justification jstring="[para(8230(a,1),7184(a,1,2))].">
      <j1 rule="para" parents="8230 7184"/>
    </justification>
  </clause>

  <clause id="8243">
    <literal><![CDATA[
      K(x,T(y,z)) * (z \ x) = (z \ x) * K(x,y)
    ]]></literal>
    <justification jstring="[para(8230(a,1),7897(a,1,1))].">
      <j1 rule="para" parents="8230 7897"/>
    </justification>
  </clause>

  <clause id="8244">
    <literal><![CDATA[
      K((x \ y) \ z,T(y,x)) = K(z / (x \ y),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,7907,a(flip),b,8233,a),flip(a)].">
      <j1 rule="hyper" parents="58 7907 8233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8245">
    <literal><![CDATA[
      (x \ y) * K(z,T(y,x)) = K(z,y) * (x \ y)
    ]]></literal>
    <justification jstring="[para(8233(a,1),7179(a,1,2))].">
      <j1 rule="para" parents="8233 7179"/>
    </justification>
  </clause>

  <clause id="8246">
    <literal><![CDATA[
      K(x,T(y,z)) * (1 / z) = (1 / z) * K(x,y)
    ]]></literal>
    <justification jstring="[para(8235(a,1),7897(a,1,1))].">
      <j1 rule="para" parents="8235 7897"/>
    </justification>
  </clause>

  <clause id="8247">
    <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),8223(a,1,2)),flip(a)].">
      <j1 rule="para" parents="213 8223"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8248">
    <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),8231(a,1,2)),flip(a)].">
      <j1 rule="para" parents="172 8231"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8249">
    <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),8231(a,2,2))].">
      <j1 rule="para" parents="173 8231"/>
    </justification>
  </clause>

  <clause id="8250">
    <literal><![CDATA[
      K(x / y,T(z,x \ y)) = K(x / y,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,5193,a(flip),b,8238,a),flip(a)].">
      <j1 rule="hyper" parents="320 5193 8238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8251">
    <literal><![CDATA[
      K(x,T(y,z \ y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8238(a,1),7257(a,1))].">
      <j1 rule="para" parents="8238 7257"/>
    </justification>
  </clause>

  <clause id="8252">
    <literal><![CDATA[
      K(x,T(y,z \ x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8238(a,1),7714(a,1))].">
      <j1 rule="para" parents="8238 7714"/>
    </justification>
  </clause>

  <clause id="8253">
    <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,7947,a,b,7854,a),flip(a)].">
      <j1 rule="hyper" parents="320 7947 7854"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8254">
    <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(854(a,2),7917(a,1,1))].">
      <j1 rule="para" parents="854 7917"/>
    </justification>
  </clause>

  <clause id="8255">
    <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(862(a,2),7917(a,1,1))].">
      <j1 rule="para" parents="862 7917"/>
    </justification>
  </clause>

  <clause id="8256">
    <literal><![CDATA[
      K(x * K(y,x),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z,y)) = u
    ]]></literal>
    <justification jstring="[para(4752(a,1),7917(a,1,1))].">
      <j1 rule="para" parents="4752 7917"/>
    </justification>
  </clause>

  <clause id="8257">
    <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(4874(a,2),7917(a,1,1))].">
      <j1 rule="para" parents="4874 7917"/>
    </justification>
  </clause>

  <clause id="8258">
    <literal><![CDATA[
      K(x,T(y,L(z,u,x))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,7930,a(flip),b,8019,a),flip(a)].">
      <j1 rule="hyper" parents="320 7930 8019"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8259">
    <literal><![CDATA[
      K(x,T(y,(x \ z) \ u)) = K(x,T(y,z \ (x * u)))
    ]]></literal>
    <justification jstring="[para(490(a,1),8258(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="490 8258"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8260">
    <literal><![CDATA[
      K(T(x,y \ z),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(T(x,z),y) = u
    ]]></literal>
    <justification jstring="[para(7928(a,2),8040(a,1))].">
      <j1 rule="para" parents="7928 8040"/>
    </justification>
  </clause>

  <clause id="8261">
    <literal><![CDATA[
      T(x \ y,K(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x \ y,K(z,y)) = u
    ]]></literal>
    <justification jstring="[para(72(a,1),8050(a,1,2,2))].">
      <j1 rule="para" parents="72 8050"/>
    </justification>
  </clause>

  <clause id="8262">
    <literal><![CDATA[
      K(x \ (y \ z),T(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K((y \ z) / x,y) = u
    ]]></literal>
    <justification jstring="[para(7097(a,1),8055(a,1))].">
      <j1 rule="para" parents="7097 8055"/>
    </justification>
  </clause>

  <clause id="8263">
    <literal><![CDATA[
      K(((x \ y) \ y) \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y / x,z) = u
    ]]></literal>
    <justification jstring="[para(7165(a,2),8055(a,1))].">
      <j1 rule="para" parents="7165 8055"/>
    </justification>
  </clause>

  <clause id="8264">
    <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(2975(a,1),8058(a,1))].">
      <j1 rule="para" parents="2975 8058"/>
    </justification>
  </clause>

  <clause id="8265">
    <literal><![CDATA[
      K(T(x \ y,x),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y / x,z) = u
    ]]></literal>
    <justification jstring="[para(7145(a,2),8058(a,1))].">
      <j1 rule="para" parents="7145 8058"/>
    </justification>
  </clause>

  <clause id="8266">
    <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(1412(a,1),8060(a,1,2,1))].">
      <j1 rule="para" parents="1412 8060"/>
    </justification>
  </clause>

  <clause id="8267">
    <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),8061(a,1,2))].">
      <j1 rule="para" parents="275 8061"/>
    </justification>
  </clause>

  <clause id="8268">
    <literal><![CDATA[
      K(x,K(y,z / u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,u / z)) = w
    ]]></literal>
    <justification jstring="[para(5351(a,1),8181(a,1,2))].">
      <j1 rule="para" parents="5351 8181"/>
    </justification>
  </clause>

  <clause id="8269">
    <literal><![CDATA[
      T(x,K(y,z / (u * z))) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,u)) = w
    ]]></literal>
    <justification jstring="[para(5350(a,2),8202(a,1,2))].">
      <j1 rule="para" parents="5350 8202"/>
    </justification>
  </clause>

  <clause id="8270">
    <literal><![CDATA[
      T(x,T(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z \ 1)) = u
    ]]></literal>
    <justification jstring="[para(2959(a,1),8221(a,1,2))].">
      <j1 rule="para" parents="2959 8221"/>
    </justification>
  </clause>

  <clause id="8271">
    <literal><![CDATA[
      K(x,T(y,z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7156(a,2),8251(a,1))].">
      <j1 rule="para" parents="7156 8251"/>
    </justification>
  </clause>

  <clause id="8272">
    <literal><![CDATA[
      K(x,T(y,z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u \ z)) = w
    ]]></literal>
    <justification jstring="[para(7534(a,1),8251(a,1))].">
      <j1 rule="para" parents="7534 8251"/>
    </justification>
  </clause>

  <clause id="8273">
    <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(8232(a,1),8252(a,1))].">
      <j1 rule="para" parents="8232 8252"/>
    </justification>
  </clause>

  <clause id="8274">
    <literal><![CDATA[
      K(x,T(y,1 / z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(2956(a,2),8271(a,1,2))].">
      <j1 rule="para" parents="2956 8271"/>
    </justification>
  </clause>

  <clause id="8275">
    <literal><![CDATA[
      K(x,T(y,z / u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u / z)) = w
    ]]></literal>
    <justification jstring="[para(4456(a,1),8271(a,1,2))].">
      <j1 rule="para" parents="4456 8271"/>
    </justification>
  </clause>

  <clause id="8276">
    <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(7663(a,1),8271(a,1,2))].">
      <j1 rule="para" parents="7663 8271"/>
    </justification>
  </clause>

  <clause id="8277">
    <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(3915(a,2),7557(a,1,2,1))].">
      <j1 rule="para" parents="3915 7557"/>
    </justification>
  </clause>

  <clause id="8278">
    <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),7559(a,1,2,1,1))].">
      <j1 rule="para" parents="18 7559"/>
    </justification>
  </clause>

  <clause id="8279">
    <literal><![CDATA[
      K(x / y,((x / (x / y)) / z) * u) = K(x / y,(y / z) * u)
    ]]></literal>
    <justification jstring="[para(244(a,1),7559(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="244 7559"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8281">
    <literal><![CDATA[
      K(((x \ y) \ 1) * z,T(y \ x,u)) = K(z * ((x \ y) \ 1),T(y \ x,u))
    ]]></literal>
    <justification jstring="[para(6173(a,1),7570(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6173 7570"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8282">
    <literal><![CDATA[
      T(T(x,y) \ T(x * z,u),x) = T(x,y) \ T(z * x,u)
    ]]></literal>
    <justification jstring="[hyper(116,a,4596,a(flip),b,7578,a),flip(a)].">
      <j1 rule="hyper" parents="116 4596 7578"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8283">
    <literal><![CDATA[
      K(x * (((y \ 1) \ z) / z),y) = K(x * (z \ ((y \ 1) \ z)),y)
    ]]></literal>
    <justification jstring="[para(4187(a,1),7582(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4187 7582"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8284">
    <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),7585(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="682 7585"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8285">
    <literal><![CDATA[
      (x * y) * (z * (((x * y) \ x) / z)) = x * K(z,y \ (z \ 1))
    ]]></literal>
    <justification jstring="[para(7593(a,1),3577(a,2,2))].">
      <j1 rule="para" parents="7593 3577"/>
    </justification>
  </clause>

  <clause id="8286">
    <literal><![CDATA[
      T(T(x,y) * (x \ z),x) = T(x,y) * (x \ T(z,x))
    ]]></literal>
    <justification jstring="[hyper(239,a,7605,a,b,1113,a)].">
      <j1 rule="hyper" parents="239 7605 1113"/>
    </justification>
  </clause>

  <clause id="8288">
    <literal><![CDATA[
      K(x,y) * K(z \ 1,x) = z * T(z \ K(x,y),x)
    ]]></literal>
    <justification jstring="[hyper(999,a,7644,a),flip(a)].">
      <j1 rule="hyper" parents="999 7644"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8289">
    <literal><![CDATA[
      (x * (y * K(z,y))) / (x * K(z,y * K(z,y))) = (x * y) / x
    ]]></literal>
    <justification jstring="[hyper(320,a,4877,a(flip),b,7654,a),flip(a)].">
      <j1 rule="hyper" parents="320 4877 7654"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8290">
    <literal><![CDATA[
      K(x,T(y \ z,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(7660(a,1),8007(a,1))].">
      <j1 rule="para" parents="7660 8007"/>
    </justification>
  </clause>

  <clause id="8291">
    <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(7216(a,1),8290(a,1))].">
      <j1 rule="para" parents="7216 8290"/>
    </justification>
  </clause>

  <clause id="8292">
    <literal><![CDATA[
      T(x,T(y,z)) * K(z,x) = T(x * K(z,x),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,7909,a(flip),b,7661,a),flip(a)].">
      <j1 rule="hyper" parents="58 7909 7661"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8293">
    <literal><![CDATA[
      K(x * K(T(x,y),z),T(u,y)) = K(K(y,x) * T(x,z),u)
    ]]></literal>
    <justification jstring="[para(7666(a,1),7888(a,1,1))].">
      <j1 rule="para" parents="7666 7888"/>
    </justification>
  </clause>

  <clause id="8294">
    <literal><![CDATA[
      T(x,T(T(y,z),y * u)) = T(x,T(T(y,z),u))
    ]]></literal>
    <justification jstring="[para(4(a,1),7689(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 7689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8295">
    <literal><![CDATA[
      K(x,T(y \ x,z / y)) = K(x,T(y \ x,y \ z))
    ]]></literal>
    <justification jstring="[para(107(a,1),7702(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="107 7702"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8296">
    <literal><![CDATA[
      K(R(K(x,y) * z,u,w),y) = K(R(z * K(x,y),u,w),y)
    ]]></literal>
    <justification jstring="[para(6351(a,1),7738(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6351 7738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8297">
    <literal><![CDATA[
      K((x \ 1) \ (y \ z),y) = K((x \ y) \ z,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,4003,a(flip),b,7748,a),flip(a)].">
      <j1 rule="hyper" parents="58 4003 7748"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8298">
    <literal><![CDATA[
      K(x,T(y \ z,u \ z)) = K(x,T(y \ z,u \ y))
    ]]></literal>
    <justification jstring="[para(5(a,1),7751(a,1,2,2,2))].">
      <j1 rule="para" parents="5 7751"/>
    </justification>
  </clause>

  <clause id="8299">
    <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(8083(a,1),7772(a,1,1))].">
      <j1 rule="para" parents="8083 7772"/>
    </justification>
  </clause>

  <clause id="8300">
    <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,4818,a(flip),b,7787,a)].">
      <j1 rule="hyper" parents="116 4818 7787"/>
    </justification>
  </clause>

  <clause id="8301">
    <literal><![CDATA[
      K(x,K(y,z)) * (z / K(x,y)) = K(y,x) * z
    ]]></literal>
    <justification jstring="[para(6335(a,2),7798(a,1,2))].">
      <j1 rule="para" parents="6335 7798"/>
    </justification>
  </clause>

  <clause id="8302">
    <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,5413,a(flip),b,7820,a)].">
      <j1 rule="hyper" parents="116 5413 7820"/>
    </justification>
  </clause>

  <clause id="8303">
    <literal><![CDATA[
      K(1 / x,y) \ K(K(1 / x,y),z) = K(1 / T(x,z),y) \ 1
    ]]></literal>
    <justification jstring="[para(5549(a,2),7822(a,2,1))].">
      <j1 rule="para" parents="5549 7822"/>
    </justification>
  </clause>

  <clause id="8304">
    <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(7882(a,1),7822(a,2,1))].">
      <j1 rule="para" parents="7882 7822"/>
    </justification>
  </clause>

  <clause id="8305">
    <literal><![CDATA[
      T(T(x,y) * z,K(x,y)) != u
    ]]></literal>
    <literal><![CDATA[
      x * (z * K(x,y)) = u
    ]]></literal>
    <justification jstring="[para(7862(a,1),7850(a,1,1))].">
      <j1 rule="para" parents="7862 7850"/>
    </justification>
  </clause>

  <clause id="8306">
    <literal><![CDATA[
      K(R(x / (x / y),z,u),w) = K(R(y,z,u),T(w,y \ x))
    ]]></literal>
    <justification jstring="[para(4346(a,1),7910(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4346 7910"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8307">
    <literal><![CDATA[
      K(K(R(x,y,z),u) * w,T(x,v5)) = K(w,T(x,v5))
    ]]></literal>
    <justification jstring="[para(7910(a,1),7418(a,1,1,1))].">
      <j1 rule="para" parents="7910 7418"/>
    </justification>
  </clause>

  <clause id="8308">
    <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,6613,a(flip),b,7911,a)].">
      <j1 rule="hyper" parents="58 6613 7911"/>
    </justification>
  </clause>

  <clause id="8309">
    <literal><![CDATA[
      K(T(x,y),T(z,y)) = K(L(x,T(x,y) \ 1,u),z)
    ]]></literal>
    <justification jstring="[hyper(58,a,6495,a(flip),b,7911,a)].">
      <j1 rule="hyper" parents="58 6495 7911"/>
    </justification>
  </clause>

  <clause id="8310">
    <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(1629(a,1),7911(a,1,1))].">
      <j1 rule="para" parents="1629 7911"/>
    </justification>
  </clause>

  <clause id="8311">
    <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(6614,a,7923,a)].">
      <j1 rule="hyper" parents="6614 7923"/>
    </justification>
  </clause>

  <clause id="8312">
    <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(1629(a,1),7923(a,1,2))].">
      <j1 rule="para" parents="1629 7923"/>
    </justification>
  </clause>

  <clause id="8313">
    <literal><![CDATA[
      K(K(x,y) * T(y,z),T(u,z)) = K(y * K(T(x,z),y),u)
    ]]></literal>
    <justification jstring="[para(7932(a,1),7888(a,1,1))].">
      <j1 rule="para" parents="7932 7888"/>
    </justification>
  </clause>

  <clause id="8314">
    <literal><![CDATA[
      (K(x,y) * T(x,z)) \ x = K(z,x) * K(y,x)
    ]]></literal>
    <justification jstring="[para(7941(a,1),7933(a,1,1))].">
      <j1 rule="para" parents="7941 7933"/>
    </justification>
  </clause>

  <clause id="8315">
    <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(7563(a,1),7944(a,1,2,1,1))].">
      <j1 rule="para" parents="7563 7944"/>
    </justification>
  </clause>

  <clause id="8316">
    <literal><![CDATA[
      T(T(x,y / z),K(z,y)) = T(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,8204,a(flip),b,7948,a)].">
      <j1 rule="hyper" parents="58 8204 7948"/>
    </justification>
  </clause>

  <clause id="8317">
    <literal><![CDATA[
      T(T(x,y \ z),K(y,z)) = T(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(7851,a,8316,a)].">
      <j1 rule="hyper" parents="7851 8316"/>
    </justification>
  </clause>

  <clause id="8318">
    <literal><![CDATA[
      T(T(x,K(y,z)),z / y) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(434,a,8316,a)].">
      <j1 rule="hyper" parents="434 8316"/>
    </justification>
  </clause>

  <clause id="8319">
    <literal><![CDATA[
      T(T(x,K(y,z)),y / z) = T(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,7845,a,b,8316,a)].">
      <j1 rule="hyper" parents="58 7845 8316"/>
    </justification>
  </clause>

  <clause id="8320">
    <literal><![CDATA[
      T(T(x,y \ z),K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(8316(a,1),7850(a,1,1))].">
      <j1 rule="para" parents="8316 7850"/>
    </justification>
  </clause>

  <clause id="8321">
    <literal><![CDATA[
      T(T(x,K(y,z)),z \ y) = T(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(58,a,7845,a,b,8317,a)].">
      <j1 rule="hyper" parents="58 7845 8317"/>
    </justification>
  </clause>

  <clause id="8323">
    <literal><![CDATA[
      T(x * K(y / z,x),z \ y) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(5205,a,8319,a)].">
      <j1 rule="hyper" parents="5205 8319"/>
    </justification>
  </clause>

  <clause id="8324">
    <literal><![CDATA[
      T(x / (y / z),z \ y) = T((y / z) \ x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(678,a,8319,a),flip(a)].">
      <j1 rule="hyper" parents="678 8319"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8325">
    <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(5321(a,1),8321(a,1,1,2))].">
      <j1 rule="para" parents="5321 8321"/>
    </justification>
  </clause>

  <clause id="8326">
    <literal><![CDATA[
      T(T(x,K(y,T(z,u))),z \ T(y,u)) = T(x,T(y,u) / z)
    ]]></literal>
    <justification jstring="[para(7160(a,1),8321(a,1,1,2))].">
      <j1 rule="para" parents="7160 8321"/>
    </justification>
  </clause>

  <clause id="8327">
    <literal><![CDATA[
      T(x,y / z) * K(z \ y,z) = K(z \ y,z) * T(x,z \ y)
    ]]></literal>
    <justification jstring="[para(7942(a,1),7950(a,1,1))].">
      <j1 rule="para" parents="7942 7950"/>
    </justification>
  </clause>

  <clause id="8328">
    <literal><![CDATA[
      T(x,K(y,z)) * T(y,z) = K(y,z) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(320,a,5089,a,b,7953,a),flip(a)].">
      <j1 rule="hyper" parents="320 5089 7953"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8329">
    <literal><![CDATA[
      K(x \ (y * z),T(y,z)) = K((x / z) \ y,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,6766,a(flip),b,7971,a),flip(a)].">
      <j1 rule="hyper" parents="320 6766 7971"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8330">
    <literal><![CDATA[
      K(x \ (y * z),T(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K((x / z) \ y,y) = u
    ]]></literal>
    <justification jstring="[para(7971(a,2),6767(a,1))].">
      <j1 rule="para" parents="7971 6767"/>
    </justification>
  </clause>

  <clause id="8331">
    <literal><![CDATA[
      K(x,T(y \ (x * z),z)) = K(x,(y / z) \ x)
    ]]></literal>
    <justification jstring="[hyper(320,a,6962,a(flip),b,7972,a),flip(a)].">
      <j1 rule="hyper" parents="320 6962 7972"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8332">
    <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(4246(a,1),7975(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="4246 7975"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8333">
    <literal><![CDATA[
      T(K(x,y),z) * (z / y) = z / T(y,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,6322,a(flip),b,7992,a),flip(a)].">
      <j1 rule="hyper" parents="320 6322 7992"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8334">
    <literal><![CDATA[
      K(x,y) * (K(z,y) / y) = K(z,y) / T(y,x)
    ]]></literal>
    <justification jstring="[para(5637(a,1),8333(a,1,1))].">
      <j1 rule="para" parents="5637 8333"/>
    </justification>
  </clause>

  <clause id="8335">
    <literal><![CDATA[
      K(x,y \ z) * (z / (z / y)) = z / T(z / y,x)
    ]]></literal>
    <justification jstring="[para(6126(a,1),8333(a,1,1))].">
      <j1 rule="para" parents="6126 8333"/>
    </justification>
  </clause>

  <clause id="8336">
    <literal><![CDATA[
      K(T(x,y),z) * (y / z) = y / T(z,x)
    ]]></literal>
    <justification jstring="[para(7145(a,2),8333(a,1,1))].">
      <j1 rule="para" parents="7145 8333"/>
    </justification>
  </clause>

  <clause id="8337">
    <literal><![CDATA[
      K(x,y) * (z / T(y,z)) = z / T(T(y,z),x)
    ]]></literal>
    <justification jstring="[para(7879(a,1),8333(a,1,1))].">
      <j1 rule="para" parents="7879 8333"/>
    </justification>
  </clause>

  <clause id="8338">
    <literal><![CDATA[
      T(x / T(y,z),y) = T(y,T(z,x)) \ x
    ]]></literal>
    <justification jstring="[para(8336(a,1),7617(a,1,1))].">
      <j1 rule="para" parents="8336 7617"/>
    </justification>
  </clause>

  <clause id="8339">
    <literal><![CDATA[
      T(x \ y,T(z,x)) != (x \ y) * u
    ]]></literal>
    <literal><![CDATA[
      K(y / x,z) = u
    ]]></literal>
    <justification jstring="[para(7998(a,1),38(a,1))].">
      <j1 rule="para" parents="7998 38"/>
    </justification>
  </clause>

  <clause id="8340">
    <literal><![CDATA[
      K(T(x * y,y) / x,z) = K(y,T(T(z,x),x * y))
    ]]></literal>
    <justification jstring="[hyper(8061,a,8005,a)].">
      <j1 rule="hyper" parents="8061 8005"/>
    </justification>
  </clause>

  <clause id="8341">
    <literal><![CDATA[
      T(x,K(y,z / y) / (z \ y)) = T(x,T(1 / (z \ y),y))
    ]]></literal>
    <justification jstring="[para(5219(a,1),8030(a,1,2,1))].">
      <j1 rule="para" parents="5219 8030"/>
    </justification>
  </clause>

  <clause id="8342">
    <literal><![CDATA[
      T(T(x,K(y,z)),y * x) = T(x,T(x * y,z))
    ]]></literal>
    <justification jstring="[hyper(4399,a,8043,a)].">
      <j1 rule="hyper" parents="4399 8043"/>
    </justification>
  </clause>

  <clause id="8343">
    <literal><![CDATA[
      K(x * T(y,z),T(u,K(y,z))) = K(K(y,z) * (x * y),u)
    ]]></literal>
    <justification jstring="[para(8091(a,1),7160(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8091 7160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8344">
    <literal><![CDATA[
      K((x / (x / y)) \ 1,z) = K(y \ 1,T(z,x))
    ]]></literal>
    <justification jstring="[para(75(a,1),8125(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="75 8125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8345">
    <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(8129(a,2),5157(a,1,1))].">
      <j1 rule="para" parents="8129 5157"/>
    </justification>
  </clause>

  <clause id="8346">
    <literal><![CDATA[
      T(x,y) * T(x \ K(x,z),x) = (x \ K(x,z)) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,8134,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 8134 17"/>
    </justification>
  </clause>

  <clause id="8347">
    <literal><![CDATA[
      T(x,1 / T(T(y,z),z)) = T(x,1 / y)
    ]]></literal>
    <justification jstring="[hyper(320,a,4805,a,b,8139,a),flip(a)].">
      <j1 rule="hyper" parents="320 4805 8139"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8348">
    <literal><![CDATA[
      T(x,1 / T(y \ z,y)) = T(x,1 / (z / y))
    ]]></literal>
    <justification jstring="[para(107(a,1),8347(a,1,2,2,1))].">
      <j1 rule="para" parents="107 8347"/>
    </justification>
  </clause>

  <clause id="8349">
    <literal><![CDATA[
      K(L(x / (y \ 1),y \ 1,y) \ 1,z) = K(T(y * x,y \ 1) \ 1,z)
    ]]></literal>
    <justification jstring="[para(864(a,1),8143(a,1,1,1))].">
      <j1 rule="para" parents="864 8143"/>
    </justification>
  </clause>

  <clause id="8350">
    <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(8145(a,2),38(a,1))].">
      <j1 rule="para" parents="8145 38"/>
    </justification>
  </clause>

  <clause id="8351">
    <literal><![CDATA[
      T(x * K(y,T(x,z)),y) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8145(a,1),4931(a,1,1))].">
      <j1 rule="para" parents="8145 4931"/>
    </justification>
  </clause>

  <clause id="8352">
    <literal><![CDATA[
      K(x,y \ T(z,z \ y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(8149(a,2),8290(a,1))].">
      <j1 rule="para" parents="8149 8290"/>
    </justification>
  </clause>

  <clause id="8353">
    <literal><![CDATA[
      x / T(y,K(x,z)) = T(x / y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,7769,a(flip),b,8160,a)].">
      <j1 rule="hyper" parents="58 7769 8160"/>
    </justification>
  </clause>

  <clause id="8354">
    <literal><![CDATA[
      x / T(y,K(z,x)) = T(x / y,K(x,z))
    ]]></literal>
    <justification jstring="[para(7832(a,1),8353(a,1,2))].">
      <j1 rule="para" parents="7832 8353"/>
    </justification>
  </clause>

  <clause id="8355">
    <literal><![CDATA[
      x / T(y,K(z,x)) = T(x / y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(320,a,7832,a,b,8354,a),flip(a)].">
      <j1 rule="hyper" parents="320 7832 8354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8356">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y / x,z) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[para(7784(a,1),8163(a,1,1))].">
      <j1 rule="para" parents="7784 8163"/>
    </justification>
  </clause>

  <clause id="8357">
    <literal><![CDATA[
      K(x,y \ z) * K(z,K(y,x)) = K(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(5163,a,8171,a)].">
      <j1 rule="hyper" parents="5163 8171"/>
    </justification>
  </clause>

  <clause id="8358">
    <literal><![CDATA[
      T(x \ y,K(y,z)) = T(x,K(y,z)) \ y
    ]]></literal>
    <justification jstring="[hyper(58,a,7826,a(flip),b,8182,a),flip(a)].">
      <j1 rule="hyper" parents="58 7826 8182"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8359">
    <literal><![CDATA[
      T(K(x,y),z \ 1) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(58,a,7763,a(flip),b,8191,a),flip(a)].">
      <j1 rule="hyper" parents="58 7763 8191"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8360">
    <literal><![CDATA[
      K(T(x,y \ 1) \ 1,z) = T(K(x \ 1,z),y)
    ]]></literal>
    <justification jstring="[hyper(5546,a,8359,a)].">
      <j1 rule="hyper" parents="5546 8359"/>
    </justification>
  </clause>

  <clause id="8361">
    <literal><![CDATA[
      T(K(x,y),z \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      T(K(x,y),z) = u
    ]]></literal>
    <justification jstring="[para(8359(a,1),3029(a,1))].">
      <j1 rule="para" parents="8359 3029"/>
    </justification>
  </clause>

  <clause id="8364">
    <literal><![CDATA[
      K(x,y) * T(y,T(z,x)) = T(y * K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(2923,a,8292,a)].">
      <j1 rule="hyper" parents="2923 8292"/>
    </justification>
  </clause>

  <clause id="8365">
    <literal><![CDATA[
      K((x \ y) \ (z * y),y) = K((x \ 1) \ z,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,7373,a(flip),b,8297,a),flip(a)].">
      <j1 rule="hyper" parents="58 7373 8297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8366">
    <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(5934(a,1),8301(a,1,1,2))].">
      <j1 rule="para" parents="5934 8301"/>
    </justification>
  </clause>

  <clause id="8367">
    <literal><![CDATA[
      (K(x,y) * T(x,K(z,u))) \ x = K(z,K(u,x)) * K(y,x)
    ]]></literal>
    <justification jstring="[para(7755(a,1),8314(a,2,1))].">
      <j1 rule="para" parents="7755 8314"/>
    </justification>
  </clause>

  <clause id="8368">
    <literal><![CDATA[
      T(T(x,K(y,z)),y / z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(8323(a,1),4931(a,1,1))].">
      <j1 rule="para" parents="8323 4931"/>
    </justification>
  </clause>

  <clause id="8369">
    <literal><![CDATA[
      x * (T(x,y) \ (K(z,x) / x)) = K(z,x) / T(x,y)
    ]]></literal>
    <justification jstring="[hyper(5263,a,8334,a)].">
      <j1 rule="hyper" parents="5263 8334"/>
    </justification>
  </clause>

  <clause id="8370">
    <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(8337(a,2),2611(a,2,1,2))].">
      <j1 rule="para" parents="8337 2611"/>
    </justification>
  </clause>

  <clause id="8371">
    <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(8337(a,2),6431(a,1,2,1,2))].">
      <j1 rule="para" parents="8337 6431"/>
    </justification>
  </clause>

  <clause id="8372">
    <literal><![CDATA[
      K(x,y) * T(z,T(z * x,y)) = T(z,x * z) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,8342,a(flip),b,108,a)].">
      <j1 rule="hyper" parents="119 8342 108"/>
    </justification>
  </clause>

  <clause id="8373">
    <literal><![CDATA[
      T(x,1 / (((y \ z) \ z) \ z)) = T(x,1 / (z / y))
    ]]></literal>
    <justification jstring="[para(4239(a,1),8348(a,1,2,2))].">
      <j1 rule="para" parents="4239 8348"/>
    </justification>
  </clause>

  <clause id="8374">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x \ y,z) = K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(29,a,7823,a,b,8356,a)].">
      <j1 rule="hyper" parents="29 7823 8356"/>
    </justification>
  </clause>

  <clause id="8375">
    <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(4912(a,1),8356(a,1,2))].">
      <j1 rule="para" parents="4912 8356"/>
    </justification>
  </clause>

  <clause id="8376">
    <literal><![CDATA[
      K(x,y \ z) * K(x,K(z,y)) = K(x,z / y)
    ]]></literal>
    <justification jstring="[para(7784(a,1),8357(a,1,2))].">
      <j1 rule="para" parents="7784 8357"/>
    </justification>
  </clause>

  <clause id="8377">
    <literal><![CDATA[
      K(T(x,y \ 1) \ 1,z) = K(T(x,y) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,5544,a,b,8360,a),flip(a)].">
      <j1 rule="hyper" parents="320 5544 8360"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8378">
    <literal><![CDATA[
      K(x,y) \ T(x,T(z,y)) = T(x * K(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(5167,a,8364,a)].">
      <j1 rule="hyper" parents="5167 8364"/>
    </justification>
  </clause>

  <clause id="8379">
    <literal><![CDATA[
      K(x,y) * T(x * K(y,x),z) = T(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(5147,a,8364,a)].">
      <j1 rule="hyper" parents="5147 8364"/>
    </justification>
  </clause>

  <clause id="8380">
    <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(8364(a,1),5148(a,1,2)),flip(b)].">
      <j1 rule="para" parents="8364 5148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8381">
    <literal><![CDATA[
      T(x,(y \ x) \ (z * x)) = 1 / (x \ K((y \ 1) \ z,x))
    ]]></literal>
    <justification jstring="[para(8365(a,1),4992(a,2,2,2))].">
      <j1 rule="para" parents="8365 4992"/>
    </justification>
  </clause>

  <clause id="8382">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x \ z,y) = K(z / x,y)
    ]]></literal>
    <justification jstring="[para(7797(a,1),8374(a,1,1))].">
      <j1 rule="para" parents="7797 8374"/>
    </justification>
  </clause>

  <clause id="8383">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,z \ y) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(5640,a,8376,a)].">
      <j1 rule="hyper" parents="5640 8376"/>
    </justification>
  </clause>

  <clause id="8384">
    <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(7032(a,1),8376(a,1,2,2))].">
      <j1 rule="para" parents="7032 8376"/>
    </justification>
  </clause>

  <clause id="8385">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y,z \ x) = K(y,x / z)
    ]]></literal>
    <justification jstring="[para(7779(a,1),8383(a,1,1))].">
      <j1 rule="para" parents="7779 8383"/>
    </justification>
  </clause>

  <clause id="8386">
    <literal><![CDATA[
      K(K(x,y),z) * K(y,z \ x) = K(y,x / z)
    ]]></literal>
    <justification jstring="[para(7783(a,2),8383(a,1,1))].">
      <j1 rule="para" parents="7783 8383"/>
    </justification>
  </clause>

  <clause id="8387">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,y \ z) = K(x,z / y)
    ]]></literal>
    <justification jstring="[para(7797(a,1),8383(a,1,1))].">
      <j1 rule="para" parents="7797 8383"/>
    </justification>
  </clause>

  <clause id="8388">
    <literal><![CDATA[
      K(x,K(y,z)) * K(z,y / x) = K(z,x \ y)
    ]]></literal>
    <justification jstring="[hyper(5147,a,8386,a)].">
      <j1 rule="hyper" parents="5147 8386"/>
    </justification>
  </clause>

  <clause id="8389">
    <literal><![CDATA[
      K(x,y / z) * K(z \ y,x) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(6344,a,8387,a)].">
      <j1 rule="hyper" parents="6344 8387"/>
    </justification>
  </clause>

  <clause id="8390">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,z / y) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(29,a,7823,a,b,8387,a)].">
      <j1 rule="hyper" parents="29 7823 8387"/>
    </justification>
  </clause>

  <clause id="8391">
    <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(7032(a,1),8387(a,1,1,2))].">
      <j1 rule="para" parents="7032 8387"/>
    </justification>
  </clause>

  <clause id="8392">
    <literal><![CDATA[
      K(x / y,z) * K(z,K(y,x)) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(5147,a,8389,a)].">
      <j1 rule="hyper" parents="5147 8389"/>
    </justification>
  </clause>

  <clause id="8393">
    <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(1409(a,1),8390(a,1,2,2))].">
      <j1 rule="para" parents="1409 8390"/>
    </justification>
  </clause>

  <clause id="8394">
    <literal><![CDATA[
      L(K(x,y),z * x,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(L(x,z,u),y) = w
    ]]></literal>
    <justification jstring="[para(7072(a,1),6499(a,1))].">
      <j1 rule="para" parents="7072 6499"/>
    </justification>
  </clause>

  <clause id="8395">
    <literal><![CDATA[
      K(T(x,y),z) * u != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z,y)) * u = w
    ]]></literal>
    <justification jstring="[para(5130(a,1),7226(a,1))].">
      <j1 rule="para" parents="5130 7226"/>
    </justification>
  </clause>

  <clause id="8396">
    <literal><![CDATA[
      x * K(T(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      x * K(y,T(u,z)) = w
    ]]></literal>
    <justification jstring="[para(6335(a,1),7232(a,1))].">
      <j1 rule="para" parents="6335 7232"/>
    </justification>
  </clause>

  <clause id="8397">
    <literal><![CDATA[
      K(x,R(y,K(z,x),u)) = K(x,y * K(z,x))
    ]]></literal>
    <justification jstring="[hyper(58,a,6955,a(flip),b,7253,a)].">
      <j1 rule="hyper" parents="58 6955 7253"/>
    </justification>
  </clause>

  <clause id="8398">
    <literal><![CDATA[
      K(x,y * K(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(7253(a,1),384(a,1)),flip(b)].">
      <j1 rule="para" parents="7253 384"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8399">
    <literal><![CDATA[
      K(x,y * x) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,x * y) = z
    ]]></literal>
    <justification jstring="[para(84(a,1),8398(a,1,2))].">
      <j1 rule="para" parents="84 8398"/>
    </justification>
  </clause>

  <clause id="8400">
    <literal><![CDATA[
      K(x,y \ T(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(1430(a,1),8398(a,1,2))].">
      <j1 rule="para" parents="1430 8398"/>
    </justification>
  </clause>

  <clause id="8401">
    <literal><![CDATA[
      K(x,T(y,x) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = u
    ]]></literal>
    <justification jstring="[para(5539(a,1),8398(a,1,2))].">
      <j1 rule="para" parents="5539 8398"/>
    </justification>
  </clause>

  <clause id="8402">
    <literal><![CDATA[
      K(x,y / (z / x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (x \ z)) = u
    ]]></literal>
    <justification jstring="[para(6221(a,1),8398(a,1,2))].">
      <j1 rule="para" parents="6221 8398"/>
    </justification>
  </clause>

  <clause id="8403">
    <literal><![CDATA[
      K(x,K(x,y) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) = u
    ]]></literal>
    <justification jstring="[para(7149(a,1),8398(a,1,2))].">
      <j1 rule="para" parents="7149 8398"/>
    </justification>
  </clause>

  <clause id="8404">
    <literal><![CDATA[
      K(L(x,y,z),y * x) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,x * y) = u
    ]]></literal>
    <justification jstring="[para(6618(a,2),8399(a,1))].">
      <j1 rule="para" parents="6618 8399"/>
    </justification>
  </clause>

  <clause id="8406">
    <literal><![CDATA[
      K(x,R(y,K(z,x),u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,7243,a(flip),b,8397,a),flip(a)].">
      <j1 rule="hyper" parents="320 7243 8397"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8408">
    <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),8406(a,1,2))].">
      <j1 rule="para" parents="26 8406"/>
    </justification>
  </clause>

  <clause id="8409">
    <literal><![CDATA[
      K(x,y \ (x \ (z * x))) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(17(a,1),8400(a,1,2,2))].">
      <j1 rule="para" parents="17 8400"/>
    </justification>
  </clause>

  <clause id="8410">
    <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),8400(a,1,2,2))].">
      <j1 rule="para" parents="22 8400"/>
    </justification>
  </clause>

  <clause id="8412">
    <literal><![CDATA[
      T(x,K(y,x) * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z) = u
    ]]></literal>
    <justification jstring="[para(7281(a,2),373(a,1)),flip(b)].">
      <j1 rule="para" parents="7281 373"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8413">
    <literal><![CDATA[
      T(x,(x \ y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,(y / x) * z) = u
    ]]></literal>
    <justification jstring="[para(5443(a,1),8412(a,1,2))].">
      <j1 rule="para" parents="5443 8412"/>
    </justification>
  </clause>

  <clause id="8415">
    <literal><![CDATA[
      K(R(x,K(y,z),u),z) = K(x * K(y,z),z)
    ]]></literal>
    <justification jstring="[hyper(58,a,6743,a(flip),b,7337,a)].">
      <j1 rule="hyper" parents="58 6743 7337"/>
    </justification>
  </clause>

  <clause id="8416">
    <literal><![CDATA[
      K(R(x,K(y,z),u),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,7333,a(flip),b,8415,a),flip(a)].">
      <j1 rule="hyper" parents="320 7333 8415"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8418">
    <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),8416(a,1,1))].">
      <j1 rule="para" parents="26 8416"/>
    </justification>
  </clause>

  <clause id="8419">
    <literal><![CDATA[
      K(L(x,K(y,z),u),y) = K(K(y,z) * x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,6615,a(flip),b,7355,a)].">
      <j1 rule="hyper" parents="58 6615 7355"/>
    </justification>
  </clause>

  <clause id="8420">
    <literal><![CDATA[
      K(L(x,K(y,z),u),y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,7343,a(flip),b,8419,a),flip(a)].">
      <j1 rule="hyper" parents="320 7343 8419"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8421">
    <literal><![CDATA[
      K(L(x,K(y,z),u),y) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = w
    ]]></literal>
    <justification jstring="[para(8419(a,2),7357(a,1))].">
      <j1 rule="para" parents="8419 7357"/>
    </justification>
  </clause>

  <clause id="8423">
    <literal><![CDATA[
      K((x * K(y,z)) \ u,y) = K(K(y,z) \ (x \ u),y)
    ]]></literal>
    <justification jstring="[para(298(a,1),8420(a,1,1))].">
      <j1 rule="para" parents="298 8420"/>
    </justification>
  </clause>

  <clause id="8424">
    <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(7500(a,1),6873(a,1))].">
      <j1 rule="para" parents="7500 6873"/>
    </justification>
  </clause>

  <clause id="8425">
    <literal><![CDATA[
      K(x,y * (z * (u * K(w,x)))) = K(x,y * (z * u))
    ]]></literal>
    <justification jstring="[para(6669(a,1),7579(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6669 7579"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8426">
    <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(4189(a,1),7594(a,2,2,2,2))].">
      <j1 rule="para" parents="4189 7594"/>
    </justification>
  </clause>

  <clause id="8427">
    <literal><![CDATA[
      K(x,T(y,z * (u * K(w,x)))) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[para(90(a,1),7668(a,1,2,2))].">
      <j1 rule="para" parents="90 7668"/>
    </justification>
  </clause>

  <clause id="8428">
    <literal><![CDATA[
      T(K(x,y),z * (u * K(w,x))) = T(K(x,y),z * u)
    ]]></literal>
    <justification jstring="[para(90(a,1),7701(a,1,2))].">
      <j1 rule="para" parents="90 7701"/>
    </justification>
  </clause>

  <clause id="8429">
    <literal><![CDATA[
      K((x * y) \ (z * y),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ z,y) = u
    ]]></literal>
    <justification jstring="[para(7467(a,2),7719(a,1))].">
      <j1 rule="para" parents="7467 7719"/>
    </justification>
  </clause>

  <clause id="8430">
    <literal><![CDATA[
      K(x \ (y * z),z) != u
    ]]></literal>
    <literal><![CDATA[
      K((z \ x) \ y,z) = u
    ]]></literal>
    <justification jstring="[para(7469(a,1),7719(a,1))].">
      <j1 rule="para" parents="7469 7719"/>
    </justification>
  </clause>

  <clause id="8432">
    <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),7742(a,1,2,1,1))].">
      <j1 rule="para" parents="6 7742"/>
    </justification>
  </clause>

  <clause id="8433">
    <literal><![CDATA[
      K(x,T(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(K(x,y),z) = u
    ]]></literal>
    <justification jstring="[para(7766(a,1),7771(a,1))].">
      <j1 rule="para" parents="7766 7771"/>
    </justification>
  </clause>

  <clause id="8434">
    <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(7815(a,2),7771(a,1,2))].">
      <j1 rule="para" parents="7815 7771"/>
    </justification>
  </clause>

  <clause id="8435">
    <literal><![CDATA[
      K((x \ y) \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      T(K(x,z),y) = u
    ]]></literal>
    <justification jstring="[para(7165(a,2),8433(a,1))].">
      <j1 rule="para" parents="7165 8433"/>
    </justification>
  </clause>

  <clause id="8436">
    <literal><![CDATA[
      K(x,y / z) != u
    ]]></literal>
    <literal><![CDATA[
      T(K(x,z \ y),z) = u
    ]]></literal>
    <justification jstring="[para(7913(a,1),8433(a,1))].">
      <j1 rule="para" parents="7913 8433"/>
    </justification>
  </clause>

  <clause id="8437">
    <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(8132(a,2),8048(a,1))].">
      <j1 rule="para" parents="8132 8048"/>
    </justification>
  </clause>

  <clause id="8438">
    <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(7539(a,1),8071(a,1,2))].">
      <j1 rule="para" parents="7539 8071"/>
    </justification>
  </clause>

  <clause id="8439">
    <literal><![CDATA[
      K(L(x,T(x,y) \ 1,z),u) = K(x,u)
    ]]></literal>
    <justification jstring="[hyper(8056,a,8309,a),flip(a)].">
      <j1 rule="hyper" parents="8056 8309"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8441">
    <literal><![CDATA[
      K(L(x,x \ K(y,x),z),u) = K(x,u)
    ]]></literal>
    <justification jstring="[para(4804(a,1),8439(a,1,1,2))].">
      <j1 rule="para" parents="4804 8439"/>
    </justification>
  </clause>

  <clause id="8442">
    <literal><![CDATA[
      T(T(x,K(y,z)),z \ y) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y / z) = u
    ]]></literal>
    <justification jstring="[para(7845(a,2),8320(a,1))].">
      <j1 rule="para" parents="7845 8320"/>
    </justification>
  </clause>

  <clause id="8443">
    <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(7072(a,2),8394(a,1))].">
      <j1 rule="para" parents="7072 8394"/>
    </justification>
  </clause>

  <clause id="8444">
    <literal><![CDATA[
      T(K(x,y),z) * u != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) * u = w
    ]]></literal>
    <justification jstring="[para(7145(a,1),8395(a,1,1))].">
      <j1 rule="para" parents="7145 8395"/>
    </justification>
  </clause>

  <clause id="8445">
    <literal><![CDATA[
      x * T(K(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      x * K(y,T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(7145(a,1),8396(a,1,2))].">
      <j1 rule="para" parents="7145 8396"/>
    </justification>
  </clause>

  <clause id="8446">
    <literal><![CDATA[
      K(x,(y * x) / z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (x \ z)) = u
    ]]></literal>
    <justification jstring="[para(7099(a,2),8402(a,1))].">
      <j1 rule="para" parents="7099 8402"/>
    </justification>
  </clause>

  <clause id="8447">
    <literal><![CDATA[
      K(x,(x \ y) \ z) = K(x,y \ (z * x))
    ]]></literal>
    <justification jstring="[hyper(8409,a,7436,a)].">
      <j1 rule="hyper" parents="8409 7436"/>
    </justification>
  </clause>

  <clause id="8448">
    <literal><![CDATA[
      K(x,(x * y) \ (z * x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(7049(a,2),8409(a,1))].">
      <j1 rule="para" parents="7049 8409"/>
    </justification>
  </clause>

  <clause id="8449">
    <literal><![CDATA[
      K(x,(y / x) \ z) = K(x,y \ (z * x))
    ]]></literal>
    <justification jstring="[hyper(7422,a,8447,a)].">
      <j1 rule="hyper" parents="7422 8447"/>
    </justification>
  </clause>

  <clause id="8450">
    <literal><![CDATA[
      T(x,(x \ y) \ z) = T(x,y \ (z * x))
    ]]></literal>
    <justification jstring="[hyper(118,a,8447,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 8447 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8451">
    <literal><![CDATA[
      K(x,y \ ((x \ z) * x)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,7436,a(flip),b,8447,a),flip(a)].">
      <j1 rule="hyper" parents="58 7436 8447"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8452">
    <literal><![CDATA[
      K(x,y \ (z * x)) = K(x,y \ (x * z))
    ]]></literal>
    <justification jstring="[hyper(58,a,7032,a(flip),b,8447,a),flip(a)].">
      <j1 rule="hyper" parents="58 7032 8447"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8453">
    <literal><![CDATA[
      K(x,y \ (((x \ y) * z) * x)) = K(x,z)
    ]]></literal>
    <justification jstring="[para(4(a,1),8447(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4 8447"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8454">
    <literal><![CDATA[
      L(K(x,y \ ((z \ u) * x)),z \ u,z) = K(x,(z * (x \ y)) \ u)
    ]]></literal>
    <justification jstring="[para(8447(a,1),6585(a,1,1))].">
      <j1 rule="para" parents="8447 6585"/>
    </justification>
  </clause>

  <clause id="8455">
    <literal><![CDATA[
      K(x,y) * K(x,K(y,z \ (u * y))) = K(x,T(y,(y \ z) \ u))
    ]]></literal>
    <justification jstring="[para(8447(a,1),7766(a,1,2,2))].">
      <j1 rule="para" parents="8447 7766"/>
    </justification>
  </clause>

  <clause id="8456">
    <literal><![CDATA[
      K(x,y \ (z * x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,(y / x) \ z) = u
    ]]></literal>
    <justification jstring="[para(8447(a,1),7422(a,1))].">
      <j1 rule="para" parents="8447 7422"/>
    </justification>
  </clause>

  <clause id="8457">
    <literal><![CDATA[
      T(x,(y / x) \ z) = T(x,y \ (z * x))
    ]]></literal>
    <justification jstring="[hyper(118,a,8449,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 8449 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8458">
    <literal><![CDATA[
      T(x,y \ ((x \ z) * x)) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,7512,a(flip),b,8450,a),flip(a)].">
      <j1 rule="hyper" parents="58 7512 8450"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8459">
    <literal><![CDATA[
      K(x,T(y,(y \ z) \ u)) = K(x,T(y,z \ u))
    ]]></literal>
    <justification jstring="[para(8450(a,2),7751(a,1,2))].">
      <j1 rule="para" parents="8450 7751"/>
    </justification>
  </clause>

  <clause id="8460">
    <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(8457(a,1),4806(a,1,1,1))].">
      <j1 rule="para" parents="8457 4806"/>
    </justification>
  </clause>

  <clause id="8461">
    <literal><![CDATA[
      T(x,y \ ((x \ z) * x)) != u
    ]]></literal>
    <literal><![CDATA[
      x * K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(8458(a,2),4858(a,1))].">
      <j1 rule="para" parents="8458 4858"/>
    </justification>
  </clause>

  <clause id="8462">
    <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(8458(a,1),4806(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="8458 4806"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8463">
    <literal><![CDATA[
      K(x \ y,T(x,y \ z)) = K(x \ y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(7714,a,8459,a),flip(a)].">
      <j1 rule="hyper" parents="7714 8459"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8464">
    <literal><![CDATA[
      K(x,y) * K(x,K(y,z \ u)) = K(x,T(y,(y \ z) \ u))
    ]]></literal>
    <justification jstring="[hyper(320,a,7766,a,b,8459,a)].">
      <j1 rule="hyper" parents="320 7766 8459"/>
    </justification>
  </clause>

  <clause id="8465">
    <literal><![CDATA[
      K(x,T(y,(y * z) \ u)) = K(x,T(y,z \ u))
    ]]></literal>
    <justification jstring="[para(4(a,1),8459(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="4 8459"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8466">
    <literal><![CDATA[
      K(x \ y,T(x,y * z)) = K(x \ y,T(x,z))
    ]]></literal>
    <justification jstring="[para(4(a,1),8463(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 8463"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8467">
    <literal><![CDATA[
      K(x \ (y / z),T(x,z)) = K(x \ (y / z),T(x,y))
    ]]></literal>
    <justification jstring="[para(75(a,1),8463(a,1,2,2))].">
      <j1 rule="para" parents="75 8463"/>
    </justification>
  </clause>

  <clause id="8468">
    <literal><![CDATA[
      K(x * y,T(x,y \ z)) = K(x * y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(7714,a,8465,a),flip(a)].">
      <j1 rule="hyper" parents="7714 8465"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8469">
    <literal><![CDATA[
      K(x * y,T(x,y \ z)) = K(y * x,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,5888,a,b,8468,a),flip(a)].">
      <j1 rule="hyper" parents="320 5888 8468"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8470">
    <literal><![CDATA[
      K(x * y,T(y,x \ z)) = K(x * y,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,5888,a,b,8469,a)].">
      <j1 rule="hyper" parents="58 5888 8469"/>
    </justification>
  </clause>

  <clause id="8471">
    <literal><![CDATA[
      K(x * y,T(y,x * z)) = K(x * y,T(y,z))
    ]]></literal>
    <justification jstring="[para(4(a,1),8470(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 8470"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8472">
    <literal><![CDATA[
      K((x * y) \ z,y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ (y \ z),y) = u
    ]]></literal>
    <justification jstring="[para(7641(a,1),8429(a,1))].">
      <j1 rule="para" parents="7641 8429"/>
    </justification>
  </clause>

  <clause id="8473">
    <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(7160(a,1),8442(a,1,1,2))].">
      <j1 rule="para" parents="7160 8442"/>
    </justification>
  </clause>

  <clause id="8474">
    <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(5627(a,2),8444(a,1))].">
      <j1 rule="para" parents="5627 8444"/>
    </justification>
  </clause>

  <clause id="8475">
    <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(7604(a,2),8445(a,1))].">
      <j1 rule="para" parents="7604 8445"/>
    </justification>
  </clause>

  <clause id="8476">
    <literal><![CDATA[
      L(K(x \ y,x),y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(z \ (x \ (z * y)),x) = u
    ]]></literal>
    <justification jstring="[para(6623(a,2),8472(a,1))].">
      <j1 rule="para" parents="6623 8472"/>
    </justification>
  </clause>

  <clause id="8477">
    <literal><![CDATA[
      L(K(x,y),z,T(x,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(4028,a,7041,a)].">
      <j1 rule="hyper" parents="4028 7041"/>
    </justification>
  </clause>

  <clause id="8478">
    <literal><![CDATA[
      K(x,(T(x,y) * z) \ u) = K(x,z \ (T(x,y) \ u))
    ]]></literal>
    <justification jstring="[hyper(6864,a,8477,a)].">
      <j1 rule="hyper" parents="6864 8477"/>
    </justification>
  </clause>

  <clause id="8479">
    <literal><![CDATA[
      K(x,L(y,z,T(x,u))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,6609,a(flip),b,8477,a)].">
      <j1 rule="hyper" parents="58 6609 8477"/>
    </justification>
  </clause>

  <clause id="8480">
    <literal><![CDATA[
      K(x,T(L(y,z,T(x,u)),w)) = K(x,T(y,w))
    ]]></literal>
    <justification jstring="[para(20(a,1),8479(a,1,2))].">
      <j1 rule="para" parents="20 8479"/>
    </justification>
  </clause>

  <clause id="8481">
    <literal><![CDATA[
      K(x,T(y \ (x * z),z)) = K(x,z / (x \ y))
    ]]></literal>
    <justification jstring="[hyper(8290,a,7070,a),flip(a)].">
      <j1 rule="hyper" parents="8290 7070"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8482">
    <literal><![CDATA[
      K(x,y / (x \ z)) = K(x,(z / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,8331,a(flip),b,8481,a),flip(a)].">
      <j1 rule="hyper" parents="58 8331 8481"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8483">
    <literal><![CDATA[
      K(x,(x * y) / z) = K(x,y / (x \ z))
    ]]></literal>
    <justification jstring="[hyper(58,a,7972,a(flip),b,8481,a)].">
      <j1 rule="hyper" parents="58 7972 8481"/>
    </justification>
  </clause>

  <clause id="8484">
    <literal><![CDATA[
      K(x,y / (z / x)) = K(x,(z / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(7401,a,8482,a)].">
      <j1 rule="hyper" parents="7401 8482"/>
    </justification>
  </clause>

  <clause id="8485">
    <literal><![CDATA[
      T(x,y / (x \ z)) = T(x,(z / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(118,a,8482,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 8482 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8486">
    <literal><![CDATA[
      K(x,(y * x) / z) = K(x,(z / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,7550,a,b,8482,a)].">
      <j1 rule="hyper" parents="58 7550 8482"/>
    </justification>
  </clause>

  <clause id="8487">
    <literal><![CDATA[
      K(x,((x * y) / z) \ x) = K(x,z / y)
    ]]></literal>
    <justification jstring="[para(4(a,1),8482(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 8482"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8488">
    <literal><![CDATA[
      R(K(x,(y / (z / u)) \ x),z / u,u) = K(x,z / ((x \ y) * u))
    ]]></literal>
    <justification jstring="[para(8482(a,1),6944(a,1,1))].">
      <j1 rule="para" parents="8482 6944"/>
    </justification>
  </clause>

  <clause id="8489">
    <literal><![CDATA[
      K(x,(y * x) / z) = K(x,(x * y) / z)
    ]]></literal>
    <justification jstring="[hyper(320,a,7550,a,b,8483,a)].">
      <j1 rule="hyper" parents="320 7550 8483"/>
    </justification>
  </clause>

  <clause id="8490">
    <literal><![CDATA[
      T(x,(x * y) / z) = T(x,y / (x \ z))
    ]]></literal>
    <justification jstring="[hyper(118,a,8483,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 8483 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8491">
    <literal><![CDATA[
      K(x,(x \ y) / (x \ z)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(5(a,1),8483(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 8483"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8492">
    <literal><![CDATA[
      T(x,(y * x) / z) = T(x,(z / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,7533,a,b,8485,a)].">
      <j1 rule="hyper" parents="58 7533 8485"/>
    </justification>
  </clause>

  <clause id="8493">
    <literal><![CDATA[
      T(K(x,y \ (z * x)),y) = K(x,(y / z) \ x)
    ]]></literal>
    <justification jstring="[hyper(8436,a,8486,a)].">
      <j1 rule="hyper" parents="8436 8486"/>
    </justification>
  </clause>

  <clause id="8494">
    <literal><![CDATA[
      K(x,T(y \ (z * x),z)) = K(x,(y / z) \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,7973,a,b,8486,a)].">
      <j1 rule="hyper" parents="58 7973 8486"/>
    </justification>
  </clause>

  <clause id="8495">
    <literal><![CDATA[
      K(x,(y \ (x * z)) / z) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[para(72(a,1),8487(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="72 8487"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8496">
    <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(6080(a,1),8487(a,1,2,1))].">
      <j1 rule="para" parents="6080 8487"/>
    </justification>
  </clause>

  <clause id="8497">
    <literal><![CDATA[
      K(x,(y * x) / z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,(z / y) \ x) = u
    ]]></literal>
    <justification jstring="[para(8489(a,2),6964(a,1))].">
      <j1 rule="para" parents="8489 6964"/>
    </justification>
  </clause>

  <clause id="8498">
    <literal><![CDATA[
      K(x,(x \ y) / (z / x)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(7401,a,8491,a)].">
      <j1 rule="hyper" parents="7401 8491"/>
    </justification>
  </clause>

  <clause id="8499">
    <literal><![CDATA[
      K(x,(x \ y) / z) = K(x,y / (x * z))
    ]]></literal>
    <justification jstring="[para(4(a,1),8491(a,1,2,2))].">
      <j1 rule="para" parents="4 8491"/>
    </justification>
  </clause>

  <clause id="8500">
    <literal><![CDATA[
      K(x,(y \ R(x,z,z \ 1)) / a(x,z,z \ 1)) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[para(706(a,1),8495(a,1,2,1,2))].">
      <j1 rule="para" parents="706 8495"/>
    </justification>
  </clause>

  <clause id="8501">
    <literal><![CDATA[
      K(x,(x \ y) / z) = K(x,y / (z * x))
    ]]></literal>
    <justification jstring="[para(6(a,1),8498(a,1,2,2))].">
      <j1 rule="para" parents="6 8498"/>
    </justification>
  </clause>

  <clause id="8502">
    <literal><![CDATA[
      K(x,y / (z * x)) = K(x,y / (x * z))
    ]]></literal>
    <justification jstring="[hyper(58,a,8499,a(flip),b,8501,a),flip(a)].">
      <j1 rule="hyper" parents="58 8499 8501"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8503">
    <literal><![CDATA[
      K(x,(x * y) / (z * x)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(4(a,1),8501(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4 8501"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8504">
    <literal><![CDATA[
      K(x,y / ((z * y) * x)) = K(x,z \ (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(320,a,7009,a(flip),b,8502,a),flip(a)].">
      <j1 rule="hyper" parents="320 7009 8502"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8506">
    <literal><![CDATA[
      K(x,R(y / x,x,z)) = K(x,(y * z) / (z * x))
    ]]></literal>
    <justification jstring="[para(102(a,2),8502(a,2,2)),flip(a)].">
      <j1 rule="para" parents="102 8502"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8507">
    <literal><![CDATA[
      K(x,T((y / z) \ x,y)) = K(x,y \ (z * x))
    ]]></literal>
    <justification jstring="[hyper(7898,a,8493,a)].">
      <j1 rule="hyper" parents="7898 8493"/>
    </justification>
  </clause>

  <clause id="8508">
    <literal><![CDATA[
      K(x,(y / z) \ (x \ 1)) = K(x,z / (y * x))
    ]]></literal>
    <justification jstring="[para(7(a,1),8504(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="7 8504"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8509">
    <literal><![CDATA[
      K(x,(y * (z / y)) / ((z / y) * x)) = K(x,((y \ z) / z) \ (x \ 1))
    ]]></literal>
    <justification jstring="[para(4449(a,1),8504(a,1,2,2,1))].">
      <j1 rule="para" parents="4449 8504"/>
    </justification>
  </clause>

  <clause id="8510">
    <literal><![CDATA[
      K(x,y \ ((z \ y) * x)) = K(x,T(z \ x,y))
    ]]></literal>
    <justification jstring="[para(72(a,1),8507(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="72 8507"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8511">
    <literal><![CDATA[
      K(x,(y / x) \ (z \ y)) = K(x,T(z \ x,y))
    ]]></literal>
    <justification jstring="[hyper(8456,a,8510,a)].">
      <j1 rule="hyper" parents="8456 8510"/>
    </justification>
  </clause>

  <clause id="8512">
    <literal><![CDATA[
      K(x,T(y \ x,x * z)) = K(x,z \ (y \ (x * z)))
    ]]></literal>
    <justification jstring="[hyper(8448,a,8510,a),flip(a)].">
      <j1 rule="hyper" parents="8448 8510"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8513">
    <literal><![CDATA[
      K(x \ y,T(z \ (x \ y),y)) = K(x \ y,x \ (z \ y))
    ]]></literal>
    <justification jstring="[para(72(a,1),8511(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="72 8511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8514">
    <literal><![CDATA[
      K(x,T(y \ (z * x),z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,(y / z) \ x) = u
    ]]></literal>
    <justification jstring="[para(7973(a,2),8497(a,1))].">
      <j1 rule="para" parents="7973 8497"/>
    </justification>
  </clause>

  <clause id="8515">
    <literal><![CDATA[
      K(x,R(x \ y,x,z)) = K(x,(y * z) / (z * x))
    ]]></literal>
    <justification jstring="[hyper(58,a,4914,a(flip),b,8506,a)].">
      <j1 rule="hyper" parents="58 4914 8506"/>
    </justification>
  </clause>

  <clause id="8516">
    <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(7136(a,1),1096(a,1,1,2))].">
      <j1 rule="para" parents="7136 1096"/>
    </justification>
  </clause>

  <clause id="8517">
    <literal><![CDATA[
      T(K(x,y) * (z * K(y,u)),K(y,u)) = K(y,u) * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(7136(a,1),7841(a,1,1))].">
      <j1 rule="para" parents="7136 7841"/>
    </justification>
  </clause>

  <clause id="8518">
    <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),7161(a,2,2))].">
      <j1 rule="para" parents="22 7161"/>
    </justification>
  </clause>

  <clause id="8519">
    <literal><![CDATA[
      K(x \ y,z) * K(u,y / x) = K(u,y / x) * K(x \ y,z)
    ]]></literal>
    <justification jstring="[para(2908(a,1),7189(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="2908 7189"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8520">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(x,y) * u) = K(x,T(y,z)) * u
    ]]></literal>
    <justification jstring="[para(7753(a,1),7190(a,1,1))].">
      <j1 rule="para" parents="7753 7190"/>
    </justification>
  </clause>

  <clause id="8521">
    <literal><![CDATA[
      K(1 / x,T(y,z * x)) = T(K(x \ 1,y),z)
    ]]></literal>
    <justification jstring="[hyper(8435,a,7207,a),flip(a)].">
      <j1 rule="hyper" parents="8435 7207"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8522">
    <literal><![CDATA[
      K(1 / x,T(y,z * x)) = T(K(1 / x,y),z)
    ]]></literal>
    <justification jstring="[para(3312(a,2),8521(a,2,1))].">
      <j1 rule="para" parents="3312 8521"/>
    </justification>
  </clause>

  <clause id="8523">
    <literal><![CDATA[
      K(1 / x,T(y,z * x)) = K(1 / T(x,z),y)
    ]]></literal>
    <justification jstring="[hyper(320,a,5549,a,b,8522,a),flip(a)].">
      <j1 rule="hyper" parents="320 5549 8522"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8524">
    <literal><![CDATA[
      K(1 / x,T(y,z * x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(1 / x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8522(a,2),7708(a,1))].">
      <j1 rule="para" parents="8522 7708"/>
    </justification>
  </clause>

  <clause id="8525">
    <literal><![CDATA[
      K(1 / T(x,y / x),z) = K(1 / x,T(z,y))
    ]]></literal>
    <justification jstring="[para(7(a,1),8523(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7 8523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8526">
    <literal><![CDATA[
      x * K(y \ z,x / (z / y)) = (y \ z) * (x / (y \ z))
    ]]></literal>
    <justification jstring="[hyper(119,a,7247,a,b,87,a)].">
      <j1 rule="hyper" parents="119 7247 87"/>
    </justification>
  </clause>

  <clause id="8528">
    <literal><![CDATA[
      ((x \ y) \ y) \ (z * T(x,x \ y)) = T(z,T(x,y))
    ]]></literal>
    <justification jstring="[para(660(a,1),7290(a,1,1)),flip(a)].">
      <j1 rule="para" parents="660 7290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8529">
    <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(7304(a,2),536(a,1))].">
      <j1 rule="para" parents="7304 536"/>
    </justification>
  </clause>

  <clause id="8530">
    <literal><![CDATA[
      x * K(y,(1 / x) * (z * x)) = K(y,L(z,x,x \ 1)) * x
    ]]></literal>
    <justification jstring="[para(2821(a,1),7304(a,1,2,2))].">
      <j1 rule="para" parents="2821 7304"/>
    </justification>
  </clause>

  <clause id="8531">
    <literal><![CDATA[
      K(((x \ y) \ 1) * z,y \ x) = K(z / (x \ y),y \ x)
    ]]></literal>
    <justification jstring="[hyper(320,a,6710,a,b,7315,a)].">
      <j1 rule="hyper" parents="320 6710 7315"/>
    </justification>
  </clause>

  <clause id="8532">
    <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),7367(a,2,2))].">
      <j1 rule="para" parents="22 7367"/>
    </justification>
  </clause>

  <clause id="8533">
    <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(7477(a,1),7388(a,1,2,1))].">
      <j1 rule="para" parents="7477 7388"/>
    </justification>
  </clause>

  <clause id="8534">
    <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),7426(a,1,2,1))].">
      <j1 rule="para" parents="22 7426"/>
    </justification>
  </clause>

  <clause id="8535">
    <literal><![CDATA[
      (((x \ y) * x) * z) \ (y * z) = K(x,z \ (x \ (y * z)))
    ]]></literal>
    <justification jstring="[para(6(a,1),7452(a,1,1,1,1,2))].">
      <j1 rule="para" parents="6 7452"/>
    </justification>
  </clause>

  <clause id="8536">
    <literal><![CDATA[
      (x * ((y \ (x \ z)) * y)) \ z = K(y,x \ (y \ z))
    ]]></literal>
    <justification jstring="[para(4628(a,1),7452(a,1,1))].">
      <j1 rule="para" parents="4628 7452"/>
    </justification>
  </clause>

  <clause id="8537">
    <literal><![CDATA[
      (x * y) * K(z,x \ (z \ (x * y))) = x * (z * (y / z))
    ]]></literal>
    <justification jstring="[hyper(58,a,4624,a(flip),b,7453,a),flip(a)].">
      <j1 rule="hyper" parents="58 4624 7453"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8538">
    <literal><![CDATA[
      x * K(y,z \ (y \ x)) = z * (y * ((z \ x) / y))
    ]]></literal>
    <justification jstring="[hyper(58,a,4623,a(flip),b,7453,a),flip(a)].">
      <j1 rule="hyper" parents="58 4623 7453"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8539">
    <literal><![CDATA[
      x \ (y * K(z,T(x,u))) = (x \ y) * T(K(z,x),u)
    ]]></literal>
    <justification jstring="[para(7158(a,2),7465(a,1,2,2))].">
      <j1 rule="para" parents="7158 7465"/>
    </justification>
  </clause>

  <clause id="8540">
    <literal><![CDATA[
      (x * K(y \ (z \ x),z)) * u = (y * ((z \ (y \ x)) * z)) * u
    ]]></literal>
    <justification jstring="[hyper(52,a,7471,a)].">
      <j1 rule="hyper" parents="52 7471"/>
    </justification>
  </clause>

  <clause id="8541">
    <literal><![CDATA[
      (x * ((y \ (x \ z)) * y)) \ z != u
    ]]></literal>
    <literal><![CDATA[
      K(y,x \ (y \ z)) = u
    ]]></literal>
    <justification jstring="[para(7471(a,1),6345(a,1,1))].">
      <j1 rule="para" parents="7471 6345"/>
    </justification>
  </clause>

  <clause id="8542">
    <literal><![CDATA[
      T(x,y) * (L(T(x,y),z,x) \ u) = x * (L(x,z,x) \ u)
    ]]></literal>
    <justification jstring="[hyper(119,a,7474,a(flip),b,5175,a)].">
      <j1 rule="hyper" parents="119 7474 5175"/>
    </justification>
  </clause>

  <clause id="8543">
    <literal><![CDATA[
      K(x,T(y * (z * K(u,x)),w)) = K(x,T(y * z,w))
    ]]></literal>
    <justification jstring="[hyper(320,a,7158,a,b,7581,a),flip(a)].">
      <j1 rule="hyper" parents="320 7158 7581"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8544">
    <literal><![CDATA[
      K(x \ (y \ z),T(y,z)) = K(z / (y * x),y)
    ]]></literal>
    <justification jstring="[hyper(8055,a,7610,a),flip(a)].">
      <j1 rule="hyper" parents="8055 7610"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8545">
    <literal><![CDATA[
      K(x \ (y * z),T(y,z)) = K(z / (y \ x),y)
    ]]></literal>
    <justification jstring="[hyper(8055,a,7612,a),flip(a)].">
      <j1 rule="hyper" parents="8055 7612"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8546">
    <literal><![CDATA[
      K((x * y) / z,x) = K(y / (x \ z),x)
    ]]></literal>
    <justification jstring="[hyper(58,a,7971,a(flip),b,8545,a)].">
      <j1 rule="hyper" parents="58 7971 8545"/>
    </justification>
  </clause>

  <clause id="8547">
    <literal><![CDATA[
      K(x / (y \ z),y) * ((y * x) / z) = T((y * x) / z,y)
    ]]></literal>
    <justification jstring="[para(8546(a,1),4770(a,2,1)),flip(a)].">
      <j1 rule="para" parents="8546 4770"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8548">
    <literal><![CDATA[
      T(x * K(y,z / x),x \ z) = T(x \ z,y) \ z
    ]]></literal>
    <justification jstring="[para(7989(a,1),7614(a,1,1))].">
      <j1 rule="para" parents="7989 7614"/>
    </justification>
  </clause>

  <clause id="8549">
    <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(3785(a,1),7623(a,1,1))].">
      <j1 rule="para" parents="3785 7623"/>
    </justification>
  </clause>

  <clause id="8550">
    <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(5896(a,1),7627(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="5896 7627"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8551">
    <literal><![CDATA[
      K(x,(y * K(z,x)) \ u) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[hyper(320,a,6387,a(flip),b,7638,a),flip(a)].">
      <j1 rule="hyper" parents="320 6387 7638"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8552">
    <literal><![CDATA[
      K(x,(y * K(z,x)) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ u) = w
    ]]></literal>
    <justification jstring="[para(7638(a,2),6419(a,1))].">
      <j1 rule="para" parents="7638 6419"/>
    </justification>
  </clause>

  <clause id="8553">
    <literal><![CDATA[
      T(x,(y * K(z,x)) \ u) = T(x,y \ u)
    ]]></literal>
    <justification jstring="[hyper(118,a,8551,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 8551 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8554">
    <literal><![CDATA[
      K(x,(y \ T(z,x)) \ u) = K(x,(y \ z) \ u)
    ]]></literal>
    <justification jstring="[para(1430(a,1),8551(a,1,2,1))].">
      <j1 rule="para" parents="1430 8551"/>
    </justification>
  </clause>

  <clause id="8556">
    <literal><![CDATA[
      K(x,(y * K(x,z)) \ u) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[para(6329(a,1),8551(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6329 8551"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8557">
    <literal><![CDATA[
      K(x,(y * (z / x)) \ u) = K(x,(y * (x \ z)) \ u)
    ]]></literal>
    <justification jstring="[para(6475(a,1),8551(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6475 8551"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8558">
    <literal><![CDATA[
      K(x,(K(x,y) * z) \ u) = K(x,z \ u)
    ]]></literal>
    <justification jstring="[para(7148(a,1),8551(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7148 8551"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8559">
    <literal><![CDATA[
      K(x,(K(y,x) * z) \ u) = K(x,z \ u)
    ]]></literal>
    <justification jstring="[para(7150(a,1),8551(a,1,2,1))].">
      <j1 rule="para" parents="7150 8551"/>
    </justification>
  </clause>

  <clause id="8560">
    <literal><![CDATA[
      K(T(x,y),(z * K(u,x)) \ w) = K(T(x,y),z \ w)
    ]]></literal>
    <justification jstring="[para(7215(a,1),8551(a,1,2,1,2))].">
      <j1 rule="para" parents="7215 8551"/>
    </justification>
  </clause>

  <clause id="8561">
    <literal><![CDATA[
      T(x,(K(y,x) * z) \ u) = T(x,z \ u)
    ]]></literal>
    <justification jstring="[para(7150(a,1),8553(a,1,2,1))].">
      <j1 rule="para" parents="7150 8553"/>
    </justification>
  </clause>

  <clause id="8562">
    <literal><![CDATA[
      K(x,(y * (z * x)) \ u) = K(x,(y * (x * z)) \ u)
    ]]></literal>
    <justification jstring="[para(6633(a,1),8556(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6633 8556"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8564">
    <literal><![CDATA[
      K(x,y \ K(x,z)) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(6489,a,8558,a),flip(a)].">
      <j1 rule="hyper" parents="6489 8558"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8565">
    <literal><![CDATA[
      K(x,y \ T(x,z)) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,6599,a(flip),b,8558,a),flip(a)].">
      <j1 rule="hyper" parents="58 6599 8558"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8566">
    <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),8558(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9 8558"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8567">
    <literal><![CDATA[
      K(x,(y * (K(z,x) * u)) \ w) = K(x,(y * u) \ w)
    ]]></literal>
    <justification jstring="[para(6038(a,1),8558(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6038 8558"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8568">
    <literal><![CDATA[
      T(x,y \ K(x,z)) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(118,a,8564,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 8564 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8569">
    <literal><![CDATA[
      T(x,y \ T(x,z)) = T(x,y \ x)
    ]]></literal>
    <justification jstring="[hyper(118,a,8565,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 8565 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8570">
    <literal><![CDATA[
      K(x,T(y \ x,z)) = K(x,T(y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,7201,a(flip),b,8565,a)].">
      <j1 rule="hyper" parents="58 7201 8565"/>
    </justification>
  </clause>

  <clause id="8571">
    <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),8565(a,1,2,2))].">
      <j1 rule="para" parents="18 8565"/>
    </justification>
  </clause>

  <clause id="8572">
    <literal><![CDATA[
      K(x / y,z \ (x / y)) = K(x / y,z \ (y \ x))
    ]]></literal>
    <justification jstring="[para(107(a,1),8565(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="107 8565"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8573">
    <literal><![CDATA[
      (x \ K(x,y)) * (T(x,x \ 1) * z) = (K(x,y) / x) * (x * z)
    ]]></literal>
    <justification jstring="[para(8568(a,1),4564(a,1,2,1))].">
      <j1 rule="para" parents="8568 4564"/>
    </justification>
  </clause>

  <clause id="8574">
    <literal><![CDATA[
      T(x,T(x,y) / z) = T(x,z \ x)
    ]]></literal>
    <justification jstring="[hyper(7154,a,8569,a)].">
      <j1 rule="hyper" parents="7154 8569"/>
    </justification>
  </clause>

  <clause id="8575">
    <literal><![CDATA[
      K(x,y \ (K(x,z) * u)) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,7510,a(flip),b,8559,a)].">
      <j1 rule="hyper" parents="58 7510 8559"/>
    </justification>
  </clause>

  <clause id="8576">
    <literal><![CDATA[
      K(x,T(y,K(z,z \ x)) \ x) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[hyper(8062,a,8570,a),flip(a)].">
      <j1 rule="hyper" parents="8062 8570"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8578">
    <literal><![CDATA[
      K(x,T(((y \ z) \ 1) \ x,z)) = K(x,y \ ((((y \ z) \ 1) \ y) * x))
    ]]></literal>
    <justification jstring="[hyper(320,a,6596,a(flip),b,8570,a),flip(a)].">
      <j1 rule="hyper" parents="320 6596 8570"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8580">
    <literal><![CDATA[
      K(x,y \ (T(x,z) \ u)) = K(x,y \ (x \ u))
    ]]></literal>
    <justification jstring="[para(5081(a,1),8575(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5081 8575"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8581">
    <literal><![CDATA[
      K(x,y \ (z \ T(u,x))) = K(x,y \ (z \ u))
    ]]></literal>
    <justification jstring="[para(5408(a,1),8575(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5408 8575"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8582">
    <literal><![CDATA[
      K(x,y \ (z * (K(u,x) * w))) = K(x,y \ (z * w))
    ]]></literal>
    <justification jstring="[para(6038(a,1),8575(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6038 8575"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8583">
    <literal><![CDATA[
      K(x,T(y \ (K(x,z) * u),w)) = T(K(x,y \ u),w)
    ]]></literal>
    <justification jstring="[para(8575(a,1),7158(a,2,1))].">
      <j1 rule="para" parents="8575 7158"/>
    </justification>
  </clause>

  <clause id="8584">
    <literal><![CDATA[
      K(x,y \ (z * K(x,u))) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(7897(a,1),8575(a,1,2,2))].">
      <j1 rule="para" parents="7897 8575"/>
    </justification>
  </clause>

  <clause id="8585">
    <literal><![CDATA[
      K(x,y \ (z * (u / x))) = K(x,y \ (z * (x \ u)))
    ]]></literal>
    <justification jstring="[para(6101(a,1),8584(a,1,2,2))].">
      <j1 rule="para" parents="6101 8584"/>
    </justification>
  </clause>

  <clause id="8586">
    <literal><![CDATA[
      K(x,y \ (z * (u * x))) = K(x,y \ (z * (x * u)))
    ]]></literal>
    <justification jstring="[para(6633(a,1),8584(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6633 8584"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8587">
    <literal><![CDATA[
      K(x,(K(y \ x,y) * z) \ x) = K(x,(z * K(y \ x,y)) \ x)
    ]]></literal>
    <justification jstring="[para(6337(a,1),8576(a,1,2,1))].">
      <j1 rule="para" parents="6337 8576"/>
    </justification>
  </clause>

  <clause id="8588">
    <literal><![CDATA[
      K(x,y \ ((T(z,x) / u) \ z)) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[para(75(a,1),8581(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="75 8581"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8589">
    <literal><![CDATA[
      K(x,((T(y,x) / z) \ 1) \ z) = z \ ((T(y,x) / z) \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,6581,a(flip),b,8588,a),flip(a)].">
      <j1 rule="hyper" parents="58 6581 8588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8590">
    <literal><![CDATA[
      K(x,(T(y,x) * z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * z) \ u) = w
    ]]></literal>
    <justification jstring="[para(5539(a,1),8552(a,1,2,1))].">
      <j1 rule="para" parents="5539 8552"/>
    </justification>
  </clause>

  <clause id="8591">
    <literal><![CDATA[
      K(x,(K(y,x) * z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ u) = w
    ]]></literal>
    <justification jstring="[para(7150(a,1),8552(a,1,2,1))].">
      <j1 rule="para" parents="7150 8552"/>
    </justification>
  </clause>

  <clause id="8592">
    <literal><![CDATA[
      K(x,y \ (K(x,z) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ u) = w
    ]]></literal>
    <justification jstring="[para(7510(a,1),8591(a,1))].">
      <j1 rule="para" parents="7510 8591"/>
    </justification>
  </clause>

  <clause id="8593">
    <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(5872(a,1),8592(a,1,2,2))].">
      <j1 rule="para" parents="5872 8592"/>
    </justification>
  </clause>

  <clause id="8594">
    <literal><![CDATA[
      (x / y) * K(x,T(z,y)) = K(x,z) * (x / y)
    ]]></literal>
    <justification jstring="[para(8230(a,1),7649(a,1,2))].">
      <j1 rule="para" parents="8230 7649"/>
    </justification>
  </clause>

  <clause id="8595">
    <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(7673(a,1),6877(a,1,3,2))].">
      <j1 rule="para" parents="7673 6877"/>
    </justification>
  </clause>

  <clause id="8596">
    <literal><![CDATA[
      K(x,T(y,(z * x) * u)) = K(x,T(y,(x * z) * u))
    ]]></literal>
    <justification jstring="[para(84(a,1),7685(a,1,2,2,1))].">
      <j1 rule="para" parents="84 7685"/>
    </justification>
  </clause>

  <clause id="8597">
    <literal><![CDATA[
      T(x,y \ (K(z,x) * u)) = T(x,y \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,8561,a(flip),b,7721,a)].">
      <j1 rule="hyper" parents="58 8561 7721"/>
    </justification>
  </clause>

  <clause id="8599">
    <literal><![CDATA[
      T(x,y \ ((z / x) \ u)) = T(x,y \ ((x \ z) \ u))
    ]]></literal>
    <justification jstring="[para(5399(a,1),8597(a,1,2,2))].">
      <j1 rule="para" parents="5399 8597"/>
    </justification>
  </clause>

  <clause id="8600">
    <literal><![CDATA[
      T(x,y) * K(y * L(x,z,u),x) = R(x,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[para(7745(a,1),6847(a,1,2))].">
      <j1 rule="para" parents="7745 6847"/>
    </justification>
  </clause>

  <clause id="8601">
    <literal><![CDATA[
      (x * K(y,z)) * T(K(z,y),u) = x * K(z,K(y,u))
    ]]></literal>
    <justification jstring="[para(6329(a,1),7770(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6329 7770"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8602">
    <literal><![CDATA[
      L(K(x,K(y,z)),u,w) = K(L(K(x,y),u,w),z)
    ]]></literal>
    <justification jstring="[para(5750(a,1),7775(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5750 7775"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8603">
    <literal><![CDATA[
      x * K(L(K(y,z),u,w),x) = T(x,L(K(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(8602(a,1),7811(a,1,2))].">
      <j1 rule="para" parents="8602 7811"/>
    </justification>
  </clause>

  <clause id="8604">
    <literal><![CDATA[
      T(x,K(y,z \ x)) / z = T(x / z,K(x,y))
    ]]></literal>
    <justification jstring="[para(4755(a,2),7814(a,1,1))].">
      <j1 rule="para" parents="4755 7814"/>
    </justification>
  </clause>

  <clause id="8605">
    <literal><![CDATA[
      R(x,T(K(y,z),u),u) = R(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(320,a,8129,a(flip),b,7874,a),flip(a)].">
      <j1 rule="hyper" parents="320 8129 7874"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8607">
    <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,6669,a(flip),b,7885,a),flip(a)].">
      <j1 rule="hyper" parents="117 6669 7885"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8608">
    <literal><![CDATA[
      ((1 / x) * (K(y,z) * x)) * x = x * L(K(y,z),x,x \ 1)
    ]]></literal>
    <justification jstring="[para(2821(a,1),7885(a,1,1))].">
      <j1 rule="para" parents="2821 7885"/>
    </justification>
  </clause>

  <clause id="8609">
    <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),7886(a,1,1))].">
      <j1 rule="para" parents="22 7886"/>
    </justification>
  </clause>

  <clause id="8610">
    <literal><![CDATA[
      T(T(x,L(K(y,z),u,w)),L(K(y,z),u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(4683,a,7887,a)].">
      <j1 rule="hyper" parents="4683 7887"/>
    </justification>
  </clause>

  <clause id="8611">
    <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,8610,a)].">
      <j1 rule="hyper" parents="678 8610"/>
    </justification>
  </clause>

  <clause id="8612">
    <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(7122(a,1),7902(a,1,1,1,2))].">
      <j1 rule="para" parents="7122 7902"/>
    </justification>
  </clause>

  <clause id="8613">
    <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(7988(a,2),537(a,1))].">
      <j1 rule="para" parents="7988 537"/>
    </justification>
  </clause>

  <clause id="8614">
    <literal><![CDATA[
      T(x,K(y,z \ 1) / z) = x * K(T(x,y),z \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,3798,a,b,8016,a)].">
      <j1 rule="hyper" parents="58 3798 8016"/>
    </justification>
  </clause>

  <clause id="8615">
    <literal><![CDATA[
      K(T(x,y * K(z,y)),u) = u / T(u,x * K(T(x,z),y))
    ]]></literal>
    <justification jstring="[para(8021(a,1),4794(a,2,2))].">
      <j1 rule="para" parents="8021 4794"/>
    </justification>
  </clause>

  <clause id="8616">
    <literal><![CDATA[
      K(x * K(y,z),(x / u) \ 1) = K(K(y,z) * x,x \ u)
    ]]></literal>
    <justification jstring="[hyper(30,a,7565,a,b,8024,a)].">
      <j1 rule="hyper" parents="30 7565 8024"/>
    </justification>
  </clause>

  <clause id="8617">
    <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),8026(a,2,2))].">
      <j1 rule="para" parents="22 8026"/>
    </justification>
  </clause>

  <clause id="8618">
    <literal><![CDATA[
      K(x \ y,x) * (z * (y / x)) = T(z * (x \ y),K(x,y))
    ]]></literal>
    <justification jstring="[para(6475(a,1),8042(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6475 8042"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8619">
    <literal><![CDATA[
      T(K(x,y),K(z,y) \ u) = T(K(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(320,a,7763,a(flip),b,8073,a),flip(a)].">
      <j1 rule="hyper" parents="320 7763 8073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8620">
    <literal><![CDATA[
      T(K(x,y),T(z,K(y,u))) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(320,a,7764,a(flip),b,8074,a),flip(a)].">
      <j1 rule="hyper" parents="320 7764 8074"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8621">
    <literal><![CDATA[
      T(K(x,y),z / K(u,y)) = T(K(x,y),K(u,y) \ z)
    ]]></literal>
    <justification jstring="[para(5629(a,1),8620(a,1,2))].">
      <j1 rule="para" parents="5629 8620"/>
    </justification>
  </clause>

  <clause id="8622">
    <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(4307(a,1),8082(a,1,2,2,2))].">
      <j1 rule="para" parents="4307 8082"/>
    </justification>
  </clause>

  <clause id="8623">
    <literal><![CDATA[
      K(x \ 1,T(y,x \ z)) = K(x \ 1,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,8344,a(flip),b,8105,a),flip(a)].">
      <j1 rule="hyper" parents="58 8344 8105"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8624">
    <literal><![CDATA[
      K(T(x,y),T(z,x \ u)) = K(T(x,y),T(z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,8014,a(flip),b,8109,a),flip(a)].">
      <j1 rule="hyper" parents="58 8014 8109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8625">
    <literal><![CDATA[
      K(T(x,y),T(z,x * u)) = K(T(x,y),T(z,u))
    ]]></literal>
    <justification jstring="[para(4(a,1),8624(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 8624"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8626">
    <literal><![CDATA[
      K(x,T(T(T(x,y) * z,u),w)) = K(x,T(T(x * z,u),w))
    ]]></literal>
    <justification jstring="[para(4819(a,1),8124(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="4819 8124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8627">
    <literal><![CDATA[
      K(1 / (x / (x / y)),z) = K(1 / y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(58,a,8525,a(flip),b,8137,a),flip(a)].">
      <j1 rule="hyper" parents="58 8525 8137"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8628">
    <literal><![CDATA[
      K(1 / (x \ y),T(z,y)) = K(1 / (y / x),z)
    ]]></literal>
    <justification jstring="[para(72(a,1),8627(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="72 8627"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8629">
    <literal><![CDATA[
      K(1 / (x / y),T(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(1 / (y \ x),z) = u
    ]]></literal>
    <justification jstring="[para(8628(a,1),8007(a,1))].">
      <j1 rule="para" parents="8628 8007"/>
    </justification>
  </clause>

  <clause id="8630">
    <literal><![CDATA[
      K(x,(1 / y) * ((z \ ((1 / y) \ 1)) * z)) = K(x,K(y \ z,z))
    ]]></literal>
    <justification jstring="[para(5369(a,1),8194(a,2,2))].">
      <j1 rule="para" parents="5369 8194"/>
    </justification>
  </clause>

  <clause id="8631">
    <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),8234(a,2,2))].">
      <j1 rule="para" parents="20 8234"/>
    </justification>
  </clause>

  <clause id="8632">
    <literal><![CDATA[
      T(x,y) * K(y * R(x,z,u),x) = R(x,y,R(x,z,u))
    ]]></literal>
    <justification jstring="[para(8248(a,1),4947(a,1,2))].">
      <j1 rule="para" parents="8248 4947"/>
    </justification>
  </clause>

  <clause id="8633">
    <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(8248(a,2),7790(a,2,1))].">
      <j1 rule="para" parents="8248 7790"/>
    </justification>
  </clause>

  <clause id="8634">
    <literal><![CDATA[
      K(T(L(x,y,z) * u,u),x) = K(L(x,y,z) * u,x)
    ]]></literal>
    <justification jstring="[hyper(7310,a,8249,a)].">
      <j1 rule="hyper" parents="7310 8249"/>
    </justification>
  </clause>

  <clause id="8635">
    <literal><![CDATA[
      T(x,y) * (x \ T(x * z,x)) = T(T(x,y) * z,x)
    ]]></literal>
    <justification jstring="[para(4(a,1),8286(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4 8286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8637">
    <literal><![CDATA[
      K(x,T(x \ y,z \ y)) = K(x,T(x \ y,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,8230,a(flip),b,8298,a),flip(a)].">
      <j1 rule="hyper" parents="320 8230 8298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8638">
    <literal><![CDATA[
      K(x,T(x \ y,z \ y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(x \ y,z)) = u
    ]]></literal>
    <justification jstring="[para(8298(a,2),8252(a,1))].">
      <j1 rule="para" parents="8298 8252"/>
    </justification>
  </clause>

  <clause id="8639">
    <literal><![CDATA[
      K(L(x,y,x),z) = K(T(u * x,x) / u,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,7912,a,b,8340,a)].">
      <j1 rule="hyper" parents="320 7912 8340"/>
    </justification>
  </clause>

  <clause id="8640">
    <literal><![CDATA[
      K(T(x * y,y) / x,z) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(8421,a,8639,a),flip(a)].">
      <j1 rule="hyper" parents="8421 8639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8642">
    <literal><![CDATA[
      K(T(x,y) / (x / y),z) = K(y,z)
    ]]></literal>
    <justification jstring="[para(7(a,1),8640(a,1,1,1,1))].">
      <j1 rule="para" parents="7 8640"/>
    </justification>
  </clause>

  <clause id="8643">
    <literal><![CDATA[
      T(x,y) \ ((x \ 1) \ K(z,x)) = x * (K(z,x) / T(x,y))
    ]]></literal>
    <justification jstring="[para(8369(a,1),3494(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8369 3494"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8644">
    <literal><![CDATA[
      K((x * K(y,z)) \ u,y) = K(x \ u,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,7344,a(flip),b,8423,a),flip(a)].">
      <j1 rule="hyper" parents="320 7344 8423"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8646">
    <literal><![CDATA[
      K(T(x \ T(y,x),z) \ u,z) = K((T(x,y) \ y) \ u,z)
    ]]></literal>
    <justification jstring="[para(4828(a,1),8644(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4828 8644"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8647">
    <literal><![CDATA[
      K((x * K(y,z)) \ u,z) = K(x \ u,z)
    ]]></literal>
    <justification jstring="[para(6329(a,1),8644(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6329 8644"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8648">
    <literal><![CDATA[
      K((x * T(y,z)) \ u,z) = K((x * y) \ u,z)
    ]]></literal>
    <justification jstring="[para(6331(a,1),8644(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6331 8644"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8649">
    <literal><![CDATA[
      K((x * (y / z)) \ u,z) = K((x * (z \ y)) \ u,z)
    ]]></literal>
    <justification jstring="[para(6101(a,1),8644(a,1,1,1))].">
      <j1 rule="para" parents="6101 8644"/>
    </justification>
  </clause>

  <clause id="8650">
    <literal><![CDATA[
      K((x * (y * z)) \ u,z) = K((x * (z * y)) \ u,z)
    ]]></literal>
    <justification jstring="[para(6633(a,1),8644(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6633 8644"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8651">
    <literal><![CDATA[
      K((K(x,y) * z) \ u,y) = K(z \ u,y)
    ]]></literal>
    <justification jstring="[para(7176(a,1),8644(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7176 8644"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8652">
    <literal><![CDATA[
      K((x * K(y,z)) \ u,T(y,w)) = K(x \ u,T(y,w))
    ]]></literal>
    <justification jstring="[para(7888(a,1),8644(a,1,1,1,2))].">
      <j1 rule="para" parents="7888 8644"/>
    </justification>
  </clause>

  <clause id="8653">
    <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(6197(a,2),8647(a,1,1))].">
      <j1 rule="para" parents="6197 8647"/>
    </justification>
  </clause>

  <clause id="8654">
    <literal><![CDATA[
      K(x \ (K(y,z) * u),y) = K(x \ u,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,7505,a(flip),b,8651,a)].">
      <j1 rule="hyper" parents="58 7505 8651"/>
    </justification>
  </clause>

  <clause id="8656">
    <literal><![CDATA[
      K(x \ (K(y,z) * u),z) = K(x \ u,z)
    ]]></literal>
    <justification jstring="[para(5133(a,1),8654(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5133 8654"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8657">
    <literal><![CDATA[
      K(x \ (y / z),z \ y) = K(x \ (z \ y),z \ y)
    ]]></literal>
    <justification jstring="[para(4997(a,1),8654(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4997 8654"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8658">
    <literal><![CDATA[
      K(x \ (T(y,z) \ u),y) = K(x \ (y \ u),y)
    ]]></literal>
    <justification jstring="[para(5081(a,1),8654(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5081 8654"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8660">
    <literal><![CDATA[
      K(x \ (K(y,z) * u),T(y,w)) = K(x \ u,T(y,w))
    ]]></literal>
    <justification jstring="[para(7888(a,1),8654(a,1,1,2,1))].">
      <j1 rule="para" parents="7888 8654"/>
    </justification>
  </clause>

  <clause id="8661">
    <literal><![CDATA[
      K(x \ (y * K(z,u)),z) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[para(7897(a,1),8654(a,1,1,2))].">
      <j1 rule="para" parents="7897 8654"/>
    </justification>
  </clause>

  <clause id="8662">
    <literal><![CDATA[
      K(x \ (y / (z * y)),z \ 1) = K(x \ ((z * y) \ y),z \ 1)
    ]]></literal>
    <justification jstring="[para(5354(a,1),8656(a,1,1,2))].">
      <j1 rule="para" parents="5354 8656"/>
    </justification>
  </clause>

  <clause id="8663">
    <literal><![CDATA[
      K(x \ (y * T(z,u)),u) = K(x \ (y * z),u)
    ]]></literal>
    <justification jstring="[para(5555(a,1),8656(a,1,1,2))].">
      <j1 rule="para" parents="5555 8656"/>
    </justification>
  </clause>

  <clause id="8664">
    <literal><![CDATA[
      K(x \ (y * (z * u)),u) = K(x \ (y * (u * z)),u)
    ]]></literal>
    <justification jstring="[para(6633(a,1),8661(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6633 8661"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8665">
    <literal><![CDATA[
      K((T(x,y) * z) \ u,x) = K(z \ (x \ u),x)
    ]]></literal>
    <justification jstring="[hyper(58,a,7511,a,b,8658,a)].">
      <j1 rule="hyper" parents="58 7511 8658"/>
    </justification>
  </clause>

  <clause id="8666">
    <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),8663(a,1,1)),flip(a)].">
      <j1 rule="para" parents="228 8663"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8668">
    <literal><![CDATA[
      K((T(x,y) * z) \ u,K(x,w)) = K(w,K(z \ (x \ u),x))
    ]]></literal>
    <justification jstring="[para(8665(a,1),7784(a,2,2))].">
      <j1 rule="para" parents="8665 7784"/>
    </justification>
  </clause>

  <clause id="8669">
    <literal><![CDATA[
      K(T(x,y * (z * K(u,w))),w) = (v5 * K(w,T(x,y * z))) \ v5
    ]]></literal>
    <justification jstring="[para(8427(a,1),6338(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="8427 6338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8670">
    <literal><![CDATA[
      K(x,(T(x,y) * z) \ u) = K(x,z \ (x \ u))
    ]]></literal>
    <justification jstring="[hyper(320,a,8580,a(flip),b,8478,a),flip(a)].">
      <j1 rule="hyper" parents="320 8580 8478"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8672">
    <literal><![CDATA[
      K(x,y \ (z \ (x * y))) = K(x,T(z \ x,y))
    ]]></literal>
    <justification jstring="[hyper(7710,a,8512,a),flip(a)].">
      <j1 rule="hyper" parents="7710 8512"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8673">
    <literal><![CDATA[
      R(K(x,T(y,z)),y * u,w) = K(x,R(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(7158(a,2),8518(a,1,1))].">
      <j1 rule="para" parents="7158 8518"/>
    </justification>
  </clause>

  <clause id="8674">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(x,x \ y) * u) = K(x,T(x \ y,z)) * u
    ]]></literal>
    <justification jstring="[para(7965(a,1),8520(a,1,1))].">
      <j1 rule="para" parents="7965 8520"/>
    </justification>
  </clause>

  <clause id="8675">
    <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),8532(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="4 8532"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8676">
    <literal><![CDATA[
      K(x,(y * (z * x)) \ u) = K(x,(y * z) \ (x \ u))
    ]]></literal>
    <justification jstring="[hyper(58,a,6902,a(flip),b,8536,a)].">
      <j1 rule="hyper" parents="58 6902 8536"/>
    </justification>
  </clause>

  <clause id="8677">
    <literal><![CDATA[
      (x * (y * ((z \ (y \ (x \ u))) * z))) \ u = K(z,(x * y) \ (z \ u))
    ]]></literal>
    <justification jstring="[para(3544(a,1),8536(a,1,1))].">
      <j1 rule="para" parents="3544 8536"/>
    </justification>
  </clause>

  <clause id="8678">
    <literal><![CDATA[
      x * (y * ((x \ z) / y)) != z * u
    ]]></literal>
    <literal><![CDATA[
      K(y,x \ (y \ z)) = u
    ]]></literal>
    <justification jstring="[para(8538(a,1),38(a,1))].">
      <j1 rule="para" parents="8538 38"/>
    </justification>
  </clause>

  <clause id="8679">
    <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(1323,a,8539,a),flip(a)].">
      <j1 rule="hyper" parents="1323 8539"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8680">
    <literal><![CDATA[
      K(x,T(y * (z / T(u,x)),w)) = K(x,T(y * (z / u),w))
    ]]></literal>
    <justification jstring="[para(6188(a,1),8543(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="6188 8543"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8681">
    <literal><![CDATA[
      (x \ 1) / (x \ K(x,(y * (x \ z)) \ u)) = K((y * (z / x)) \ u,x)
    ]]></literal>
    <justification jstring="[para(8557(a,1),5138(a,1,2,2))].">
      <j1 rule="para" parents="8557 5138"/>
    </justification>
  </clause>

  <clause id="8682">
    <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(8562(a,1),6615(a,1,1))].">
      <j1 rule="para" parents="8562 6615"/>
    </justification>
  </clause>

  <clause id="8683">
    <literal><![CDATA[
      K(x,(y * (K(x,z) * u)) \ w) = K(x,(y * u) \ w)
    ]]></literal>
    <justification jstring="[para(5133(a,1),8567(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="5133 8567"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8684">
    <literal><![CDATA[
      K(x / y,z \ (y \ x)) = K(y \ x,(z * y) \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,8118,a(flip),b,8572,a),flip(a)].">
      <j1 rule="hyper" parents="58 8118 8572"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8685">
    <literal><![CDATA[
      K(x,y \ (z * (K(x,u) * w))) = K(x,y \ (z * w))
    ]]></literal>
    <justification jstring="[para(5133(a,1),8582(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="5133 8582"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8686">
    <literal><![CDATA[
      K(x,T(y \ (K(x,z) * u),w)) = K(x,T(y \ u,w))
    ]]></literal>
    <justification jstring="[hyper(320,a,7158,a,b,8583,a),flip(a)].">
      <j1 rule="hyper" parents="320 7158 8583"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8687">
    <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,7681,a(flip),b,8585,a),flip(a)].">
      <j1 rule="hyper" parents="58 7681 8585"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8688">
    <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(8599(a,1),4806(a,1,1,1))].">
      <j1 rule="para" parents="8599 4806"/>
    </justification>
  </clause>

  <clause id="8689">
    <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(5500(a,1),8601(a,1,1))].">
      <j1 rule="para" parents="5500 8601"/>
    </justification>
  </clause>

  <clause id="8690">
    <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,8609,a(flip),b,4105,a(flip))].">
      <j1 rule="hyper" parents="239 8609 4105"/>
    </justification>
  </clause>

  <clause id="8691">
    <literal><![CDATA[
      K(x,K(y,z \ 1) / z) = K(T(x,y),z \ 1)
    ]]></literal>
    <justification jstring="[hyper(4837,a,8614,a)].">
      <j1 rule="hyper" parents="4837 8614"/>
    </justification>
  </clause>

  <clause id="8692">
    <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(5435(a,1),8691(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5435 8691"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8693">
    <literal><![CDATA[
      T(x,R(T(y,y \ z),u,w)) = T(x,R(z / (z / y),u,w))
    ]]></literal>
    <justification jstring="[para(4343(a,1),8617(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4343 8617"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8694">
    <literal><![CDATA[
      T(K(x,y),z / K(u,y)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(320,a,8619,a(flip),b,8621,a),flip(a)].">
      <j1 rule="hyper" parents="320 8619 8621"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8696">
    <literal><![CDATA[
      T(K(x,y),z * K(y,u)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(6335(a,1),8694(a,1,2))].">
      <j1 rule="para" parents="6335 8694"/>
    </justification>
  </clause>

  <clause id="8697">
    <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(8696(a,1),8605(a,1,2))].">
      <j1 rule="para" parents="8696 8605"/>
    </justification>
  </clause>

  <clause id="8698">
    <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(1754(a,1),8635(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1754 8635"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8699">
    <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(1899(a,1),8635(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1899 8635"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8700">
    <literal><![CDATA[
      K(((x \ 1) * (y * x)) \ z,x) = K(L(y,x,x \ 1) \ z,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,4008,a(flip),b,8650,a),flip(a)].">
      <j1 rule="hyper" parents="320 4008 8650"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8701">
    <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(8657(a,1),5526(a,1,1,1,2))].">
      <j1 rule="para" parents="8657 5526"/>
    </justification>
  </clause>

  <clause id="8702">
    <literal><![CDATA[
      K(x \ (y * z),T(z,u)) = K(x \ (z * y),T(z,u))
    ]]></literal>
    <justification jstring="[para(4813(a,1),8660(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4813 8660"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8703">
    <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),8664(a,2,1))].">
      <j1 rule="para" parents="477 8664"/>
    </justification>
  </clause>

  <clause id="8704">
    <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),8673(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5 8673"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8705">
    <literal><![CDATA[
      K(x,(x * y) \ ((x * z) * y)) = K(x,R(T(z,y),x,y))
    ]]></literal>
    <justification jstring="[hyper(5038,a,8675,a)].">
      <j1 rule="hyper" parents="5038 8675"/>
    </justification>
  </clause>

  <clause id="8706">
    <literal><![CDATA[
      K(x,(y * (x * z)) \ u) = K(x,(y * z) \ (x \ u))
    ]]></literal>
    <justification jstring="[hyper(58,a,8562,a(flip),b,8676,a)].">
      <j1 rule="hyper" parents="58 8562 8676"/>
    </justification>
  </clause>

  <clause id="8707">
    <literal><![CDATA[
      K(x,(y * (z / x)) \ (x \ u)) = K(x,(y * z) \ u)
    ]]></literal>
    <justification jstring="[para(7(a,1),8676(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="7 8676"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8708">
    <literal><![CDATA[
      K(x,((1 / y) * y) \ (x \ z)) = K(x,L(x,y,y \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(2820(a,1),8676(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2820 8676"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8709">
    <literal><![CDATA[
      (x * K(y,(z * u) \ (y \ w))) \ x = K((z * (u * y)) \ w,y)
    ]]></literal>
    <justification jstring="[para(8676(a,1),6338(a,1,1,2))].">
      <j1 rule="para" parents="8676 6338"/>
    </justification>
  </clause>

  <clause id="8710">
    <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),8685(a,1,2))].">
      <j1 rule="para" parents="477 8685"/>
    </justification>
  </clause>

  <clause id="8711">
    <literal><![CDATA[
      K(x,T(y \ T(x,z),u)) = K(x,T(y \ x,u))
    ]]></literal>
    <justification jstring="[para(4770(a,2),8686(a,1,2,1,2))].">
      <j1 rule="para" parents="4770 8686"/>
    </justification>
  </clause>

  <clause id="8712">
    <literal><![CDATA[
      K(x,T(y \ T(T(x,z),u),w)) = K(x,T(y \ T(x,u),w))
    ]]></literal>
    <justification jstring="[para(7227(a,1),8686(a,1,2,1,2))].">
      <j1 rule="para" parents="7227 8686"/>
    </justification>
  </clause>

  <clause id="8713">
    <literal><![CDATA[
      K(x \ (y * z),T(z,y)) = K((x / y) \ z,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,8329,a(flip),b,8702,a),flip(a)].">
      <j1 rule="hyper" parents="320 8329 8702"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8714">
    <literal><![CDATA[
      K((x \ y) \ z,T(z,x)) = K((y / x) \ z,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,7399,a,b,8713,a)].">
      <j1 rule="hyper" parents="58 7399 8713"/>
    </justification>
  </clause>

  <clause id="8715">
    <literal><![CDATA[
      K(((x * y) / x) \ z,z) = K(y \ z,T(z,x))
    ]]></literal>
    <justification jstring="[para(4(a,1),8714(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4 8714"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8716">
    <literal><![CDATA[
      K(x * (y \ K(y,z)),x) = K(y \ x,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,5366,a(flip),b,8715,a)].">
      <j1 rule="hyper" parents="58 5366 8715"/>
    </justification>
  </clause>

  <clause id="8717">
    <literal><![CDATA[
      K((x \ K(x,y)) * z,z) = K(x \ z,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(7419,a,8716,a)].">
      <j1 rule="hyper" parents="7419 8716"/>
    </justification>
  </clause>

  <clause id="8718">
    <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,8704,a),flip(a)].">
      <j1 rule="hyper" parents="320 379 8704"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8719">
    <literal><![CDATA[
      K(x,R(T(y,z),y \ 1,u)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(320,a,7158,a(flip),b,8718,a),flip(a)].">
      <j1 rule="hyper" parents="320 7158 8718"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8720">
    <literal><![CDATA[
      K(x,(y * (x \ z)) \ (x \ u)) = K(x,(y * z) \ u)
    ]]></literal>
    <justification jstring="[para(5(a,1),8706(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="5 8706"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8721">
    <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(8706(a,1),6615(a,1,1))].">
      <j1 rule="para" parents="8706 6615"/>
    </justification>
  </clause>

  <clause id="8722">
    <literal><![CDATA[
      K(x,(y * (z / x)) \ u) = K(x,(y * z) \ (u * x))
    ]]></literal>
    <justification jstring="[hyper(8409,a,8707,a)].">
      <j1 rule="hyper" parents="8409 8707"/>
    </justification>
  </clause>

  <clause id="8723">
    <literal><![CDATA[
      K(x,(y * (x \ z)) \ u) = K(x,(y * z) \ (u * x))
    ]]></literal>
    <justification jstring="[hyper(8409,a,8720,a)].">
      <j1 rule="hyper" parents="8409 8720"/>
    </justification>
  </clause>

  <clause id="8724">
    <literal><![CDATA[
      (x \ 1) / (x \ K(x,(y * z) \ (u * x))) = K((y * (z / x)) \ u,x)
    ]]></literal>
    <justification jstring="[para(8722(a,1),5138(a,1,2,2))].">
      <j1 rule="para" parents="8722 5138"/>
    </justification>
  </clause>

  <clause id="8725">
    <literal><![CDATA[
      L(K(x,(y * z) \ ((u \ w) * x)),u \ w,u) = K(x,(u * (y * (z / x))) \ w)
    ]]></literal>
    <justification jstring="[para(8722(a,1),6585(a,1,1))].">
      <j1 rule="para" parents="8722 6585"/>
    </justification>
  </clause>

  <clause id="8726">
    <literal><![CDATA[
      K(x,((y * K(x \ z,y)) * z) \ (u * x)) = K(x,((x \ z) * y) \ u)
    ]]></literal>
    <justification jstring="[para(4774(a,1),8723(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4774 8723"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8727">
    <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(7209(a,1),39(a,1))].">
      <j1 rule="para" parents="7209 39"/>
    </justification>
  </clause>

  <clause id="8728">
    <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(1405(a,1),7261(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1405 7261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8729">
    <literal><![CDATA[
      K(x,y \ (x \ (y * (z * x)))) = K(x,L(z,x,y))
    ]]></literal>
    <justification jstring="[hyper(320,a,4911,a(flip),b,7595,a),flip(a)].">
      <j1 rule="hyper" parents="320 4911 7595"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8730">
    <literal><![CDATA[
      K(x,y \ (x \ (y * (z * x)))) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,L(z,x,y)) = u
    ]]></literal>
    <justification jstring="[para(7595(a,2),5037(a,1))].">
      <j1 rule="para" parents="7595 5037"/>
    </justification>
  </clause>

  <clause id="8731">
    <literal><![CDATA[
      K(x,y) * K(x * y,x) = T(x \ R(x,y,x),y)
    ]]></literal>
    <justification jstring="[para(6457(a,1),7616(a,1,2))].">
      <j1 rule="para" parents="6457 7616"/>
    </justification>
  </clause>

  <clause id="8732">
    <literal><![CDATA[
      T(x \ R(x,y,x),y) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(5483,a,8731,a),flip(a)].">
      <j1 rule="hyper" parents="5483 8731"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8733">
    <literal><![CDATA[
      (x * (y \ R(y,x,y))) / x = y \ R(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(271,a,8732,a)].">
      <j1 rule="hyper" parents="271 8732"/>
    </justification>
  </clause>

  <clause id="8734">
    <literal><![CDATA[
      (T(x * y,x) / x) / y = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[para(6573(a,1),8733(a,1,1))].">
      <j1 rule="para" parents="6573 8733"/>
    </justification>
  </clause>

  <clause id="8735">
    <literal><![CDATA[
      K(x,T(y,z) \ x) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y \ x,z)) = u
    ]]></literal>
    <justification jstring="[para(8565(a,1),7705(a,1))].">
      <j1 rule="para" parents="8565 7705"/>
    </justification>
  </clause>

  <clause id="8737">
    <literal><![CDATA[
      T(x * y,T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x * y,T(z,x)) = u
    ]]></literal>
    <justification jstring="[para(8220(a,1),7722(a,1))].">
      <j1 rule="para" parents="8220 7722"/>
    </justification>
  </clause>

  <clause id="8738">
    <literal><![CDATA[
      K(x,T(y,K(L(x,z,u),w) * v5)) = K(x,T(y,v5))
    ]]></literal>
    <justification jstring="[hyper(320,a,7930,a(flip),b,8020,a),flip(a)].">
      <j1 rule="hyper" parents="320 7930 8020"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8739">
    <literal><![CDATA[
      K(x,T(y,L(x,z,u) * (u * z))) = K(x,T(y,u * (z * x)))
    ]]></literal>
    <justification jstring="[para(5003(a,1),8738(a,1,2,2))].">
      <j1 rule="para" parents="5003 8738"/>
    </justification>
  </clause>

  <clause id="8740">
    <literal><![CDATA[
      K(1 / T(T(x,y),y * x),z) = K(1 / L(x,y,x),z)
    ]]></literal>
    <justification jstring="[para(4316(a,1),8138(a,1,1,2))].">
      <j1 rule="para" parents="4316 8138"/>
    </justification>
  </clause>

  <clause id="8741">
    <literal><![CDATA[
      (x \ 1) * K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,T(z,x)) * (x \ 1) = u
    ]]></literal>
    <justification jstring="[para(7883(a,1),8240(a,1,2))].">
      <j1 rule="para" parents="7883 8240"/>
    </justification>
  </clause>

  <clause id="8742">
    <literal><![CDATA[
      (x \ y) * K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,T(z,x)) * (x \ y) = u
    ]]></literal>
    <justification jstring="[para(7883(a,1),8242(a,1,2))].">
      <j1 rule="para" parents="7883 8242"/>
    </justification>
  </clause>

  <clause id="8743">
    <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,8603,a,b,8253,a)].">
      <j1 rule="hyper" parents="58 8603 8253"/>
    </justification>
  </clause>

  <clause id="8744">
    <literal><![CDATA[
      K(x / (y * z),y) != u
    ]]></literal>
    <literal><![CDATA[
      K((y \ x) / z,y) = u
    ]]></literal>
    <justification jstring="[para(8544(a,1),8262(a,1))].">
      <j1 rule="para" parents="8544 8262"/>
    </justification>
  </clause>

  <clause id="8746">
    <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,8600,a(flip),b,4778,a),flip(a)].">
      <j1 rule="hyper" parents="116 8600 4778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8747">
    <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(8600(a,1),13(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="8600 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8748">
    <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(8600(a,1),5096(a,1,2))].">
      <j1 rule="para" parents="8600 5096"/>
    </justification>
  </clause>

  <clause id="8749">
    <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,8632,a(flip),b,4778,a),flip(a)].">
      <j1 rule="hyper" parents="116 8632 4778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8750">
    <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(8632(a,1),5466(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8632 5466"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8751">
    <literal><![CDATA[
      K(x,T(x \ y,y \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(x \ y,z)) = u
    ]]></literal>
    <justification jstring="[para(8238(a,1),8638(a,1))].">
      <j1 rule="para" parents="8238 8638"/>
    </justification>
  </clause>

  <clause id="8752">
    <literal><![CDATA[
      K(x,y \ (x \ ((x * z) * y))) = K(x,R(T(z,y),x,y))
    ]]></literal>
    <justification jstring="[hyper(7393,a,8705,a)].">
      <j1 rule="hyper" parents="7393 8705"/>
    </justification>
  </clause>

  <clause id="8753">
    <literal><![CDATA[
      K(1 / T(x,y),T(z,y * x)) = K(1 / L(x,y,x),z)
    ]]></literal>
    <justification jstring="[hyper(7713,a,8740,a)].">
      <j1 rule="hyper" parents="7713 8740"/>
    </justification>
  </clause>

  <clause id="8754">
    <literal><![CDATA[
      K(1 / x,T(T(y,z * x),z)) = K(1 / L(x,z,x),y)
    ]]></literal>
    <justification jstring="[hyper(7713,a,8753,a)].">
      <j1 rule="hyper" parents="7713 8753"/>
    </justification>
  </clause>

  <clause id="8755">
    <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),8754(a,1,2))].">
      <j1 rule="para" parents="18 8754"/>
    </justification>
  </clause>

  <clause id="8756">
    <literal><![CDATA[
      K(1 / L(x,y,x),z) = K(1 / x,T(T(z,y),y))
    ]]></literal>
    <justification jstring="[hyper(8524,a,8755,a),flip(a)].">
      <j1 rule="hyper" parents="8524 8755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8757">
    <literal><![CDATA[
      K(1 / L(x,y,x),z) = K(1 / x,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,7883,a(flip),b,8756,a),flip(a)].">
      <j1 rule="hyper" parents="320 7883 8756"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8759">
    <literal><![CDATA[
      L(K(x,y),z,L(x,u,w)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(4028,a,7042,a)].">
      <j1 rule="hyper" parents="4028 7042"/>
    </justification>
  </clause>

  <clause id="8760">
    <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(7042(a,1),6345(a,1,1))].">
      <j1 rule="para" parents="7042 6345"/>
    </justification>
  </clause>

  <clause id="8761">
    <literal><![CDATA[
      K(L(x,y,L(x,z,u)),w) = K(x,w)
    ]]></literal>
    <justification jstring="[hyper(8394,a,8759,a)].">
      <j1 rule="hyper" parents="8394 8759"/>
    </justification>
  </clause>

  <clause id="8762">
    <literal><![CDATA[
      x * K(L(x,y,L(x,z,u)),w) = T(x,w)
    ]]></literal>
    <justification jstring="[hyper(119,a,8761,a,b,4729,a(flip))].">
      <j1 rule="hyper" parents="119 8761 4729"/>
    </justification>
  </clause>

  <clause id="8763">
    <literal><![CDATA[
      K(x,(R(x,y,z) \ u) \ w) = K(x,u \ (R(x,y,z) * w))
    ]]></literal>
    <justification jstring="[hyper(6714,a,7043,a),flip(a)].">
      <j1 rule="hyper" parents="6714 7043"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8764">
    <literal><![CDATA[
      K(x,x \ (x * y)) = K(x,K(z \ x,z) * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,6838,a(flip),b,7071,a)].">
      <j1 rule="hyper" parents="58 6838 7071"/>
    </justification>
  </clause>

  <clause id="8766">
    <literal><![CDATA[
      K(x,K(y \ x,y) * z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(4(a,1),8764(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4 8764"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8767">
    <literal><![CDATA[
      K(x,y * K(z \ x,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,7330,a(flip),b,8766,a)].">
      <j1 rule="hyper" parents="58 7330 8766"/>
    </justification>
  </clause>

  <clause id="8769">
    <literal><![CDATA[
      K(x * y,K(x,y) * z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(4963(a,1),8766(a,1,2,1))].">
      <j1 rule="para" parents="4963 8766"/>
    </justification>
  </clause>

  <clause id="8770">
    <literal><![CDATA[
      K(x,K(y,y \ x) * z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(5133(a,1),8766(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5133 8766"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8771">
    <literal><![CDATA[
      K(x,(x / y) * z) = K(x,(y \ x) * z)
    ]]></literal>
    <justification jstring="[para(5443(a,1),8766(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5443 8766"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8773">
    <literal><![CDATA[
      K(x,y \ T(z,((y \ 1) \ (y \ z)) \ x)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(6567(a,1),8767(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6567 8767"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8774">
    <literal><![CDATA[
      T(x,K(y,y \ x) * z) = T(x,z)
    ]]></literal>
    <justification jstring="[hyper(118,a,8770,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 8770 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8775">
    <literal><![CDATA[
      T(x * y,K(y,x) * z) = T(x * y,z)
    ]]></literal>
    <justification jstring="[para(4910(a,1),8774(a,1,2,1))].">
      <j1 rule="para" parents="4910 8774"/>
    </justification>
  </clause>

  <clause id="8776">
    <literal><![CDATA[
      (K(x,y) * z) * T(y * x,z) = (y * x) * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(119,a,8775,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 8775 17"/>
    </justification>
  </clause>

  <clause id="8777">
    <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(8775(a,1),284(a,1,2))].">
      <j1 rule="para" parents="8775 284"/>
    </justification>
  </clause>

  <clause id="8778">
    <literal><![CDATA[
      K(x \ (x * y),x) = K(K(z \ x,z) * y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,6729,a(flip),b,7075,a)].">
      <j1 rule="hyper" parents="58 6729 7075"/>
    </justification>
  </clause>

  <clause id="8779">
    <literal><![CDATA[
      K(K(x \ y,x) * z,y) = K(z,y)
    ]]></literal>
    <justification jstring="[hyper(6299,a,8778,a),flip(a)].">
      <j1 rule="hyper" parents="6299 8778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8781">
    <literal><![CDATA[
      K(K(x \ y,x) * z,y) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,y) = u
    ]]></literal>
    <justification jstring="[para(8778(a,1),1359(a,1))].">
      <j1 rule="para" parents="8778 1359"/>
    </justification>
  </clause>

  <clause id="8783">
    <literal><![CDATA[
      (K(x \ y,x) * z) * K(z,y) = T(K(x \ y,x) * z,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,8779,a(flip),b,4729,a(flip))].">
      <j1 rule="hyper" parents="119 8779 4729"/>
    </justification>
  </clause>

  <clause id="8784">
    <literal><![CDATA[
      K(K(x,y) * z,y * x) = K(z,y * x)
    ]]></literal>
    <justification jstring="[para(4(a,1),8779(a,1,1,1,1))].">
      <j1 rule="para" parents="4 8779"/>
    </justification>
  </clause>

  <clause id="8785">
    <literal><![CDATA[
      K(T(x,y) * z,y * x) = K(x * z,y * x)
    ]]></literal>
    <justification jstring="[para(4781(a,1),8784(a,1,1))].">
      <j1 rule="para" parents="4781 8784"/>
    </justification>
  </clause>

  <clause id="8786">
    <literal><![CDATA[
      K(((x \ y) \ y) \ z,y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ z,y) = u
    ]]></literal>
    <justification jstring="[para(5235(a,2),8781(a,1,1))].">
      <j1 rule="para" parents="5235 8781"/>
    </justification>
  </clause>

  <clause id="8787">
    <literal><![CDATA[
      K((x \ y) * z,y) != u
    ]]></literal>
    <literal><![CDATA[
      K((y / x) * z,y) = u
    ]]></literal>
    <justification jstring="[para(5443(a,1),8781(a,1,1))].">
      <j1 rule="para" parents="5443 8781"/>
    </justification>
  </clause>

  <clause id="8788">
    <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,6643,a(flip),b,7321,a),flip(a)].">
      <j1 rule="hyper" parents="58 6643 7321"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8789">
    <literal><![CDATA[
      K(x,y / R(T(x,z),u,w)) = K(x,R(x,u,w) \ y)
    ]]></literal>
    <justification jstring="[hyper(320,a,8534,a(flip),b,7323,a),flip(a)].">
      <j1 rule="hyper" parents="320 8534 7323"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8791">
    <literal><![CDATA[
      K(x,y / (T(z,u) / u)) = K(x,y / (z / T(u,z)))
    ]]></literal>
    <justification jstring="[hyper(7400,a,7332,a),flip(a)].">
      <j1 rule="hyper" parents="7400 7332"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8792">
    <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,6743,a(flip),b,7369,a),flip(a)].">
      <j1 rule="hyper" parents="58 6743 7369"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8793">
    <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,8792,a,b,5139,a),flip(a)].">
      <j1 rule="hyper" parents="115 8792 5139"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8794">
    <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),8792(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 8792"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8795">
    <literal><![CDATA[
      L(K(x,y),z,L(y,u,w)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(4028,a,7461,a)].">
      <j1 rule="hyper" parents="4028 7461"/>
    </justification>
  </clause>

  <clause id="8796">
    <literal><![CDATA[
      K(L(x,y,L(z,u,w)),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(8394,a,8795,a)].">
      <j1 rule="hyper" parents="8394 8795"/>
    </justification>
  </clause>

  <clause id="8797">
    <literal><![CDATA[
      K(x,L(y,z,L(y,u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,6609,a(flip),b,8795,a)].">
      <j1 rule="hyper" parents="58 6609 8795"/>
    </justification>
  </clause>

  <clause id="8798">
    <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(4354(a,1),8796(a,1,1))].">
      <j1 rule="para" parents="4354 8796"/>
    </justification>
  </clause>

  <clause id="8799">
    <literal><![CDATA[
      R(K(x,y),z,R(x,u,w)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(4038,a,7486,a)].">
      <j1 rule="hyper" parents="4038 7486"/>
    </justification>
  </clause>

  <clause id="8800">
    <literal><![CDATA[
      K(x,y) * ((y * x) * R(x,z,u)) = (x * y) * R(x,z,u)
    ]]></literal>
    <justification jstring="[para(4813(a,1),7486(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4813 7486"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8801">
    <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(7486(a,1),5094(a,1,1,2))].">
      <j1 rule="para" parents="7486 5094"/>
    </justification>
  </clause>

  <clause id="8802">
    <literal><![CDATA[
      K(x,(y * R(x,z,u)) / w) = K(x,y / (w / R(x,z,u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,6945,a(flip),b,8799,a)].">
      <j1 rule="hyper" parents="58 6945 8799"/>
    </justification>
  </clause>

  <clause id="8803">
    <literal><![CDATA[
      K(R(x,y,R(x,z,u)),w) = K(x,w)
    ]]></literal>
    <justification jstring="[hyper(58,a,6743,a(flip),b,8799,a)].">
      <j1 rule="hyper" parents="58 6743 8799"/>
    </justification>
  </clause>

  <clause id="8804">
    <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(8803(a,1),4770(a,2,1)),flip(a)].">
      <j1 rule="para" parents="8803 4770"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8805">
    <literal><![CDATA[
      T(L(x / y,z,x / y),y) = L(y \ x,z,T(y \ x,u))
    ]]></literal>
    <justification jstring="[para(7496(a,2),7495(a,1,1))].">
      <j1 rule="para" parents="7496 7495"/>
    </justification>
  </clause>

  <clause id="8806">
    <literal><![CDATA[
      K(x * (R(y,z,y) \ u),y) = K(x * (u / T(y,z)),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,7583,a(flip),b,7516,a),flip(a)].">
      <j1 rule="hyper" parents="58 7583 7516"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8807">
    <literal><![CDATA[
      K(x * (R(x,y,x) \ z),x) = K(z,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,7386,a(flip),b,8806,a),flip(a)].">
      <j1 rule="hyper" parents="320 7386 8806"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8808">
    <literal><![CDATA[
      K(R(x,y,x) * z,x) = K(x * z,x)
    ]]></literal>
    <justification jstring="[para(4(a,1),8807(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4 8807"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8809">
    <literal><![CDATA[
      K(x * R(y,z,y),y) = K(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,7433,a(flip),b,8808,a)].">
      <j1 rule="hyper" parents="58 7433 8808"/>
    </justification>
  </clause>

  <clause id="8810">
    <literal><![CDATA[
      T(x,y * R(x,z,x)) = 1 / (x \ K(x * y,x))
    ]]></literal>
    <justification jstring="[para(8809(a,1),4992(a,2,2,2))].">
      <j1 rule="para" parents="8809 4992"/>
    </justification>
  </clause>

  <clause id="8811">
    <literal><![CDATA[
      T(x,y * R(x,z,x)) = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(320,a,4992,a,b,8810,a),flip(a)].">
      <j1 rule="hyper" parents="320 4992 8810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8812">
    <literal><![CDATA[
      T(x,y * R(x,z,x)) = x * K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(320,a,4755,a(flip),b,8811,a),flip(a)].">
      <j1 rule="hyper" parents="320 4755 8811"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8813">
    <literal><![CDATA[
      K(x,y * R(x,z,x)) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(4837,a,8812,a)].">
      <j1 rule="hyper" parents="4837 8812"/>
    </justification>
  </clause>

  <clause id="8814">
    <literal><![CDATA[
      K(x,R(x,y,x) * z) = K(x,x * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,7425,a,b,8813,a)].">
      <j1 rule="hyper" parents="58 7425 8813"/>
    </justification>
  </clause>

  <clause id="8815">
    <literal><![CDATA[
      K(R(x,y,x),R(x,z,x) * u) = K(x,x * u)
    ]]></literal>
    <justification jstring="[hyper(7395,a,8814,a)].">
      <j1 rule="hyper" parents="7395 8814"/>
    </justification>
  </clause>

  <clause id="8816">
    <literal><![CDATA[
      T(T(x,1 / y),K(1 / y,z)) = T(x,1 / T(y,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,4755,a,b,7589,a),flip(a)].">
      <j1 rule="hyper" parents="320 4755 7589"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8817">
    <literal><![CDATA[
      T(T(x,1 / y),K(z,1 / y)) = T(x,1 / T(y,z))
    ]]></literal>
    <justification jstring="[hyper(7866,a,8816,a)].">
      <j1 rule="hyper" parents="7866 8816"/>
    </justification>
  </clause>

  <clause id="8818">
    <literal><![CDATA[
      T(x,1 / T(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(1 / y,z)) = u
    ]]></literal>
    <justification jstring="[para(8816(a,1),7703(a,1))].">
      <j1 rule="para" parents="8816 7703"/>
    </justification>
  </clause>

  <clause id="8819">
    <literal><![CDATA[
      T(T(x,1 / (y / z)),K(u,z / y)) = T(x,1 / T(y / z,u))
    ]]></literal>
    <justification jstring="[para(5356(a,1),8817(a,1,2))].">
      <j1 rule="para" parents="5356 8817"/>
    </justification>
  </clause>

  <clause id="8820">
    <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),7671(a,2,1))].">
      <j1 rule="para" parents="22 7671"/>
    </justification>
  </clause>

  <clause id="8821">
    <literal><![CDATA[
      T(x / y,z) * T(y,K(z,x / y)) = x * K(x / y,z)
    ]]></literal>
    <justification jstring="[para(7832(a,1),7729(a,1,2))].">
      <j1 rule="para" parents="7832 7729"/>
    </justification>
  </clause>

  <clause id="8822">
    <literal><![CDATA[
      R(K(x,K(y,z)),u,w) = K(R(K(x,y),u,w),z)
    ]]></literal>
    <justification jstring="[para(5709(a,1),7767(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5709 7767"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8823">
    <literal><![CDATA[
      R(K(x,K(y,z \ 1)),u,w) = K(x,K(y,R(z,u,w) \ 1))
    ]]></literal>
    <justification jstring="[para(7755(a,1),7768(a,1,1))].">
      <j1 rule="para" parents="7755 7768"/>
    </justification>
  </clause>

  <clause id="8824">
    <literal><![CDATA[
      K(R(K(x,y),z,u),w) = K(y,R(K(x,w),z,u))
    ]]></literal>
    <justification jstring="[para(5709(a,1),7800(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5709 7800"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8825">
    <literal><![CDATA[
      R(K(x,K(y,z)),u,w) = K(y,R(K(x,z),u,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,8822,a,b,8824,a)].">
      <j1 rule="hyper" parents="58 8822 8824"/>
    </justification>
  </clause>

  <clause id="8826">
    <literal><![CDATA[
      R(K(x,K(y,z)),u,w) = K(x,R(K(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(7779(a,1),8825(a,1,1))].">
      <j1 rule="para" parents="7779 8825"/>
    </justification>
  </clause>

  <clause id="8827">
    <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),7806(a,1,2,1))].">
      <j1 rule="para" parents="7 7806"/>
    </justification>
  </clause>

  <clause id="8828">
    <literal><![CDATA[
      T(x * K(y,z),K(u,y)) = T(x,K(u,y)) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(7789,a,7872,a),flip(a)].">
      <j1 rule="hyper" parents="7789 7872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8829">
    <literal><![CDATA[
      T(K(x,y) * z,K(u,y)) = K(x,y) * T(z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(6035,a,8828,a),flip(a)].">
      <j1 rule="hyper" parents="6035 8828"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8830">
    <literal><![CDATA[
      T(K(x,y) * z,K(u,y)) = K(x,y) * T(z,K(y,u))
    ]]></literal>
    <justification jstring="[para(7832(a,1),8829(a,2,2))].">
      <j1 rule="para" parents="7832 8829"/>
    </justification>
  </clause>

  <clause id="8831">
    <literal><![CDATA[
      T(K(x,y) * z,K(y,u)) = K(x,y) * T(z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(7866,a,8830,a)].">
      <j1 rule="hyper" parents="7866 8830"/>
    </justification>
  </clause>

  <clause id="8832">
    <literal><![CDATA[
      K(x,y) * T(K(x,y) \ z,K(x,u)) = T(z,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(6048,a,8831,a)].">
      <j1 rule="hyper" parents="6048 8831"/>
    </justification>
  </clause>

  <clause id="8833">
    <literal><![CDATA[
      T(x * K(y,z),K(y,u)) = T(x,K(y,u)) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(6041,a,8831,a),flip(a)].">
      <j1 rule="hyper" parents="6041 8831"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8834">
    <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),8832(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4 8832"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8835">
    <literal><![CDATA[
      T(x * K(y,z),K(z,u)) = T(x,K(z,u)) * K(y,z)
    ]]></literal>
    <justification jstring="[para(8832(a,1),5979(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8832 5979"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8836">
    <literal><![CDATA[
      T(x * K(y,z * x),K(y,z)) = K(y,z * x) * x
    ]]></literal>
    <justification jstring="[hyper(320,a,8098,a(flip),b,8833,a),flip(a)].">
      <j1 rule="hyper" parents="320 8098 8833"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8837">
    <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(7786(a,1),8834(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7786 8834"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8838">
    <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(5687(a,1),8835(a,2,2))].">
      <j1 rule="para" parents="5687 8835"/>
    </justification>
  </clause>

  <clause id="8839">
    <literal><![CDATA[
      T(x * K(y,z),K(z,u)) \ T(x,K(z,u)) = K(z,y)
    ]]></literal>
    <justification jstring="[para(8835(a,2),6338(a,1,1))].">
      <j1 rule="para" parents="8835 6338"/>
    </justification>
  </clause>

  <clause id="8840">
    <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(8836(a,1),4269(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8836 4269"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8841">
    <literal><![CDATA[
      R(K(x,y),T(y,z) * u,w) = K(x,R(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(320,a,7924,a(flip),b,7935,a),flip(a)].">
      <j1 rule="hyper" parents="320 7924 7935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8842">
    <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(7935(a,2),8067(a,1))].">
      <j1 rule="para" parents="7935 8067"/>
    </justification>
  </clause>

  <clause id="8844">
    <literal><![CDATA[
      K(x,R(y,T(y,z) \ u,w)) = R(K(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(5(a,1),8841(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5 8841"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8845">
    <literal><![CDATA[
      R(K(x,y),K(z,y) * u,w) = R(K(x,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(58,a,6957,a,b,8844,a)].">
      <j1 rule="hyper" parents="58 6957 8844"/>
    </justification>
  </clause>

  <clause id="8847">
    <literal><![CDATA[
      R(K(x,y),K(y,z) * u,w) = R(K(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(5133(a,1),8845(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5133 8845"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8848">
    <literal><![CDATA[
      R(K(x,y),y \ K(y,z),u) = R(K(x,y),y \ 1,u)
    ]]></literal>
    <justification jstring="[para(5137(a,1),8845(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5137 8845"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8849">
    <literal><![CDATA[
      R(K(x,y),z * K(u,y),w) = R(K(x,y),z,w)
    ]]></literal>
    <justification jstring="[para(7288(a,1),8845(a,1,2))].">
      <j1 rule="para" parents="7288 8845"/>
    </justification>
  </clause>

  <clause id="8850">
    <literal><![CDATA[
      R(K(x,y),z * (K(u,y) * w),v5) = R(K(x,y),z * w,v5)
    ]]></literal>
    <justification jstring="[para(6038(a,1),8847(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6038 8847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8851">
    <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(8848(a,2),1637(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="8848 1637"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8852">
    <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),8842(a,1,2,1))].">
      <j1 rule="para" parents="104 8842"/>
    </justification>
  </clause>

  <clause id="8853">
    <literal><![CDATA[
      K(x \ y,T(z,y)) = K((K(z,u) * y) / x,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,8660,a(flip),b,7977,a)].">
      <j1 rule="hyper" parents="58 8660 7977"/>
    </justification>
  </clause>

  <clause id="8854">
    <literal><![CDATA[
      K((K(x,y) * z) / u,x) = K(z / u,x)
    ]]></literal>
    <justification jstring="[hyper(8055,a,8853,a),flip(a)].">
      <j1 rule="hyper" parents="8055 8853"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8856">
    <literal><![CDATA[
      K(x,(K(x,y) * z) / u) = (w * K(z / u,x)) \ w
    ]]></literal>
    <justification jstring="[para(8854(a,1),6338(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="8854 6338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8857">
    <literal><![CDATA[
      K(x,(K(x,y) * z) / u) = K(x,z / u)
    ]]></literal>
    <justification jstring="[hyper(320,a,6338,a(flip),b,8856,a),flip(a)].">
      <j1 rule="hyper" parents="320 6338 8856"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8858">
    <literal><![CDATA[
      K(x,(T(y,x) * z) / u) = K(x,(y * z) / u)
    ]]></literal>
    <justification jstring="[para(4819(a,1),8857(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4819 8857"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8859">
    <literal><![CDATA[
      K(x,(T(y / (z \ u),x) * K(z \ u,z)) / w) = K(x,(y / (u / z)) / w)
    ]]></literal>
    <justification jstring="[para(6470(a,1),8858(a,2,2,1))].">
      <j1 rule="para" parents="6470 8858"/>
    </justification>
  </clause>

  <clause id="8860">
    <literal><![CDATA[
      K(x \ y,T(z,x)) = K(y / (x * K(z,u)),z)
    ]]></literal>
    <justification jstring="[hyper(58,a,8652,a(flip),b,8004,a)].">
      <j1 rule="hyper" parents="58 8652 8004"/>
    </justification>
  </clause>

  <clause id="8861">
    <literal><![CDATA[
      K(x / (y * K(z,u)),z) = K(x / y,z)
    ]]></literal>
    <justification jstring="[hyper(8061,a,8860,a),flip(a)].">
      <j1 rule="hyper" parents="8061 8860"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8863">
    <literal><![CDATA[
      K(x / ((y * K(z,u)) * w),u) = K(x / (y * w),u)
    ]]></literal>
    <justification jstring="[para(6818(a,1),8861(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6818 8861"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8864">
    <literal><![CDATA[
      K(x / ((K(y,z) * u) * w),y) = K(x / (u * w),y)
    ]]></literal>
    <justification jstring="[para(7148(a,1),8863(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7148 8863"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8865">
    <literal><![CDATA[
      K(x / ((K(y,z) * u) * w),z) = K(x / (u * w),z)
    ]]></literal>
    <justification jstring="[para(7150(a,1),8863(a,1,1,2,1))].">
      <j1 rule="para" parents="7150 8863"/>
    </justification>
  </clause>

  <clause id="8866">
    <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),8865(a,1,1))].">
      <j1 rule="para" parents="510 8865"/>
    </justification>
  </clause>

  <clause id="8867">
    <literal><![CDATA[
      K(T(x,y),y \ z) = K(x,z / (y * K(u,x)))
    ]]></literal>
    <justification jstring="[hyper(58,a,8560,a(flip),b,8017,a)].">
      <j1 rule="hyper" parents="58 8560 8017"/>
    </justification>
  </clause>

  <clause id="8868">
    <literal><![CDATA[
      K(x,y / (z * K(u,x))) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(8068,a,8867,a),flip(a)].">
      <j1 rule="hyper" parents="8068 8867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8870">
    <literal><![CDATA[
      K(x,y / (T(z,x) / u)) = K(x,y / (z / u))
    ]]></literal>
    <justification jstring="[para(1439(a,1),8868(a,1,2,2))].">
      <j1 rule="para" parents="1439 8868"/>
    </justification>
  </clause>

  <clause id="8871">
    <literal><![CDATA[
      K(x,y / K(z,z \ K(u,x))) = K(x,y / (z * (K(u,x) / z)))
    ]]></literal>
    <justification jstring="[para(4783(a,1),8868(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4783 8868"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8872">
    <literal><![CDATA[
      K(x,y / (T(z,x) * u)) = K(x,y / (z * u))
    ]]></literal>
    <justification jstring="[para(5539(a,1),8868(a,1,2,2))].">
      <j1 rule="para" parents="5539 8868"/>
    </justification>
  </clause>

  <clause id="8873">
    <literal><![CDATA[
      K(x,y / (z * K(x,u))) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(6329(a,1),8868(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6329 8868"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8874">
    <literal><![CDATA[
      K(x,y / (K(x,z) * u)) = K(x,y / u)
    ]]></literal>
    <justification jstring="[para(7148(a,1),8868(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7148 8868"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8875">
    <literal><![CDATA[
      K(x,y / ((z * K(u,x)) * w)) = K(x,y / (z * w))
    ]]></literal>
    <justification jstring="[para(6818(a,1),8873(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6818 8873"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8876">
    <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),8874(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15 8874"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8877">
    <literal><![CDATA[
      K(x,y / (T(z \ T(u,z),x) / w)) = K(x,y / ((T(z,u) \ u) / w))
    ]]></literal>
    <justification jstring="[para(4392(a,1),8870(a,1,2,2,1))].">
      <j1 rule="para" parents="4392 8870"/>
    </justification>
  </clause>

  <clause id="8878">
    <literal><![CDATA[
      K(x,y / ((z * x) * u)) = K(x,y / ((x * z) * u))
    ]]></literal>
    <justification jstring="[para(84(a,1),8875(a,1,2,2,1))].">
      <j1 rule="para" parents="84 8875"/>
    </justification>
  </clause>

  <clause id="8879">
    <literal><![CDATA[
      K(x,y / (((x \ z) * x) * u)) = K(x,y / (z * u))
    ]]></literal>
    <justification jstring="[para(302(a,1),8875(a,1,2,2,1))].">
      <j1 rule="para" parents="302 8875"/>
    </justification>
  </clause>

  <clause id="8880">
    <literal><![CDATA[
      K(x,y / ((K(x,z) * u) * w)) = K(x,y / (u * w))
    ]]></literal>
    <justification jstring="[para(7148(a,1),8875(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="7148 8875"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8881">
    <literal><![CDATA[
      K(x,y / ((K(z,x) * u) * w)) = K(x,y / (u * w))
    ]]></literal>
    <justification jstring="[para(7150(a,1),8875(a,1,2,2,1))].">
      <j1 rule="para" parents="7150 8875"/>
    </justification>
  </clause>

  <clause id="8882">
    <literal><![CDATA[
      K(x,y / ((z * (K(u,x) * w)) * v5)) = K(x,y / ((z * w) * v5))
    ]]></literal>
    <justification jstring="[para(6038(a,1),8880(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="6038 8880"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8883">
    <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),8881(a,1,2))].">
      <j1 rule="para" parents="510 8881"/>
    </justification>
  </clause>

  <clause id="8884">
    <literal><![CDATA[
      K(x,R(y,K(x,z),u)) = K(x,y * K(x,z))
    ]]></literal>
    <justification jstring="[para(6(a,1),8876(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6 8876"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8885">
    <literal><![CDATA[
      K(x,R(y,K(x,z),u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,7238,a(flip),b,8884,a),flip(a)].">
      <j1 rule="hyper" parents="320 7238 8884"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8888">
    <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),8885(a,1,2))].">
      <j1 rule="para" parents="26 8885"/>
    </justification>
  </clause>

  <clause id="8889">
    <literal><![CDATA[
      ((x * (y * K(z,y))) / x) / ((x * y) / x) = K(T(z,x),y)
    ]]></literal>
    <justification jstring="[para(4752(a,1),8018(a,1,1,1,2))].">
      <j1 rule="para" parents="4752 8018"/>
    </justification>
  </clause>

  <clause id="8890">
    <literal><![CDATA[
      T(K(x,y),T(z,x \ u)) = T(K(x,y),T(z,u))
    ]]></literal>
    <justification jstring="[hyper(7760,a,8072,a),flip(a)].">
      <j1 rule="hyper" parents="7760 8072"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8891">
    <literal><![CDATA[
      T(K(x,y),T(z,x * u)) = T(K(x,y),T(z,u))
    ]]></literal>
    <justification jstring="[para(4(a,1),8890(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 8890"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8892">
    <literal><![CDATA[
      1 / (K(x,y) * T(x,z)) = K(y,x) / T(x,z)
    ]]></literal>
    <justification jstring="[para(7888(a,1),8108(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7888 8108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8893">
    <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(8892(a,1),4023(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="8892 4023"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8894">
    <literal><![CDATA[
      (K(x,y) / T(y,z)) \ 1 = K(y,z) * T(y,x)
    ]]></literal>
    <justification jstring="[para(8892(a,1),5455(a,1,1))].">
      <j1 rule="para" parents="8892 5455"/>
    </justification>
  </clause>

  <clause id="8896">
    <literal><![CDATA[
      K(x \ 1,y) * K(y,x \ K(x,z)) = K(y,K(z,x \ 1))
    ]]></literal>
    <justification jstring="[hyper(320,a,7784,a,b,8120,a),flip(a)].">
      <j1 rule="hyper" parents="320 7784 8120"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8897">
    <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,8110,a,b,8121,a)].">
      <j1 rule="hyper" parents="320 8110 8121"/>
    </justification>
  </clause>

  <clause id="8898">
    <literal><![CDATA[
      T(x,R(y / (y / z),u,w)) = x * K(T(x,z \ y),R(z,u,w))
    ]]></literal>
    <justification jstring="[para(4343(a,1),8126(a,1,2,1))].">
      <j1 rule="para" parents="4343 8126"/>
    </justification>
  </clause>

  <clause id="8899">
    <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(7045(a,1),8130(a,2,2))].">
      <j1 rule="para" parents="7045 8130"/>
    </justification>
  </clause>

  <clause id="8900">
    <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(6205(a,1),8278(a,2,2,1,1))].">
      <j1 rule="para" parents="6205 8278"/>
    </justification>
  </clause>

  <clause id="8901">
    <literal><![CDATA[
      K(R(x / (x / y),z,u),w) = K(R(y,z,u),T(w,x))
    ]]></literal>
    <justification jstring="[hyper(320,a,8792,a(flip),b,8306,a),flip(a)].">
      <j1 rule="hyper" parents="320 8792 8306"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8902">
    <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),8901(a,1,1)),flip(a)].">
      <j1 rule="para" parents="102 8901"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8903">
    <literal><![CDATA[
      K(L(x,y / T(x,z),u),w) = L(K(x,w),y,u)
    ]]></literal>
    <justification jstring="[para(7888(a,1),8308(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7888 8308"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8904">
    <literal><![CDATA[
      L(K(x,y),z * T(x,u),w) = K(L(x,z,w),y)
    ]]></literal>
    <justification jstring="[para(6(a,1),8903(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6 8903"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8905">
    <literal><![CDATA[
      L(K(x,y),x * z,u) = K(L(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(187(a,1),8903(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="187 8903"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8906">
    <literal><![CDATA[
      K(L(x,x \ y,z),u) = L(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(265(a,1),8903(a,1,1,2))].">
      <j1 rule="para" parents="265 8903"/>
    </justification>
  </clause>

  <clause id="8908">
    <literal><![CDATA[
      K(L(x,y,z),x * y) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(6122,a,8905,a),flip(a)].">
      <j1 rule="hyper" parents="6122 8905"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8909">
    <literal><![CDATA[
      K(L(x,y,z),y) = K(x,L(y,x,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,6609,a(flip),b,8905,a),flip(a)].">
      <j1 rule="hyper" parents="58 6609 8905"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8910">
    <literal><![CDATA[
      K(L(x,y,z),(z \ u) \ (x * y)) = K(x,u \ (z * (x * y)))
    ]]></literal>
    <justification jstring="[hyper(58,a,6584,a(flip),b,8905,a),flip(a)].">
      <j1 rule="hyper" parents="58 6584 8905"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8911">
    <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(7888(a,1),8905(a,1,1))].">
      <j1 rule="para" parents="7888 8905"/>
    </justification>
  </clause>

  <clause id="8912">
    <literal><![CDATA[
      L(K(x,y),K(z,x),u) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,8441,a(flip),b,8906,a),flip(a)].">
      <j1 rule="hyper" parents="58 8441 8906"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8913">
    <literal><![CDATA[
      (x * K(y,z)) * K(z,u) = x * (K(y,z) * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(119,a,8912,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="119 8912 13"/>
    </justification>
  </clause>

  <clause id="8914">
    <literal><![CDATA[
      L(L(K(x,y),z,u),K(w,x),v5) = L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(8912(a,1),25(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8912 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8915">
    <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(8912(a,1),447(a,1,2,1))].">
      <j1 rule="para" parents="8912 447"/>
    </justification>
  </clause>

  <clause id="8916">
    <literal><![CDATA[
      L(K(x,y),L(K(z,x),u,w),v5) = K(x,y)
    ]]></literal>
    <justification jstring="[para(4823(a,1),8912(a,1,2))].">
      <j1 rule="para" parents="4823 8912"/>
    </justification>
  </clause>

  <clause id="8917">
    <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,8916,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="119 8916 13"/>
    </justification>
  </clause>

  <clause id="8918">
    <literal><![CDATA[
      K(L(x,y * K(x,z),u),w) = K(L(x,y,u),w)
    ]]></literal>
    <justification jstring="[hyper(58,a,6617,a(flip),b,8904,a)].">
      <j1 rule="hyper" parents="58 6617 8904"/>
    </justification>
  </clause>

  <clause id="8920">
    <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(8918(a,1),8839(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="8918 8839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8921">
    <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(8914(a,2),6668(a,1,2))].">
      <j1 rule="para" parents="8914 6668"/>
    </justification>
  </clause>

  <clause id="8922">
    <literal><![CDATA[
      (x * (K(y,z) * K(z,u))) * K(u,z) = x * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(6344,a,8913,a)].">
      <j1 rule="hyper" parents="6344 8913"/>
    </justification>
  </clause>

  <clause id="8923">
    <literal><![CDATA[
      R(x,K(y,z),K(z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(515,a,8913,a)].">
      <j1 rule="hyper" parents="515 8913"/>
    </justification>
  </clause>

  <clause id="8924">
    <literal><![CDATA[
      (x * K(y,z)) * K(u,y) = x * (K(u,y) * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,6822,a,b,8913,a)].">
      <j1 rule="hyper" parents="58 6822 8913"/>
    </justification>
  </clause>

  <clause id="8925">
    <literal><![CDATA[
      x * (K(y,z) * K(z,z * y)) = (x / R(z,y,z)) * z
    ]]></literal>
    <justification jstring="[hyper(58,a,6660,a(flip),b,8913,a),flip(a)].">
      <j1 rule="hyper" parents="58 6660 8913"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8926">
    <literal><![CDATA[
      (x * K(y,z)) * K(z,u) = x * (K(z,u) * K(y,z))
    ]]></literal>
    <justification jstring="[para(2003(a,2),8913(a,2,2))].">
      <j1 rule="para" parents="2003 8913"/>
    </justification>
  </clause>

  <clause id="8927">
    <literal><![CDATA[
      R(x,K(y,z),K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      w = x
    ]]></literal>
    <justification jstring="[para(8923(a,1),46(a,1)),flip(a)].">
      <j1 rule="para" parents="8923 46"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8928">
    <literal><![CDATA[
      R(x,T(K(y,z),u),K(z,w)) = x
    ]]></literal>
    <justification jstring="[para(1533(a,1),8923(a,1,2))].">
      <j1 rule="para" parents="1533 8923"/>
    </justification>
  </clause>

  <clause id="8929">
    <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(8923(a,1),2547(a,1,1,1))].">
      <j1 rule="para" parents="8923 2547"/>
    </justification>
  </clause>

  <clause id="8930">
    <literal><![CDATA[
      (x * y) \ (y * T(x,z)) = K(y,x) * K(x,z)
    ]]></literal>
    <justification jstring="[para(8923(a,1),6157(a,1,1))].">
      <j1 rule="para" parents="8923 6157"/>
    </justification>
  </clause>

  <clause id="8931">
    <literal><![CDATA[
      R(x,T(K(y,z),u),T(K(z,w),v5)) = x
    ]]></literal>
    <justification jstring="[para(5510(a,1),8928(a,1,3))].">
      <j1 rule="para" parents="5510 8928"/>
    </justification>
  </clause>

  <clause id="8932">
    <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(8931(a,1),938(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8931 938"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8933">
    <literal><![CDATA[
      (x * y) \ (y * T(x,z)) = K(x,z) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,2003,a,b,8930,a),flip(a)].">
      <j1 rule="hyper" parents="320 2003 8930"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8934">
    <literal><![CDATA[
      K(x,y) * K(y,y \ x) = a(y,x / y,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,4294,a(flip),b,8930,a),flip(a)].">
      <j1 rule="hyper" parents="58 4294 8930"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8935">
    <literal><![CDATA[
      (x * y) \ (y * T(x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) * K(y,x) = u
    ]]></literal>
    <justification jstring="[para(8930(a,2),2009(a,1))].">
      <j1 rule="para" parents="8930 2009"/>
    </justification>
  </clause>

  <clause id="8937">
    <literal><![CDATA[
      x \ R(x,x \ y,x) = a(x,y / x,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,5499,a,b,8934,a)].">
      <j1 rule="hyper" parents="58 5499 8934"/>
    </justification>
  </clause>

  <clause id="8938">
    <literal><![CDATA[
      a(x,y / x,x) \ K(y,x) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[para(8934(a,1),6338(a,1,1))].">
      <j1 rule="para" parents="8934 6338"/>
    </justification>
  </clause>

  <clause id="8939">
    <literal><![CDATA[
      a(x,y / x,x) * K(x,y) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[para(8934(a,1),6341(a,1,1))].">
      <j1 rule="para" parents="8934 6341"/>
    </justification>
  </clause>

  <clause id="8940">
    <literal><![CDATA[
      a(x,(x * y) / x,x) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[para(4(a,1),8937(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 8937"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8941">
    <literal><![CDATA[
      x \ R(x,T(y,x),x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[para(225(a,1),8940(a,1,2)),flip(a)].">
      <j1 rule="para" parents="225 8940"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8942">
    <literal><![CDATA[
      x \ R(x,y,x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[para(4429(a,1),8941(a,1,2))].">
      <j1 rule="para" parents="4429 8941"/>
    </justification>
  </clause>

  <clause id="8943">
    <literal><![CDATA[
      T(x,y) \ R(T(x,y),z,x) = a(x,z,x)
    ]]></literal>
    <justification jstring="[hyper(7642,a,8942,a)].">
      <j1 rule="hyper" parents="7642 8942"/>
    </justification>
  </clause>

  <clause id="8944">
    <literal><![CDATA[
      R(x,y,x) / x = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(5919,a,8942,a)].">
      <j1 rule="hyper" parents="5919 8942"/>
    </justification>
  </clause>

  <clause id="8945">
    <literal><![CDATA[
      K(x,y) * K(y * x,x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(5504,a,8942,a)].">
      <j1 rule="hyper" parents="5504 8942"/>
    </justification>
  </clause>

  <clause id="8946">
    <literal><![CDATA[
      K(x * y,y) * K(y,x) = a(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(5503,a,8942,a)].">
      <j1 rule="hyper" parents="5503 8942"/>
    </justification>
  </clause>

  <clause id="8947">
    <literal><![CDATA[
      K(x * y,x) * K(x,y) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(5491,a,8942,a)].">
      <j1 rule="hyper" parents="5491 8942"/>
    </justification>
  </clause>

  <clause id="8948">
    <literal><![CDATA[
      K(x,y) * K(x * y,x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(5481,a,8942,a)].">
      <j1 rule="hyper" parents="5481 8942"/>
    </justification>
  </clause>

  <clause id="8949">
    <literal><![CDATA[
      x * a(x,y,x) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(134,a,8942,a)].">
      <j1 rule="hyper" parents="134 8942"/>
    </justification>
  </clause>

  <clause id="8950">
    <literal><![CDATA[
      K(x,y \ z) * K(y \ (z * x),x) = a(x,(z \ y) \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,6855,a,b,8942,a)].">
      <j1 rule="hyper" parents="58 6855 8942"/>
    </justification>
  </clause>

  <clause id="8951">
    <literal><![CDATA[
      T(x,y) * a(x,z,x) = R(T(x,y),z,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,8942,a(flip),b,7479,a)].">
      <j1 rule="hyper" parents="119 8942 7479"/>
    </justification>
  </clause>

  <clause id="8952">
    <literal><![CDATA[
      T(x,y) \ R(x,z,x) = K(y,x) * a(x,z,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,8942,a(flip),b,5129,a),flip(a)].">
      <j1 rule="hyper" parents="119 8942 5129"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8953">
    <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(8942(a,1),5180(a,1,2))].">
      <j1 rule="para" parents="8942 5180"/>
    </justification>
  </clause>

  <clause id="8954">
    <literal><![CDATA[
      K(x,x * y) * a(x,y,x) = K(x,y)
    ]]></literal>
    <justification jstring="[para(8942(a,1),5493(a,1,2))].">
      <j1 rule="para" parents="8942 5493"/>
    </justification>
  </clause>

  <clause id="8955">
    <literal><![CDATA[
      a(x,x \ (y \ x),x) = x \ R(x,y \ 1,x)
    ]]></literal>
    <justification jstring="[para(5790(a,1),8942(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5790 8942"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8956">
    <literal><![CDATA[
      a(x,y,x) * x = R(x,y,x)
    ]]></literal>
    <justification jstring="[para(8942(a,1),5921(a,1,1))].">
      <j1 rule="para" parents="8942 5921"/>
    </justification>
  </clause>

  <clause id="8957">
    <literal><![CDATA[
      a(x,y,x) \ K(x,y) = K(x,x * y)
    ]]></literal>
    <justification jstring="[para(8942(a,1),6362(a,1,1))].">
      <j1 rule="para" parents="8942 6362"/>
    </justification>
  </clause>

  <clause id="8958">
    <literal><![CDATA[
      a(x,y,x) \ K(x * y,x) = K(y,x)
    ]]></literal>
    <justification jstring="[para(8942(a,1),6363(a,1,1))].">
      <j1 rule="para" parents="8942 6363"/>
    </justification>
  </clause>

  <clause id="8959">
    <literal><![CDATA[
      T(x * y,x) / x = y * a(x,y,x)
    ]]></literal>
    <justification jstring="[para(8942(a,1),6573(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8942 6573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8960">
    <literal><![CDATA[
      R(x,y,x) \ x = a(x,y,x) \ 1
    ]]></literal>
    <justification jstring="[para(8942(a,1),6760(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8942 6760"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8961">
    <literal><![CDATA[
      x \ R(T(x,y),z,x) = K(x,y) * a(x,z,x)
    ]]></literal>
    <justification jstring="[para(8942(a,1),7603(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8942 7603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8962">
    <literal><![CDATA[
      x \ R(x,y,x) != z
    ]]></literal>
    <literal><![CDATA[
      a(x,y,x) = z
    ]]></literal>
    <justification jstring="[para(8949(a,1),287(a,1,2)),flip(b)].">
      <j1 rule="para" parents="8949 287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8963">
    <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(8949(a,1),232(a,1,1))].">
      <j1 rule="para" parents="8949 232"/>
    </justification>
  </clause>

  <clause id="8964">
    <literal><![CDATA[
      K(x,y) * a(y,x,y) = K(x * y,y)
    ]]></literal>
    <justification jstring="[hyper(5147,a,8945,a)].">
      <j1 rule="hyper" parents="5147 8945"/>
    </justification>
  </clause>

  <clause id="8965">
    <literal><![CDATA[
      a(x,y,x) * K(y,x) = K(y * x,x)
    ]]></literal>
    <justification jstring="[hyper(6344,a,8946,a)].">
      <j1 rule="hyper" parents="6344 8946"/>
    </justification>
  </clause>

  <clause id="8966">
    <literal><![CDATA[
      a(x,y,x) * K(y,x) = K(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(6344,a,8947,a)].">
      <j1 rule="hyper" parents="6344 8947"/>
    </justification>
  </clause>

  <clause id="8967">
    <literal><![CDATA[
      a(x,y,x) * K(x,x * y) = K(x,y)
    ]]></literal>
    <justification jstring="[para(8947(a,1),6341(a,1,1))].">
      <j1 rule="para" parents="8947 6341"/>
    </justification>
  </clause>

  <clause id="8968">
    <literal><![CDATA[
      K(x,y) * a(y,x,y) = K(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(5147,a,8948,a)].">
      <j1 rule="hyper" parents="5147 8948"/>
    </justification>
  </clause>

  <clause id="8969">
    <literal><![CDATA[
      (x * y) * a(y,x,y) = T(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,8948,a(flip),b,6722,a)].">
      <j1 rule="hyper" parents="119 8948 6722"/>
    </justification>
  </clause>

  <clause id="8970">
    <literal><![CDATA[
      a(x,y,x) * (y * x) = T(x * y,x)
    ]]></literal>
    <justification jstring="[para(8948(a,1),6721(a,1,1))].">
      <j1 rule="para" parents="8948 6721"/>
    </justification>
  </clause>

  <clause id="8971">
    <literal><![CDATA[
      K(x,y) * a(x,x \ y,x) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[para(5(a,1),8954(a,1,1,2))].">
      <j1 rule="para" parents="5 8954"/>
    </justification>
  </clause>

  <clause id="8972">
    <literal><![CDATA[
      a(x,y \ 1,x) \ K(y \ x,x) = K(y \ 1,x)
    ]]></literal>
    <justification jstring="[para(5363(a,1),8958(a,1,2))].">
      <j1 rule="para" parents="5363 8958"/>
    </justification>
  </clause>

  <clause id="8973">
    <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,1901,a,b,8959,a)].">
      <j1 rule="hyper" parents="58 1901 8959"/>
    </justification>
  </clause>

  <clause id="8974">
    <literal><![CDATA[
      (x \ y) * a(x,x \ y,x) = T(y,x) / x
    ]]></literal>
    <justification jstring="[para(5(a,1),8959(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5 8959"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8975">
    <literal><![CDATA[
      T(x * a(y,x,y),y) = y \ T(y * x,y)
    ]]></literal>
    <justification jstring="[para(8959(a,1),107(a,1,1))].">
      <j1 rule="para" parents="8959 107"/>
    </justification>
  </clause>

  <clause id="8976">
    <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(8959(a,2),231(a,1,2,2))].">
      <j1 rule="para" parents="8959 231"/>
    </justification>
  </clause>

  <clause id="8977">
    <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(8959(a,2),476(a,1,2,2))].">
      <j1 rule="para" parents="8959 476"/>
    </justification>
  </clause>

  <clause id="8978">
    <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(8959(a,2),833(a,1,2,2,2))].">
      <j1 rule="para" parents="8959 833"/>
    </justification>
  </clause>

  <clause id="8979">
    <literal><![CDATA[
      K(x,y) * K(x * y,x) != z
    ]]></literal>
    <literal><![CDATA[
      a(x,y,x) = z
    ]]></literal>
    <justification jstring="[para(5293(a,2),8962(a,1))].">
      <j1 rule="para" parents="5293 8962"/>
    </justification>
  </clause>

  <clause id="8980">
    <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(6210(a,1),8966(a,2,1))].">
      <j1 rule="para" parents="6210 8966"/>
    </justification>
  </clause>

  <clause id="8981">
    <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(8969(a,1),950(a,1,1,2))].">
      <j1 rule="para" parents="8969 950"/>
    </justification>
  </clause>

  <clause id="8982">
    <literal><![CDATA[
      a(x,x \ y,x) = T(x,y) \ ((x \ y) \ y)
    ]]></literal>
    <justification jstring="[para(4375(a,1),8943(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4375 8943"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8983">
    <literal><![CDATA[
      a(x,y,x) * T(x,z) = R(T(x,z),y,x)
    ]]></literal>
    <justification jstring="[para(8943(a,1),5921(a,1,1))].">
      <j1 rule="para" parents="8943 5921"/>
    </justification>
  </clause>

  <clause id="8984">
    <literal><![CDATA[
      R(T(x / y,K(y,x)),z,x / y) = a(x / y,z,x / y) * (x / y)
    ]]></literal>
    <justification jstring="[para(6374(a,1),8983(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6374 8983"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8985">
    <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(8952(a,2),8395(a,1))].">
      <j1 rule="para" parents="8952 8395"/>
    </justification>
  </clause>

  <clause id="8986">
    <literal><![CDATA[
      a(x,x \ (y \ x),x) = a(x,y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,8942,a(flip),b,8955,a),flip(a)].">
      <j1 rule="hyper" parents="320 8942 8955"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8987">
    <literal><![CDATA[
      T(x,y \ x) \ ((x \ (y \ x)) \ (y \ x)) = a(x,y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,8982,a(flip),b,8986,a)].">
      <j1 rule="hyper" parents="58 8982 8986"/>
    </justification>
  </clause>

  <clause id="8988">
    <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(8961(a,1),91(a,1,2,2,1))].">
      <j1 rule="para" parents="8961 91"/>
    </justification>
  </clause>

  <clause id="8989">
    <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(8961(a,1),4122(a,1,1,1))].">
      <j1 rule="para" parents="8961 4122"/>
    </justification>
  </clause>

  <clause id="8990">
    <literal><![CDATA[
      L(K(x,y),K(z,y),u) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(6673,a,8922,a)].">
      <j1 rule="hyper" parents="6673 8922"/>
    </justification>
  </clause>

  <clause id="8991">
    <literal><![CDATA[
      (x * (K(y,z) * K(u,y))) * K(z,y) = x * K(u,y)
    ]]></literal>
    <justification jstring="[para(2003(a,2),8922(a,1,1,2))].">
      <j1 rule="para" parents="2003 8922"/>
    </justification>
  </clause>

  <clause id="8992">
    <literal><![CDATA[
      (x * K(y,z)) * K(u,z) = x * (K(y,z) * K(u,z))
    ]]></literal>
    <justification jstring="[hyper(119,a,8990,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="119 8990 13"/>
    </justification>
  </clause>

  <clause id="8993">
    <literal><![CDATA[
      (x * K(y,z)) * K(u,y) = x * (K(y,z) * K(u,y))
    ]]></literal>
    <justification jstring="[para(2003(a,2),8924(a,2,2))].">
      <j1 rule="para" parents="2003 8924"/>
    </justification>
  </clause>

  <clause id="8994">
    <literal><![CDATA[
      (x / T(y,z)) * T(y,u) = x * (K(y,u) * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(6487,a,8926,a)].">
      <j1 rule="hyper" parents="6487 8926"/>
    </justification>
  </clause>

  <clause id="8995">
    <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,8926,a,b,632,a)].">
      <j1 rule="hyper" parents="239 8926 632"/>
    </justification>
  </clause>

  <clause id="8996">
    <literal><![CDATA[
      (x / y) * (K(y,z) * K(u,y)) = (x / T(y,u)) * K(y,z)
    ]]></literal>
    <justification jstring="[para(6322(a,1),8926(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6322 8926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8997">
    <literal><![CDATA[
      (x * (K(y,z) * K(u,y))) * (K(z,y) * K(y,u)) = x
    ]]></literal>
    <justification jstring="[hyper(30,a,8922,a,b,8991,a(flip))].">
      <j1 rule="hyper" parents="30 8922 8991"/>
    </justification>
  </clause>

  <clause id="8998">
    <literal><![CDATA[
      (x * K(y,z)) * (K(u,y) * K(z,y)) = x * K(u,y)
    ]]></literal>
    <justification jstring="[hyper(6824,a,8992,a),flip(a)].">
      <j1 rule="hyper" parents="6824 8992"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8999">
    <literal><![CDATA[
      R(x,K(y,z),K(u,y)) = x
    ]]></literal>
    <justification jstring="[hyper(515,a,8993,a)].">
      <j1 rule="hyper" parents="515 8993"/>
    </justification>
  </clause>

  <clause id="9000">
    <literal><![CDATA[
      L(K(x,y),K(y,z),u) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(479,a,8993,a)].">
      <j1 rule="hyper" parents="479 8993"/>
    </justification>
  </clause>

  <clause id="9001">
    <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(2972(a,1),8993(a,1,1))].">
      <j1 rule="para" parents="2972 8993"/>
    </justification>
  </clause>

  <clause id="9002">
    <literal><![CDATA[
      (x * K(y,z)) * (K(z,y) * K(u,z)) = x * K(u,z)
    ]]></literal>
    <justification jstring="[para(6329(a,1),8993(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6329 8993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9003">
    <literal><![CDATA[
      R(x / K(y,z),K(u,w),K(v5,u)) = x * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,6335,a(flip),b,8999,a),flip(a)].">
      <j1 rule="hyper" parents="320 6335 8999"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9004">
    <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(9000(a,1),286(a,1,2))].">
      <j1 rule="para" parents="9000 286"/>
    </justification>
  </clause>

  <clause id="9005">
    <literal><![CDATA[
      L(K(x,T(y,z)),K(y,u),w) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(7888(a,1),9000(a,1,2))].">
      <j1 rule="para" parents="7888 9000"/>
    </justification>
  </clause>

  <clause id="9006">
    <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,9005,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="119 9005 13"/>
    </justification>
  </clause>

  <clause id="9007">
    <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(9003(a,1),1368(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9003 1368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9008">
    <literal><![CDATA[
      (x * y) * (K(y,z) * K(u,y)) = (x * K(u,y)) * T(y,z)
    ]]></literal>
    <justification jstring="[para(6319(a,1),8994(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6319 8994"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9009">
    <literal><![CDATA[
      x / (K(y,z) * K(u,y)) = x * (K(z,y) * K(y,u))
    ]]></literal>
    <justification jstring="[hyper(326,a,8997,a),flip(a)].">
      <j1 rule="hyper" parents="326 8997"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9010">
    <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(8997(a,1),327(a,1,1)),flip(b)].">
      <j1 rule="para" parents="8997 327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9011">
    <literal><![CDATA[
      (K(x,y) * K(x,z)) \ 1 = K(y,x) * K(z,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,4973,a(flip),b,8998,a)].">
      <j1 rule="hyper" parents="116 4973 8998"/>
    </justification>
  </clause>

  <clause id="9012">
    <literal><![CDATA[
      (K(x,y) * K(x,z)) \ 1 = K(z,x) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,5642,a,b,9011,a),flip(a)].">
      <j1 rule="hyper" parents="320 5642 9011"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9013">
    <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(9011(a,1),6879(a,2,1))].">
      <j1 rule="para" parents="9011 6879"/>
    </justification>
  </clause>

  <clause id="9014">
    <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(9002(a,1),4905(a,1,1,1))].">
      <j1 rule="para" parents="9002 4905"/>
    </justification>
  </clause>

  <clause id="9015">
    <literal><![CDATA[
      (K(x,y) * K(z,x)) \ 1 = K(y,x) * K(x,z)
    ]]></literal>
    <justification jstring="[hyper(3961,a,9009,a)].">
      <j1 rule="hyper" parents="3961 9009"/>
    </justification>
  </clause>

  <clause id="9016">
    <literal><![CDATA[
      x / (K(y,z) * K(z,u)) = x * (K(u,z) * K(z,y))
    ]]></literal>
    <justification jstring="[para(2003(a,1),9009(a,1,2))].">
      <j1 rule="para" parents="2003 9009"/>
    </justification>
  </clause>

  <clause id="9017">
    <literal><![CDATA[
      (x / R(y,z,y)) * y = x * (y \ L(y,z,y))
    ]]></literal>
    <justification jstring="[para(5490(a,1),8925(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5490 8925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9018">
    <literal><![CDATA[
      K(x,L(y,z / T(y,u),w)) = L(K(x,y),z,w)
    ]]></literal>
    <justification jstring="[para(7888(a,1),8311(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7888 8311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9019">
    <literal><![CDATA[
      L(K(x,y),y * z,u) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(187(a,1),9018(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="187 9018"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9020">
    <literal><![CDATA[
      K(x,L(y,y \ z,u)) = L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(265(a,1),9018(a,1,2,2))].">
      <j1 rule="para" parents="265 9018"/>
    </justification>
  </clause>

  <clause id="9021">
    <literal><![CDATA[
      L(K(x,y),z * K(y,u),w) = K(x,L(y,z / y,w))
    ]]></literal>
    <justification jstring="[para(6148(a,1),9018(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6148 9018"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9023">
    <literal><![CDATA[
      K(x * y,L(x,y,z)) = K(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(6118,a,9019,a),flip(a)].">
      <j1 rule="hyper" parents="6118 9019"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9024">
    <literal><![CDATA[
      K((x \ y) \ (z * u),L(z,u,x)) = K(y \ (x * (z * u)),z)
    ]]></literal>
    <justification jstring="[hyper(58,a,6626,a(flip),b,9019,a),flip(a)].">
      <j1 rule="hyper" parents="58 6626 9019"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9025">
    <literal><![CDATA[
      (x * (y * z)) * K(u,L(y,z,x)) = x * ((y * z) * K(u,y))
    ]]></literal>
    <justification jstring="[hyper(119,a,9019,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="119 9019 13"/>
    </justification>
  </clause>

  <clause id="9026">
    <literal><![CDATA[
      L(K(x,y / z),y,u) = K(x,L(y / z,z,u))
    ]]></literal>
    <justification jstring="[para(7(a,1),9019(a,1,2))].">
      <j1 rule="para" parents="7 9019"/>
    </justification>
  </clause>

  <clause id="9027">
    <literal><![CDATA[
      L(K(x,y),T(y,z) * u,w) = K(x,L(y,K(y,z) * u,w))
    ]]></literal>
    <justification jstring="[para(4778(a,1),9019(a,1,2))].">
      <j1 rule="para" parents="4778 9019"/>
    </justification>
  </clause>

  <clause id="9028">
    <literal><![CDATA[
      K(x,L(y,x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(L(x,y,z),y) = u
    ]]></literal>
    <justification jstring="[para(9019(a,1),8394(a,1))].">
      <j1 rule="para" parents="9019 8394"/>
    </justification>
  </clause>

  <clause id="9029">
    <literal><![CDATA[
      L(K(x,y),z * K(y,u),w) = L(K(x,y),z,w)
    ]]></literal>
    <justification jstring="[hyper(320,a,6607,a(flip),b,9021,a),flip(a)].">
      <j1 rule="hyper" parents="320 6607 9021"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9030">
    <literal><![CDATA[
      K(x,y) * L(K(y,x),z * K(x,u),w) = a(w,z,K(x,y))
    ]]></literal>
    <justification jstring="[para(9029(a,2),5892(a,1,2))].">
      <j1 rule="para" parents="9029 5892"/>
    </justification>
  </clause>

  <clause id="9031">
    <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(9029(a,2),8602(a,2,1)),flip(a)].">
      <j1 rule="para" parents="9029 8602"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9032">
    <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,7930,a(flip),b,8313,a),flip(a)].">
      <j1 rule="hyper" parents="320 7930 8313"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9033">
    <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(8313(a,2),8256(a,1))].">
      <j1 rule="para" parents="8313 8256"/>
    </justification>
  </clause>

  <clause id="9034">
    <literal><![CDATA[
      T(T(x,K(y,T(z,z))),z \ T(y,z)) = T(x,y / T(z,y))
    ]]></literal>
    <justification jstring="[para(4246(a,1),8326(a,2,2))].">
      <j1 rule="para" parents="4246 8326"/>
    </justification>
  </clause>

  <clause id="9035">
    <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,8307,a(flip),b,8343,a),flip(a)].">
      <j1 rule="hyper" parents="320 8307 8343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9036">
    <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(7780(a,1),8367(a,2,2))].">
      <j1 rule="para" parents="7780 8367"/>
    </justification>
  </clause>

  <clause id="9037">
    <literal><![CDATA[
      K(x,y) * T(z,T(x * z,y)) = T(z,x * z) * K(x,y)
    ]]></literal>
    <justification jstring="[para(4610(a,2),8372(a,1,2))].">
      <j1 rule="para" parents="4610 8372"/>
    </justification>
  </clause>

  <clause id="9038">
    <literal><![CDATA[
      T(x,(y \ x) \ (z * x)) = T(x,(y \ 1) \ z)
    ]]></literal>
    <justification jstring="[hyper(320,a,4992,a,b,8381,a),flip(a)].">
      <j1 rule="hyper" parents="320 4992 8381"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9039">
    <literal><![CDATA[
      T(x,(y \ 1) \ (x \ z)) = x * K(x,(y \ x) \ z)
    ]]></literal>
    <justification jstring="[hyper(8461,a,9038,a),flip(a)].">
      <j1 rule="hyper" parents="8461 9038"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9040">
    <literal><![CDATA[
      K(x,(y \ 1) \ (x \ z)) = K(x,(y \ x) \ z)
    ]]></literal>
    <justification jstring="[hyper(4837,a,9039,a)].">
      <j1 rule="hyper" parents="4837 9039"/>
    </justification>
  </clause>

  <clause id="9041">
    <literal><![CDATA[
      K(x / y,z \ (y \ x)) = K(y \ x,y \ (z \ x))
    ]]></literal>
    <justification jstring="[hyper(8055,a,8513,a)].">
      <j1 rule="hyper" parents="8055 8513"/>
    </justification>
  </clause>

  <clause id="9042">
    <literal><![CDATA[
      K(x \ y,(z * x) \ y) = K(x \ y,x \ (z \ y))
    ]]></literal>
    <justification jstring="[hyper(58,a,8684,a(flip),b,9041,a)].">
      <j1 rule="hyper" parents="58 8684 9041"/>
    </justification>
  </clause>

  <clause id="9043">
    <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),9042(a,2,2))].">
      <j1 rule="para" parents="75 9042"/>
    </justification>
  </clause>

  <clause id="9044">
    <literal><![CDATA[
      K((((x * y) \ x) \ 1) * z,x \ (x * y)) = K(z / ((x * y) \ x),y)
    ]]></literal>
    <justification jstring="[para(4(a,1),8531(a,2,2))].">
      <j1 rule="para" parents="4 8531"/>
    </justification>
  </clause>

  <clause id="9045">
    <literal><![CDATA[
      K(x,y \ (x \ ((x * z) * y))) = ((z * x) * y) \ ((x * z) * y)
    ]]></literal>
    <justification jstring="[para(4(a,1),8535(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4 8535"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9046">
    <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(8571(a,1),7704(a,1))].">
      <j1 rule="para" parents="8571 7704"/>
    </justification>
  </clause>

  <clause id="9048">
    <literal><![CDATA[
      K(T(x,y * K(z,y)),u) = K(x * K(T(x,z),y),u)
    ]]></literal>
    <justification jstring="[hyper(320,a,4794,a,b,8615,a),flip(a)].">
      <j1 rule="hyper" parents="320 4794 8615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9049">
    <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(5203(a,1),9048(a,2,1,2,1))].">
      <j1 rule="para" parents="5203 9048"/>
    </justification>
  </clause>

  <clause id="9050">
    <literal><![CDATA[
      K(T(x,y * K(z * x,y)),u) = K(x * K(T(x,z),y),u)
    ]]></literal>
    <justification jstring="[para(7144(a,1),9048(a,2,1,2))].">
      <j1 rule="para" parents="7144 9048"/>
    </justification>
  </clause>

  <clause id="9051">
    <literal><![CDATA[
      T(x * (y \ z),K(y,z)) = (y \ z) * T(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(58,a,5583,a(flip),b,8618,a),flip(a)].">
      <j1 rule="hyper" parents="58 5583 8618"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9052">
    <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(8643(a,1),490(a,1,1,1))].">
      <j1 rule="para" parents="8643 490"/>
    </justification>
  </clause>

  <clause id="9053">
    <literal><![CDATA[
      K((T(x,y) \ y) \ z,u) = K((x \ T(y,x)) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(7420,a,8646,a),flip(a)].">
      <j1 rule="hyper" parents="7420 8646"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9054">
    <literal><![CDATA[
      K((T(x,y) * z) \ u,K(x,w)) = K(x,K(w,z \ (x \ u)))
    ]]></literal>
    <justification jstring="[hyper(320,a,7784,a(flip),b,8668,a),flip(a)].">
      <j1 rule="hyper" parents="320 7784 8668"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9055">
    <literal><![CDATA[
      K(x,T(y \ T(T(x,z),u),w)) = K(x,T(y \ x,w))
    ]]></literal>
    <justification jstring="[hyper(320,a,8711,a(flip),b,8712,a),flip(a)].">
      <j1 rule="hyper" parents="320 8711 8712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9057">
    <literal><![CDATA[
      T(K(x \ y,x) * z,y) = K(x \ y,x) * T(z,y)
    ]]></literal>
    <justification jstring="[hyper(6199,a,8783,a),flip(a)].">
      <j1 rule="hyper" parents="6199 8783"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9058">
    <literal><![CDATA[
      T(K(x \ (y * x),x) * z,y * x) = K(y,x) * T(z,y * x)
    ]]></literal>
    <justification jstring="[para(4963(a,1),9057(a,2,1))].">
      <j1 rule="para" parents="4963 9057"/>
    </justification>
  </clause>

  <clause id="9059">
    <literal><![CDATA[
      K(T(x,y \ z),R(y,u,w)) = K(T(x,z),R(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(4984,a,8793,a),flip(a)].">
      <j1 rule="hyper" parents="4984 8793"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9060">
    <literal><![CDATA[
      K(x,y) * ((y * R(x,z,u)) * x) = (x * y) * R(x,z,u)
    ]]></literal>
    <justification jstring="[para(1875(a,2),8800(a,1,2))].">
      <j1 rule="para" parents="1875 8800"/>
    </justification>
  </clause>

  <clause id="9061">
    <literal><![CDATA[
      K(x,(y * R(x,z,u)) / w) = K(x,y / (R(x,z,u) \ w))
    ]]></literal>
    <justification jstring="[hyper(320,a,7561,a(flip),b,8802,a),flip(a)].">
      <j1 rule="hyper" parents="320 7561 8802"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9062">
    <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,8804,a),flip(a)].">
      <j1 rule="hyper" parents="320 22 8804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9063">
    <literal><![CDATA[
      L(x \ y,z,T(x \ y,u)) = L(x \ y,z,y / x)
    ]]></literal>
    <justification jstring="[hyper(860,a,8805,a),flip(a)].">
      <j1 rule="hyper" parents="860 8805"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9064">
    <literal><![CDATA[
      L(x \ y,z,y / x) = L(x \ y,z,x \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,7491,a(flip),b,9063,a),flip(a)].">
      <j1 rule="hyper" parents="58 7491 9063"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9065">
    <literal><![CDATA[
      L(x \ y,x,x \ y) = T(y / x,y)
    ]]></literal>
    <justification jstring="[hyper(761,a,9064,a),flip(a)].">
      <j1 rule="hyper" parents="761 9064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9066">
    <literal><![CDATA[
      L(T(x \ y,z),x,x \ y) = T(T(y / x,y),z)
    ]]></literal>
    <justification jstring="[para(9065(a,1),20(a,2,1))].">
      <j1 rule="para" parents="9065 20"/>
    </justification>
  </clause>

  <clause id="9067">
    <literal><![CDATA[
      T(x / y,z) * T(y,K(x,z)) = x * K(x / y,z)
    ]]></literal>
    <justification jstring="[para(8044(a,1),8821(a,1,2))].">
      <j1 rule="para" parents="8044 8821"/>
    </justification>
  </clause>

  <clause id="9068">
    <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(4246(a,2),9067(a,2,2,1))].">
      <j1 rule="para" parents="4246 9067"/>
    </justification>
  </clause>

  <clause id="9069">
    <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,8173,a(flip),b,8823,a),flip(a)].">
      <j1 rule="hyper" parents="320 8173 8823"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9070">
    <literal><![CDATA[
      R(K(x,K(y,z)),u,w) = K(x,K(y,R(z,u,w)))
    ]]></literal>
    <justification jstring="[para(8173(a,1),9069(a,1,1))].">
      <j1 rule="para" parents="8173 9069"/>
    </justification>
  </clause>

  <clause id="9071">
    <literal><![CDATA[
      R(K(x,K(y,z)),u,w) = K(y,K(z,R(x,u,w)))
    ]]></literal>
    <justification jstring="[para(8176(a,1),9069(a,1,1))].">
      <j1 rule="para" parents="8176 9069"/>
    </justification>
  </clause>

  <clause id="9072">
    <literal><![CDATA[
      K(x,R(K(y,z),u,w)) = K(x,K(y,R(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(58,a,8826,a(flip),b,9070,a)].">
      <j1 rule="hyper" parents="58 8826 9070"/>
    </justification>
  </clause>

  <clause id="9073">
    <literal><![CDATA[
      K(x,K(y,R(z,u,w))) = K(z,K(x,R(y,u,w)))
    ]]></literal>
    <justification jstring="[hyper(58,a,9070,a(flip),b,9071,a),flip(a)].">
      <j1 rule="hyper" parents="58 9070 9071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9074">
    <literal><![CDATA[
      K(x,R(K(y,z),u,w)) = K(x,K(z,R(y,u,w)))
    ]]></literal>
    <justification jstring="[hyper(58,a,8825,a(flip),b,9071,a)].">
      <j1 rule="hyper" parents="58 8825 9071"/>
    </justification>
  </clause>

  <clause id="9075">
    <literal><![CDATA[
      T(x,R(K(y,z),u,w)) = T(x,K(y,R(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(118,a,9072,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 9072 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9076">
    <literal><![CDATA[
      T(x,R(K(y,z),u,w)) = T(x,K(z,R(y,u,w)))
    ]]></literal>
    <justification jstring="[hyper(118,a,9074,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 9074 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9077">
    <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(6947(a,1),9074(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6947 9074"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9078">
    <literal><![CDATA[
      T(x,K(y,R(z,u,w))) = T(x,K(z,R(y,u,w)))
    ]]></literal>
    <justification jstring="[hyper(58,a,9075,a(flip),b,9076,a)].">
      <j1 rule="hyper" parents="58 9075 9076"/>
    </justification>
  </clause>

  <clause id="9079">
    <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(9078(a,1),8834(a,2,2))].">
      <j1 rule="para" parents="9078 8834"/>
    </justification>
  </clause>

  <clause id="9080">
    <literal><![CDATA[
      K(T(x,y),z) * ((y * z) / y) = (y * (z * K(x,z))) / y
    ]]></literal>
    <justification jstring="[hyper(133,a,8889,a)].">
      <j1 rule="hyper" parents="133 8889"/>
    </justification>
  </clause>

  <clause id="9081">
    <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(8896(a,1),6315(a,1,1))].">
      <j1 rule="para" parents="8896 6315"/>
    </justification>
  </clause>

  <clause id="9082">
    <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(8911(a,2),8065(a,1))].">
      <j1 rule="para" parents="8911 8065"/>
    </justification>
  </clause>

  <clause id="9083">
    <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),9082(a,1,2,1))].">
      <j1 rule="para" parents="104 9082"/>
    </justification>
  </clause>

  <clause id="9084">
    <literal><![CDATA[
      (x / y) * (K(y,z) * K(y * z,y)) = x / L(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,6646,a(flip),b,8996,a),flip(a)].">
      <j1 rule="hyper" parents="320 6646 8996"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9085">
    <literal><![CDATA[
      (x / y) * a(y,z,y) = x / L(y,z,y)
    ]]></literal>
    <justification jstring="[para(8948(a,1),9084(a,1,2))].">
      <j1 rule="para" parents="8948 9084"/>
    </justification>
  </clause>

  <clause id="9086">
    <literal><![CDATA[
      L(x,y,x) \ x = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(29,a,6062,a,b,9085,a)].">
      <j1 rule="hyper" parents="29 6062 9085"/>
    </justification>
  </clause>

  <clause id="9087">
    <literal><![CDATA[
      (x * y) / L(y,z,y) = x * a(y,z,y)
    ]]></literal>
    <justification jstring="[para(6(a,1),9085(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6 9085"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9088">
    <literal><![CDATA[
      L(x,y,x) \ 1 = x \ a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,9086,a(flip),b,1413,a),flip(a)].">
      <j1 rule="hyper" parents="116 9086 1413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9089">
    <literal><![CDATA[
      a(x,y,x) \ x = L(x,y,x)
    ]]></literal>
    <justification jstring="[para(9086(a,1),5948(a,1,1))].">
      <j1 rule="para" parents="9086 5948"/>
    </justification>
  </clause>

  <clause id="9090">
    <literal><![CDATA[
      L(x \ L(y,z,y),x,a(y,z,y)) = (a(y,z,y) * x) \ y
    ]]></literal>
    <justification jstring="[para(9089(a,1),298(a,1,1,2))].">
      <j1 rule="para" parents="9089 298"/>
    </justification>
  </clause>

  <clause id="9091">
    <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(9088(a,1),6750(a,1,1,2))].">
      <j1 rule="para" parents="9088 6750"/>
    </justification>
  </clause>

  <clause id="9092">
    <literal><![CDATA[
      (x / L(y,z,y)) * y = x * a(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(1650,a,9087,a)].">
      <j1 rule="hyper" parents="1650 9087"/>
    </justification>
  </clause>

  <clause id="9093">
    <literal><![CDATA[
      (x * a(y,z,y)) \ (x * y) = L(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(188,a,9087,a)].">
      <j1 rule="hyper" parents="188 9087"/>
    </justification>
  </clause>

  <clause id="9094">
    <literal><![CDATA[
      x * (L(x,y,x) \ z) = z * a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,7513,a(flip),b,9092,a)].">
      <j1 rule="hyper" parents="58 7513 9092"/>
    </justification>
  </clause>

  <clause id="9095">
    <literal><![CDATA[
      (x * L(y,z,y)) * a(y,z,y) = x * y
    ]]></literal>
    <justification jstring="[para(6(a,1),9092(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6 9092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9096">
    <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(906(a,1),9093(a,1,2))].">
      <j1 rule="para" parents="906 9093"/>
    </justification>
  </clause>

  <clause id="9097">
    <literal><![CDATA[
      (T(x * y,x) / x) \ (y * x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[para(8959(a,2),9093(a,1,1))].">
      <j1 rule="para" parents="8959 9093"/>
    </justification>
  </clause>

  <clause id="9098">
    <literal><![CDATA[
      L(x,y,x) * (x \ z) = z / a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(573,a,9094,a),flip(a)].">
      <j1 rule="hyper" parents="573 9094"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9099">
    <literal><![CDATA[
      T(x,y) * (L(T(x,y),z,x) \ u) = u * a(x,z,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,8542,a,b,9094,a)].">
      <j1 rule="hyper" parents="58 8542 9094"/>
    </justification>
  </clause>

  <clause id="9100">
    <literal><![CDATA[
      L(x,y,x) \ (x * z) = z * a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,1412,a,b,9094,a)].">
      <j1 rule="hyper" parents="58 1412 9094"/>
    </justification>
  </clause>

  <clause id="9101">
    <literal><![CDATA[
      K(x,y) * (z * a(x,u,x)) = T(x,y) * (L(x,u,x) \ z)
    ]]></literal>
    <justification jstring="[hyper(119,a,9094,a(flip),b,4782,a)].">
      <j1 rule="hyper" parents="119 9094 4782"/>
    </justification>
  </clause>

  <clause id="9102">
    <literal><![CDATA[
      x * a(y,y \ x,y) = y * (T(x,y) / y)
    ]]></literal>
    <justification jstring="[para(4506(a,1),9094(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4506 9094"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9103">
    <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(7503(a,1),9094(a,1,2,1))].">
      <j1 rule="para" parents="7503 9094"/>
    </justification>
  </clause>

  <clause id="9104">
    <literal><![CDATA[
      (x / y) \ (x / a(y,z,y)) = L(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(116,a,9098,a(flip),b,7514,a(flip))].">
      <j1 rule="hyper" parents="116 9098 7514"/>
    </justification>
  </clause>

  <clause id="9105">
    <literal><![CDATA[
      (x \ y) * a(x,z,x) = L(x,z,x) \ y
    ]]></literal>
    <justification jstring="[para(5(a,1),9100(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5 9100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9106">
    <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(7955(a,1),9097(a,1,2))].">
      <j1 rule="para" parents="7955 9097"/>
    </justification>
  </clause>

  <clause id="9107">
    <literal><![CDATA[
      x * a(y,y \ x,y) = T(y * (x / y),y)
    ]]></literal>
    <justification jstring="[hyper(320,a,4574,a,b,9102,a),flip(a)].">
      <j1 rule="hyper" parents="320 4574 9102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9108">
    <literal><![CDATA[
      K(x,y) * (z * a(y,u,y)) = y * (L(T(y,x),u,y) \ z)
    ]]></literal>
    <justification jstring="[hyper(119,a,9099,a(flip),b,5099,a)].">
      <j1 rule="hyper" parents="119 9099 5099"/>
    </justification>
  </clause>

  <clause id="9109">
    <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(9099(a,2),38(a,1))].">
      <j1 rule="para" parents="9099 38"/>
    </justification>
  </clause>

  <clause id="9110">
    <literal><![CDATA[
      (x * y) * (K(y,z) * K(u,y)) = x * (K(u,y) * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,6310,a(flip),b,9008,a),flip(a)].">
      <j1 rule="hyper" parents="320 6310 9008"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9111">
    <literal><![CDATA[
      a(x,y * K(z,u),K(z,w)) = a(x,y,K(z,w))
    ]]></literal>
    <justification jstring="[hyper(5899,a,9030,a)].">
      <j1 rule="hyper" parents="5899 9030"/>
    </justification>
  </clause>

  <clause id="9112">
    <literal><![CDATA[
      a(x,y * K(z,u),K(u,w)) = a(x,y,K(u,w))
    ]]></literal>
    <justification jstring="[para(6329(a,1),9111(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6329 9111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9113">
    <literal><![CDATA[
      (x * y) \ ((x * (y * K(z,u))) * K(u,z)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,6343,a,b,9112,a)].">
      <j1 rule="hyper" parents="58 6343 9112"/>
    </justification>
  </clause>

  <clause id="9114">
    <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,7775,a,b,9031,a),flip(a)].">
      <j1 rule="hyper" parents="320 7775 9031"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9115">
    <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),9034(a,1,1,2,2))].">
      <j1 rule="para" parents="104 9034"/>
    </justification>
  </clause>

  <clause id="9116">
    <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,9062,a(flip),b,5102,a),flip(a)].">
      <j1 rule="hyper" parents="116 9062 5102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9117">
    <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(9062(a,1),7103(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9062 7103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9118">
    <literal><![CDATA[
      ((x * y) / x) / ((x * (y * K(z,y))) / x) = K(y,T(z,x))
    ]]></literal>
    <justification jstring="[para(9080(a,1),5142(a,1,2))].">
      <j1 rule="para" parents="9080 5142"/>
    </justification>
  </clause>

  <clause id="9119">
    <literal><![CDATA[
      K(x,x * y) * (z * a(x,y,x)) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(320,a,6971,a(flip),b,9101,a),flip(a)].">
      <j1 rule="hyper" parents="320 6971 9101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9120">
    <literal><![CDATA[
      K(x,x * y) * z != K(x,y) * u
    ]]></literal>
    <literal><![CDATA[
      u * a(x,y,x) = z
    ]]></literal>
    <justification jstring="[para(9119(a,1),38(a,1)),flip(a)].">
      <j1 rule="para" parents="9119 38"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9121">
    <literal><![CDATA[
      K(x,y) * (z * L(x,y,x)) = K(x,x * y) * (z * x)
    ]]></literal>
    <justification jstring="[para(9095(a,1),9119(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9095 9119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9122">
    <literal><![CDATA[
      (x * y) * (K(y,z) * K(y * z,y)) = x * R(y,z,y)
    ]]></literal>
    <justification jstring="[para(5093(a,1),9110(a,2,2))].">
      <j1 rule="para" parents="5093 9110"/>
    </justification>
  </clause>

  <clause id="9123">
    <literal><![CDATA[
      (x * y) * a(y,z,y) = x * R(y,z,y)
    ]]></literal>
    <justification jstring="[para(8948(a,1),9122(a,1,2))].">
      <j1 rule="para" parents="8948 9122"/>
    </justification>
  </clause>

  <clause id="9124">
    <literal><![CDATA[
      (x / y) * R(y,z,y) = x * a(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(326,a,9123,a),flip(a)].">
      <j1 rule="hyper" parents="326 9123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9125">
    <literal><![CDATA[
      (x * y) \ (x * R(y,z,y)) = a(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(123,a,9123,a)].">
      <j1 rule="hyper" parents="123 9123"/>
    </justification>
  </clause>

  <clause id="9126">
    <literal><![CDATA[
      (x / R(y,z,y)) * y = x / a(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(117,a,7,a(flip),b,9123,a),flip(a)].">
      <j1 rule="hyper" parents="117 7 9123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9127">
    <literal><![CDATA[
      R(x,y,x) * (x \ z) = z * a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,7139,a,b,9124,a)].">
      <j1 rule="hyper" parents="58 7139 9124"/>
    </justification>
  </clause>

  <clause id="9128">
    <literal><![CDATA[
      (x * a(y,z,y)) \ (x * R(y,z,y)) = y
    ]]></literal>
    <justification jstring="[para(9124(a,1),1881(a,1,1))].">
      <j1 rule="para" parents="9124 1881"/>
    </justification>
  </clause>

  <clause id="9129">
    <literal><![CDATA[
      (x / y) * ((y \ z) \ T(z,y)) = x * a(y,y \ z,y)
    ]]></literal>
    <justification jstring="[para(4335(a,1),9124(a,1,2))].">
      <j1 rule="para" parents="4335 9124"/>
    </justification>
  </clause>

  <clause id="9130">
    <literal><![CDATA[
      K(x,y) * ((z / y) * R(y,u,y)) = y * (L(T(y,x),u,y) \ z)
    ]]></literal>
    <justification jstring="[para(9124(a,2),9108(a,1,2))].">
      <j1 rule="para" parents="9124 9108"/>
    </justification>
  </clause>

  <clause id="9131">
    <literal><![CDATA[
      (x * y) * a(y,z,y) != u
    ]]></literal>
    <literal><![CDATA[
      x * R(y,z,y) = u
    ]]></literal>
    <justification jstring="[para(9125(a,1),255(a,1,2)),flip(b)].">
      <j1 rule="para" parents="9125 255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9132">
    <literal><![CDATA[
      x * (y \ L(y,z,y)) = x / a(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,9017,a(flip),b,9126,a)].">
      <j1 rule="hyper" parents="58 9017 9126"/>
    </justification>
  </clause>

  <clause id="9133">
    <literal><![CDATA[
      (x * y) * a(x,z,x) = R(x,z,x) * y
    ]]></literal>
    <justification jstring="[hyper(585,a,9127,a),flip(a)].">
      <j1 rule="hyper" parents="585 9127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9134">
    <literal><![CDATA[
      (R(x,y,x) \ z) * a(x,y,x) = x \ z
    ]]></literal>
    <justification jstring="[hyper(58,a,1312,a(flip),b,9127,a),flip(a)].">
      <j1 rule="hyper" parents="58 1312 9127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9135">
    <literal><![CDATA[
      x * (y * a(x,z,x)) = R(x,z,x) * y
    ]]></literal>
    <justification jstring="[hyper(119,a,9127,a(flip),b,1311,a)].">
      <j1 rule="hyper" parents="119 9127 1311"/>
    </justification>
  </clause>

  <clause id="9136">
    <literal><![CDATA[
      (x / R(y,z,y)) * a(y,z,y) = x / y
    ]]></literal>
    <justification jstring="[para(9128(a,1),324(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9128 324"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9137">
    <literal><![CDATA[
      K(x,T((y \ z) / z,u)) = ((u * x) / u) / ((u * (x * K(y \ 1,x))) / u)
    ]]></literal>
    <justification jstring="[para(5434(a,1),9118(a,1,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5434 9118"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9138">
    <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(8864(a,1),9118(a,1,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="8864 9118"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9139">
    <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),7143(a,1,2,1,1))].">
      <j1 rule="para" parents="72 7143"/>
    </justification>
  </clause>

  <clause id="9140">
    <literal><![CDATA[
      L(x,T(y,K(x,z)),x) = T(x,x * y) * K(y,x)
    ]]></literal>
    <justification jstring="[para(7871(a,1),7152(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7871 7152"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9141">
    <literal><![CDATA[
      L(x,T(y,K(x,z)),x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,5284,a(flip),b,9140,a),flip(a)].">
      <j1 rule="hyper" parents="320 5284 9140"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9143">
    <literal><![CDATA[
      L(x,T(y,T(x,z)),x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,7446,a(flip),b,9141,a)].">
      <j1 rule="hyper" parents="58 7446 9141"/>
    </justification>
  </clause>

  <clause id="9145">
    <literal><![CDATA[
      L(x,y / T(x,z),x) = L(x,T(x,z) \ y,x)
    ]]></literal>
    <justification jstring="[para(107(a,1),9143(a,1,2)),flip(a)].">
      <j1 rule="para" parents="107 9143"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9146">
    <literal><![CDATA[
      L(K(x,T((y \ z) \ u,w)),u,y) = K(x,T(z \ (y * u),w))
    ]]></literal>
    <justification jstring="[para(7158(a,2),7162(a,1,1))].">
      <j1 rule="para" parents="7158 7162"/>
    </justification>
  </clause>

  <clause id="9147">
    <literal><![CDATA[
      L(K(x,T(y \ z,u)),y \ z,w) = K(x,T((z \ y) \ 1,u))
    ]]></literal>
    <justification jstring="[para(7158(a,2),7163(a,1,1))].">
      <j1 rule="para" parents="7158 7163"/>
    </justification>
  </clause>

  <clause id="9149">
    <literal><![CDATA[
      x \ R(x,y * K(x,z),x) = K(x,y) * K(y * x,x)
    ]]></literal>
    <justification jstring="[para(7341(a,1),7249(a,2,2))].">
      <j1 rule="para" parents="7341 7249"/>
    </justification>
  </clause>

  <clause id="9150">
    <literal><![CDATA[
      R(x,y * K(x,z),x) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(5502,a,9149,a),flip(a)].">
      <j1 rule="hyper" parents="5502 9149"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9152">
    <literal><![CDATA[
      a(x,y * K(x,z),x) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,9150,a(flip),b,8949,a),flip(a)].">
      <j1 rule="hyper" parents="116 9150 8949"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9153">
    <literal><![CDATA[
      a(x,y * K(x,z),x) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,x) = u
    ]]></literal>
    <justification jstring="[para(9152(a,2),8962(a,1))].">
      <j1 rule="para" parents="9152 8962"/>
    </justification>
  </clause>

  <clause id="9154">
    <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(5631(a,1),7531(a,1,2,1))].">
      <j1 rule="para" parents="5631 7531"/>
    </justification>
  </clause>

  <clause id="9155">
    <literal><![CDATA[
      T((x \ 1) * y,K(x,z)) = (x \ 1) * T(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(842,a,7639,a),flip(a)].">
      <j1 rule="hyper" parents="842 7639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9156">
    <literal><![CDATA[
      K(x,y) * T((x \ 1) * z,K(x,y)) = (x \ 1) * (z * K(x,y))
    ]]></literal>
    <justification jstring="[para(9155(a,2),6010(a,1,2))].">
      <j1 rule="para" parents="9155 6010"/>
    </justification>
  </clause>

  <clause id="9157">
    <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,7160,a(flip),b,7737,a),flip(a)].">
      <j1 rule="hyper" parents="320 7160 7737"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9158">
    <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(5637(a,1),7904(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5637 7904"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9159">
    <literal><![CDATA[
      L(K(x,T(T(y,z),u * z)),z,u) = (u * (K(x,y) * z)) / (u * z)
    ]]></literal>
    <justification jstring="[para(7179(a,1),7985(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7179 7985"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9160">
    <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(8066,a,8310,a),flip(a)].">
      <j1 rule="hyper" parents="8066 8310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9161">
    <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(7753(a,1),8474(a,1,1))].">
      <j1 rule="para" parents="7753 8474"/>
    </justification>
  </clause>

  <clause id="9162">
    <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(7779(a,1),8474(a,1,1))].">
      <j1 rule="para" parents="7779 8474"/>
    </justification>
  </clause>

  <clause id="9163">
    <literal><![CDATA[
      x * K(y,(x \ 1) * (z * x)) = K(y,L(z,x,x \ 1)) * x
    ]]></literal>
    <justification jstring="[para(5322(a,1),8530(a,1,2))].">
      <j1 rule="para" parents="5322 8530"/>
    </justification>
  </clause>

  <clause id="9164">
    <literal><![CDATA[
      K(x,(y * (z * x)) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * z) \ (x \ u)) = w
    ]]></literal>
    <justification jstring="[para(6902(a,1),8541(a,1))].">
      <j1 rule="para" parents="6902 8541"/>
    </justification>
  </clause>

  <clause id="9165">
    <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(631(a,1),8566(a,1,2))].">
      <j1 rule="para" parents="631 8566"/>
    </justification>
  </clause>

  <clause id="9166">
    <literal><![CDATA[
      K(x,a(K(x,y),z,u)) = 1
    ]]></literal>
    <justification jstring="[hyper(58,a,5515,a(flip),b,9165,a),flip(a)].">
      <j1 rule="hyper" parents="58 5515 9165"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9167">
    <literal><![CDATA[
      a(K(x,y),z,u) * x = x * a(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(5572,a,9166,a),flip(a)].">
      <j1 rule="hyper" parents="5572 9166"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9168">
    <literal><![CDATA[
      T(a(K(x,y),z,u),x) = a(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(4953,a,9166,a)].">
      <j1 rule="hyper" parents="4953 9166"/>
    </justification>
  </clause>

  <clause id="9170">
    <literal><![CDATA[
      T(x,a(K(x,y),z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(51,a,9166,a)].">
      <j1 rule="hyper" parents="51 9166"/>
    </justification>
  </clause>

  <clause id="9171">
    <literal><![CDATA[
      T(T(x,y),a(K(x,z),u,w)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(9170(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9170 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9172">
    <literal><![CDATA[
      K(x,y) * a(K(x,z),u,w) = a(K(x,z),u,w) * K(x,y)
    ]]></literal>
    <justification jstring="[para(9170(a,1),7150(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9170 7150"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9173">
    <literal><![CDATA[
      K(a(K(x,y),z,u),w) * x = x * K(a(K(x,y),z,u),w)
    ]]></literal>
    <justification jstring="[para(9168(a,1),7150(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9168 7150"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9174">
    <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(8666(a,1),7755(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8666 7755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9175">
    <literal><![CDATA[
      K(x,L(x,y,y \ 1) \ z) = K(x,x \ z)
    ]]></literal>
    <justification jstring="[para(164(a,1),8708(a,1,2)),flip(a)].">
      <j1 rule="para" parents="164 8708"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9177">
    <literal><![CDATA[
      K((x \ 1) \ y,((x \ 1) \ y) \ z) = K((x \ 1) \ y,(x * y) \ z)
    ]]></literal>
    <justification jstring="[para(2818(a,1),9175(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2818 9175"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9178">
    <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(8743(a,2),39(a,1))].">
      <j1 rule="para" parents="8743 39"/>
    </justification>
  </clause>

  <clause id="9179">
    <literal><![CDATA[
      K(x,y) * (y \ R(y,x,L(y,z,u))) = K(x * L(y,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(5147,a,8746,a)].">
      <j1 rule="hyper" parents="5147 8746"/>
    </justification>
  </clause>

  <clause id="9180">
    <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,8933,a,b,8746,a)].">
      <j1 rule="hyper" parents="58 8933 8746"/>
    </justification>
  </clause>

  <clause id="9181">
    <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(8746(a,1),2005(a,1))].">
      <j1 rule="para" parents="8746 2005"/>
    </justification>
  </clause>

  <clause id="9182">
    <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,8933,a,b,8749,a)].">
      <j1 rule="hyper" parents="58 8933 8749"/>
    </justification>
  </clause>

  <clause id="9183">
    <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(8749(a,1),2005(a,1))].">
      <j1 rule="para" parents="8749 2005"/>
    </justification>
  </clause>

  <clause id="9184">
    <literal><![CDATA[
      K(R(x,y / x,z),u) = K((y * z) / ((y / x) * z),T(u,y))
    ]]></literal>
    <justification jstring="[hyper(8007,a,8902,a)].">
      <j1 rule="hyper" parents="8007 8902"/>
    </justification>
  </clause>

  <clause id="9185">
    <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),8910(a,2,2))].">
      <j1 rule="para" parents="477 8910"/>
    </justification>
  </clause>

  <clause id="9186">
    <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(829,a,8921,a)].">
      <j1 rule="hyper" parents="829 8921"/>
    </justification>
  </clause>

  <clause id="9187">
    <literal><![CDATA[
      (x * (y * z)) * K(u,L(y,z,x)) = x * (y * (z * K(u,y)))
    ]]></literal>
    <justification jstring="[para(7055(a,1),9025(a,2,2))].">
      <j1 rule="para" parents="7055 9025"/>
    </justification>
  </clause>

  <clause id="9189">
    <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,4935,a,b,9113,a)].">
      <j1 rule="hyper" parents="320 4935 9113"/>
    </justification>
  </clause>

  <clause id="9190">
    <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,9113,a(flip),b,155,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 9113 155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9191">
    <literal><![CDATA[
      K(x,T((y \ z) \ x,u)) = K(x,T(z \ (y * x),u))
    ]]></literal>
    <justification jstring="[hyper(6118,a,9146,a)].">
      <j1 rule="hyper" parents="6118 9146"/>
    </justification>
  </clause>

  <clause id="9192">
    <literal><![CDATA[
      K(x,T((y \ z) \ x,y)) = K(x,(z / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(320,a,8494,a(flip),b,9191,a),flip(a)].">
      <j1 rule="hyper" parents="320 8494 9191"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9193">
    <literal><![CDATA[
      K(x,T((y \ z) \ x,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,(z / y) \ x) = u
    ]]></literal>
    <justification jstring="[para(9191(a,2),8514(a,1))].">
      <j1 rule="para" parents="9191 8514"/>
    </justification>
  </clause>

  <clause id="9194">
    <literal><![CDATA[
      K(x,((y * z) / y) \ x) = K(x,T(z \ x,y))
    ]]></literal>
    <justification jstring="[para(4(a,1),9192(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="4 9192"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9195">
    <literal><![CDATA[
      K(x,T(y \ x,y \ z)) = K(x,(z / (z / y)) \ x)
    ]]></literal>
    <justification jstring="[para(4343(a,1),9194(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4343 9194"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9196">
    <literal><![CDATA[
      K(x,T((y / (z * y)) \ x,z)) = K(x,R(1 / (1 / (1 / z)),z,y) \ x)
    ]]></literal>
    <justification jstring="[para(4408(a,2),9194(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4408 9194"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9197">
    <literal><![CDATA[
      K(x,T((y \ z) \ 1,u)) = K(x,T(z \ y,u))
    ]]></literal>
    <justification jstring="[hyper(7389,a,9147,a),flip(a)].">
      <j1 rule="hyper" parents="7389 9147"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9198">
    <literal><![CDATA[
      K(x,T((y \ z) \ 1,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z \ y,u)) = w
    ]]></literal>
    <justification jstring="[para(9147(a,1),3666(a,1))].">
      <j1 rule="para" parents="9147 3666"/>
    </justification>
  </clause>

  <clause id="9199">
    <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,7611,a,b,9197,a)].">
      <j1 rule="hyper" parents="58 7611 9197"/>
    </justification>
  </clause>

  <clause id="9200">
    <literal><![CDATA[
      K(x,T(y,z * R(x,u,w))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,8803,a(flip),b,9157,a)].">
      <j1 rule="hyper" parents="58 8803 9157"/>
    </justification>
  </clause>

  <clause id="9202">
    <literal><![CDATA[
      K(x,T(y,z / R(x,u,w))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(7(a,1),9200(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7 9200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9203">
    <literal><![CDATA[
      K(x,T(y,R(x,z,u) \ w)) = K(x,T(y,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,7723,a(flip),b,9202,a)].">
      <j1 rule="hyper" parents="58 7723 9202"/>
    </justification>
  </clause>

  <clause id="9205">
    <literal><![CDATA[
      K(x,T(y,R(x,z,u) * w)) = K(x,T(y,w))
    ]]></literal>
    <justification jstring="[para(4(a,1),9203(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 9203"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9206">
    <literal><![CDATA[
      K(x,T(y,(x * z) * u)) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[para(184(a,1),9203(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="184 9203"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9207">
    <literal><![CDATA[
      K(x,T(y \ (R(x,z,u) * w),w)) = K(x,(R(x,z,u) * w) / y)
    ]]></literal>
    <justification jstring="[hyper(8290,a,9205,a),flip(a)].">
      <j1 rule="hyper" parents="8290 9205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9208">
    <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,7766,a,b,9205,a),flip(a)].">
      <j1 rule="hyper" parents="320 7766 9205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9209">
    <literal><![CDATA[
      K(x,T(y,(z * x) * u)) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,8596,a,b,9206,a)].">
      <j1 rule="hyper" parents="58 8596 9206"/>
    </justification>
  </clause>

  <clause id="9210">
    <literal><![CDATA[
      K(x,T(y / ((z * x) * u),z * u)) = K(x,((z * x) * u) \ y)
    ]]></literal>
    <justification jstring="[para(107(a,1),9209(a,1,2)),flip(a)].">
      <j1 rule="para" parents="107 9209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9211">
    <literal><![CDATA[
      K(x,K(y,R(x,z,u) * w)) = K(x,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(8076,a,9208,a)].">
      <j1 rule="hyper" parents="8076 9208"/>
    </justification>
  </clause>

  <clause id="9212">
    <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(9208(a,2),8071(a,1))].">
      <j1 rule="para" parents="9208 8071"/>
    </justification>
  </clause>

  <clause id="9213">
    <literal><![CDATA[
      K(x,K(y,R(x,z,u) \ w)) = K(x,K(y,w))
    ]]></literal>
    <justification jstring="[para(5(a,1),9211(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5 9211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9214">
    <literal><![CDATA[
      K(x,K(y,(x * z) * u)) = K(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[para(101(a,1),9211(a,1,2,2))].">
      <j1 rule="para" parents="101 9211"/>
    </justification>
  </clause>

  <clause id="9215">
    <literal><![CDATA[
      K(x,K(y,z \ R(x,u,w))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(8216,a,9213,a)].">
      <j1 rule="hyper" parents="8216 9213"/>
    </justification>
  </clause>

  <clause id="9216">
    <literal><![CDATA[
      K(x,K(y,R(x,z,u) / w)) = K(x,K(y,w))
    ]]></literal>
    <justification jstring="[para(75(a,1),9215(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="75 9215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9217">
    <literal><![CDATA[
      K(x,K(y,z * R(x,u,w))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(8214,a,9216,a),flip(a)].">
      <j1 rule="hyper" parents="8214 9216"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9218">
    <literal><![CDATA[
      K(x,K(y,(y * z) * u)) = K(y,K(x,z * u))
    ]]></literal>
    <justification jstring="[hyper(7781,a,9214,a)].">
      <j1 rule="hyper" parents="7781 9214"/>
    </justification>
  </clause>

  <clause id="9219">
    <literal><![CDATA[
      K(x,T(y,L(x,z,u) * w)) = K(x,T(y,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,8761,a(flip),b,9160,a)].">
      <j1 rule="hyper" parents="58 8761 9160"/>
    </justification>
  </clause>

  <clause id="9221">
    <literal><![CDATA[
      K(x,T(y,z * (u * x))) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,8739,a(flip),b,9219,a)].">
      <j1 rule="hyper" parents="58 8739 9219"/>
    </justification>
  </clause>

  <clause id="9223">
    <literal><![CDATA[
      K(x,T(y,z * (x * u))) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,7684,a(flip),b,9221,a)].">
      <j1 rule="hyper" parents="58 7684 9221"/>
    </justification>
  </clause>

  <clause id="9224">
    <literal><![CDATA[
      K(x,T(y,z * (u / x))) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[para(7(a,1),9221(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="7 9221"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9225">
    <literal><![CDATA[
      K(x,T(y,z * u)) * (z * (u * x)) = (z * (u * x)) * K(x,y)
    ]]></literal>
    <justification jstring="[para(9221(a,1),7897(a,1,1))].">
      <j1 rule="para" parents="9221 7897"/>
    </justification>
  </clause>

  <clause id="9226">
    <literal><![CDATA[
      K(x,T(x * y,z * y)) = K(x,T(x * y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,7157,a(flip),b,9223,a),flip(a)].">
      <j1 rule="hyper" parents="58 7157 9223"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9227">
    <literal><![CDATA[
      K(x,T(y,z * (x \ u))) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[para(5(a,1),9223(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="5 9223"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9228">
    <literal><![CDATA[
      K(x,T(x * y,z * y)) = K(x,T(y * x,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,5388,a,b,9226,a),flip(a)].">
      <j1 rule="hyper" parents="320 5388 9226"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9229">
    <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(9227(a,1),8060(a,1))].">
      <j1 rule="para" parents="9227 8060"/>
    </justification>
  </clause>

  <clause id="9230">
    <literal><![CDATA[
      K(x,T((y \ 1) * (z * y),y)) = K(x,L(z,y,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(7901,a,9163,a)].">
      <j1 rule="hyper" parents="7901 9163"/>
    </justification>
  </clause>

  <clause id="9231">
    <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,8013,a(flip),b,9184,a)].">
      <j1 rule="hyper" parents="320 8013 9184"/>
    </justification>
  </clause>

  <clause id="9232">
    <literal><![CDATA[
      K(R(x,y / x,z),u) = R(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(7883(a,1),9231(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7883 9231"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9234">
    <literal><![CDATA[
      R(K(x,y),z * x,u) = K(R(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(6(a,1),9232(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6 9232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9235">
    <literal><![CDATA[
      K(x,R(y,z / y,u)) = w / (R(K(y,x),z,u) * w)
    ]]></literal>
    <justification jstring="[para(9232(a,1),5142(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9232 5142"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9236">
    <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(7345(a,1),9234(a,1,1))].">
      <j1 rule="para" parents="7345 9234"/>
    </justification>
  </clause>

  <clause id="9237">
    <literal><![CDATA[
      K(x,R(y,z / y,u)) = R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(320,a,6932,a(flip),b,9235,a),flip(a)].">
      <j1 rule="hyper" parents="320 6932 9235"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9238">
    <literal><![CDATA[
      K(x,R(y,z / y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      R(K(x,y),z,u) = w
    ]]></literal>
    <justification jstring="[para(9235(a,2),6936(a,1))].">
      <j1 rule="para" parents="9235 6936"/>
    </justification>
  </clause>

  <clause id="9239">
    <literal><![CDATA[
      K(x,R(y,z / y,u)) = K(x,R(y,y \ z,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,6949,a,b,9237,a),flip(a)].">
      <j1 rule="hyper" parents="320 6949 9237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9240">
    <literal><![CDATA[
      R(K(x,y),z * y,u) = K(x,R(y,z,u))
    ]]></literal>
    <justification jstring="[para(6(a,1),9237(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6 9237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9241">
    <literal><![CDATA[
      R(K(x,y \ z),z,u) = K(x,R(y \ z,y,u))
    ]]></literal>
    <justification jstring="[para(72(a,1),9237(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="72 9237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9242">
    <literal><![CDATA[
      R(K(x,y),z * T(y,u),w) = K(x,R(y,z * K(y,u),w))
    ]]></literal>
    <justification jstring="[para(6193(a,1),9237(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6193 9237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9243">
    <literal><![CDATA[
      R(K(x,y),z * K(u,y),w) = K(x,R(y,z / T(y,u),w))
    ]]></literal>
    <justification jstring="[para(6342(a,1),9237(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6342 9237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9244">
    <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(7243(a,1),9240(a,1,1))].">
      <j1 rule="para" parents="7243 9240"/>
    </justification>
  </clause>

  <clause id="9245">
    <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(5923(a,1),9241(a,2,2))].">
      <j1 rule="para" parents="5923 9241"/>
    </justification>
  </clause>

  <clause id="9246">
    <literal><![CDATA[
      K(x,R(y,y \ z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      R(K(x,y),z,u) = w
    ]]></literal>
    <justification jstring="[para(9239(a,1),9238(a,1))].">
      <j1 rule="para" parents="9239 9238"/>
    </justification>
  </clause>

  <clause id="9247">
    <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),9246(a,1,2,2))].">
      <j1 rule="para" parents="184 9246"/>
    </justification>
  </clause>

  <clause id="9248">
    <literal><![CDATA[
      K(x,R(y,z / T(y,u),w)) = R(K(x,y),z,w)
    ]]></literal>
    <justification jstring="[hyper(58,a,8849,a(flip),b,9243,a),flip(a)].">
      <j1 rule="hyper" parents="58 8849 9243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9250">
    <literal><![CDATA[
      R(K(x,y),z * T(y,u),w) = K(x,R(y,z,w))
    ]]></literal>
    <justification jstring="[para(6(a,1),9248(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6 9248"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9251">
    <literal><![CDATA[
      K(x,R(y,z * K(y,u),w)) = K(x,R(y,z,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,9242,a(flip),b,9250,a)].">
      <j1 rule="hyper" parents="58 9242 9250"/>
    </justification>
  </clause>

  <clause id="9253">
    <literal><![CDATA[
      K(x,R(y,K(y,z) * u,w)) = K(x,R(y,u,w))
    ]]></literal>
    <justification jstring="[para(7179(a,1),9251(a,1,2,2))].">
      <j1 rule="para" parents="7179 9251"/>
    </justification>
  </clause>

  <clause id="9254">
    <literal><![CDATA[
      K(R(x,K(x,y) * z,u),w) = (v5 * K(w,R(x,z,u))) \ v5
    ]]></literal>
    <justification jstring="[para(9253(a,1),6338(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9253 6338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9255">
    <literal><![CDATA[
      K(R(x,K(x,y) * z,u),w) = K(R(x,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(320,a,6338,a(flip),b,9254,a),flip(a)].">
      <j1 rule="hyper" parents="320 6338 9254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9256">
    <literal><![CDATA[
      R(K(x,y),K(x,z) * u,w) = K(R(x,x \ u,w),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,6747,a(flip),b,9255,a)].">
      <j1 rule="hyper" parents="58 6747 9255"/>
    </justification>
  </clause>

  <clause id="9257">
    <literal><![CDATA[
      K(R(x,K(y,x) * z,u),w) = K(R(x,z,u),w)
    ]]></literal>
    <justification jstring="[para(5133(a,1),9255(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5133 9255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9259">
    <literal><![CDATA[
      R(K(x,y),K(x,z) * u,w) = R(K(x,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(320,a,6745,a(flip),b,9256,a),flip(a)].">
      <j1 rule="hyper" parents="320 6745 9256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9260">
    <literal><![CDATA[
      R(K(x,y),z / x,u) = R(K(x,y),x \ z,u)
    ]]></literal>
    <justification jstring="[para(4859(a,1),9259(a,1,2))].">
      <j1 rule="para" parents="4859 9259"/>
    </justification>
  </clause>

  <clause id="9261">
    <literal><![CDATA[
      R(K(x,y),z * (K(u,x) * w),v5) = R(K(x,y),z * w,v5)
    ]]></literal>
    <justification jstring="[para(6038(a,1),9259(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6038 9259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9262">
    <literal><![CDATA[
      R(K(x,y),x \ y,z) * ((y / T(x,y)) * z) = (y / x) * z
    ]]></literal>
    <justification jstring="[para(9260(a,1),6934(a,1,1))].">
      <j1 rule="para" parents="9260 6934"/>
    </justification>
  </clause>

  <clause id="9263">
    <literal><![CDATA[
      R(K(x,y),z * (u * K(w,x)),v5) = R(K(x,y),z * u,v5)
    ]]></literal>
    <justification jstring="[para(7288(a,1),9261(a,1,2,2))].">
      <j1 rule="para" parents="7288 9261"/>
    </justification>
  </clause>

  <clause id="9264">
    <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(4628(a,2),9187(a,2,2))].">
      <j1 rule="para" parents="4628 9187"/>
    </justification>
  </clause>

  <clause id="9265">
    <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(9262(a,1),39(a,1)),flip(a)].">
      <j1 rule="para" parents="9262 39"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9266">
    <literal><![CDATA[
      K(L(x,y,z),R(z,u,w)) = K(x,R(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(320,a,5524,a(flip),b,7074,a),flip(a)].">
      <j1 rule="hyper" parents="320 5524 7074"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9267">
    <literal><![CDATA[
      K((x \ 1) \ y,R(x,z,u)) = K(x * y,R(x,z,u))
    ]]></literal>
    <justification jstring="[para(489(a,1),9266(a,1,1)),flip(a)].">
      <j1 rule="para" parents="489 9266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9268">
    <literal><![CDATA[
      K((x \ 1) * y,R(x \ 1,z,u)) = K(x \ y,R(x \ 1,z,u))
    ]]></literal>
    <justification jstring="[hyper(5966,a,9267,a),flip(a)].">
      <j1 rule="hyper" parents="5966 9267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9269">
    <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(7193(a,2),8437(a,1))].">
      <j1 rule="para" parents="7193 8437"/>
    </justification>
  </clause>

  <clause id="9270">
    <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(7204(a,2),7704(a,1))].">
      <j1 rule="para" parents="7204 7704"/>
    </justification>
  </clause>

  <clause id="9271">
    <literal><![CDATA[
      (x * K(y,T(z,u))) * K(z,w) = (x * K(z,w)) * K(y,T(z,u))
    ]]></literal>
    <justification jstring="[para(7160(a,1),7233(a,1,1,2))].">
      <j1 rule="para" parents="7160 7233"/>
    </justification>
  </clause>

  <clause id="9272">
    <literal><![CDATA[
      K((((x * y) \ x) \ 1) * z,y) = K(z * (1 / ((x * y) \ x)),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,3981,a(flip),b,7372,a)].">
      <j1 rule="hyper" parents="58 3981 7372"/>
    </justification>
  </clause>

  <clause id="9273">
    <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(7375(a,1),7542(a,1,1,1,1,2))].">
      <j1 rule="para" parents="7375 7542"/>
    </justification>
  </clause>

  <clause id="9274">
    <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(7596(a,1),8394(a,1))].">
      <j1 rule="para" parents="7596 8394"/>
    </justification>
  </clause>

  <clause id="9275">
    <literal><![CDATA[
      K(x,(y \ K(x,z)) \ u) = (y \ T(y * u,x)) \ u
    ]]></literal>
    <justification jstring="[para(7647(a,1),6387(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7647 6387"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9276">
    <literal><![CDATA[
      K(x,(y \ K(x,z)) \ u) = K(x,(y \ 1) \ u)
    ]]></literal>
    <justification jstring="[hyper(320,a,6464,a(flip),b,9275,a),flip(a)].">
      <j1 rule="hyper" parents="320 6464 9275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9277">
    <literal><![CDATA[
      K(x,((y \ 1) \ K(x,z)) \ u) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[hyper(320,a,5321,a(flip),b,9276,a),flip(a)].">
      <j1 rule="hyper" parents="320 5321 9276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9278">
    <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,7648,a),flip(a)].">
      <j1 rule="hyper" parents="320 453 7648"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9279">
    <literal><![CDATA[
      (1 / (x \ y)) * K(y / x,z) = K(y / x,z) / (x \ y)
    ]]></literal>
    <justification jstring="[para(7907(a,1),8003(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7907 8003"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9280">
    <literal><![CDATA[
      K(1 / x,y) / (x \ 1) = x * K(1 / x,y)
    ]]></literal>
    <justification jstring="[hyper(348,a,9279,a),flip(a)].">
      <j1 rule="hyper" parents="348 9279"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9281">
    <literal><![CDATA[
      1 / (x \ K(y,1 / x)) = x * K(1 / x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,5880,a(flip),b,9280,a)].">
      <j1 rule="hyper" parents="58 5880 9280"/>
    </justification>
  </clause>

  <clause id="9282">
    <literal><![CDATA[
      1 / ((x * (y \ 1)) / x) = y * K(1 / y,x)
    ]]></literal>
    <justification jstring="[para(4895(a,1),9281(a,1,2))].">
      <j1 rule="para" parents="4895 9281"/>
    </justification>
  </clause>

  <clause id="9283">
    <literal><![CDATA[
      1 / ((x * ((y / z) \ 1)) / x) = (y / z) * K(z / y,x)
    ]]></literal>
    <justification jstring="[para(5429(a,1),9282(a,2,2))].">
      <j1 rule="para" parents="5429 9282"/>
    </justification>
  </clause>

  <clause id="9284">
    <literal><![CDATA[
      x / (K(T(y,z),x) * K(x,z)) = T(x * K(z,x),y)
    ]]></literal>
    <justification jstring="[para(4970(a,1),8022(a,1,2,2))].">
      <j1 rule="para" parents="4970 8022"/>
    </justification>
  </clause>

  <clause id="9285">
    <literal><![CDATA[
      T(x * K(y,x),z) \ x = K(T(z,y),x) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(188,a,9284,a)].">
      <j1 rule="hyper" parents="188 9284"/>
    </justification>
  </clause>

  <clause id="9287">
    <literal><![CDATA[
      T((x * y) / x,z) \ y = K(T(z,x),y) * K(y,x)
    ]]></literal>
    <justification jstring="[para(4752(a,2),9285(a,1,1,1))].">
      <j1 rule="para" parents="4752 9285"/>
    </justification>
  </clause>

  <clause id="9288">
    <literal><![CDATA[
      T((x * y) / x,z) \ y = K(y,x) * K(T(z,x),y)
    ]]></literal>
    <justification jstring="[hyper(320,a,2003,a,b,9287,a),flip(a)].">
      <j1 rule="hyper" parents="320 2003 9287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9289">
    <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(1627(a,1),9288(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1627 9288"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9290">
    <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(8092(a,1),7678(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8092 7678"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9291">
    <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(7796(a,1),8094(a,1,1))].">
      <j1 rule="para" parents="7796 8094"/>
    </justification>
  </clause>

  <clause id="9292">
    <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(442(a,1),8283(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="442 8283"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9293">
    <literal><![CDATA[
      K(x,(y * z) \ (x \ y)) = K(x,z \ (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(8678,a,8285,a)].">
      <j1 rule="hyper" parents="8678 8285"/>
    </justification>
  </clause>

  <clause id="9294">
    <literal><![CDATA[
      K((x * y) \ (z \ x),z) = (u * K(z,y \ (z \ 1))) \ u
    ]]></literal>
    <justification jstring="[para(9293(a,1),6338(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9293 6338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9295">
    <literal><![CDATA[
      K((x * y) \ (z \ x),z) = K(y \ (z \ 1),z)
    ]]></literal>
    <justification jstring="[hyper(320,a,6338,a(flip),b,9294,a),flip(a)].">
      <j1 rule="hyper" parents="320 6338 9294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9296">
    <literal><![CDATA[
      K((x \ y) \ (z \ 1),z) = K(y \ (z \ x),z)
    ]]></literal>
    <justification jstring="[para(5(a,1),9295(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5 9295"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9297">
    <literal><![CDATA[
      (x * (y * K(z,y))) / (x * K(z,y)) = (x * y) / x
    ]]></literal>
    <justification jstring="[para(4869(a,1),8289(a,1,2,2))].">
      <j1 rule="para" parents="4869 8289"/>
    </justification>
  </clause>

  <clause id="9299">
    <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(8303(a,2),4985(a,1))].">
      <j1 rule="para" parents="8303 4985"/>
    </justification>
  </clause>

  <clause id="9300">
    <literal><![CDATA[
      T(x,y / z) * K(z \ y,z) = (y / z) \ (x * (z \ y))
    ]]></literal>
    <justification jstring="[hyper(320,a,5593,a(flip),b,8327,a),flip(a)].">
      <j1 rule="hyper" parents="320 5593 8327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9301">
    <literal><![CDATA[
      x \ ((y / z) \ (x * (z \ y))) = K(x,y / z) * K(z \ y,z)
    ]]></literal>
    <justification jstring="[hyper(116,a,9300,a(flip),b,4778,a)].">
      <j1 rule="hyper" parents="116 9300 4778"/>
    </justification>
  </clause>

  <clause id="9302">
    <literal><![CDATA[
      K(x,K(y,z \ (u * y))) = K(x,K(y,z \ u))
    ]]></literal>
    <justification jstring="[hyper(29,a,8464,a,b,8455,a),flip(a)].">
      <j1 rule="hyper" parents="29 8464 8455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9303">
    <literal><![CDATA[
      K(x,K(y,z \ (u * y))) = K(y,K(x,z \ u))
    ]]></literal>
    <justification jstring="[hyper(320,a,7779,a,b,9302,a),flip(a)].">
      <j1 rule="hyper" parents="320 7779 9302"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9304">
    <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(1311(a,1),9302(a,1,2,2))].">
      <j1 rule="para" parents="1311 9302"/>
    </justification>
  </clause>

  <clause id="9305">
    <literal><![CDATA[
      K(x,K(y,z \ (y \ u))) = K(x,K(y,z \ u))
    ]]></literal>
    <justification jstring="[para(8451(a,1),9302(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8451 9302"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9306">
    <literal><![CDATA[
      K(x,K(y,z \ (y * u))) = K(x,K(y,z \ u))
    ]]></literal>
    <justification jstring="[para(8452(a,1),9302(a,1,2))].">
      <j1 rule="para" parents="8452 9302"/>
    </justification>
  </clause>

  <clause id="9307">
    <literal><![CDATA[
      K(x,K(y,z \ (u * x))) = K(x,K(y,z \ u))
    ]]></literal>
    <justification jstring="[hyper(7781,a,9303,a)].">
      <j1 rule="hyper" parents="7781 9303"/>
    </justification>
  </clause>

  <clause id="9308">
    <literal><![CDATA[
      K(x,K(y,z \ (u * x))) = K(x,K(y,u \ z))
    ]]></literal>
    <justification jstring="[hyper(320,a,8190,a,b,9307,a),flip(a)].">
      <j1 rule="hyper" parents="320 8190 9307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9309">
    <literal><![CDATA[
      T(K(x,y),(z \ (u * x)) \ 1) = K(x,y) * K(x,K(y,z \ u))
    ]]></literal>
    <justification jstring="[para(9307(a,1),8191(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9307 8191"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9310">
    <literal><![CDATA[
      K(x,K(y,(z * x) \ u)) = K(x,K(y,z \ u))
    ]]></literal>
    <justification jstring="[hyper(8216,a,9308,a)].">
      <j1 rule="hyper" parents="8216 9308"/>
    </justification>
  </clause>

  <clause id="9311">
    <literal><![CDATA[
      K(x,K(y,(z / x) \ u)) = K(x,K(y,z \ u))
    ]]></literal>
    <justification jstring="[para(7(a,1),9310(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="7 9310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9312">
    <literal><![CDATA[
      K(x,K(y,(x \ z) \ u)) = K(x,K(y,z \ u))
    ]]></literal>
    <justification jstring="[hyper(58,a,8131,a(flip),b,9311,a)].">
      <j1 rule="hyper" parents="58 8131 9311"/>
    </justification>
  </clause>

  <clause id="9313">
    <literal><![CDATA[
      K(x,K(y,z \ (x \ u))) = K(x,K(y,u \ z))
    ]]></literal>
    <justification jstring="[hyper(8216,a,9312,a)].">
      <j1 rule="hyper" parents="8216 9312"/>
    </justification>
  </clause>

  <clause id="9314">
    <literal><![CDATA[
      K(x,y) * K(x,K(y,z \ u)) = K(x,T(y,(x \ z) \ u))
    ]]></literal>
    <justification jstring="[para(9312(a,1),7766(a,1,2))].">
      <j1 rule="para" parents="9312 7766"/>
    </justification>
  </clause>

  <clause id="9315">
    <literal><![CDATA[
      K((T(x,y) * z) \ u,K(x,w)) = K(x,K(w,u \ z))
    ]]></literal>
    <justification jstring="[hyper(58,a,9054,a,b,9313,a)].">
      <j1 rule="hyper" parents="58 9054 9313"/>
    </justification>
  </clause>

  <clause id="9316">
    <literal><![CDATA[
      K(x,K(y,(T(x,z) * u) \ w)) = K(x,K(y,w \ u))
    ]]></literal>
    <justification jstring="[hyper(7821,a,9315,a)].">
      <j1 rule="hyper" parents="7821 9315"/>
    </justification>
  </clause>

  <clause id="9317">
    <literal><![CDATA[
      K(x,T(y,(x \ z) \ u)) = K(x,T(y,z \ u))
    ]]></literal>
    <justification jstring="[hyper(8071,a,9314,a),flip(a)].">
      <j1 rule="hyper" parents="8071 9314"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9318">
    <literal><![CDATA[
      K(x,T(y,z \ (x * u))) = K(x,T(y,z \ u))
    ]]></literal>
    <justification jstring="[hyper(58,a,8259,a(flip),b,9317,a)].">
      <j1 rule="hyper" parents="58 8259 9317"/>
    </justification>
  </clause>

  <clause id="9319">
    <literal><![CDATA[
      K(x,T(y,(x * z) \ u)) = K(x,T(y,z \ u))
    ]]></literal>
    <justification jstring="[para(4(a,1),9317(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="4 9317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9320">
    <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),9319(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 9319"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9321">
    <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(631(a,1),9320(a,1,2,2))].">
      <j1 rule="para" parents="631 9320"/>
    </justification>
  </clause>

  <clause id="9322">
    <literal><![CDATA[
      K(x,T(y,a(x,z,u))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(8063,a,9321,a),flip(a)].">
      <j1 rule="hyper" parents="8063 9321"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9323">
    <literal><![CDATA[
      K(x,y / a(x,z,u)) = K(x,a(x,z,u) \ y)
    ]]></literal>
    <justification jstring="[hyper(8060,a,9322,a)].">
      <j1 rule="hyper" parents="8060 9322"/>
    </justification>
  </clause>

  <clause id="9325">
    <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,9323,a(flip),b,8500,a)].">
      <j1 rule="hyper" parents="58 9323 8500"/>
    </justification>
  </clause>

  <clause id="9326">
    <literal><![CDATA[
      K(x,y) * (K(z,x) * (u * K(y,x))) = T(K(z,x) * u,K(x,y))
    ]]></literal>
    <justification jstring="[para(6329(a,1),8517(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6329 8517"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9327">
    <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(6454(a,1),8517(a,1,1,2))].">
      <j1 rule="para" parents="6454 8517"/>
    </justification>
  </clause>

  <clause id="9328">
    <literal><![CDATA[
      K(x,y / z) * K(z \ y,z) = z \ (y / T(y / z,x))
    ]]></literal>
    <justification jstring="[hyper(58,a,6372,a(flip),b,8519,a),flip(a)].">
      <j1 rule="hyper" parents="58 6372 8519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9329">
    <literal><![CDATA[
      (x \ ((y \ (x * z)) * y)) * u = (z * K((x \ 1) \ (y \ z),y)) * u
    ]]></literal>
    <justification jstring="[para(3545(a,1),8540(a,2,1)),flip(a)].">
      <j1 rule="para" parents="3545 8540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9330">
    <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(8573(a,1),5368(a,1,2,1))].">
      <j1 rule="para" parents="8573 5368"/>
    </justification>
  </clause>

  <clause id="9331">
    <literal><![CDATA[
      K(x,(K(y \ x,y) * z) \ x) = K(x,z \ x)
    ]]></literal>
    <justification jstring="[hyper(320,a,6841,a(flip),b,8587,a),flip(a)].">
      <j1 rule="hyper" parents="320 6841 8587"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9333">
    <literal><![CDATA[
      K(x,y \ (K(z,z \ x) * x)) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,6592,a(flip),b,9331,a)].">
      <j1 rule="hyper" parents="58 6592 9331"/>
    </justification>
  </clause>

  <clause id="9334">
    <literal><![CDATA[
      K(x,y \ (z * (x / z))) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[para(4783(a,1),9333(a,1,2,2))].">
      <j1 rule="para" parents="4783 9333"/>
    </justification>
  </clause>

  <clause id="9335">
    <literal><![CDATA[
      K(x,y \ ((z \ x) * z)) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[para(72(a,1),9334(a,1,2,2,2))].">
      <j1 rule="para" parents="72 9334"/>
    </justification>
  </clause>

  <clause id="9336">
    <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(9335(a,1),6632(a,1))].">
      <j1 rule="para" parents="9335 6632"/>
    </justification>
  </clause>

  <clause id="9337">
    <literal><![CDATA[
      T(K(x,y),T(z,u * x)) = T(K(x,y),T(z,x * u))
    ]]></literal>
    <justification jstring="[hyper(8434,a,8622,a),flip(a)].">
      <j1 rule="hyper" parents="8434 8622"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9338">
    <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,7450,a(flip),b,9337,a),flip(a)].">
      <j1 rule="hyper" parents="58 7450 9337"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9339">
    <literal><![CDATA[
      K(x,(1 / y) * ((z \ ((1 / y) \ 1)) * z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,8154,a(flip),b,8630,a),flip(a)].">
      <j1 rule="hyper" parents="320 8154 8630"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9340">
    <literal><![CDATA[
      K(x,(1 / y) * ((z \ y) * z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(75(a,1),9339(a,1,2,2,1,2))].">
      <j1 rule="para" parents="75 9339"/>
    </justification>
  </clause>

  <clause id="9341">
    <literal><![CDATA[
      K(x,(y \ 1) * ((z \ y) * z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,5322,a(flip),b,9340,a)].">
      <j1 rule="hyper" parents="58 5322 9340"/>
    </justification>
  </clause>

  <clause id="9342">
    <literal><![CDATA[
      K(T(x,y * (z * K(u,w))),w) = K(x,T(w,y * z))
    ]]></literal>
    <justification jstring="[hyper(320,a,7203,a(flip),b,8669,a),flip(a)].">
      <j1 rule="hyper" parents="320 7203 8669"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9343">
    <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(8674(a,1),5656(a,1))].">
      <j1 rule="para" parents="8674 5656"/>
    </justification>
  </clause>

  <clause id="9344">
    <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(7158(a,2),8697(a,1,2))].">
      <j1 rule="para" parents="7158 8697"/>
    </justification>
  </clause>

  <clause id="9345">
    <literal><![CDATA[
      K((x * (y * z)) \ u,z) != w
    ]]></literal>
    <literal><![CDATA[
      K((x * y) \ (z \ u),z) = w
    ]]></literal>
    <justification jstring="[para(8709(a,1),6345(a,1))].">
      <j1 rule="para" parents="8709 6345"/>
    </justification>
  </clause>

  <clause id="9346">
    <literal><![CDATA[
      K((x * (y * z)) \ u,y) != w
    ]]></literal>
    <literal><![CDATA[
      K((x * z) \ (y \ u),y) = w
    ]]></literal>
    <justification jstring="[para(8650(a,1),9345(a,1))].">
      <j1 rule="para" parents="8650 9345"/>
    </justification>
  </clause>

  <clause id="9347">
    <literal><![CDATA[
      T(T(x,1 / (y / z)),K(y,z)) = T(x,1 / T(y / z,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,7958,a(flip),b,8819,a)].">
      <j1 rule="hyper" parents="58 7958 8819"/>
    </justification>
  </clause>

  <clause id="9348">
    <literal><![CDATA[
      T(T(x,1 / (y / z)),K(z,z / y)) = T(x,1 / (z \ y))
    ]]></literal>
    <justification jstring="[para(107(a,1),8819(a,2,2,2))].">
      <j1 rule="para" parents="107 8819"/>
    </justification>
  </clause>

  <clause id="9349">
    <literal><![CDATA[
      T(T(x,1 / (y / z)),K(y,z)) = T(x,1 / (z \ y))
    ]]></literal>
    <justification jstring="[hyper(58,a,8204,a(flip),b,9348,a)].">
      <j1 rule="hyper" parents="58 8204 9348"/>
    </justification>
  </clause>

  <clause id="9350">
    <literal><![CDATA[
      T(x,1 / T(y / z,y)) = T(x,1 / (z \ y))
    ]]></literal>
    <justification jstring="[hyper(58,a,9347,a(flip),b,9349,a)].">
      <j1 rule="hyper" parents="58 9347 9349"/>
    </justification>
  </clause>

  <clause id="9351">
    <literal><![CDATA[
      T(x,T(1 / (y / z),y)) = T(x,1 / (z \ y))
    ]]></literal>
    <justification jstring="[hyper(8818,a,9350,a)].">
      <j1 rule="hyper" parents="8818 9350"/>
    </justification>
  </clause>

  <clause id="9352">
    <literal><![CDATA[
      T(x,1 / ((y \ z) \ z)) = T(x,T(1 / y,z))
    ]]></literal>
    <justification jstring="[para(72(a,1),9351(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="72 9351"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9353">
    <literal><![CDATA[
      T(x,T(1 / (y \ z),z)) = T(x,1 / (z / y))
    ]]></literal>
    <justification jstring="[hyper(58,a,8373,a(flip),b,9352,a),flip(a)].">
      <j1 rule="hyper" parents="58 8373 9352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9354">
    <literal><![CDATA[
      T(x,K(y,z / y) / (z \ y)) = T(x,1 / (y / z))
    ]]></literal>
    <justification jstring="[hyper(58,a,8341,a,b,9353,a)].">
      <j1 rule="hyper" parents="58 8341 9353"/>
    </justification>
  </clause>

  <clause id="9355">
    <literal><![CDATA[
      K(x,y / (z * (K(u,x) / z))) = K(x,y * K(z \ K(u,x),z))
    ]]></literal>
    <justification jstring="[para(6335(a,1),8871(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6335 8871"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9356">
    <literal><![CDATA[
      T(x,R(y / (y / z),u,w)) = x * K(T(x,y),R(z,u,w))
    ]]></literal>
    <justification jstring="[para(9059(a,1),8898(a,2,2))].">
      <j1 rule="para" parents="9059 8898"/>
    </justification>
  </clause>

  <clause id="9357">
    <literal><![CDATA[
      T(x,R((y * z) / y,u,w)) = T(x,R(y / (y / z),u,w))
    ]]></literal>
    <justification jstring="[hyper(320,a,8126,a,b,9356,a)].">
      <j1 rule="hyper" parents="320 8126 9356"/>
    </justification>
  </clause>

  <clause id="9358">
    <literal><![CDATA[
      T(x,R(y / (y / z),u,w)) = T(x,R(T(z,y),u,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,8617,a(flip),b,9357,a),flip(a)].">
      <j1 rule="hyper" parents="58 8617 9357"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9359">
    <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,8693,a,b,9358,a)].">
      <j1 rule="hyper" parents="58 8693 9358"/>
    </justification>
  </clause>

  <clause id="9360">
    <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),9359(a,1,2,1))].">
      <j1 rule="para" parents="106 9359"/>
    </justification>
  </clause>

  <clause id="9361">
    <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(3815(a,1),9360(a,1,2,1,1))].">
      <j1 rule="para" parents="3815 9360"/>
    </justification>
  </clause>

  <clause id="9362">
    <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(8959(a,1),8973(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8959 8973"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9363">
    <literal><![CDATA[
      ((x * y) * z) \ ((y * x) * z) = K(y,R(T(x,z),y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,8752,a(flip),b,9045,a),flip(a)].">
      <j1 rule="hyper" parents="58 8752 9045"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9364">
    <literal><![CDATA[
      T(K(x,y) * z,x * y) = K(x,y) * T(z,x * y)
    ]]></literal>
    <justification jstring="[para(4963(a,1),9058(a,1,1,1))].">
      <j1 rule="para" parents="4963 9058"/>
    </justification>
  </clause>

  <clause id="9365">
    <literal><![CDATA[
      T(x * K(y,z),z * y) = T(x,z * y) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(6041,a,9364,a),flip(a)].">
      <j1 rule="hyper" parents="6041 9364"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9366">
    <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(9365(a,2),481(a,2,2))].">
      <j1 rule="para" parents="9365 481"/>
    </justification>
  </clause>

  <clause id="9367">
    <literal><![CDATA[
      a(T(x,y),z,T(x,y)) = a(x,z,x)
    ]]></literal>
    <justification jstring="[hyper(9109,a,9103,a),flip(a)].">
      <j1 rule="hyper" parents="9109 9103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9369">
    <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(5688(a,1),9114(a,2,1,1))].">
      <j1 rule="para" parents="5688 9114"/>
    </justification>
  </clause>

  <clause id="9370">
    <literal><![CDATA[
      R(x,y,x) * (T(x,z) \ u) = x * (L(T(x,z),y,x) \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,7734,a(flip),b,9130,a)].">
      <j1 rule="hyper" parents="58 7734 9130"/>
    </justification>
  </clause>

  <clause id="9371">
    <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(9370(a,1),7085(a,1,2))].">
      <j1 rule="para" parents="9370 7085"/>
    </justification>
  </clause>

  <clause id="9372">
    <literal><![CDATA[
      ((x \ 1) * y) * K(x,z) = (x \ 1) * (y * K(x,z))
    ]]></literal>
    <justification jstring="[hyper(284,a,9156,a)].">
      <j1 rule="hyper" parents="284 9156"/>
    </justification>
  </clause>

  <clause id="9374">
    <literal><![CDATA[
      a(x \ 1,y,K(x,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,9372,a(flip),b,80,a),flip(a)].">
      <j1 rule="hyper" parents="115 9372 80"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9375">
    <literal><![CDATA[
      L(K(x,y),z,y \ 1) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(5893,a,9374,a)].">
      <j1 rule="hyper" parents="5893 9374"/>
    </justification>
  </clause>

  <clause id="9376">
    <literal><![CDATA[
      a(x,y,K(x \ 1,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(58,a,4064,a(flip),b,9374,a)].">
      <j1 rule="hyper" parents="58 4064 9374"/>
    </justification>
  </clause>

  <clause id="9377">
    <literal><![CDATA[
      (x * y) * K(x \ 1,z) = x * (y * K(x \ 1,z))
    ]]></literal>
    <justification jstring="[hyper(977,a,9376,a)].">
      <j1 rule="hyper" parents="977 9376"/>
    </justification>
  </clause>

  <clause id="9378">
    <literal><![CDATA[
      L(K(x \ 1,y),z,x) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(47,a,9376,a)].">
      <j1 rule="hyper" parents="47 9376"/>
    </justification>
  </clause>

  <clause id="9379">
    <literal><![CDATA[
      K(L(x,y,z \ 1),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(9083,a,9375,a)].">
      <j1 rule="hyper" parents="9083 9375"/>
    </justification>
  </clause>

  <clause id="9382">
    <literal><![CDATA[
      K(((x \ 1) * y) \ (z * (x \ 1)),x) = K(y \ T(z,x \ 1),x)
    ]]></literal>
    <justification jstring="[hyper(58,a,6625,a(flip),b,9375,a)].">
      <j1 rule="hyper" parents="58 6625 9375"/>
    </justification>
  </clause>

  <clause id="9383">
    <literal><![CDATA[
      K(((x \ 1) * y) \ z,T(x,y)) = K(((x \ 1) \ z) / y,x)
    ]]></literal>
    <justification jstring="[hyper(8255,a,9379,a)].">
      <j1 rule="hyper" parents="8255 9379"/>
    </justification>
  </clause>

  <clause id="9385">
    <literal><![CDATA[
      K(L(x,y,x) \ 1,z) = K(x \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(5721,a,9378,a)].">
      <j1 rule="hyper" parents="5721 9378"/>
    </justification>
  </clause>

  <clause id="9387">
    <literal><![CDATA[
      K(R(x,y,x) \ 1,z) = K(x \ 1,z)
    ]]></literal>
    <justification jstring="[para(4673(a,1),9385(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4673 9385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9388">
    <literal><![CDATA[
      R(K(x,y),z,x \ 1) = K((x \ 1) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,5709,a(flip),b,9387,a)].">
      <j1 rule="hyper" parents="58 5709 9387"/>
    </justification>
  </clause>

  <clause id="9389">
    <literal><![CDATA[
      (K(x \ 1,y) * z) * x = K(x \ 1,y) * (z * x)
    ]]></literal>
    <justification jstring="[para(9387(a,1),5707(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9387 5707"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9390">
    <literal><![CDATA[
      R(K(x,y),z,x \ 1) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,3317,a(flip),b,9388,a),flip(a)].">
      <j1 rule="hyper" parents="320 3317 9388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9391">
    <literal><![CDATA[
      K(x,R(y,z,x \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(8852,a,9390,a)].">
      <j1 rule="hyper" parents="8852 9390"/>
    </justification>
  </clause>

  <clause id="9392">
    <literal><![CDATA[
      (K(x,y) * z) * (x \ 1) = K(x,y) * (z * (x \ 1))
    ]]></literal>
    <justification jstring="[para(9390(a,1),101(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9390 101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9393">
    <literal><![CDATA[
      R(x * K(y,x),z,y \ 1) = R(x,z,y \ 1) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,9391,a(flip),b,5524,a),flip(a)].">
      <j1 rule="hyper" parents="119 9391 5524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9394">
    <literal><![CDATA[
      R(x,y,K(x \ 1,z)) = x
    ]]></literal>
    <justification jstring="[hyper(4038,a,9377,a)].">
      <j1 rule="hyper" parents="4038 9377"/>
    </justification>
  </clause>

  <clause id="9395">
    <literal><![CDATA[
      x * (y * K(x \ 1,x * y)) = y / R(1 / x,x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,5936,a(flip),b,9377,a),flip(a)].">
      <j1 rule="hyper" parents="58 5936 9377"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9397">
    <literal><![CDATA[
      R(T(x,y),z,K(x \ 1,u)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(9394(a,1),22(a,2,1))].">
      <j1 rule="para" parents="9394 22"/>
    </justification>
  </clause>

  <clause id="9399">
    <literal><![CDATA[
      T(x,y * K(x \ 1,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,5831,a(flip),b,9397,a),flip(a)].">
      <j1 rule="hyper" parents="58 5831 9397"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9401">
    <literal><![CDATA[
      K(x,y * K(x \ 1,z)) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(116,a,9399,a(flip),b,4755,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="116 9399 4755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9403">
    <literal><![CDATA[
      T(x,K(y,x \ 1) * z) = T(x,z)
    ]]></literal>
    <justification jstring="[para(7176(a,1),9399(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7176 9399"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9404">
    <literal><![CDATA[
      T(x,K(x \ 1,y) * z) = T(x,z)
    ]]></literal>
    <justification jstring="[para(7179(a,1),9399(a,1,2))].">
      <j1 rule="para" parents="7179 9399"/>
    </justification>
  </clause>

  <clause id="9405">
    <literal><![CDATA[
      T(x,K(y,1 / x) * z) = T(x,z)
    ]]></literal>
    <justification jstring="[para(3558(a,2),9403(a,1,2,1))].">
      <j1 rule="para" parents="3558 9403"/>
    </justification>
  </clause>

  <clause id="9406">
    <literal><![CDATA[
      T(x \ 1,K(x,y) * z) = T(x \ 1,z)
    ]]></literal>
    <justification jstring="[para(3317(a,1),9404(a,1,2,1))].">
      <j1 rule="para" parents="3317 9404"/>
    </justification>
  </clause>

  <clause id="9407">
    <literal><![CDATA[
      K(K(x,1 / y) * z,y) = y / T(y,z)
    ]]></literal>
    <justification jstring="[para(9405(a,1),4794(a,2,2))].">
      <j1 rule="para" parents="9405 4794"/>
    </justification>
  </clause>

  <clause id="9408">
    <literal><![CDATA[
      K(x,y * K(x \ 1,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,4729,a,b,9401,a),flip(a)].">
      <j1 rule="hyper" parents="320 4729 9401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9410">
    <literal><![CDATA[
      K(x,y * K(z,x \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(6329(a,1),9408(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6329 9408"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9411">
    <literal><![CDATA[
      K(x \ y,z * K(u,y \ x)) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[para(6108(a,1),9410(a,1,2,2))].">
      <j1 rule="para" parents="6108 9410"/>
    </justification>
  </clause>

  <clause id="9412">
    <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(9406(a,1),925(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9406 925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9414">
    <literal><![CDATA[
      K(K(x,1 / y) * z,y) = K(z,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,4794,a,b,9407,a),flip(a)].">
      <j1 rule="hyper" parents="320 4794 9407"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9415">
    <literal><![CDATA[
      K(K(x,y) * z,y \ 1) = K(z,y \ 1)
    ]]></literal>
    <justification jstring="[para(72(a,1),9414(a,1,1,1,2))].">
      <j1 rule="para" parents="72 9414"/>
    </justification>
  </clause>

  <clause id="9416">
    <literal><![CDATA[
      K(K(x,y \ 1) * z,y) = K(z,y)
    ]]></literal>
    <justification jstring="[para(3558(a,1),9414(a,1,1,1))].">
      <j1 rule="para" parents="3558 9414"/>
    </justification>
  </clause>

  <clause id="9417">
    <literal><![CDATA[
      K(T(x,1 / y) / z,y) = K(x / z,y)
    ]]></literal>
    <justification jstring="[para(5738(a,1),9414(a,1,1))].">
      <j1 rule="para" parents="5738 9414"/>
    </justification>
  </clause>

  <clause id="9419">
    <literal><![CDATA[
      (K(x,y \ 1) * z) * K(z,y) = T(K(x,y \ 1) * z,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,9416,a(flip),b,4729,a(flip))].">
      <j1 rule="hyper" parents="119 9416 4729"/>
    </justification>
  </clause>

  <clause id="9420">
    <literal><![CDATA[
      K(K(x,x \ y) * z,x / y) = K(z,x / y)
    ]]></literal>
    <justification jstring="[para(5214(a,1),9416(a,1,1,1))].">
      <j1 rule="para" parents="5214 9416"/>
    </justification>
  </clause>

  <clause id="9421">
    <literal><![CDATA[
      K(x \ T(y,z \ 1),z) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[para(5553(a,1),9416(a,1,1))].">
      <j1 rule="para" parents="5553 9416"/>
    </justification>
  </clause>

  <clause id="9422">
    <literal><![CDATA[
      K(x * K(y,z \ 1),z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(7288(a,1),9416(a,1,1))].">
      <j1 rule="para" parents="7288 9416"/>
    </justification>
  </clause>

  <clause id="9423">
    <literal><![CDATA[
      K(x * K(y,z \ u),u \ z) = K(x,u \ z)
    ]]></literal>
    <justification jstring="[para(6108(a,1),9422(a,1,1,2))].">
      <j1 rule="para" parents="6108 9422"/>
    </justification>
  </clause>

  <clause id="9424">
    <literal><![CDATA[
      K(((x * y) \ x) * z,y) = K(z * ((x * y) \ x),y)
    ]]></literal>
    <justification jstring="[para(6184(a,1),9422(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6184 9422"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9425">
    <literal><![CDATA[
      K(T(x / (1 / (1 / y)),1 / z) / (1 / y),z) = K((x / y) / (y \ 1),z)
    ]]></literal>
    <justification jstring="[para(2733(a,1),9417(a,2,1))].">
      <j1 rule="para" parents="2733 9417"/>
    </justification>
  </clause>

  <clause id="9426">
    <literal><![CDATA[
      K(x \ y,(y \ x) * z) = K(x \ y,z * (y \ x))
    ]]></literal>
    <justification jstring="[para(84(a,1),9411(a,1,2)),flip(a)].">
      <j1 rule="para" parents="84 9411"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9427">
    <literal><![CDATA[
      K(x \ y,z * (x / y)) = K(x \ y,z * (y \ x))
    ]]></literal>
    <justification jstring="[para(6101(a,1),9411(a,1,2))].">
      <j1 rule="para" parents="6101 9411"/>
    </justification>
  </clause>

  <clause id="9428">
    <literal><![CDATA[
      K((x / y) \ z,y / x) = K((y \ x) \ z,y / x)
    ]]></literal>
    <justification jstring="[para(5414(a,1),9420(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5414 9420"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9429">
    <literal><![CDATA[
      K(x * (y / z),y \ z) = K(x * (z \ y),y \ z)
    ]]></literal>
    <justification jstring="[para(6101(a,1),9423(a,1,1))].">
      <j1 rule="para" parents="6101 9423"/>
    </justification>
  </clause>

  <clause id="9430">
    <literal><![CDATA[
      L(x,y,K(x \ 1,z)) = x
    ]]></literal>
    <justification jstring="[hyper(4028,a,9389,a)].">
      <j1 rule="hyper" parents="4028 9389"/>
    </justification>
  </clause>

  <clause id="9433">
    <literal><![CDATA[
      L(x \ 1,y,K(x,z)) = x \ 1
    ]]></literal>
    <justification jstring="[para(3317(a,1),9430(a,1,3))].">
      <j1 rule="para" parents="3317 9430"/>
    </justification>
  </clause>

  <clause id="9434">
    <literal><![CDATA[
      (K(x,y) * (z * x)) \ (K(x,y) * z) = L(x \ 1,x,z)
    ]]></literal>
    <justification jstring="[para(9433(a,1),917(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9433 917"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9438">
    <literal><![CDATA[
      (x \ 1) * T(K(x,y) * z,x \ 1) = K(x,y) * (z * (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(285,a,9392,a)].">
      <j1 rule="hyper" parents="285 9392"/>
    </justification>
  </clause>

  <clause id="9439">
    <literal><![CDATA[
      T(K(x,y) * z,x \ 1) = K(x,y) * T(z,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(239,a,9392,a,b,6006,a)].">
      <j1 rule="hyper" parents="239 9392 6006"/>
    </justification>
  </clause>

  <clause id="9440">
    <literal><![CDATA[
      (1 / (x \ y)) * (z / (1 / (x \ y))) = z * K(y \ x,z * (y / x))
    ]]></literal>
    <justification jstring="[para(9427(a,2),6282(a,2,2))].">
      <j1 rule="para" parents="9427 6282"/>
    </justification>
  </clause>

  <clause id="9441">
    <literal><![CDATA[
      ((1 / (x \ y)) \ z) * (1 / (x \ y)) = z * K(z * (y / x),y \ x)
    ]]></literal>
    <justification jstring="[para(9429(a,2),6169(a,2,2))].">
      <j1 rule="para" parents="9429 6169"/>
    </justification>
  </clause>

  <clause id="9442">
    <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),9439(a,2,2))].">
      <j1 rule="para" parents="20 9439"/>
    </justification>
  </clause>

  <clause id="9443">
    <literal><![CDATA[
      x * (((x * y) \ y) * (x * y)) = y / R(1 / x,x,y)
    ]]></literal>
    <justification jstring="[para(5439(a,2),9395(a,1,2))].">
      <j1 rule="para" parents="5439 9395"/>
    </justification>
  </clause>

  <clause id="9444">
    <literal><![CDATA[
      x * (((x * y) \ y) * (x * y)) = y / (y / (x * y))
    ]]></literal>
    <justification jstring="[para(219(a,1),9443(a,2,2))].">
      <j1 rule="para" parents="219 9443"/>
    </justification>
  </clause>

  <clause id="9445">
    <literal><![CDATA[
      R(x * K(y,x),z,y \ 1) = K(y,x) * R(x,z,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,2899,a(flip),b,9393,a),flip(a)].">
      <j1 rule="hyper" parents="320 2899 9393"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9446">
    <literal><![CDATA[
      T(K(x,y \ 1) * z,y) = K(x,y \ 1) * T(z,y)
    ]]></literal>
    <justification jstring="[hyper(6199,a,9419,a),flip(a)].">
      <j1 rule="hyper" parents="6199 9419"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9448">
    <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,9445,a,b,5236,a)].">
      <j1 rule="hyper" parents="116 9445 5236"/>
    </justification>
  </clause>

  <clause id="9449">
    <literal><![CDATA[
      R(K(x,y),z * y,u) = K(x,R(y * K(w,x),z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,9263,a(flip),b,9244,a)].">
      <j1 rule="hyper" parents="58 9263 9244"/>
    </justification>
  </clause>

  <clause id="9451">
    <literal><![CDATA[
      K(x,R(y * K(z,x),u,w)) = K(x,R(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,9240,a(flip),b,9449,a),flip(a)].">
      <j1 rule="hyper" parents="58 9240 9449"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9452">
    <literal><![CDATA[
      K(x,R(y * K(x,z),u,w)) = K(x,R(y,u,w))
    ]]></literal>
    <justification jstring="[para(6329(a,1),9451(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6329 9451"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9453">
    <literal><![CDATA[
      K(x,R(K(y,x) * z,u,w)) = K(x,R(z * K(y,x),u,w))
    ]]></literal>
    <justification jstring="[para(7758(a,1),9452(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7758 9452"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9454">
    <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(650(a,1),9268(a,1,2)),flip(a)].">
      <j1 rule="para" parents="650 9268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9455">
    <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,9006,a(flip),b,9271,a),flip(a)].">
      <j1 rule="hyper" parents="320 9006 9271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9456">
    <literal><![CDATA[
      K((((x * y) \ x) \ 1) * z,y) = K(z * (((x * y) \ x) \ 1),y)
    ]]></literal>
    <justification jstring="[hyper(320,a,3975,a(flip),b,9272,a),flip(a)].">
      <j1 rule="hyper" parents="320 3975 9272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9457">
    <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),9278(a,1,2,2,1,2))].">
      <j1 rule="para" parents="4 9278"/>
    </justification>
  </clause>

  <clause id="9458">
    <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,7520,a,b,9291,a)].">
      <j1 rule="hyper" parents="58 7520 9291"/>
    </justification>
  </clause>

  <clause id="9459">
    <literal><![CDATA[
      x \ ((y / z) \ (x * (z \ y))) = z \ (y / T(y / z,x))
    ]]></literal>
    <justification jstring="[hyper(320,a,9328,a(flip),b,9301,a),flip(a)].">
      <j1 rule="hyper" parents="320 9328 9301"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9460">
    <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(9304(a,2),8216(a,1))].">
      <j1 rule="para" parents="9304 8216"/>
    </justification>
  </clause>

  <clause id="9461">
    <literal><![CDATA[
      T(K(x,y),(z \ (u * x)) \ 1) = T(K(x,y),z \ u)
    ]]></literal>
    <justification jstring="[hyper(320,a,7763,a(flip),b,9309,a),flip(a)].">
      <j1 rule="hyper" parents="320 7763 9309"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9462">
    <literal><![CDATA[
      T(K(x,y),z \ (u * x)) = T(K(x,y),z \ u)
    ]]></literal>
    <justification jstring="[hyper(8361,a,9461,a)].">
      <j1 rule="hyper" parents="8361 9461"/>
    </justification>
  </clause>

  <clause id="9463">
    <literal><![CDATA[
      T(K(x,y),z \ (u / x)) = T(K(x,y),z \ u)
    ]]></literal>
    <justification jstring="[para(7(a,1),9462(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7 9462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9464">
    <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(9463(a,1),4764(a,1,2,1))].">
      <j1 rule="para" parents="9463 4764"/>
    </justification>
  </clause>

  <clause id="9465">
    <literal><![CDATA[
      T(K(x,y \ (z * x)),T(y,z)) = T(K(x,y \ (z * x)),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,8891,a(flip),b,9338,a)].">
      <j1 rule="hyper" parents="58 8891 9338"/>
    </justification>
  </clause>

  <clause id="9466">
    <literal><![CDATA[
      K(x,T(y \ (z * x),T(y,z))) = T(K(x,y \ (z * x)),y)
    ]]></literal>
    <justification jstring="[hyper(7708,a,9465,a)].">
      <j1 rule="hyper" parents="7708 9465"/>
    </justification>
  </clause>

  <clause id="9467">
    <literal><![CDATA[
      K(x,T(y \ (z * x),T(y,z))) = K(x,(y / z) \ x)
    ]]></literal>
    <justification jstring="[hyper(320,a,8493,a(flip),b,9466,a),flip(a)].">
      <j1 rule="hyper" parents="320 8493 9466"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9468">
    <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,6780,a(flip),b,9467,a),flip(a)].">
      <j1 rule="hyper" parents="320 6780 9467"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9469">
    <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,5579,a(flip),b,9355,a),flip(a)].">
      <j1 rule="hyper" parents="58 5579 9355"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9470">
    <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(5716(a,1),9457(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5716 9457"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9471">
    <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(8444,a,9458,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="8444 9458"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9472">
    <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),7258(a,1,1))].">
      <j1 rule="para" parents="22 7258"/>
    </justification>
  </clause>

  <clause id="9473">
    <literal><![CDATA[
      K(R(x,y,z),u * K(x,w)) = K(R(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(320,a,5526,a(flip),b,7349,a),flip(a)].">
      <j1 rule="hyper" parents="320 5526 7349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9474">
    <literal><![CDATA[
      K(R(x,y,z),u * K(w,x)) = K(R(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(6329(a,1),9473(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6329 9473"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9475">
    <literal><![CDATA[
      K(L(x,y,z),T(u,x \ w)) = K(L(x,y,z),T(u,w))
    ]]></literal>
    <justification jstring="[hyper(5031,a,7380,a),flip(a)].">
      <j1 rule="hyper" parents="5031 7380"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9476">
    <literal><![CDATA[
      K(T(x,y \ z),L(y,u,w)) = 1 / K(L(y,u,w),T(x,z))
    ]]></literal>
    <justification jstring="[para(9475(a,1),4971(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9475 4971"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9477">
    <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,7230,a(flip),b,9476,a),flip(a)].">
      <j1 rule="hyper" parents="114 7230 9476"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9478">
    <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),9477(a,2,2))].">
      <j1 rule="para" parents="20 9477"/>
    </justification>
  </clause>

  <clause id="9479">
    <literal><![CDATA[
      K(x,T(L(y,z,u),y \ w)) = K(x,L(T(y,w),z,u))
    ]]></literal>
    <justification jstring="[hyper(7704,a,9478,a)].">
      <j1 rule="hyper" parents="7704 9478"/>
    </justification>
  </clause>

  <clause id="9480">
    <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),9479(a,1,2))].">
      <j1 rule="para" parents="317 9479"/>
    </justification>
  </clause>

  <clause id="9481">
    <literal><![CDATA[
      T(x,L((y \ z) \ z,u,w)) = T(x,L(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[hyper(118,a,9480,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 9480 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9482">
    <literal><![CDATA[
      K(x,L(T(y,z * y),u,w)) = K(x,L(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(4268(a,2),9480(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4268 9480"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9483">
    <literal><![CDATA[
      T(x,L(T(y,z * y),u,w)) = T(x,L(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(4268(a,2),9481(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4268 9481"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9484">
    <literal><![CDATA[
      L(x \ 1,x,K(x,y) * z) = L(x \ 1,x,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,9434,a(flip),b,7484,a),flip(a)].">
      <j1 rule="hyper" parents="58 9434 7484"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9486">
    <literal><![CDATA[
      L(x \ 1,x,y * K(x,z)) = L(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[para(7897(a,1),9484(a,1,3))].">
      <j1 rule="para" parents="7897 9484"/>
    </justification>
  </clause>

  <clause id="9487">
    <literal><![CDATA[
      L(x \ 1,T(x,y),z) = L(x \ 1,x,z)
    ]]></literal>
    <justification jstring="[hyper(6688,a,9486,a)].">
      <j1 rule="hyper" parents="6688 9486"/>
    </justification>
  </clause>

  <clause id="9489">
    <literal><![CDATA[
      T(x * L(x \ 1,x,y),z) = T(x,z) * ((y * T(x,z)) \ y)
    ]]></literal>
    <justification jstring="[para(9487(a,1),2144(a,1,1,2))].">
      <j1 rule="para" parents="9487 2144"/>
    </justification>
  </clause>

  <clause id="9492">
    <literal><![CDATA[
      a(x,y * K(x,z),x) = a(x,y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(691,a,7730,a),flip(a)].">
      <j1 rule="hyper" parents="691 7730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9493">
    <literal><![CDATA[
      a(x,y,T(x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,x) = u
    ]]></literal>
    <justification jstring="[para(9492(a,1),9153(a,1))].">
      <j1 rule="para" parents="9492 9153"/>
    </justification>
  </clause>

  <clause id="9494">
    <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),7736(a,2,1))].">
      <j1 rule="para" parents="24 7736"/>
    </justification>
  </clause>

  <clause id="9495">
    <literal><![CDATA[
      K(x,K(y,(z * u) \ ((z * x) * u))) = 1
    ]]></literal>
    <justification jstring="[para(7927(a,1),8078(a,1,2))].">
      <j1 rule="para" parents="7927 8078"/>
    </justification>
  </clause>

  <clause id="9496">
    <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,7956,a(flip),b,6929,a(flip))].">
      <j1 rule="hyper" parents="116 7956 6929"/>
    </justification>
  </clause>

  <clause id="9497">
    <literal><![CDATA[
      R(K(x,T(T(y,z),z * u)),z,u) = (z * u) \ ((z * K(x,y)) * u)
    ]]></literal>
    <justification jstring="[para(7158(a,2),7984(a,1,1))].">
      <j1 rule="para" parents="7158 7984"/>
    </justification>
  </clause>

  <clause id="9498">
    <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(7230(a,1),7990(a,1,1))].">
      <j1 rule="para" parents="7230 7990"/>
    </justification>
  </clause>

  <clause id="9499">
    <literal><![CDATA[
      L(K(x,y \ ((z \ u) * x)),z \ u,z) = K(x,(z * y) \ (u * x))
    ]]></literal>
    <justification jstring="[hyper(320,a,8723,a(flip),b,8454,a),flip(a)].">
      <j1 rule="hyper" parents="320 8723 8454"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9500">
    <literal><![CDATA[
      T(x,y / T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z) / z) = u
    ]]></literal>
    <justification jstring="[para(9034(a,1),8473(a,1))].">
      <j1 rule="para" parents="9034 8473"/>
    </justification>
  </clause>

  <clause id="9501">
    <literal><![CDATA[
      x / (x / R(K(y,z),u,w)) = (R(K(y,z),u,w) \ x) \ x
    ]]></literal>
    <justification jstring="[para(8690(a,1),4305(a,1,2))].">
      <j1 rule="para" parents="8690 4305"/>
    </justification>
  </clause>

  <clause id="9502">
    <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,7155,a(flip),b,8728,a),flip(a)].">
      <j1 rule="hyper" parents="320 7155 8728"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9503">
    <literal><![CDATA[
      K(x,((y \ z) * u) \ (z * u)) = R(K(x,T(y,z * u)),z,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,8704,a(flip),b,9139,a),flip(a)].">
      <j1 rule="hyper" parents="58 8704 9139"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9504">
    <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,5987,a,b,9159,a),flip(a)].">
      <j1 rule="hyper" parents="320 5987 9159"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9505">
    <literal><![CDATA[
      L(T(K(x,T(y,z * u)),u),u,z) = (z * (K(x,y) * u)) / (z * u)
    ]]></literal>
    <justification jstring="[para(7181(a,1),9159(a,1,1))].">
      <j1 rule="para" parents="7181 9159"/>
    </justification>
  </clause>

  <clause id="9506">
    <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(9190(a,1),39(a,1)),flip(a)].">
      <j1 rule="para" parents="9190 39"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9507">
    <literal><![CDATA[
      K(x,y) * K(L(x,z,u) * y,x) = L(x,y,L(x,z,u)) \ x
    ]]></literal>
    <justification jstring="[para(8634(a,1),9289(a,1,2))].">
      <j1 rule="para" parents="8634 9289"/>
    </justification>
  </clause>

  <clause id="9508">
    <literal><![CDATA[
      K(L(x,y,z) * u,x) * K(x,u) = L(x,u,L(x,y,z)) \ x
    ]]></literal>
    <justification jstring="[hyper(2005,a,9507,a)].">
      <j1 rule="hyper" parents="2005 9507"/>
    </justification>
  </clause>

  <clause id="9509">
    <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(2652(a,1),9472(a,2,1,1))].">
      <j1 rule="para" parents="2652 9472"/>
    </justification>
  </clause>

  <clause id="9510">
    <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(8254,a,9494,a)].">
      <j1 rule="hyper" parents="8254 9494"/>
    </justification>
  </clause>

  <clause id="9511">
    <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),9510(a,1,2))].">
      <j1 rule="para" parents="18 9510"/>
    </justification>
  </clause>

  <clause id="9512">
    <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,8794,a(flip),b,9511,a)].">
      <j1 rule="hyper" parents="58 8794 9511"/>
    </justification>
  </clause>

  <clause id="9513">
    <literal><![CDATA[
      K(L(R(x,y,z),u,x),w) = K(R(x,y,z),w)
    ]]></literal>
    <justification jstring="[hyper(8007,a,9512,a),flip(a)].">
      <j1 rule="hyper" parents="8007 9512"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9515">
    <literal><![CDATA[
      K(R(L(x,y,x),z,u),w) = K(R(x,z,u),w)
    ]]></literal>
    <justification jstring="[para(24(a,2),9513(a,1,1))].">
      <j1 rule="para" parents="24 9513"/>
    </justification>
  </clause>

  <clause id="9516">
    <literal><![CDATA[
      K(R(x,x \ a(x,y,x),z),u) = K(L(x,y,x),u)
    ]]></literal>
    <justification jstring="[hyper(58,a,9091,a(flip),b,9515,a),flip(a)].">
      <j1 rule="hyper" parents="58 9091 9515"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9517">
    <literal><![CDATA[
      K(R(x,x \ a(x,y,x),z),u) = K(x,u)
    ]]></literal>
    <justification jstring="[hyper(320,a,7051,a(flip),b,9516,a),flip(a)].">
      <j1 rule="hyper" parents="320 7051 9516"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9520">
    <literal><![CDATA[
      (K(x,y) * a(x,z,x)) * u = K(x,y) * (a(x,z,x) * u)
    ]]></literal>
    <justification jstring="[para(9517(a,1),6751(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9517 6751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9521">
    <literal><![CDATA[
      K(x,x * y) * (a(x,y,x) * z) = K(x,y) * z
    ]]></literal>
    <justification jstring="[para(8954(a,1),9520(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8954 9520"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9522">
    <literal><![CDATA[
      a(x,y,x) * z = z * a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(9120,a,9521,a),flip(a)].">
      <j1 rule="hyper" parents="9120 9521"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9523">
    <literal><![CDATA[
      K(x * y,x) * (K(x,y) * z) = a(x,y,x) * z
    ]]></literal>
    <justification jstring="[hyper(5147,a,9521,a)].">
      <j1 rule="hyper" parents="5147 9521"/>
    </justification>
  </clause>

  <clause id="9524">
    <literal><![CDATA[
      K(x,y) * (a(x,y,x) \ z) = K(x,x * y) * z
    ]]></literal>
    <justification jstring="[hyper(342,a,9521,a),flip(a)].">
      <j1 rule="hyper" parents="342 9521"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9525">
    <literal><![CDATA[
      x / a(y,z,y) = a(y,z,y) \ x
    ]]></literal>
    <justification jstring="[hyper(337,a,9522,a)].">
      <j1 rule="hyper" parents="337 9522"/>
    </justification>
  </clause>

  <clause id="9526">
    <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,9362,a(flip),b,9522,a),flip(a)].">
      <j1 rule="hyper" parents="320 9362 9522"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9527">
    <literal><![CDATA[
      a(x,y,x) * (R(x,y,x) \ z) = x \ z
    ]]></literal>
    <justification jstring="[hyper(320,a,9134,a(flip),b,9522,a),flip(a)].">
      <j1 rule="hyper" parents="320 9134 9522"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9528">
    <literal><![CDATA[
      a(x,y,x) * (x * z) = R(x,y,x) * z
    ]]></literal>
    <justification jstring="[hyper(320,a,9133,a(flip),b,9522,a),flip(a)].">
      <j1 rule="hyper" parents="320 9133 9522"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9529">
    <literal><![CDATA[
      a(x,y,x) * (z * x) = z * R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,9123,a(flip),b,9522,a),flip(a)].">
      <j1 rule="hyper" parents="320 9123 9522"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9530">
    <literal><![CDATA[
      a(x,x \ y,x) * y = T(x * (y / x),x)
    ]]></literal>
    <justification jstring="[hyper(320,a,9107,a(flip),b,9522,a),flip(a)].">
      <j1 rule="hyper" parents="320 9107 9522"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9531">
    <literal><![CDATA[
      a(x,y,x) * (x \ z) = L(x,y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(320,a,9105,a(flip),b,9522,a),flip(a)].">
      <j1 rule="hyper" parents="320 9105 9522"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9532">
    <literal><![CDATA[
      a(x,y,x) * (z / x) = z / L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,9085,a(flip),b,9522,a),flip(a)].">
      <j1 rule="hyper" parents="320 9085 9522"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9533">
    <literal><![CDATA[
      (a(x,y,x) \ z) * a(x,y,x) = z
    ]]></literal>
    <justification jstring="[hyper(256,a,9522,a),flip(a)].">
      <j1 rule="hyper" parents="256 9522"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9534">
    <literal><![CDATA[
      T(x,a(y,z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(242,a,9522,a)].">
      <j1 rule="hyper" parents="242 9522"/>
    </justification>
  </clause>

  <clause id="9535">
    <literal><![CDATA[
      T(a(x,y,x),z) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(239,a,9522,a,b,xx)].">
      <j1 rule="hyper" parents="239 9522"/>
    </justification>
  </clause>

  <clause id="9536">
    <literal><![CDATA[
      (x * a(y,z,y)) / x = a(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(131,a,9522,a)].">
      <j1 rule="hyper" parents="131 9522"/>
    </justification>
  </clause>

  <clause id="9537">
    <literal><![CDATA[
      a(x,y,x) \ (z * a(x,y,x)) = z
    ]]></literal>
    <justification jstring="[hyper(123,a,9522,a)].">
      <j1 rule="hyper" parents="123 9522"/>
    </justification>
  </clause>

  <clause id="9538">
    <literal><![CDATA[
      (x * R(y,z,y)) / (x * y) = a(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(117,a,9123,a(flip),b,9522,a)].">
      <j1 rule="hyper" parents="117 9123 9522"/>
    </justification>
  </clause>

  <clause id="9539">
    <literal><![CDATA[
      a(x,y,x) \ (z / x) = z / R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,9136,a(flip),b,9522,a)].">
      <j1 rule="hyper" parents="116 9136 9522"/>
    </justification>
  </clause>

  <clause id="9540">
    <literal><![CDATA[
      a(x,y,x) \ (x \ z) = R(x,y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(116,a,9134,a(flip),b,9522,a)].">
      <j1 rule="hyper" parents="116 9134 9522"/>
    </justification>
  </clause>

  <clause id="9541">
    <literal><![CDATA[
      x \ (a(x,y,x) * z) = L(x,y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(116,a,9522,a,b,9094,a)].">
      <j1 rule="hyper" parents="116 9522 9094"/>
    </justification>
  </clause>

  <clause id="9542">
    <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,9522,a,b,639,a)].">
      <j1 rule="hyper" parents="116 9522 639"/>
    </justification>
  </clause>

  <clause id="9543">
    <literal><![CDATA[
      K(x,a(y,z,y)) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,9522,a,b,84,a),flip(a)].">
      <j1 rule="hyper" parents="115 9522 84"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9544">
    <literal><![CDATA[
      (a(x,y,x) * z) \ u = (z * a(x,y,x)) \ u
    ]]></literal>
    <justification jstring="[hyper(56,a,9522,a)].">
      <j1 rule="hyper" parents="56 9522"/>
    </justification>
  </clause>

  <clause id="9545">
    <literal><![CDATA[
      a(x,y,x) * z != z * u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,x) = u
    ]]></literal>
    <justification jstring="[para(9522(a,2),38(a,1))].">
      <j1 rule="para" parents="9522 38"/>
    </justification>
  </clause>

  <clause id="9546">
    <literal><![CDATA[
      (a(x,y,x) \ z) * a(x,y,x) != u
    ]]></literal>
    <literal><![CDATA[
      z = u
    ]]></literal>
    <justification jstring="[para(9522(a,1),256(a,1))].">
      <j1 rule="para" parents="9522 256"/>
    </justification>
  </clause>

  <clause id="9547">
    <literal><![CDATA[
      (x * y) \ ((x * a(z,u,z)) * y) = R(T(a(z,u,z),x * y),x,y)
    ]]></literal>
    <justification jstring="[para(9522(a,1),631(a,1,2,1))].">
      <j1 rule="para" parents="9522 631"/>
    </justification>
  </clause>

  <clause id="9548">
    <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(9522(a,1),773(a,1,1))].">
      <j1 rule="para" parents="9522 773"/>
    </justification>
  </clause>

  <clause id="9549">
    <literal><![CDATA[
      a(x,y,x) * (z * x) != u
    ]]></literal>
    <literal><![CDATA[
      z * R(x,y,x) = u
    ]]></literal>
    <justification jstring="[para(9522(a,2),9131(a,1))].">
      <j1 rule="para" parents="9522 9131"/>
    </justification>
  </clause>

  <clause id="9550">
    <literal><![CDATA[
      a(x,y,x) * z != u
    ]]></literal>
    <literal><![CDATA[
      z * a(x,y,x) = u
    ]]></literal>
    <justification jstring="[para(9534(a,1),284(a,1,2))].">
      <j1 rule="para" parents="9534 284"/>
    </justification>
  </clause>

  <clause id="9551">
    <literal><![CDATA[
      x * K(y,a(z,u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(9543(a,2),128(a,1,2))].">
      <j1 rule="para" parents="9543 128"/>
    </justification>
  </clause>

  <clause id="9552">
    <literal><![CDATA[
      T(a(x,y,x),z) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,8942,a,b,9535,a),flip(a)].">
      <j1 rule="hyper" parents="320 8942 9535"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9553">
    <literal><![CDATA[
      x * a(y,z,y) != u
    ]]></literal>
    <literal><![CDATA[
      a(y,z,y) * x = u
    ]]></literal>
    <justification jstring="[para(9535(a,1),284(a,1,2))].">
      <j1 rule="para" parents="9535 284"/>
    </justification>
  </clause>

  <clause id="9554">
    <literal><![CDATA[
      R(a(x,y,x),z,u) * w = w * R(a(x,y,x),z,u)
    ]]></literal>
    <justification jstring="[para(9535(a,1),238(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9535 238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9555">
    <literal><![CDATA[
      x * (y \ L(y,z,y)) = a(y,z,y) \ x
    ]]></literal>
    <justification jstring="[hyper(58,a,9132,a,b,9525,a)].">
      <j1 rule="hyper" parents="58 9132 9525"/>
    </justification>
  </clause>

  <clause id="9556">
    <literal><![CDATA[
      L(x,y,x) * (x \ z) = a(x,y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(58,a,9098,a,b,9525,a)].">
      <j1 rule="hyper" parents="58 9098 9525"/>
    </justification>
  </clause>

  <clause id="9557">
    <literal><![CDATA[
      (x / y) \ (a(y,z,y) \ x) = L(y,z,y)
    ]]></literal>
    <justification jstring="[para(9525(a,1),9104(a,1,2))].">
      <j1 rule="para" parents="9525 9104"/>
    </justification>
  </clause>

  <clause id="9558">
    <literal><![CDATA[
      (x * (y * a(z,u,z))) / (x * y) = L(a(z,u,z),y,x)
    ]]></literal>
    <justification jstring="[para(9536(a,1),850(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9536 850"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9559">
    <literal><![CDATA[
      (a(x,y,x) * z) \ u != w
    ]]></literal>
    <literal><![CDATA[
      (z * a(x,y,x)) \ u = w
    ]]></literal>
    <justification jstring="[para(9537(a,1),350(a,1,1,2))].">
      <j1 rule="para" parents="9537 350"/>
    </justification>
  </clause>

  <clause id="9560">
    <literal><![CDATA[
      K(x,a(y,z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      1 = u
    ]]></literal>
    <justification jstring="[para(2(a,1),9551(a,1))].">
      <j1 rule="para" parents="2 9551"/>
    </justification>
  </clause>

  <clause id="9561">
    <literal><![CDATA[
      T(a(x / y,z,x / y),u) = (x / y) \ R(x / y,z,y \ x)
    ]]></literal>
    <justification jstring="[para(7118(a,1),9552(a,2,2))].">
      <j1 rule="para" parents="7118 9552"/>
    </justification>
  </clause>

  <clause id="9563">
    <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(9528(a,1),518(a,1,1,1))].">
      <j1 rule="para" parents="9528 518"/>
    </justification>
  </clause>

  <clause id="9564">
    <literal><![CDATA[
      (x * R(x \ y,z,x \ y)) / y = a(x \ y,z,x \ y)
    ]]></literal>
    <justification jstring="[hyper(117,a,9529,a(flip),b,151,a(flip))].">
      <j1 rule="hyper" parents="117 9529 151"/>
    </justification>
  </clause>

  <clause id="9565">
    <literal><![CDATA[
      (x * R(y,z,y)) / (x * y) != u
    ]]></literal>
    <literal><![CDATA[
      a(y,z,y) = u
    ]]></literal>
    <justification jstring="[para(9529(a,1),327(a,1,1)),flip(b)].">
      <j1 rule="para" parents="9529 327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9566">
    <literal><![CDATA[
      a(x,y,x) \ y = x \ ((x * (y * x)) / x)
    ]]></literal>
    <justification jstring="[hyper(116,a,4372,a(flip),b,9531,a)].">
      <j1 rule="hyper" parents="116 4372 9531"/>
    </justification>
  </clause>

  <clause id="9567">
    <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),9538(a,1,2))].">
      <j1 rule="para" parents="90 9538"/>
    </justification>
  </clause>

  <clause id="9568">
    <literal><![CDATA[
      a(x,y,x) \ (x * z) = L(x,y,x) * z
    ]]></literal>
    <justification jstring="[hyper(625,a,9541,a),flip(a)].">
      <j1 rule="hyper" parents="625 9541"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9569">
    <literal><![CDATA[
      a(x,y,x) * (L(x,y,x) * z) = x * z
    ]]></literal>
    <justification jstring="[hyper(119,a,4,a(flip),b,9541,a),flip(a)].">
      <j1 rule="hyper" parents="119 4 9541"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9570">
    <literal><![CDATA[
      L(x,y,x) \ z != x \ u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,x) * z = u
    ]]></literal>
    <justification jstring="[para(9541(a,1),42(a,1))].">
      <j1 rule="para" parents="9541 42"/>
    </justification>
  </clause>

  <clause id="9571">
    <literal><![CDATA[
      a(x,y,x) \ x != z
    ]]></literal>
    <literal><![CDATA[
      L(x,y,x) = z
    ]]></literal>
    <justification jstring="[para(9555(a,1),255(a,1)),flip(b)].">
      <j1 rule="para" parents="9555 255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9572">
    <literal><![CDATA[
      (x / y) * L(y,z,y) = a(y,z,y) \ x
    ]]></literal>
    <justification jstring="[hyper(58,a,7514,a(flip),b,9556,a)].">
      <j1 rule="hyper" parents="58 7514 9556"/>
    </justification>
  </clause>

  <clause id="9573">
    <literal><![CDATA[
      (x / y) \ (a(y,z,y) \ x) != u
    ]]></literal>
    <literal><![CDATA[
      L(y,z,y) = u
    ]]></literal>
    <justification jstring="[para(9572(a,1),287(a,1,2)),flip(b)].">
      <j1 rule="para" parents="9572 287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9574">
    <literal><![CDATA[
      K(x * y,y) * (K(y,x) * z) = a(y,x,y) * z
    ]]></literal>
    <justification jstring="[para(5266(a,2),9523(a,1,1))].">
      <j1 rule="para" parents="5266 9523"/>
    </justification>
  </clause>

  <clause id="9575">
    <literal><![CDATA[
      K(x,y) * (K(y,y * x) * z) = a(y,x,y) \ z
    ]]></literal>
    <justification jstring="[hyper(5147,a,9524,a)].">
      <j1 rule="hyper" parents="5147 9524"/>
    </justification>
  </clause>

  <clause id="9576">
    <literal><![CDATA[
      K(x * y,y) * (x * (K(y,x) * z)) = a(y,x,y) * (x * z)
    ]]></literal>
    <justification jstring="[para(5256(a,1),9574(a,1,2))].">
      <j1 rule="para" parents="5256 9574"/>
    </justification>
  </clause>

  <clause id="9577">
    <literal><![CDATA[
      K(x,y) * (K(y,x * y) * z) = a(y,x,y) \ z
    ]]></literal>
    <justification jstring="[para(5385(a,2),9575(a,1,2,1))].">
      <j1 rule="para" parents="5385 9575"/>
    </justification>
  </clause>

  <clause id="9578">
    <literal><![CDATA[
      K(x,y) * (K(y,y * x) * z) = (y \ R(y,x,y)) \ z
    ]]></literal>
    <justification jstring="[para(8942(a,2),9575(a,2,1))].">
      <j1 rule="para" parents="8942 9575"/>
    </justification>
  </clause>

  <clause id="9579">
    <literal><![CDATA[
      T(x,R(a(y,z,y),u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(242,a,9554,a)].">
      <j1 rule="hyper" parents="242 9554"/>
    </justification>
  </clause>

  <clause id="9580">
    <literal><![CDATA[
      (x * (y * R(z,u,z))) / (x * (y * z)) = L(a(z,u,z),y * z,x)
    ]]></literal>
    <justification jstring="[para(9123(a,1),9558(a,1,1,2))].">
      <j1 rule="para" parents="9123 9558"/>
    </justification>
  </clause>

  <clause id="9581">
    <literal><![CDATA[
      (x \ R(x,y,x)) \ (K(x * y,x) * z) = K(y,x) * z
    ]]></literal>
    <justification jstring="[para(5133(a,1),9578(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5133 9578"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9582">
    <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(9497(a,1),6930(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9497 6930"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9583">
    <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(8466(a,1),9505(a,1,1,1))].">
      <j1 rule="para" parents="8466 9505"/>
    </justification>
  </clause>

  <clause id="9584">
    <literal><![CDATA[
      (x * y) \ ((x * a(z,u,z)) * y) = R(a(z,u,z),x,y)
    ]]></literal>
    <justification jstring="[para(9535(a,1),9547(a,2,1))].">
      <j1 rule="para" parents="9535 9547"/>
    </justification>
  </clause>

  <clause id="9585">
    <literal><![CDATA[
      (x * y) \ ((T(z * x,z) / z) * y) = R(a(z,x,z),x,y)
    ]]></literal>
    <justification jstring="[para(8959(a,2),9584(a,1,2,1))].">
      <j1 rule="para" parents="8959 9584"/>
    </justification>
  </clause>

  <clause id="9587">
    <literal><![CDATA[
      T(x * K(y,x),K(x,z) * u) = T(x,u) * K(y,T(x,u))
    ]]></literal>
    <justification jstring="[para(7265(a,1),7272(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7265 7272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9588">
    <literal><![CDATA[
      T(x * K(y,x),K(x,z) * u) = T(x * K(y,x),u)
    ]]></literal>
    <justification jstring="[hyper(320,a,5202,a(flip),b,9587,a),flip(a)].">
      <j1 rule="hyper" parents="320 5202 9587"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9590">
    <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,5378,a(flip),b,9588,a),flip(a)].">
      <j1 rule="hyper" parents="58 5378 9588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9591">
    <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,4806,a(flip),b,7424,a),flip(a)].">
      <j1 rule="hyper" parents="320 4806 7424"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9592">
    <literal><![CDATA[
      K(x * K(y,z),L(y,u,w)) = K(x,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(372(a,1),9591(a,1,1,2,1))].">
      <j1 rule="para" parents="372 9591"/>
    </justification>
  </clause>

  <clause id="9593">
    <literal><![CDATA[
      K(x * y,L(y,z,u)) = K(y * x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(84(a,1),9592(a,1,1)),flip(a)].">
      <j1 rule="para" parents="84 9592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9594">
    <literal><![CDATA[
      K(x \ T(y,z),L(z,u,w)) = K(x \ y,L(z,u,w))
    ]]></literal>
    <justification jstring="[para(6567(a,1),9592(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6567 9592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9595">
    <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),9594(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="107 9594"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9596">
    <literal><![CDATA[
      L(K(x,T(y,z)),u,L(y,w,v5)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(4028,a,7463,a)].">
      <j1 rule="hyper" parents="4028 7463"/>
    </justification>
  </clause>

  <clause id="9597">
    <literal><![CDATA[
      K(x,T(y,L(y,z,u) * w)) = K(x,T(y,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,9502,a(flip),b,9596,a)].">
      <j1 rule="hyper" parents="58 9502 9596"/>
    </justification>
  </clause>

  <clause id="9599">
    <literal><![CDATA[
      K(x,T(y,L(y,z,u) \ w)) = K(x,T(y,w))
    ]]></literal>
    <justification jstring="[para(5(a,1),9597(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5 9597"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9600">
    <literal><![CDATA[
      K(x,T(y,z * (u * y))) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[para(7423(a,1),9597(a,1,2))].">
      <j1 rule="para" parents="7423 9597"/>
    </justification>
  </clause>

  <clause id="9601">
    <literal><![CDATA[
      K(x,T(y \ z,u * z)) = K(x,T(y \ z,u * y))
    ]]></literal>
    <justification jstring="[para(5(a,1),9600(a,1,2,2,2))].">
      <j1 rule="para" parents="5 9600"/>
    </justification>
  </clause>

  <clause id="9602">
    <literal><![CDATA[
      K(x,T(y,z * (y * u))) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[para(7135(a,1),9600(a,1,2))].">
      <j1 rule="para" parents="7135 9600"/>
    </justification>
  </clause>

  <clause id="9603">
    <literal><![CDATA[
      K(x * y,T(x,z * y)) = K(x * y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(7724,a,9602,a),flip(a)].">
      <j1 rule="hyper" parents="7724 9602"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9605">
    <literal><![CDATA[
      K(x * y,T(y,z * x)) = K(y * x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,5888,a,b,9603,a)].">
      <j1 rule="hyper" parents="58 5888 9603"/>
    </justification>
  </clause>

  <clause id="9606">
    <literal><![CDATA[
      K(x,T(y \ x,z * y)) = K(x,T(y \ x,z))
    ]]></literal>
    <justification jstring="[hyper(7724,a,9601,a),flip(a)].">
      <j1 rule="hyper" parents="7724 9601"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9607">
    <literal><![CDATA[
      K(x,T(y \ x,z / y)) = K(x,T(y \ x,z))
    ]]></literal>
    <justification jstring="[para(7(a,1),9606(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7 9606"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9608">
    <literal><![CDATA[
      K(x,T(y \ x,y \ z)) = K(x,T(y \ x,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,8295,a(flip),b,9607,a)].">
      <j1 rule="hyper" parents="58 8295 9607"/>
    </justification>
  </clause>

  <clause id="9609">
    <literal><![CDATA[
      K(x,(y / (y / z)) \ x) = K(x,T(z \ x,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,9195,a(flip),b,9608,a)].">
      <j1 rule="hyper" parents="58 9195 9608"/>
    </justification>
  </clause>

  <clause id="9610">
    <literal><![CDATA[
      K(x,T(y \ x,x * z)) = K(x,((x * z) / y) / z)
    ]]></literal>
    <justification jstring="[hyper(58,a,8487,a(flip),b,9609,a),flip(a)].">
      <j1 rule="hyper" parents="58 8487 9609"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9611">
    <literal><![CDATA[
      K(x,((x * y) / z) / y) = K(x,T(z \ x,y))
    ]]></literal>
    <justification jstring="[hyper(7710,a,9610,a),flip(a)].">
      <j1 rule="hyper" parents="7710 9610"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9612">
    <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,8789,a(flip),b,9611,a)].">
      <j1 rule="hyper" parents="58 8789 9611"/>
    </justification>
  </clause>

  <clause id="9613">
    <literal><![CDATA[
      R(x,y,T(x * K(z,x),u)) = R(x,y,x * K(z,x))
    ]]></literal>
    <justification jstring="[para(4816(a,1),7532(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4816 7532"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9614">
    <literal><![CDATA[
      R(x,y,x * K(z,x)) = R(x,y,x)
    ]]></literal>
    <justification jstring="[para(4816(a,1),9613(a,1,3)),flip(a)].">
      <j1 rule="para" parents="4816 9613"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9615">
    <literal><![CDATA[
      R(x \ y,z,y / x) = R(x \ y,z,x \ y)
    ]]></literal>
    <justification jstring="[para(4776(a,1),9614(a,1,3))].">
      <j1 rule="para" parents="4776 9614"/>
    </justification>
  </clause>

  <clause id="9616">
    <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(4725(a,1),7696(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4725 7696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9617">
    <literal><![CDATA[
      T(x / y,T((y * z) \ x,y)) = T(x / y,T(z \ (y \ x),y))
    ]]></literal>
    <justification jstring="[hyper(7318,a,7743,a),flip(a)].">
      <j1 rule="hyper" parents="7318 7743"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9618">
    <literal><![CDATA[
      T(x / y,T(z \ (y \ x),y)) = T(x / y,x / (y * z))
    ]]></literal>
    <justification jstring="[hyper(58,a,8036,a(flip),b,9617,a),flip(a)].">
      <j1 rule="hyper" parents="58 8036 9617"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9619">
    <literal><![CDATA[
      K(x,(T(y,z) / u) / (y / u)) * (y / u) = T(y,K(x,z)) / u
    ]]></literal>
    <justification jstring="[para(7834(a,1),7812(a,1,1))].">
      <j1 rule="para" parents="7834 7812"/>
    </justification>
  </clause>

  <clause id="9620">
    <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(9619(a,1),103(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9619 103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9621">
    <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(9619(a,1),5146(a,1,2))].">
      <j1 rule="para" parents="9619 5146"/>
    </justification>
  </clause>

  <clause id="9622">
    <literal><![CDATA[
      T(x / y,K(((x / y) \ (1 / y)) \ 1,z)) = T(x,K(z,y \ x)) / y
    ]]></literal>
    <justification jstring="[para(6181(a,1),7873(a,2,1))].">
      <j1 rule="para" parents="6181 7873"/>
    </justification>
  </clause>

  <clause id="9623">
    <literal><![CDATA[
      T(x,T((y \ z) / z,T(y,u))) = T(x,(((y \ 1) \ 1) \ z) / z)
    ]]></literal>
    <justification jstring="[hyper(58,a,7944,a(flip),b,8027,a)].">
      <j1 rule="hyper" parents="58 7944 8027"/>
    </justification>
  </clause>

  <clause id="9624">
    <literal><![CDATA[
      T(x,T((y \ z) / z,T(y,u))) = T(x,((y \ 1) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,4453,a(flip),b,9623,a),flip(a)].">
      <j1 rule="hyper" parents="320 4453 9623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9626">
    <literal><![CDATA[
      T(x,T((y \ z) / z,T(y,u))) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,3768,a(flip),b,9624,a),flip(a)].">
      <j1 rule="hyper" parents="320 3768 9624"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9627">
    <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,9455,a(flip),b,8039,a)].">
      <j1 rule="hyper" parents="58 9455 8039"/>
    </justification>
  </clause>

  <clause id="9628">
    <literal><![CDATA[
      K(x,K(y,z)) * ((K(x,y) * z) \ u) = (z * K(x,y)) \ u
    ]]></literal>
    <justification jstring="[para(6351(a,1),8299(a,2,1))].">
      <j1 rule="para" parents="6351 8299"/>
    </justification>
  </clause>

  <clause id="9629">
    <literal><![CDATA[
      K(x,y * ((K(x,z) * u) \ w)) = K(x,y * ((u * K(x,z)) \ w))
    ]]></literal>
    <justification jstring="[para(9628(a,1),7555(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9628 7555"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9630">
    <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,4969,a(flip),b,8304,a),flip(a)].">
      <j1 rule="hyper" parents="320 4969 8304"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9631">
    <literal><![CDATA[
      K(x,1 / T(T(y,z),z)) = K(x,1 / y)
    ]]></literal>
    <justification jstring="[hyper(9299,a,9630,a)].">
      <j1 rule="hyper" parents="9299 9630"/>
    </justification>
  </clause>

  <clause id="9632">
    <literal><![CDATA[
      K(x,1 / ((y * z) / y)) = K(x,1 / T(z,y))
    ]]></literal>
    <justification jstring="[para(224(a,1),9631(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="224 9631"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9633">
    <literal><![CDATA[
      K(x,1 / T(y,z / y)) = K(x,1 / (z / (z / y)))
    ]]></literal>
    <justification jstring="[para(244(a,1),9631(a,1,2,2,1))].">
      <j1 rule="para" parents="244 9631"/>
    </justification>
  </clause>

  <clause id="9634">
    <literal><![CDATA[
      K(x,K(y,z) / y) = K(x,1 / T(y,z))
    ]]></literal>
    <justification jstring="[para(4952(a,2),9632(a,1,2))].">
      <j1 rule="para" parents="4952 9632"/>
    </justification>
  </clause>

  <clause id="9635">
    <literal><![CDATA[
      K(x,K(1 / y,z) / (1 / y)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(320,a,5513,a(flip),b,9634,a),flip(a)].">
      <j1 rule="hyper" parents="320 5513 9634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9636">
    <literal><![CDATA[
      K(x,1 / (K(y,z \ 1) / z)) = T(K(x,z),y)
    ]]></literal>
    <justification jstring="[para(5272(a,1),9635(a,1,2))].">
      <j1 rule="para" parents="5272 9635"/>
    </justification>
  </clause>

  <clause id="9637">
    <literal><![CDATA[
      K(x,y * K(y \ 1,z)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(58,a,6359,a(flip),b,9636,a)].">
      <j1 rule="hyper" parents="58 6359 9636"/>
    </justification>
  </clause>

  <clause id="9638">
    <literal><![CDATA[
      K(x,y * K(1 / y,z)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(3312(a,2),9637(a,1,2,2))].">
      <j1 rule="para" parents="3312 9637"/>
    </justification>
  </clause>

  <clause id="9639">
    <literal><![CDATA[
      T(K(x,y),z / (1 / y)) = K(x,1 / (z / (z / (1 / y))))
    ]]></literal>
    <justification jstring="[hyper(58,a,5513,a(flip),b,9633,a)].">
      <j1 rule="hyper" parents="58 5513 9633"/>
    </justification>
  </clause>

  <clause id="9640">
    <literal><![CDATA[
      K(T(x,y) / y,z) = K(x / T(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(29,a,7975,a(flip),b,8332,a)].">
      <j1 rule="hyper" parents="29 7975 8332"/>
    </justification>
  </clause>

  <clause id="9641">
    <literal><![CDATA[
      K(x,(y * (z / y)) / ((z / y) * x)) = K(x,z / ((y \ z) * x))
    ]]></literal>
    <justification jstring="[hyper(320,a,8508,a(flip),b,8509,a),flip(a)].">
      <j1 rule="hyper" parents="320 8508 8509"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9642">
    <literal><![CDATA[
      K(x,R(x \ y,x,z / y)) = K(x,z / ((y \ z) * x))
    ]]></literal>
    <justification jstring="[hyper(58,a,8515,a,b,9641,a)].">
      <j1 rule="hyper" parents="58 8515 9641"/>
    </justification>
  </clause>

  <clause id="9643">
    <literal><![CDATA[
      K(x,R(x \ (y / z),x,y / (y / z))) = K(x,y / (z * x))
    ]]></literal>
    <justification jstring="[para(75(a,1),9642(a,2,2,2,1))].">
      <j1 rule="para" parents="75 9642"/>
    </justification>
  </clause>

  <clause id="9644">
    <literal><![CDATA[
      K(x,y * (z * a(u,w,K(x,v5)))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(320,a,7580,a(flip),b,8550,a),flip(a)].">
      <j1 rule="hyper" parents="320 7580 8550"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9646">
    <literal><![CDATA[
      K(x,T(1 \ ((y \ z) * x),z)) = K(x,y \ ((((y \ z) \ 1) \ y) * x))
    ]]></literal>
    <justification jstring="[hyper(58,a,9191,a(flip),b,8578,a)].">
      <j1 rule="hyper" parents="58 9191 8578"/>
    </justification>
  </clause>

  <clause id="9647">
    <literal><![CDATA[
      (x * (y \ ((z \ (y * (x \ u))) * z))) \ u = K(z,(x * (y \ 1)) \ (z \ u))
    ]]></literal>
    <justification jstring="[para(3545(a,1),8677(a,1,1,2))].">
      <j1 rule="para" parents="3545 8677"/>
    </justification>
  </clause>

  <clause id="9648">
    <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,7544,a(flip),b,8679,a),flip(a)].">
      <j1 rule="hyper" parents="320 7544 8679"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9649">
    <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,8689,a(flip),b,9648,a)].">
      <j1 rule="hyper" parents="58 8689 9648"/>
    </justification>
  </clause>

  <clause id="9650">
    <literal><![CDATA[
      T(x,T(y,z)) \ R(x,y,x) = K(y * x,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(8438,a,9649,a),flip(a)].">
      <j1 rule="hyper" parents="8438 9649"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9651">
    <literal><![CDATA[
      K(x,T(y,z)) * a(y,x,y) = K(x * y,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(8985,a,9650,a)].">
      <j1 rule="hyper" parents="8985 9650"/>
    </justification>
  </clause>

  <clause id="9652">
    <literal><![CDATA[
      K(x,T(y,z)) * a(y,x,y) = K(y * x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,5888,a(flip),b,9651,a),flip(a)].">
      <j1 rule="hyper" parents="320 5888 9651"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9653">
    <literal><![CDATA[
      K(x / y,z) * a(z,y \ x,z) = K((y \ x) * z,T(z,y))
    ]]></literal>
    <justification jstring="[para(7907(a,1),9651(a,1,1))].">
      <j1 rule="para" parents="7907 9651"/>
    </justification>
  </clause>

  <clause id="9654">
    <literal><![CDATA[
      K(x * y,T(y,z)) \ (K(x,T(y,z)) * y) = L(y,x,y)
    ]]></literal>
    <justification jstring="[para(9651(a,1),9093(a,1,1))].">
      <j1 rule="para" parents="9651 9093"/>
    </justification>
  </clause>

  <clause id="9655">
    <literal><![CDATA[
      a(x,y,x) * K(y,T(x,z)) = K(x * y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(9553,a,9652,a)].">
      <j1 rule="hyper" parents="9553 9652"/>
    </justification>
  </clause>

  <clause id="9656">
    <literal><![CDATA[
      K(x * y,T(x,z)) * K(x,T(y,z)) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(7231,a,9655,a)].">
      <j1 rule="hyper" parents="7231 9655"/>
    </justification>
  </clause>

  <clause id="9657">
    <literal><![CDATA[
      K(x * y,T(y,z)) \ (y * K(x,T(y,z))) = L(y,x,y)
    ]]></literal>
    <justification jstring="[para(2907(a,1),9654(a,1,2))].">
      <j1 rule="para" parents="2907 9654"/>
    </justification>
  </clause>

  <clause id="9658">
    <literal><![CDATA[
      T(x,T(y * x,z)) * K(y,T(x,z)) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(7228,a,9657,a)].">
      <j1 rule="hyper" parents="7228 9657"/>
    </justification>
  </clause>

  <clause id="9659">
    <literal><![CDATA[
      T(x,T(x * y,z)) * K(y,T(x,z)) = L(x,y,x)
    ]]></literal>
    <justification jstring="[para(4610(a,1),9658(a,1,1))].">
      <j1 rule="para" parents="4610 9658"/>
    </justification>
  </clause>

  <clause id="9660">
    <literal><![CDATA[
      K((x * (y / z)) \ u,z) != w
    ]]></literal>
    <literal><![CDATA[
      K((x * (z \ y)) \ u,z) = w
    ]]></literal>
    <justification jstring="[para(8681(a,1),5241(a,1))].">
      <j1 rule="para" parents="8681 5241"/>
    </justification>
  </clause>

  <clause id="9661">
    <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,4287,a(flip),b,8698,a),flip(a)].">
      <j1 rule="hyper" parents="320 4287 8698"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9662">
    <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,4286,a(flip),b,8699,a),flip(a)].">
      <j1 rule="hyper" parents="320 4286 8699"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9663">
    <literal><![CDATA[
      K((x * (y / z)) \ u,z) = K((x * y) \ (u * z),z)
    ]]></literal>
    <justification jstring="[hyper(5241,a,8724,a),flip(a)].">
      <j1 rule="hyper" parents="5241 8724"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9664">
    <literal><![CDATA[
      K((x * (y \ z)) \ u,y) = K((x * z) \ (u * y),y)
    ]]></literal>
    <justification jstring="[hyper(9660,a,9663,a)].">
      <j1 rule="hyper" parents="9660 9663"/>
    </justification>
  </clause>

  <clause id="9665">
    <literal><![CDATA[
      K((x * (y \ 1)) \ z,y) = K(x \ (z * y),y)
    ]]></literal>
    <justification jstring="[para(3(a,1),9664(a,2,1,1))].">
      <j1 rule="para" parents="3 9664"/>
    </justification>
  </clause>

  <clause id="9666">
    <literal><![CDATA[
      L(K(x * (y \ z),x),y \ z,y) = K(y \ (z * x),x)
    ]]></literal>
    <justification jstring="[hyper(58,a,6656,a,b,9665,a)].">
      <j1 rule="hyper" parents="58 6656 9665"/>
    </justification>
  </clause>

  <clause id="9667">
    <literal><![CDATA[
      L(K(x * y,x),y,z) = K(z \ ((z * y) * x),x)
    ]]></literal>
    <justification jstring="[hyper(58,a,6636,a,b,9665,a)].">
      <j1 rule="hyper" parents="58 6636 9665"/>
    </justification>
  </clause>

  <clause id="9668">
    <literal><![CDATA[
      K(x \ ((x * y) * z),z) \ K(z * y,z) = a(x,y,K(z * y,z))
    ]]></literal>
    <justification jstring="[para(9667(a,1),1932(a,1,1))].">
      <j1 rule="para" parents="9667 1932"/>
    </justification>
  </clause>

  <clause id="9669">
    <literal><![CDATA[
      L(K(x * y,y),x,z) = K(z \ ((z * x) * y),y)
    ]]></literal>
    <justification jstring="[para(5266(a,2),9667(a,1,1))].">
      <j1 rule="para" parents="5266 9667"/>
    </justification>
  </clause>

  <clause id="9670">
    <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),9669(a,2,1,2))].">
      <j1 rule="para" parents="105 9669"/>
    </justification>
  </clause>

  <clause id="9671">
    <literal><![CDATA[
      K(x,y \ ((y * z) * x)) * K(x * z,x) = a(y,z,K(x * z,x))
    ]]></literal>
    <justification jstring="[hyper(5163,a,9668,a)].">
      <j1 rule="hyper" parents="5163 9668"/>
    </justification>
  </clause>

  <clause id="9672">
    <literal><![CDATA[
      L(K(x,x * y),y,z) = K(x,z \ ((z * y) * x))
    ]]></literal>
    <justification jstring="[hyper(30,a,5890,a,b,9671,a)].">
      <j1 rule="hyper" parents="30 5890 9671"/>
    </justification>
  </clause>

  <clause id="9673">
    <literal><![CDATA[
      L(K(x,x * (y \ z)),y \ z,y) = K(x,y \ (z * x))
    ]]></literal>
    <justification jstring="[para(5(a,1),9672(a,2,2,2,1))].">
      <j1 rule="para" parents="5 9672"/>
    </justification>
  </clause>

  <clause id="9674">
    <literal><![CDATA[
      L(K(x,y * x),y,z) = K(x,z \ ((z * y) * x))
    ]]></literal>
    <justification jstring="[para(5385(a,2),9672(a,1,1))].">
      <j1 rule="para" parents="5385 9672"/>
    </justification>
  </clause>

  <clause id="9675">
    <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),9674(a,2,2))].">
      <j1 rule="para" parents="296 9674"/>
    </justification>
  </clause>

  <clause id="9676">
    <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,6622,a(flip),b,9675,a),flip(a)].">
      <j1 rule="hyper" parents="320 6622 9675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9678">
    <literal><![CDATA[
      K(x,(((K(y,x \ z) / y) \ 1) * z) \ (u * x)) = K(x,((x \ z) * y) \ u)
    ]]></literal>
    <justification jstring="[para(5270(a,2),8726(a,1,2,1,1))].">
      <j1 rule="para" parents="5270 8726"/>
    </justification>
  </clause>

  <clause id="9679">
    <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),8788(a,1,2,2))].">
      <j1 rule="para" parents="176 8788"/>
    </justification>
  </clause>

  <clause id="9680">
    <literal><![CDATA[
      K(x,y / ((T(z,u) \ u) / w)) = K(x,y / ((z \ T(u,z)) / w))
    ]]></literal>
    <justification jstring="[hyper(58,a,8870,a(flip),b,8877,a),flip(a)].">
      <j1 rule="hyper" parents="58 8870 8877"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9681">
    <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(2011(a,2),8915(a,2,2))].">
      <j1 rule="para" parents="2011 8915"/>
    </justification>
  </clause>

  <clause id="9682">
    <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(6329(a,1),8915(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6329 8915"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9683">
    <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(2006(a,1),8917(a,2,2))].">
      <j1 rule="para" parents="2006 8917"/>
    </justification>
  </clause>

  <clause id="9684">
    <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(8984(a,2),39(a,1))].">
      <j1 rule="para" parents="8984 39"/>
    </justification>
  </clause>

  <clause id="9685">
    <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(7784(a,1),9036(a,1,1,1))].">
      <j1 rule="para" parents="7784 9036"/>
    </justification>
  </clause>

  <clause id="9686">
    <literal><![CDATA[
      K((((x * y) \ x) \ 1) * z,y) = K(z / ((x * y) \ x),y)
    ]]></literal>
    <justification jstring="[para(4(a,1),9044(a,1,2))].">
      <j1 rule="para" parents="4 9044"/>
    </justification>
  </clause>

  <clause id="9687">
    <literal><![CDATA[
      K(x * (((y * z) \ y) \ 1),z) = K(x / ((y * z) \ y),z)
    ]]></literal>
    <justification jstring="[hyper(58,a,9456,a(flip),b,9686,a)].">
      <j1 rule="hyper" parents="58 9456 9686"/>
    </justification>
  </clause>

  <clause id="9688">
    <literal><![CDATA[
      K(x * (((y * z) \ y) \ 1),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(((y * z) \ y) \ x,z) = u
    ]]></literal>
    <justification jstring="[para(9687(a,2),7999(a,1))].">
      <j1 rule="para" parents="9687 7999"/>
    </justification>
  </clause>

  <clause id="9689">
    <literal><![CDATA[
      T(x / T(y,x),z) * T(y,T(x,z)) = x * K(T(x,y) / y,z)
    ]]></literal>
    <justification jstring="[para(7438(a,1),9068(a,1,2))].">
      <j1 rule="para" parents="7438 9068"/>
    </justification>
  </clause>

  <clause id="9690">
    <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(9177(a,1),6283(a,1,2))].">
      <j1 rule="para" parents="9177 6283"/>
    </justification>
  </clause>

  <clause id="9691">
    <literal><![CDATA[
      (x / a(y,z,K(u,w))) * K(u,w) = x * L(K(u,w),z,y)
    ]]></literal>
    <justification jstring="[para(5892(a,1),9186(a,1,1,2))].">
      <j1 rule="para" parents="5892 9186"/>
    </justification>
  </clause>

  <clause id="9692">
    <literal><![CDATA[
      (x * K((y \ 1) \ (z \ x),z)) * y = (z \ (x * y)) * z
    ]]></literal>
    <justification jstring="[hyper(4663,a,9329,a),flip(a)].">
      <j1 rule="hyper" parents="4663 9329"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9693">
    <literal><![CDATA[
      (x * K((y \ z) \ x,z)) * y = (z \ (x * y)) * z
    ]]></literal>
    <justification jstring="[para(8297(a,1),9692(a,1,1,2))].">
      <j1 rule="para" parents="8297 9692"/>
    </justification>
  </clause>

  <clause id="9694">
    <literal><![CDATA[
      x \ R(x * K(y,x),y,y \ 1) = K(y,x) * a(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[para(705(a,1),9448(a,2,2))].">
      <j1 rule="para" parents="705 9448"/>
    </justification>
  </clause>

  <clause id="9695">
    <literal><![CDATA[
      K(x,y) * a(y,x,x \ 1) = y \ ((x * y) * (x \ 1))
    ]]></literal>
    <justification jstring="[para(4930(a,1),9694(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4930 9694"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9696">
    <literal><![CDATA[
      K(x,(x \ ((y * x) * (y \ 1))) \ z) = K(x,a(x,y,y \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(9695(a,1),8559(a,1,2,1))].">
      <j1 rule="para" parents="9695 8559"/>
    </justification>
  </clause>

  <clause id="9697">
    <literal><![CDATA[
      K(x,((y * x) * (y \ 1)) \ (x * z)) = K(x,a(x,y,y \ 1) \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,7032,a(flip),b,9696,a)].">
      <j1 rule="hyper" parents="58 7032 9696"/>
    </justification>
  </clause>

  <clause id="9698">
    <literal><![CDATA[
      T(x / y,K(((x / y) \ (1 / y)) \ 1,z)) = T(x / y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,8604,a(flip),b,9622,a),flip(a)].">
      <j1 rule="hyper" parents="320 8604 9622"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9699">
    <literal><![CDATA[
      T(x / y,K(z,((x / y) \ (1 / y)) \ 1)) = T(x / y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(7866,a,9698,a)].">
      <j1 rule="hyper" parents="7866 9698"/>
    </justification>
  </clause>

  <clause id="9700">
    <literal><![CDATA[
      T(x / y,K(z,(1 / y) \ (x / y))) = T(x / y,K(x,z))
    ]]></literal>
    <justification jstring="[para(6108(a,1),9699(a,1,2))].">
      <j1 rule="para" parents="6108 9699"/>
    </justification>
  </clause>

  <clause id="9701">
    <literal><![CDATA[
      (x / T(y / (y / z),u)) * z = x * (T(y / (y / z),u) \ z)
    ]]></literal>
    <justification jstring="[para(8038(a,1),9627(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8038 9627"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9702">
    <literal><![CDATA[
      (x / T(1 / (1 / y),z)) * y = x * (y * (1 / T(y,z)))
    ]]></literal>
    <justification jstring="[para(6804(a,1),9701(a,2,2))].">
      <j1 rule="para" parents="6804 9701"/>
    </justification>
  </clause>

  <clause id="9703">
    <literal><![CDATA[
      K(x,T((y \ z) * x,z)) = K(x,y \ ((((y \ z) \ 1) \ y) * x))
    ]]></literal>
    <justification jstring="[para(60(a,1),9646(a,1,2,1))].">
      <j1 rule="para" parents="60 9646"/>
    </justification>
  </clause>

  <clause id="9704">
    <literal><![CDATA[
      K(x,T(((y \ z) \ 1) \ x,y)) = K(x,T((y \ z) * x,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,8510,a(flip),b,9703,a)].">
      <j1 rule="hyper" parents="320 8510 9703"/>
    </justification>
  </clause>

  <clause id="9705">
    <literal><![CDATA[
      K(x,T(1 \ ((y \ z) * x),y)) = K(x,T((y \ z) * x,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,9191,a(flip),b,9704,a)].">
      <j1 rule="hyper" parents="58 9191 9704"/>
    </justification>
  </clause>

  <clause id="9706">
    <literal><![CDATA[
      K(x,T((y \ z) * x,z)) = K(x,T((y \ z) * x,y))
    ]]></literal>
    <justification jstring="[para(60(a,1),9705(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="60 9705"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9707">
    <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,6954,a(flip),b,9682,a)].">
      <j1 rule="hyper" parents="117 6954 9682"/>
    </justification>
  </clause>

  <clause id="9708">
    <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(6344,a,9683,a)].">
      <j1 rule="hyper" parents="6344 9683"/>
    </justification>
  </clause>

  <clause id="9709">
    <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(8837(a,1),9685(a,1,1))].">
      <j1 rule="para" parents="8837 9685"/>
    </justification>
  </clause>

  <clause id="9710">
    <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(7784(a,1),9709(a,2,1))].">
      <j1 rule="para" parents="7784 9709"/>
    </justification>
  </clause>

  <clause id="9711">
    <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(7779(a,1),9710(a,2,2))].">
      <j1 rule="para" parents="7779 9710"/>
    </justification>
  </clause>

  <clause id="9712">
    <literal><![CDATA[
      (x * a(y,z,K(u,w))) * K(w,u) = x * L(K(w,u),z,y)
    ]]></literal>
    <justification jstring="[para(5892(a,1),9708(a,1,1,2))].">
      <j1 rule="para" parents="5892 9708"/>
    </justification>
  </clause>

  <clause id="9713">
    <literal><![CDATA[
      x / a(y,z,K(u,w)) = x * a(y,z,K(w,u))
    ]]></literal>
    <justification jstring="[hyper(30,a,9691,a,b,9712,a)].">
      <j1 rule="hyper" parents="30 9691 9712"/>
    </justification>
  </clause>

  <clause id="9714">
    <literal><![CDATA[
      (x * a(y,z,K(u,w))) \ x = a(y,z,K(w,u))
    ]]></literal>
    <justification jstring="[hyper(572,a,9713,a)].">
      <j1 rule="hyper" parents="572 9713"/>
    </justification>
  </clause>

  <clause id="9715">
    <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(9713(a,1),438(a,1,1))].">
      <j1 rule="para" parents="9713 438"/>
    </justification>
  </clause>

  <clause id="9716">
    <literal><![CDATA[
      K(x,y) * T(y,K(z,y) * (x * y)) = L(y,K(z,y) * x,y)
    ]]></literal>
    <justification jstring="[para(7345(a,1),7522(a,1,1))].">
      <j1 rule="para" parents="7345 7522"/>
    </justification>
  </clause>

  <clause id="9717">
    <literal><![CDATA[
      L(x,K(y,x) * z,x) = K(z,x) * T(x,z * x)
    ]]></literal>
    <justification jstring="[para(7270(a,1),9716(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7270 9716"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9719">
    <literal><![CDATA[
      L(x,K(y,x) * z,x) = L(x,z,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,5091,a(flip),b,9717,a),flip(a)].">
      <j1 rule="hyper" parents="320 5091 9717"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9721">
    <literal><![CDATA[
      L(x,T(x,y) \ z,x) = L(x,x \ z,x)
    ]]></literal>
    <justification jstring="[para(5131(a,1),9719(a,1,2))].">
      <j1 rule="para" parents="5131 9719"/>
    </justification>
  </clause>

  <clause id="9722">
    <literal><![CDATA[
      L(x,y / T(x,z),x) = L(x,x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,9145,a,b,9721,a)].">
      <j1 rule="hyper" parents="58 9145 9721"/>
    </justification>
  </clause>

  <clause id="9724">
    <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,7018,a,b,9722,a)].">
      <j1 rule="hyper" parents="58 7018 9722"/>
    </justification>
  </clause>

  <clause id="9726">
    <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(5923(a,2),8002(a,1,1))].">
      <j1 rule="para" parents="5923 8002"/>
    </justification>
  </clause>

  <clause id="9727">
    <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,7766,a,b,8008,a)].">
      <j1 rule="hyper" parents="320 7766 8008"/>
    </justification>
  </clause>

  <clause id="9728">
    <literal><![CDATA[
      L(x,y,x) \ (T(x * y,x) \ z) = ((y * x) / y) \ ((x * y) \ z)
    ]]></literal>
    <justification jstring="[para(4117(a,1),8028(a,1,2,1))].">
      <j1 rule="para" parents="4117 8028"/>
    </justification>
  </clause>

  <clause id="9729">
    <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,8377,a(flip),b,8349,a),flip(a)].">
      <j1 rule="hyper" parents="320 8377 8349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9730">
    <literal><![CDATA[
      K((x / y) \ z,L(y,u,w)) = K(x \ (z * y),L(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(5026,a,8460,a),flip(a)].">
      <j1 rule="hyper" parents="5026 8460"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9731">
    <literal><![CDATA[
      K(x \ ((y \ z) * y),L(y,u,w)) = K(x \ z,L(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(320,a,4806,a(flip),b,8462,a),flip(a)].">
      <j1 rule="hyper" parents="320 4806 8462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9732">
    <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),9731(a,1,1,2,1))].">
      <j1 rule="para" parents="4 9731"/>
    </justification>
  </clause>

  <clause id="9733">
    <literal><![CDATA[
      (x * y) / (x * (y * K(z,u))) = L(T(K(u,z),x * y),y,x)
    ]]></literal>
    <justification jstring="[para(8428(a,1),8607(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8428 8607"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9734">
    <literal><![CDATA[
      (x * y) / (x * (y * K(z,u))) = L(K(u,T(z,x * y)),y,x)
    ]]></literal>
    <justification jstring="[para(7158(a,2),9733(a,2,1))].">
      <j1 rule="para" parents="7158 9733"/>
    </justification>
  </clause>

  <clause id="9736">
    <literal><![CDATA[
      L(K(x,T(x * y,z * y)),y,z) = (z * y) / (z * (x \ T(x * y,x)))
    ]]></literal>
    <justification jstring="[para(6384(a,2),9734(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6384 9734"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9737">
    <literal><![CDATA[
      L(K(x,T(T(y,z),u * z)),z,u) = (u * z) / (u * (K(y,x) * z))
    ]]></literal>
    <justification jstring="[para(7150(a,1),9734(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7150 9734"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9738">
    <literal><![CDATA[
      K((x * y) / (x * (z \ y)),u) = (x * y) / (x * (K(u,z) * y))
    ]]></literal>
    <justification jstring="[hyper(58,a,9504,a(flip),b,9737,a)].">
      <j1 rule="hyper" parents="58 9504 9737"/>
    </justification>
  </clause>

  <clause id="9739">
    <literal><![CDATA[
      K((x * y) / (x * (z \ y)),u) = K(z,(x * y) / (x * (u \ y)))
    ]]></literal>
    <justification jstring="[hyper(320,a,6044,a,b,9738,a),flip(a)].">
      <j1 rule="hyper" parents="320 6044 9738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9740">
    <literal><![CDATA[
      K(x,(y * z) / (y * (u \ z))) = (y * (K(x,u) * z)) / (y * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,5987,a(flip),b,9739,a),flip(a)].">
      <j1 rule="hyper" parents="58 5987 9739"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9741">
    <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(9135(a,1),8963(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9135 8963"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9742">
    <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,9741,a),flip(a)].">
      <j1 rule="hyper" parents="320 4 9741"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9744">
    <literal><![CDATA[
      L(x,a(y,z,y),y) = x
    ]]></literal>
    <justification jstring="[para(9534(a,1),9742(a,1,1))].">
      <j1 rule="para" parents="9534 9742"/>
    </justification>
  </clause>

  <clause id="9746">
    <literal><![CDATA[
      L(x,a(y,z,y),T(y,u)) = x
    ]]></literal>
    <justification jstring="[para(9367(a,1),9744(a,1,2))].">
      <j1 rule="para" parents="9367 9744"/>
    </justification>
  </clause>

  <clause id="9747">
    <literal><![CDATA[
      (T(x,y) * a(x,z,x)) * u = T(x,y) * (a(x,z,x) * u)
    ]]></literal>
    <justification jstring="[hyper(1338,a,9746,a),flip(a)].">
      <j1 rule="hyper" parents="1338 9746"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9748">
    <literal><![CDATA[
      T(x,y) * (a(x,z,x) * u) = R(T(x,y),z,x) * u
    ]]></literal>
    <justification jstring="[para(8951(a,1),9747(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8951 9747"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9749">
    <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,7780,a(flip),b,9174,a),flip(a)].">
      <j1 rule="hyper" parents="320 7780 9174"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9750">
    <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(7543(a,1),9582(a,1,1))].">
      <j1 rule="para" parents="7543 9582"/>
    </justification>
  </clause>

  <clause id="9751">
    <literal><![CDATA[
      (x * (K(y \ x,y) * z)) / (x * z) = L(K(y \ x,y),z,x)
    ]]></literal>
    <justification jstring="[para(7879(a,1),9583(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7879 9583"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9752">
    <literal><![CDATA[
      L(K(x \ y,x),z,y) * (y * z) = y * (K(x \ y,x) * z)
    ]]></literal>
    <justification jstring="[hyper(133,a,9751,a)].">
      <j1 rule="hyper" parents="133 9751"/>
    </justification>
  </clause>

  <clause id="9754">
    <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),9752(a,1,1,1,1))].">
      <j1 rule="para" parents="4 9752"/>
    </justification>
  </clause>

  <clause id="9755">
    <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(5156(a,1),9726(a,2,2))].">
      <j1 rule="para" parents="5156 9726"/>
    </justification>
  </clause>

  <clause id="9756">
    <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(9726(a,1),8166(a,2,2))].">
      <j1 rule="para" parents="9726 8166"/>
    </justification>
  </clause>

  <clause id="9757">
    <literal><![CDATA[
      (x * y) / (x * (z \ T(z * y,z))) = L(K(z,T(y * z,x)),y,x)
    ]]></literal>
    <justification jstring="[para(9228(a,1),9736(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9228 9736"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9758">
    <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(7821,a,9749,a)].">
      <j1 rule="hyper" parents="7821 9749"/>
    </justification>
  </clause>

  <clause id="9759">
    <literal><![CDATA[
      ((x * y) \ ((x * K(z,u)) * y)) \ 1 = (x * y) \ ((x * K(u,z)) * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,9497,a(flip),b,9750,a),flip(a)].">
      <j1 rule="hyper" parents="58 9497 9750"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9760">
    <literal><![CDATA[
      K(((x / y) * z) \ (x * z),u) \ 1 = (x * z) \ ((x * K(u,y)) * z)
    ]]></literal>
    <justification jstring="[para(6820(a,2),9759(a,1,1))].">
      <j1 rule="para" parents="6820 9759"/>
    </justification>
  </clause>

  <clause id="9761">
    <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(9760(a,1),4985(a,1))].">
      <j1 rule="para" parents="9760 4985"/>
    </justification>
  </clause>

  <clause id="9762">
    <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(1336(a,1),7370(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1336 7370"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9763">
    <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(6925(a,1),7475(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6925 7475"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9764">
    <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,3351,a,b,9763,a),flip(a)].">
      <j1 rule="hyper" parents="320 3351 9763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9765">
    <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,6676,a,b,8116,a),flip(a)].">
      <j1 rule="hyper" parents="320 6676 8116"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9766">
    <literal><![CDATA[
      K(x,K((1 / y) / z,(z * y) / u)) = (T(z * y,K(x,u)) / y) / z
    ]]></literal>
    <justification jstring="[hyper(8211,a,8169,a)].">
      <j1 rule="hyper" parents="8211 8169"/>
    </justification>
  </clause>

  <clause id="9767">
    <literal><![CDATA[
      K(x,K((1 / y) / z,(z * y) / u)) = K(x,K(u,(1 / y) / z))
    ]]></literal>
    <justification jstring="[hyper(320,a,8210,a(flip),b,9766,a),flip(a)].">
      <j1 rule="hyper" parents="320 8210 9766"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9768">
    <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),9767(a,1,2,2))].">
      <j1 rule="para" parents="524 9767"/>
    </justification>
  </clause>

  <clause id="9769">
    <literal><![CDATA[
      T((1 / ((x * y) \ x)) * K(y,z),y) = (y \ (1 / ((x * y) \ x))) * T(y,z)
    ]]></literal>
    <justification jstring="[para(6059(a,1),8284(a,2,1))].">
      <j1 rule="para" parents="6059 8284"/>
    </justification>
  </clause>

  <clause id="9770">
    <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,9681,a(flip),b,8612,a),flip(a)].">
      <j1 rule="hyper" parents="320 9681 8612"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9771">
    <literal><![CDATA[
      K(L(x,y,z),(u * (w * x)) \ v5) = K(L(x,y,z),(u * (x * w)) \ v5)
    ]]></literal>
    <justification jstring="[hyper(8394,a,8682,a),flip(a)].">
      <j1 rule="hyper" parents="8394 8682"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9772">
    <literal><![CDATA[
      K((x * (y * z)) \ (x * ((z * u) * y)),y) = K(L(u,y * z,x),y)
    ]]></literal>
    <justification jstring="[hyper(320,a,7073,a(flip),b,8703,a),flip(a)].">
      <j1 rule="hyper" parents="320 7073 8703"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9773">
    <literal><![CDATA[
      K((x * y) \ (z \ (x * ((y * u) * z))),z) = K(L(u,z * y,x),z)
    ]]></literal>
    <justification jstring="[hyper(9346,a,9772,a)].">
      <j1 rule="hyper" parents="9346 9772"/>
    </justification>
  </clause>

  <clause id="9775">
    <literal><![CDATA[
      K(L(x,y,z),(u * (x * w)) \ v5) = K(L(x,y,z),(u * w) \ (x \ v5))
    ]]></literal>
    <justification jstring="[hyper(8394,a,8721,a),flip(a)].">
      <j1 rule="hyper" parents="8394 8721"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9776">
    <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,9771,a,b,9775,a)].">
      <j1 rule="hyper" parents="58 9771 9775"/>
    </justification>
  </clause>

  <clause id="9777">
    <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(6771(a,1),8893(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6771 8893"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9778">
    <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(7158(a,2),8897(a,1,2))].">
      <j1 rule="para" parents="7158 8897"/>
    </justification>
  </clause>

  <clause id="9779">
    <literal><![CDATA[
      x \ (K(y,z) * (K(u,y) * x)) = T(K(u,y),x) * T(K(y,z),x)
    ]]></literal>
    <justification jstring="[para(7667(a,1),8932(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7667 8932"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9781">
    <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(1551(a,1),8976(a,1,2,2))].">
      <j1 rule="para" parents="1551 8976"/>
    </justification>
  </clause>

  <clause id="9782">
    <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(7779(a,1),9081(a,1,1))].">
      <j1 rule="para" parents="7779 9081"/>
    </justification>
  </clause>

  <clause id="9783">
    <literal><![CDATA[
      ((x * y) * a(y,z,y)) \ ((y * x) * y) = L(T(y,x),z,T(y,x))
    ]]></literal>
    <justification jstring="[para(9367(a,1),9096(a,1,1,2))].">
      <j1 rule="para" parents="9367 9096"/>
    </justification>
  </clause>

  <clause id="9784">
    <literal><![CDATA[
      (x * R(y,z,y)) \ ((y * x) * y) = L(T(y,x),z,T(y,x))
    ]]></literal>
    <justification jstring="[para(9123(a,1),9783(a,1,1))].">
      <j1 rule="para" parents="9123 9783"/>
    </justification>
  </clause>

  <clause id="9786">
    <literal><![CDATA[
      (x * R(y,z,y)) \ ((y * x) * y) = L(T(y,x),z,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,7503,a(flip),b,9784,a),flip(a)].">
      <j1 rule="hyper" parents="320 7503 9784"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9788">
    <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(9786(a,2),8424(a,1))].">
      <j1 rule="para" parents="9786 8424"/>
    </justification>
  </clause>

  <clause id="9789">
    <literal><![CDATA[
      K(x,T((y \ z) / z,u)) = K(x,T(y \ 1,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,9118,a(flip),b,9137,a),flip(a)].">
      <j1 rule="hyper" parents="320 9118 9137"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9790">
    <literal><![CDATA[
      T(x,T((y \ z) / z,u)) = T(x,T(y \ 1,u))
    ]]></literal>
    <justification jstring="[hyper(118,a,9789,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 9789 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9791">
    <literal><![CDATA[
      K(x,T((y / z) \ 1,u)) = K(x,T(z / y,u))
    ]]></literal>
    <justification jstring="[para(75(a,1),9789(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="75 9789"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9792">
    <literal><![CDATA[
      T(x,T((y / z) \ 1,u)) = T(x,T(z / y,u))
    ]]></literal>
    <justification jstring="[para(75(a,1),9790(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="75 9790"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9793">
    <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(9791(a,1),9656(a,1,1))].">
      <j1 rule="para" parents="9791 9656"/>
    </justification>
  </clause>

  <clause id="9794">
    <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(6224(a,1),9792(a,2,2,1))].">
      <j1 rule="para" parents="6224 9792"/>
    </justification>
  </clause>

  <clause id="9795">
    <literal><![CDATA[
      K(((x \ y) \ 1) * z,T(y \ x,u)) = K((x \ y) \ z,T(y \ x,u))
    ]]></literal>
    <justification jstring="[hyper(9198,a,9199,a)].">
      <j1 rule="hyper" parents="9198 9199"/>
    </justification>
  </clause>

  <clause id="9796">
    <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,8281,a(flip),b,9795,a)].">
      <j1 rule="hyper" parents="58 8281 9795"/>
    </justification>
  </clause>

  <clause id="9797">
    <literal><![CDATA[
      K(x * ((y \ z) \ 1),T(z \ y,z)) = K((y \ z) \ x,y / z)
    ]]></literal>
    <justification jstring="[hyper(320,a,7913,a(flip),b,9796,a),flip(a)].">
      <j1 rule="hyper" parents="320 7913 9796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9798">
    <literal><![CDATA[
      K(x * ((y \ z) \ 1),y / z) = K((y \ z) \ x,y / z)
    ]]></literal>
    <justification jstring="[hyper(8060,a,9797,a)].">
      <j1 rule="hyper" parents="8060 9797"/>
    </justification>
  </clause>

  <clause id="9799">
    <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(8831(a,2),9327(a,1,1))].">
      <j1 rule="para" parents="8831 9327"/>
    </justification>
  </clause>

  <clause id="9800">
    <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(5041,a,9371,a),flip(a)].">
      <j1 rule="hyper" parents="5041 9371"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9801">
    <literal><![CDATA[
      K((x / y) / (y \ 1),1 / y) = K((y \ x) / (y \ 1),1 / y)
    ]]></literal>
    <justification jstring="[para(3075(a,1),9425(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3075 9425"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9802">
    <literal><![CDATA[
      K((x / y) / (y \ 1),1 / y) = K((y \ x) / (1 / y),1 / y)
    ]]></literal>
    <justification jstring="[hyper(320,a,3976,a,b,9801,a),flip(a)].">
      <j1 rule="hyper" parents="320 3976 9801"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9803">
    <literal><![CDATA[
      K((x / y) / (1 / y),1 / y) = K((y \ x) / (1 / y),1 / y)
    ]]></literal>
    <justification jstring="[hyper(58,a,3976,a,b,9802,a)].">
      <j1 rule="hyper" parents="58 3976 9802"/>
    </justification>
  </clause>

  <clause id="9804">
    <literal><![CDATA[
      (x / y) / ((x / y) / (1 / y)) = (1 / y) * K((y \ x) / (1 / y),1 / y)
    ]]></literal>
    <justification jstring="[para(9803(a,1),4753(a,2,2))].">
      <j1 rule="para" parents="9803 4753"/>
    </justification>
  </clause>

  <clause id="9805">
    <literal><![CDATA[
      K(x,(y * (z \ 1)) \ (x \ u)) = K(x,(y * (z \ x)) \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,6679,a(flip),b,9647,a),flip(a)].">
      <j1 rule="hyper" parents="58 6679 9647"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9806">
    <literal><![CDATA[
      K(x,(y * (z \ x)) \ (u * x)) = K(x,(y * (z \ 1)) \ u)
    ]]></literal>
    <justification jstring="[hyper(8409,a,9805,a),flip(a)].">
      <j1 rule="hyper" parents="8409 9805"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9807">
    <literal><![CDATA[
      K(x,(y * ((z \ x) \ 1)) \ u) = K(x,(y * z) \ (u * x))
    ]]></literal>
    <justification jstring="[hyper(58,a,6839,a(flip),b,9806,a),flip(a)].">
      <j1 rule="hyper" parents="58 6839 9806"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9808">
    <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(5520(a,1),9807(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5520 9807"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9809">
    <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),9661(a,1,1,2,1))].">
      <j1 rule="para" parents="4 9661"/>
    </justification>
  </clause>

  <clause id="9810">
    <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),9662(a,1,1,2,1))].">
      <j1 rule="para" parents="4 9662"/>
    </justification>
  </clause>

  <clause id="9811">
    <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,5326,a,b,9678,a)].">
      <j1 rule="hyper" parents="58 5326 9678"/>
    </justification>
  </clause>

  <clause id="9812">
    <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,7645,a,b,9762,a)].">
      <j1 rule="hyper" parents="58 7645 9762"/>
    </justification>
  </clause>

  <clause id="9813">
    <literal><![CDATA[
      K(x / y,z) * K(K(y \ x,z) * x,x) = K(x / T(y,x),z)
    ]]></literal>
    <justification jstring="[para(4503(a,1),9765(a,2,1))].">
      <j1 rule="para" parents="4503 9765"/>
    </justification>
  </clause>

  <clause id="9814">
    <literal><![CDATA[
      T(x * K(x / y,z),x) = x * K(x / T(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(119,a,9813,a(flip),b,8116,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 9813 8116"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9815">
    <literal><![CDATA[
      T(x * K(x / y,z),x) = x * K(T(x,y) / y,z)
    ]]></literal>
    <justification jstring="[para(4246(a,2),9814(a,2,2,1))].">
      <j1 rule="para" parents="4246 9814"/>
    </justification>
  </clause>

  <clause id="9816">
    <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(7232,a,9778,a),flip(a)].">
      <j1 rule="hyper" parents="7232 9778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9817">
    <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),9781(a,1,2)),flip(a)].">
      <j1 rule="para" parents="105 9781"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9818">
    <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,9585,a(flip),b,9817,a),flip(a)].">
      <j1 rule="hyper" parents="320 9585 9817"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9819">
    <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(4816(a,1),9818(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4816 9818"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9820">
    <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(5718(a,1),9782(a,1,2))].">
      <j1 rule="para" parents="5718 9782"/>
    </justification>
  </clause>

  <clause id="9821">
    <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(7829,a,9820,a)].">
      <j1 rule="hyper" parents="7829 9820"/>
    </justification>
  </clause>

  <clause id="9822">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(z,x) * T(z \ 1,y)) = T(z \ K(z,x),y)
    ]]></literal>
    <justification jstring="[para(8173(a,1),9821(a,1,1))].">
      <j1 rule="para" parents="8173 9821"/>
    </justification>
  </clause>

  <clause id="9823">
    <literal><![CDATA[
      K(x,T(y,z)) * T(x \ 1,z) = T(x \ K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(9162,a,9822,a)].">
      <j1 rule="hyper" parents="9162 9822"/>
    </justification>
  </clause>

  <clause id="9824">
    <literal><![CDATA[
      K(x,y) * (K(z,x) * (K(x,y) \ u)) = K(z,x) * u
    ]]></literal>
    <justification jstring="[hyper(7850,a,9799,a),flip(a)].">
      <j1 rule="hyper" parents="7850 9799"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9826">
    <literal><![CDATA[
      K(x,y) * (K(z,x) * u) = K(z,x) * (K(x,y) * u)
    ]]></literal>
    <justification jstring="[para(4(a,1),9824(a,1,2,2))].">
      <j1 rule="para" parents="4 9824"/>
    </justification>
  </clause>

  <clause id="9827">
    <literal><![CDATA[
      K(x,y) * (K(z,x) * (K(y,x) * u)) = K(z,x) * u
    ]]></literal>
    <justification jstring="[para(5130(a,1),9824(a,1,2,2))].">
      <j1 rule="para" parents="5130 9824"/>
    </justification>
  </clause>

  <clause id="9828">
    <literal><![CDATA[
      T(x,y) \ (T(x,z) * u) = K(x,z) * (K(y,x) * u)
    ]]></literal>
    <justification jstring="[hyper(320,a,5233,a,b,9826,a)].">
      <j1 rule="hyper" parents="320 5233 9826"/>
    </justification>
  </clause>

  <clause id="9829">
    <literal><![CDATA[
      K(x,y) * (K(x * y,x) * z) = a(x,y,x) * z
    ]]></literal>
    <justification jstring="[hyper(320,a,9523,a(flip),b,9826,a),flip(a)].">
      <j1 rule="hyper" parents="320 9523 9826"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9830">
    <literal><![CDATA[
      K(x,y) * (K(y,z) * (K(y,x) * u)) = K(y,z) * u
    ]]></literal>
    <justification jstring="[para(5133(a,1),9826(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5133 9826"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9831">
    <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(6613(a,1),9826(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6613 9826"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9832">
    <literal><![CDATA[
      a(x,y,x) * (K(x,x * y) * z) = K(x,y) * z
    ]]></literal>
    <justification jstring="[para(5133(a,1),9829(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5133 9829"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9833">
    <literal><![CDATA[
      a(x,x \ y,x) * (K(x,y) * z) = K(x,x \ y) * z
    ]]></literal>
    <justification jstring="[para(5(a,1),9832(a,1,2,1,2))].">
      <j1 rule="para" parents="5 9832"/>
    </justification>
  </clause>

  <clause id="9834">
    <literal><![CDATA[
      K(x,y) * (K(z,y) * u) = K(z,y) * (K(x,y) * u)
    ]]></literal>
    <justification jstring="[hyper(5147,a,9827,a)].">
      <j1 rule="hyper" parents="5147 9827"/>
    </justification>
  </clause>

  <clause id="9835">
    <literal><![CDATA[
      K(x,y) * (K(x,z) * u) = K(x,z) * (K(x,y) * u)
    ]]></literal>
    <justification jstring="[hyper(5147,a,9830,a)].">
      <j1 rule="hyper" parents="5147 9830"/>
    </justification>
  </clause>

  <clause id="9836">
    <literal><![CDATA[
      K(x,y) * (K(y,T(x,z)) * u) = K(y,K(x,z)) * u
    ]]></literal>
    <justification jstring="[para(8520(a,1),9830(a,1,2))].">
      <j1 rule="para" parents="8520 9830"/>
    </justification>
  </clause>

  <clause id="9837">
    <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(9834(a,1),1637(a,1,1,1,1))].">
      <j1 rule="para" parents="9834 1637"/>
    </justification>
  </clause>

  <clause id="9838">
    <literal><![CDATA[
      K(x,y) * (K(x,K(y,z)) * u) = K(x,T(y,z)) * u
    ]]></literal>
    <justification jstring="[hyper(9161,a,9835,a),flip(a)].">
      <j1 rule="hyper" parents="9161 9835"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9839">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(z,u) * w) = K(z,u) * (K(z,K(x,y)) * w)
    ]]></literal>
    <justification jstring="[para(7784(a,2),9835(a,1,1))].">
      <j1 rule="para" parents="7784 9835"/>
    </justification>
  </clause>

  <clause id="9840">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(z,u) * w) = K(z,u) * (K(x,K(y,z)) * w)
    ]]></literal>
    <justification jstring="[para(7784(a,2),9839(a,2,2,1))].">
      <j1 rule="para" parents="7784 9839"/>
    </justification>
  </clause>

  <clause id="9841">
    <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,9840,a),flip(a)].">
      <j1 rule="hyper" parents="342 9840"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9842">
    <literal><![CDATA[
      K(x,y) * (K(z,K(x,u)) * (K(x,y) \ w)) = K(u,K(z,x)) * w
    ]]></literal>
    <justification jstring="[para(7784(a,2),9841(a,1,2,1))].">
      <j1 rule="para" parents="7784 9841"/>
    </justification>
  </clause>

  <clause id="9843">
    <literal><![CDATA[
      (x / y) / ((x / y) / (1 / y)) = (1 / y) * K((y \ x) * y,1 / y)
    ]]></literal>
    <justification jstring="[para(5864(a,1),9804(a,2,2))].">
      <j1 rule="para" parents="5864 9804"/>
    </justification>
  </clause>

  <clause id="9844">
    <literal><![CDATA[
      (x / y) / ((x / y) / (1 / y)) = (1 / y) * K(x,1 / y)
    ]]></literal>
    <justification jstring="[para(5874(a,1),9843(a,2,2))].">
      <j1 rule="para" parents="5874 9843"/>
    </justification>
  </clause>

  <clause id="9845">
    <literal><![CDATA[
      (x / y) / ((x / y) / (1 / y)) = K(x,1 / y) / y
    ]]></literal>
    <justification jstring="[hyper(320,a,2356,a(flip),b,9844,a),flip(a)].">
      <j1 rule="hyper" parents="320 2356 9844"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9846">
    <literal><![CDATA[
      x / ((y / (x \ y)) / (1 / (x \ y))) = K(y,1 / (x \ y)) / (x \ y)
    ]]></literal>
    <justification jstring="[para(72(a,1),9845(a,1,1))].">
      <j1 rule="para" parents="72 9845"/>
    </justification>
  </clause>

  <clause id="9847">
    <literal><![CDATA[
      K(x,1 / (y \ x)) / (y \ x) = y / (y / (1 / (y \ x)))
    ]]></literal>
    <justification jstring="[para(72(a,1),9846(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="72 9846"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9849">
    <literal><![CDATA[
      K(x,y / x) / (y \ x) = y / (y / (1 / (y \ x)))
    ]]></literal>
    <justification jstring="[para(5219(a,1),9847(a,1,1))].">
      <j1 rule="para" parents="5219 9847"/>
    </justification>
  </clause>

  <clause id="9850">
    <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(9849(a,2),2069(a,1,2))].">
      <j1 rule="para" parents="9849 2069"/>
    </justification>
  </clause>

  <clause id="9851">
    <literal><![CDATA[
      (x / y) \ (L(y,z,u) * (y \ x)) = x \ ((L(y,z,u) * (y \ x)) * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,7483,a(flip),b,9812,a)].">
      <j1 rule="hyper" parents="58 7483 9812"/>
    </justification>
  </clause>

  <clause id="9852">
    <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,7464,a(flip),b,9816,a),flip(a)].">
      <j1 rule="hyper" parents="320 7464 9816"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9853">
    <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(6613(a,1),9831(a,1,1))].">
      <j1 rule="para" parents="6613 9831"/>
    </justification>
  </clause>

  <clause id="9854">
    <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(7187(a,2),9852(a,2,2))].">
      <j1 rule="para" parents="7187 9852"/>
    </justification>
  </clause>

  <clause id="9855">
    <literal><![CDATA[
      K(x,y) * (K(z,u) * (K(y,x) * z)) = T(z,T(u,K(x,y)))
    ]]></literal>
    <justification jstring="[hyper(8122,a,9854,a),flip(a)].">
      <j1 rule="hyper" parents="8122 9854"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9856">
    <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(5133(a,1),9855(a,1,2,2))].">
      <j1 rule="para" parents="5133 9855"/>
    </justification>
  </clause>

  <clause id="9857">
    <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(8024(a,1),9856(a,1,2))].">
      <j1 rule="para" parents="8024 9856"/>
    </justification>
  </clause>

  <clause id="9858">
    <literal><![CDATA[
      K((x \ y) \ z,L(x,u,w)) = K(y \ (x * z),L(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(5795,a,7472,a),flip(a)].">
      <j1 rule="hyper" parents="5795 7472"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9859">
    <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(7472(a,1),5795(a,1))].">
      <j1 rule="para" parents="7472 5795"/>
    </justification>
  </clause>

  <clause id="9860">
    <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,7362,a(flip),b,7577,a)].">
      <j1 rule="hyper" parents="58 7362 7577"/>
    </justification>
  </clause>

  <clause id="9862">
    <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,5378,a(flip),b,9860,a),flip(a)].">
      <j1 rule="hyper" parents="58 5378 9860"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9863">
    <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(7909(a,1),9862(a,1,2))].">
      <j1 rule="para" parents="7909 9862"/>
    </justification>
  </clause>

  <clause id="9864">
    <literal><![CDATA[
      K((x * y) \ z,L(y,u,w)) = K(x \ (y \ z),L(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(5795,a,7599,a),flip(a)].">
      <j1 rule="hyper" parents="5795 7599"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9865">
    <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,5523,a(flip),b,7635,a),flip(a)].">
      <j1 rule="hyper" parents="320 5523 7635"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9866">
    <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,5524,a(flip),b,7636,a),flip(a)].">
      <j1 rule="hyper" parents="320 5524 7636"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9867">
    <literal><![CDATA[
      K(x * y,R(y,z,u)) = K(y * x,R(y,z,u))
    ]]></literal>
    <justification jstring="[para(4847(a,1),9866(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4847 9866"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9868">
    <literal><![CDATA[
      R(x,K(y,z),u * K(z,y)) * u = (x * K(y,z)) * (K(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(7842(a,1),8345(a,1,1,3))].">
      <j1 rule="para" parents="7842 8345"/>
    </justification>
  </clause>

  <clause id="9869">
    <literal><![CDATA[
      R(x,K(y,z),u * K(z,y)) * u = (x * K(y,z)) * (K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(5130(a,1),9868(a,2,2))].">
      <j1 rule="para" parents="5130 9868"/>
    </justification>
  </clause>

  <clause id="9870">
    <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,6592,a(flip),b,8496,a)].">
      <j1 rule="hyper" parents="58 6592 8496"/>
    </justification>
  </clause>

  <clause id="9871">
    <literal><![CDATA[
      K(x,(y * (z * (u / x))) \ w) = K(x,(y * (z * u)) \ (w * x))
    ]]></literal>
    <justification jstring="[hyper(58,a,9499,a(flip),b,8725,a),flip(a)].">
      <j1 rule="hyper" parents="58 9499 8725"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9872">
    <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(7831,a,9077,a)].">
      <j1 rule="hyper" parents="7831 9077"/>
    </justification>
  </clause>

  <clause id="9873">
    <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(8097(a,1),9106(a,1,1))].">
      <j1 rule="para" parents="8097 9106"/>
    </justification>
  </clause>

  <clause id="9874">
    <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(1311(a,1),9468(a,1,2,1))].">
      <j1 rule="para" parents="1311 9468"/>
    </justification>
  </clause>

  <clause id="9875">
    <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(7417(a,1),9590(a,1,1,2))].">
      <j1 rule="para" parents="7417 9590"/>
    </justification>
  </clause>

  <clause id="9876">
    <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,5378,a(flip),b,9875,a),flip(a)].">
      <j1 rule="hyper" parents="58 5378 9875"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9878">
    <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,9620,a),flip(a)].">
      <j1 rule="hyper" parents="320 153 9620"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9879">
    <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,4744,a,b,9878,a),flip(a)].">
      <j1 rule="hyper" parents="320 4744 9878"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9881">
    <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,7779,a,b,9879,a),flip(a)].">
      <j1 rule="hyper" parents="320 7779 9879"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9882">
    <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),9754(a,2,2,1,1))].">
      <j1 rule="para" parents="4 9754"/>
    </justification>
  </clause>

  <clause id="9883">
    <literal><![CDATA[
      ((x * y) * (K(y,x) * z)) / ((x * y) * z) = L(K(y,x),z,x * y)
    ]]></literal>
    <justification jstring="[hyper(131,a,9882,a)].">
      <j1 rule="hyper" parents="131 9882"/>
    </justification>
  </clause>

  <clause id="9884">
    <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(9882(a,1),327(a,1,1)),flip(b)].">
      <j1 rule="para" parents="9882 327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9886">
    <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),9883(a,1,2))].">
      <j1 rule="para" parents="105 9883"/>
    </justification>
  </clause>

  <clause id="9887">
    <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(8776(a,2),9886(a,1,1))].">
      <j1 rule="para" parents="8776 9886"/>
    </justification>
  </clause>

  <clause id="9888">
    <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(9740(a,2),9884(a,1))].">
      <j1 rule="para" parents="9740 9884"/>
    </justification>
  </clause>

  <clause id="9889">
    <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(9872(a,1),7831(a,1))].">
      <j1 rule="para" parents="9872 7831"/>
    </justification>
  </clause>

  <clause id="9890">
    <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(7955(a,1),9873(a,1,1,2,1))].">
      <j1 rule="para" parents="7955 9873"/>
    </justification>
  </clause>

  <clause id="9891">
    <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),9874(a,1,2,2))].">
      <j1 rule="para" parents="172 9874"/>
    </justification>
  </clause>

  <clause id="9892">
    <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(9887(a,1),518(a,1))].">
      <j1 rule="para" parents="9887 518"/>
    </justification>
  </clause>

  <clause id="9893">
    <literal><![CDATA[
      ((x \ y) \ y) * (y / T(T(x,x \ y),y)) = x \ (y * ((x \ y) \ y))
    ]]></literal>
    <justification jstring="[hyper(320,a,1956,a(flip),b,4698,a),flip(a)].">
      <j1 rule="hyper" parents="320 1956 4698"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9894">
    <literal><![CDATA[
      ((x \ y) \ y) * (T(x,y) \ y) = x \ (y * ((x \ y) \ y))
    ]]></literal>
    <justification jstring="[para(7670(a,1),9893(a,1,2))].">
      <j1 rule="para" parents="7670 9893"/>
    </justification>
  </clause>

  <clause id="9895">
    <literal><![CDATA[
      ((x \ y) \ y) * (T(x,y) \ y) = x * (y / T(x,y))
    ]]></literal>
    <justification jstring="[hyper(320,a,4445,a(flip),b,9894,a),flip(a)].">
      <j1 rule="hyper" parents="320 4445 9894"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9896">
    <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(9895(a,1),718(a,1,2))].">
      <j1 rule="para" parents="9895 718"/>
    </justification>
  </clause>

  <clause id="9897">
    <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(5616(a,1),4980(a,1,2,1))].">
      <j1 rule="para" parents="5616 4980"/>
    </justification>
  </clause>

  <clause id="9898">
    <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(8444,a,9897,a)].">
      <j1 rule="hyper" parents="8444 9897"/>
    </justification>
  </clause>

  <clause id="9899">
    <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(7158(a,2),9898(a,1,2,1))].">
      <j1 rule="para" parents="7158 9898"/>
    </justification>
  </clause>

  <clause id="9900">
    <literal><![CDATA[
      L(L(x,y,K(z,u)),K(z,u) * y,K(u,z)) = y \ (y * x)
    ]]></literal>
    <justification jstring="[para(5133(a,1),5165(a,2,2))].">
      <j1 rule="para" parents="5133 5165"/>
    </justification>
  </clause>

  <clause id="9901">
    <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(9900(a,2),287(a,1))].">
      <j1 rule="para" parents="9900 287"/>
    </justification>
  </clause>

  <clause id="9903">
    <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),5239(a,1,2)),flip(a)].">
      <j1 rule="para" parents="238 5239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9904">
    <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(4969(a,1),9903(a,1,1,2,1))].">
      <j1 rule="para" parents="4969 9903"/>
    </justification>
  </clause>

  <clause id="9905">
    <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),5240(a,1,2)),flip(a)].">
      <j1 rule="para" parents="237 5240"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9906">
    <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(4969(a,1),9905(a,1,1,2,1))].">
      <j1 rule="para" parents="4969 9905"/>
    </justification>
  </clause>

  <clause id="9907">
    <literal><![CDATA[
      K(x,y) * (L(K(y,x),z,u) * w) = a(u,z,K(x,y)) * w
    ]]></literal>
    <justification jstring="[para(5892(a,1),9906(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5892 9906"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9908">
    <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,9853,a,b,9907,a)].">
      <j1 rule="hyper" parents="58 9853 9907"/>
    </justification>
  </clause>

  <clause id="9909">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (L(K(z,u),y,x) * w) = K(z,u) * w
    ]]></literal>
    <justification jstring="[para(5891(a,1),9907(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5891 9907"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9910">
    <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,5133,a(flip),b,9909,a),flip(a)].">
      <j1 rule="hyper" parents="116 5133 9909"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9911">
    <literal><![CDATA[
      a(x,y,K(z,u)) \ w = a(x,y,K(u,z)) * w
    ]]></literal>
    <justification jstring="[hyper(58,a,9908,a(flip),b,9910,a),flip(a)].">
      <j1 rule="hyper" parents="58 9908 9910"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9912">
    <literal><![CDATA[
      x / (a(y,z,K(u,w)) * x) = a(y,z,K(w,u))
    ]]></literal>
    <justification jstring="[hyper(575,a,9911,a)].">
      <j1 rule="hyper" parents="575 9911"/>
    </justification>
  </clause>

  <clause id="9913">
    <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,7406,a,b,9911,a),flip(a)].">
      <j1 rule="hyper" parents="320 7406 9911"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9914">
    <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,6843,a(flip),b,9911,a)].">
      <j1 rule="hyper" parents="119 6843 9911"/>
    </justification>
  </clause>

  <clause id="9915">
    <literal><![CDATA[
      a(x,y,K(z,u)) * w != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,K(u,z)) * v5 = w
    ]]></literal>
    <justification jstring="[para(9911(a,1),134(a,1))].">
      <j1 rule="para" parents="9911 134"/>
    </justification>
  </clause>

  <clause id="9916">
    <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(9913(a,2),38(a,1))].">
      <j1 rule="para" parents="9913 38"/>
    </justification>
  </clause>

  <clause id="9917">
    <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(5817(a,1),5722(a,1,2,2,1,2))].">
      <j1 rule="para" parents="5817 5722"/>
    </justification>
  </clause>

  <clause id="9918">
    <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(3567(a,1),5789(a,1,1))].">
      <j1 rule="para" parents="3567 5789"/>
    </justification>
  </clause>

  <clause id="9919">
    <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(3999(a,1),9918(a,1,1,1))].">
      <j1 rule="para" parents="3999 9918"/>
    </justification>
  </clause>

  <clause id="9920">
    <literal><![CDATA[
      (T(x * (y \ 1),x) / x) / (y \ 1) = y * (T(x * (y \ 1),x) / x)
    ]]></literal>
    <justification jstring="[para(5421(a,1),5909(a,1,1,1))].">
      <j1 rule="para" parents="5421 5909"/>
    </justification>
  </clause>

  <clause id="9921">
    <literal><![CDATA[
      (x \ R(x,y \ 1,x)) / (T(x * (y \ 1),x) / x) = y
    ]]></literal>
    <justification jstring="[hyper(117,a,8734,a(flip),b,9920,a(flip))].">
      <j1 rule="hyper" parents="117 8734 9920"/>
    </justification>
  </clause>

  <clause id="9922">
    <literal><![CDATA[
      x * T(K(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      w * T(K(z,y),u) = x
    ]]></literal>
    <justification jstring="[para(8931(a,1),6851(a,1)),flip(a)].">
      <j1 rule="para" parents="8931 6851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9923">
    <literal><![CDATA[
      K(x,y * (((z * K(u,z)) * u) * w)) = K(x,y * ((u * (1 / (1 / z))) * w))
    ]]></literal>
    <justification jstring="[para(5270(a,1),6853(a,1,2,2,1,1))].">
      <j1 rule="para" parents="5270 6853"/>
    </justification>
  </clause>

  <clause id="9924">
    <literal><![CDATA[
      K(x,y * ((z * (1 / (1 / u))) * w)) = K(x,y * ((z * u) * w))
    ]]></literal>
    <justification jstring="[para(4774(a,1),9923(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="4774 9923"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9925">
    <literal><![CDATA[
      ((x \ y) \ y) \ R((x \ y) \ y,z,u) = x \ (y \ ((R(x,z,u) * (x \ y)) * x))
    ]]></literal>
    <justification jstring="[hyper(1185,a,6870,a)].">
      <j1 rule="hyper" parents="1185 6870"/>
    </justification>
  </clause>

  <clause id="9926">
    <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(7888(a,1),7934(a,1,2,2,1))].">
      <j1 rule="para" parents="7888 7934"/>
    </justification>
  </clause>

  <clause id="9928">
    <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,8300,a(flip),b,8302,a),flip(a)].">
      <j1 rule="hyper" parents="58 8300 8302"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9929">
    <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),9928(a,1,2,1))].">
      <j1 rule="para" parents="460 9928"/>
    </justification>
  </clause>

  <clause id="9930">
    <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,8006,a(flip),b,9929,a)].">
      <j1 rule="hyper" parents="58 8006 9929"/>
    </justification>
  </clause>

  <clause id="9931">
    <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(7158(a,2),9930(a,1,2,1,2))].">
      <j1 rule="para" parents="7158 9930"/>
    </justification>
  </clause>

  <clause id="9932">
    <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,3786,a(flip),b,8325,a)].">
      <j1 rule="hyper" parents="58 3786 8325"/>
    </justification>
  </clause>

  <clause id="9933">
    <literal><![CDATA[
      T(x,y / (((z \ 1) \ 1) \ u)) = T(x,y / (z \ u))
    ]]></literal>
    <justification jstring="[hyper(8442,a,9932,a),flip(a)].">
      <j1 rule="hyper" parents="8442 9932"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9934">
    <literal><![CDATA[
      K(x,((y \ z) \ u) \ y) * K(x,K(y,z \ u)) = K(x,y / ((y \ z) \ u))
    ]]></literal>
    <justification jstring="[para(9306(a,1),8384(a,1,2))].">
      <j1 rule="para" parents="9306 8384"/>
    </justification>
  </clause>

  <clause id="9935">
    <literal><![CDATA[
      K(x,K(y,z \ u)) * K(x,y \ ((y \ z) \ u)) = K(x,((y \ z) \ u) / y)
    ]]></literal>
    <justification jstring="[para(9306(a,1),8391(a,1,1))].">
      <j1 rule="para" parents="9306 8391"/>
    </justification>
  </clause>

  <clause id="9936">
    <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,8549,a),flip(a)].">
      <j1 rule="hyper" parents="120 8549"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9937">
    <literal><![CDATA[
      T((x \ 1) * y,K(z,T(u,x \ y))) = T((x \ 1) * y,K(z,u))
    ]]></literal>
    <justification jstring="[para(3780(a,1),9936(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3780 9936"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9938">
    <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(5977,a,9937,a)].">
      <j1 rule="hyper" parents="5977 9937"/>
    </justification>
  </clause>

  <clause id="9939">
    <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,8691,a(flip),b,8692,a),flip(a)].">
      <j1 rule="hyper" parents="320 8691 8692"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9941">
    <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),9939(a,1,1,2,1,2,1))].">
      <j1 rule="para" parents="72 9939"/>
    </justification>
  </clause>

  <clause id="9943">
    <literal><![CDATA[
      K(T(x,(y \ 1) \ (y \ z)),y \ 1) = K(T(x,z),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,7680,a(flip),b,9941,a)].">
      <j1 rule="hyper" parents="58 7680 9941"/>
    </justification>
  </clause>

  <clause id="9944">
    <literal><![CDATA[
      K(T(x,y \ z),y \ 1) = K(T(x,z),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(8260,a,9943,a)].">
      <j1 rule="hyper" parents="8260 9943"/>
    </justification>
  </clause>

  <clause id="9945">
    <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,7327,a(flip),b,8747,a),flip(a)].">
      <j1 rule="hyper" parents="320 7327 8747"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9947">
    <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(5687(a,1),8838(a,1,1,2))].">
      <j1 rule="para" parents="5687 8838"/>
    </justification>
  </clause>

  <clause id="9948">
    <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(4618,a,9947,a),flip(a)].">
      <j1 rule="hyper" parents="4618 9947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9949">
    <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(5889(a,1),9948(a,1,1))].">
      <j1 rule="para" parents="5889 9948"/>
    </justification>
  </clause>

  <clause id="9950">
    <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,5889,a(flip),b,9949,a),flip(a)].">
      <j1 rule="hyper" parents="320 5889 9949"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9951">
    <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,9950,a),flip(a)].">
      <j1 rule="hyper" parents="320 236 9950"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9952">
    <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,8278,a(flip),b,8900,a)].">
      <j1 rule="hyper" parents="58 8278 8900"/>
    </justification>
  </clause>

  <clause id="9953">
    <literal><![CDATA[
      K(x,L(y,z * K(y,u),w)) = K(x,L(y,z,w))
    ]]></literal>
    <justification jstring="[hyper(320,a,8839,a(flip),b,8920,a),flip(a)].">
      <j1 rule="hyper" parents="320 8839 8920"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9954">
    <literal><![CDATA[
      K(x,L(y,K(y,z) * u,w)) = K(x,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(7179(a,1),9953(a,1,2,2))].">
      <j1 rule="para" parents="7179 9953"/>
    </justification>
  </clause>

  <clause id="9955">
    <literal><![CDATA[
      L(K(x,y),T(y,z) * u,w) = K(x,L(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,9027,a,b,9954,a)].">
      <j1 rule="hyper" parents="58 9027 9954"/>
    </justification>
  </clause>

  <clause id="9957">
    <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(8909(a,1),9955(a,1,1))].">
      <j1 rule="para" parents="8909 9955"/>
    </justification>
  </clause>

  <clause id="9958">
    <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),9117(a,2,1))].">
      <j1 rule="para" parents="238 9117"/>
    </justification>
  </clause>

  <clause id="9959">
    <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,9060,a(flip),b,9958,a),flip(a)].">
      <j1 rule="hyper" parents="58 9060 9958"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9960">
    <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(1656(a,1),9180(a,1,2))].">
      <j1 rule="para" parents="1656 9180"/>
    </justification>
  </clause>

  <clause id="9961">
    <literal><![CDATA[
      x \ R(x,y,L(x,z,u)) = a(x,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(691,a,9960,a),flip(a)].">
      <j1 rule="hyper" parents="691 9960"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9962">
    <literal><![CDATA[
      K(x * L(y,z,u),y) * K(y,x) = a(y,x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(9181,a,9961,a)].">
      <j1 rule="hyper" parents="9181 9961"/>
    </justification>
  </clause>

  <clause id="9963">
    <literal><![CDATA[
      K(x,y) * K(y * L(x,z,u),x) = a(x,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(8748,a,9961,a)].">
      <j1 rule="hyper" parents="8748 9961"/>
    </justification>
  </clause>

  <clause id="9964">
    <literal><![CDATA[
      K(x,y) * a(y,x,L(y,z,u)) = K(x * L(y,z,u),y)
    ]]></literal>
    <justification jstring="[para(9961(a,1),9179(a,1,2))].">
      <j1 rule="para" parents="9961 9179"/>
    </justification>
  </clause>

  <clause id="9965">
    <literal><![CDATA[
      K(L(x,y,z) * u,x) * K(x,u) = a(x,u,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(7430(a,2),9962(a,1,1))].">
      <j1 rule="para" parents="7430 9962"/>
    </justification>
  </clause>

  <clause id="9966">
    <literal><![CDATA[
      K(x,y) * K(y,x * L(y,z,u)) = a(y,x,L(y,z,u)) \ 1
    ]]></literal>
    <justification jstring="[para(9963(a,1),9015(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9963 9015"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9967">
    <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(9964(a,1),38(a,1))].">
      <j1 rule="para" parents="9964 38"/>
    </justification>
  </clause>

  <clause id="9968">
    <literal><![CDATA[
      L(x,y,L(x,z,u)) \ x = a(x,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,9508,a(flip),b,9965,a)].">
      <j1 rule="hyper" parents="58 9508 9965"/>
    </justification>
  </clause>

  <clause id="9969">
    <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(9968(a,1),6829(a,1,1,1))].">
      <j1 rule="para" parents="9968 6829"/>
    </justification>
  </clause>

  <clause id="9970">
    <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(1893(a,1),9182(a,1,2))].">
      <j1 rule="para" parents="1893 9182"/>
    </justification>
  </clause>

  <clause id="9971">
    <literal><![CDATA[
      x * a(x,y,R(x,z,u)) = R(x,y,R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(694,a,9970,a)].">
      <j1 rule="hyper" parents="694 9970"/>
    </justification>
  </clause>

  <clause id="9972">
    <literal><![CDATA[
      x \ R(x,y,R(x,z,u)) = a(x,y,R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(691,a,9970,a),flip(a)].">
      <j1 rule="hyper" parents="691 9970"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9973">
    <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(9970(a,1),691(a,1))].">
      <j1 rule="para" parents="9970 691"/>
    </justification>
  </clause>

  <clause id="9974">
    <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,9863,a,b,9971,a)].">
      <j1 rule="hyper" parents="116 9863 9971"/>
    </justification>
  </clause>

  <clause id="9975">
    <literal><![CDATA[
      K(x * R(y,z,u),y) * K(y,x) = a(y,x,R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(9183,a,9972,a)].">
      <j1 rule="hyper" parents="9183 9972"/>
    </justification>
  </clause>

  <clause id="9976">
    <literal><![CDATA[
      R(x,y,R(x,z,u)) \ x = a(x,y,R(x,z,u)) \ 1
    ]]></literal>
    <justification jstring="[para(9972(a,1),6760(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9972 6760"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9977">
    <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(9972(a,1),9116(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9972 9116"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9978">
    <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(4665(a,1),9976(a,2,1))].">
      <j1 rule="para" parents="4665 9976"/>
    </justification>
  </clause>

  <clause id="9979">
    <literal><![CDATA[
      a(x,y,R(x,z,u)) * K(x,y * R(x,z,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(9975(a,1),6341(a,1,1))].">
      <j1 rule="para" parents="9975 6341"/>
    </justification>
  </clause>

  <clause id="9980">
    <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(7434(a,1),9975(a,1,1))].">
      <j1 rule="para" parents="7434 9975"/>
    </justification>
  </clause>

  <clause id="9981">
    <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(9975(a,1),8601(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9975 8601"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9982">
    <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),9979(a,1,2,2))].">
      <j1 rule="para" parents="7 9979"/>
    </justification>
  </clause>

  <clause id="9983">
    <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(5224,a,9977,a)].">
      <j1 rule="hyper" parents="5224 9977"/>
    </justification>
  </clause>

  <clause id="9984">
    <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(5082,a,9977,a)].">
      <j1 rule="hyper" parents="5082 9977"/>
    </justification>
  </clause>

  <clause id="9985">
    <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(9984(a,1),287(a,1,2)),flip(b)].">
      <j1 rule="para" parents="9984 287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9986">
    <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(877(a,1),9985(a,1))].">
      <j1 rule="para" parents="877 9985"/>
    </justification>
  </clause>

  <clause id="9987">
    <literal><![CDATA[
      ((1 / x) * T((1 / x) \ K(y,z),y)) * u = K(y,z) * (K(x,y) * u)
    ]]></literal>
    <justification jstring="[hyper(1597,a,9470,a)].">
      <j1 rule="hyper" parents="1597 9470"/>
    </justification>
  </clause>

  <clause id="9988">
    <literal><![CDATA[
      (K(x,y) * K((1 / z) \ 1,x)) * u = K(x,y) * (K(z,x) * u)
    ]]></literal>
    <justification jstring="[para(8288(a,2),9987(a,1,1))].">
      <j1 rule="para" parents="8288 9987"/>
    </justification>
  </clause>

  <clause id="9989">
    <literal><![CDATA[
      (K(x,y) * K(z,x)) * u = K(x,y) * (K(z,x) * u)
    ]]></literal>
    <justification jstring="[para(75(a,1),9988(a,1,1,2,1))].">
      <j1 rule="para" parents="75 9988"/>
    </justification>
  </clause>

  <clause id="9990">
    <literal><![CDATA[
      L(x,K(y,z),K(z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(479,a,9989,a)].">
      <j1 rule="hyper" parents="479 9989"/>
    </justification>
  </clause>

  <clause id="9991">
    <literal><![CDATA[
      (K(x,y) * K(z,x)) * u = K(z,x) * (K(x,y) * u)
    ]]></literal>
    <justification jstring="[hyper(320,a,9826,a(flip),b,9989,a),flip(a)].">
      <j1 rule="hyper" parents="320 9826 9989"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9992">
    <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(9989(a,1),288(a,1,2))].">
      <j1 rule="para" parents="9989 288"/>
    </justification>
  </clause>

  <clause id="9994">
    <literal><![CDATA[
      (K(x,y) * K(y,z)) * u = K(y,z) * (K(x,y) * u)
    ]]></literal>
    <justification jstring="[para(2003(a,1),9989(a,1,1))].">
      <j1 rule="para" parents="2003 9989"/>
    </justification>
  </clause>

  <clause id="9995">
    <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(9989(a,1),6931(a,1,2))].">
      <j1 rule="para" parents="9989 6931"/>
    </justification>
  </clause>

  <clause id="9998">
    <literal><![CDATA[
      (K(x,y) * K(z,x)) \ u = K(x,z) * (K(y,x) * u)
    ]]></literal>
    <justification jstring="[hyper(58,a,5766,a(flip),b,9990,a)].">
      <j1 rule="hyper" parents="58 5766 9990"/>
    </justification>
  </clause>

  <clause id="10000">
    <literal><![CDATA[
      L(x,K(y,T(z,u)),K(z,w)) = x
    ]]></literal>
    <justification jstring="[para(7160(a,1),9990(a,1,2))].">
      <j1 rule="para" parents="7160 9990"/>
    </justification>
  </clause>

  <clause id="10001">
    <literal><![CDATA[
      (K(x,y) * K(z,T(x,u))) * w = K(x,y) * (K(z,T(x,u)) * w)
    ]]></literal>
    <justification jstring="[hyper(1338,a,10000,a),flip(a)].">
      <j1 rule="hyper" parents="1338 10000"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10002">
    <literal><![CDATA[
      (K(x,y) * K(y,z)) * u = K(x,y) * (K(y,z) * u)
    ]]></literal>
    <justification jstring="[para(2003(a,1),9991(a,1,1))].">
      <j1 rule="para" parents="2003 9991"/>
    </justification>
  </clause>

  <clause id="10003">
    <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(4766,a,9994,a),flip(a)].">
      <j1 rule="hyper" parents="4766 9994"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10004">
    <literal><![CDATA[
      (K(x,y) * z) / (K(u,y) * z) = K(x,y) * K(y,u)
    ]]></literal>
    <justification jstring="[hyper(117,a,9827,a(flip),b,9994,a)].">
      <j1 rule="hyper" parents="117 9827 9994"/>
    </justification>
  </clause>

  <clause id="10005">
    <literal><![CDATA[
      (K(x,y) * K(y,z)) \ u = K(y,x) * (K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(2003(a,1),9998(a,1,1))].">
      <j1 rule="para" parents="2003 9998"/>
    </justification>
  </clause>

  <clause id="10006">
    <literal><![CDATA[
      R(K(x,y),K(y,z),u) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(3476,a,10002,a)].">
      <j1 rule="hyper" parents="3476 10002"/>
    </justification>
  </clause>

  <clause id="10007">
    <literal><![CDATA[
      L(x,K(y,z),K(u,y)) = x
    ]]></literal>
    <justification jstring="[hyper(479,a,10002,a)].">
      <j1 rule="hyper" parents="479 10002"/>
    </justification>
  </clause>

  <clause id="10008">
    <literal><![CDATA[
      (K(x,y) * z) / (K(x,u) * z) = K(u,x) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(117,a,9830,a(flip),b,10002,a)].">
      <j1 rule="hyper" parents="117 9830 10002"/>
    </justification>
  </clause>

  <clause id="10009">
    <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,10002,a(flip),b,4774,a)].">
      <j1 rule="hyper" parents="117 10002 4774"/>
    </justification>
  </clause>

  <clause id="10010">
    <literal><![CDATA[
      K(x,y) * (K(y,x * y) * z) = (y \ L(y,x,y)) * z
    ]]></literal>
    <justification jstring="[para(5501(a,1),10002(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5501 10002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10014">
    <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(10006(a,1),3603(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10006 3603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10015">
    <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(7897(a,1),10004(a,1,1))].">
      <j1 rule="para" parents="7897 10004"/>
    </justification>
  </clause>

  <clause id="10016">
    <literal><![CDATA[
      (K(x,T(y,z)) * K(y,u)) \ w = K(y,T(x,z)) * (K(u,y) * w)
    ]]></literal>
    <justification jstring="[para(7160(a,1),10005(a,1,1,1))].">
      <j1 rule="para" parents="7160 10005"/>
    </justification>
  </clause>

  <clause id="10017">
    <literal><![CDATA[
      x / (K(y \ x,z) * (y * (x / y))) = K(z,y \ x) * K(y \ x,y)
    ]]></literal>
    <justification jstring="[para(4717(a,1),10008(a,1,1))].">
      <j1 rule="para" parents="4717 10008"/>
    </justification>
  </clause>

  <clause id="10018">
    <literal><![CDATA[
      (x \ L(x,y,x)) * z = a(x,y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(58,a,9577,a(flip),b,10010,a),flip(a)].">
      <j1 rule="hyper" parents="58 9577 10010"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10019">
    <literal><![CDATA[
      (x \ L(x,y,x)) \ z = z * a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,9537,a(flip),b,10018,a)].">
      <j1 rule="hyper" parents="116 9537 10018"/>
    </justification>
  </clause>

  <clause id="10020">
    <literal><![CDATA[
      (R(x,y,x) \ x) * z = a(x,y,x) \ z
    ]]></literal>
    <justification jstring="[para(5775(a,2),10018(a,1,1))].">
      <j1 rule="para" parents="5775 10018"/>
    </justification>
  </clause>

  <clause id="10021">
    <literal><![CDATA[
      (x \ R(x,y,x)) \ z = (R(x,y,x) \ x) * z
    ]]></literal>
    <justification jstring="[para(8942(a,2),10020(a,2,1)),flip(a)].">
      <j1 rule="para" parents="8942 10020"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10022">
    <literal><![CDATA[
      (R(x,y,x) \ x) * (K(x * y,x) * z) = K(y,x) * z
    ]]></literal>
    <justification jstring="[hyper(58,a,9581,a(flip),b,10021,a),flip(a)].">
      <j1 rule="hyper" parents="58 9581 10021"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10023">
    <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(9779(a,1),9992(a,1))].">
      <j1 rule="para" parents="9779 9992"/>
    </justification>
  </clause>

  <clause id="10024">
    <literal><![CDATA[
      R(K(x,y),K(z,y),u) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(5150,a,9995,a),flip(a)].">
      <j1 rule="hyper" parents="5150 9995"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10026">
    <literal><![CDATA[
      (x * K(y,z)) / (x * K(u,z)) = K(y,T(z,x)) * K(T(z,x),u)
    ]]></literal>
    <justification jstring="[para(7897(a,1),10015(a,1,2))].">
      <j1 rule="para" parents="7897 10015"/>
    </justification>
  </clause>

  <clause id="10027">
    <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,7199,a(flip),b,10026,a),flip(a)].">
      <j1 rule="hyper" parents="320 7199 10026"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10028">
    <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),10017(a,1,2,2,2))].">
      <j1 rule="para" parents="215 10017"/>
    </justification>
  </clause>

  <clause id="10029">
    <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,9857,a(flip),b,10003,a)].">
      <j1 rule="hyper" parents="58 9857 10003"/>
    </justification>
  </clause>

  <clause id="10030">
    <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(4816(a,1),9819(a,2,2))].">
      <j1 rule="para" parents="4816 9819"/>
    </justification>
  </clause>

  <clause id="10031">
    <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(9876(a,1),9925(a,2,2,2,1,1))].">
      <j1 rule="para" parents="9876 9925"/>
    </justification>
  </clause>

  <clause id="10032">
    <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(9973,a,9974,a)].">
      <j1 rule="hyper" parents="9973 9974"/>
    </justification>
  </clause>

  <clause id="10033">
    <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(9863(a,1),9978(a,1,1))].">
      <j1 rule="para" parents="9863 9978"/>
    </justification>
  </clause>

  <clause id="10034">
    <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(9010,a,10009,a)].">
      <j1 rule="hyper" parents="9010 10009"/>
    </justification>
  </clause>

  <clause id="10035">
    <literal><![CDATA[
      T(x,R(x * K(y,x),z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(328,a,4507,a),flip(a)].">
      <j1 rule="hyper" parents="328 4507"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10037">
    <literal><![CDATA[
      T(x \ y,R(y / x,z,u)) = x \ y
    ]]></literal>
    <justification jstring="[para(4776(a,1),10035(a,1,2,1))].">
      <j1 rule="para" parents="4776 10035"/>
    </justification>
  </clause>

  <clause id="10038">
    <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(10037(a,1),7195(a,1,2))].">
      <j1 rule="para" parents="10037 7195"/>
    </justification>
  </clause>

  <clause id="10039">
    <literal><![CDATA[
      ((x * (y * ((x \ (z / u)) / y))) * u) / z = K(y,z / ((x * y) * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,6944,a(flip),b,5760,a),flip(a)].">
      <j1 rule="hyper" parents="58 6944 5760"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10040">
    <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(3610(a,1),5878(a,1,2,1,1))].">
      <j1 rule="para" parents="3610 5878"/>
    </justification>
  </clause>

  <clause id="10041">
    <literal><![CDATA[
      (x \ R(x,y,z)) * K(R(x,y,z),u) = x \ R(T(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(3317(a,1),10040(a,1,2))].">
      <j1 rule="para" parents="3317 10040"/>
    </justification>
  </clause>

  <clause id="10042">
    <literal><![CDATA[
      R(K(x,y),R(y,z,u),w) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(5933,a,6046,a)].">
      <j1 rule="hyper" parents="5933 6046"/>
    </justification>
  </clause>

  <clause id="10043">
    <literal><![CDATA[
      R(K(x,y),R(x,z,u),w) = (v5 * K(y,x)) \ v5
    ]]></literal>
    <justification jstring="[para(10042(a,1),6953(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="10042 6953"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10044">
    <literal><![CDATA[
      R(K(x,y),R(x,z,u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(10043(a,2),6345(a,1))].">
      <j1 rule="para" parents="10043 6345"/>
    </justification>
  </clause>

  <clause id="10045">
    <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(6945(a,1),10044(a,1))].">
      <j1 rule="para" parents="6945 10044"/>
    </justification>
  </clause>

  <clause id="10046">
    <literal><![CDATA[
      ((x * T(x \ (y / z),y / z)) * z) / y = K(x \ (y / z),(z / y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(5494,a,5937,a),flip(a)].">
      <j1 rule="hyper" parents="5494 5937"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10047">
    <literal><![CDATA[
      (x * (y * T(y \ (x \ z),z / y))) / z = K(x \ (z / y),(y / z) \ 1)
    ]]></literal>
    <justification jstring="[para(1576(a,1),10046(a,1,1))].">
      <j1 rule="para" parents="1576 10046"/>
    </justification>
  </clause>

  <clause id="10048">
    <literal><![CDATA[
      K(((x * y) / z) \ 1,z / y) = K(x \ (z / y),(y / z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,5530,a(flip),b,10047,a)].">
      <j1 rule="hyper" parents="58 5530 10047"/>
    </justification>
  </clause>

  <clause id="10049">
    <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(1764(a,2),6849(a,1,2))].">
      <j1 rule="para" parents="1764 6849"/>
    </justification>
  </clause>

  <clause id="10050">
    <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(7160(a,1),7991(a,2,1,2))].">
      <j1 rule="para" parents="7160 7991"/>
    </justification>
  </clause>

  <clause id="10051">
    <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(5141(a,1),8090(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5141 8090"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10052">
    <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(10051(a,2),7746(a,1))].">
      <j1 rule="para" parents="10051 7746"/>
    </justification>
  </clause>

  <clause id="10053">
    <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(8688(a,1),5026(a,1))].">
      <j1 rule="para" parents="8688 5026"/>
    </justification>
  </clause>

  <clause id="10054">
    <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(4233(a,1),8981(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4233 8981"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10055">
    <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(9990(a,1),8995(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9990 8995"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10056">
    <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(2003(a,1),10055(a,1,2,2))].">
      <j1 rule="para" parents="2003 10055"/>
    </justification>
  </clause>

  <clause id="10057">
    <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(10056(a,1),6387(a,1,1))].">
      <j1 rule="para" parents="10056 6387"/>
    </justification>
  </clause>

  <clause id="10058">
    <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(6454(a,1),10057(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6454 10057"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10059">
    <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),9035(a,1,1,2))].">
      <j1 rule="para" parents="22 9035"/>
    </justification>
  </clause>

  <clause id="10060">
    <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(7784(a,2),9158(a,1,2,1))].">
      <j1 rule="para" parents="7784 9158"/>
    </justification>
  </clause>

  <clause id="10061">
    <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(7158(a,2),9412(a,2,2,1))].">
      <j1 rule="para" parents="7158 9412"/>
    </justification>
  </clause>

  <clause id="10062">
    <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(5031,a,9464,a),flip(a)].">
      <j1 rule="hyper" parents="5031 9464"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10063">
    <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(9542(a,1),9548(a,1))].">
      <j1 rule="para" parents="9542 9548"/>
    </justification>
  </clause>

  <clause id="10064">
    <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(9612(a,2),8063(a,1))].">
      <j1 rule="para" parents="9612 8063"/>
    </justification>
  </clause>

  <clause id="10065">
    <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(7571(a,1),9670(a,1,1))].">
      <j1 rule="para" parents="7571 9670"/>
    </justification>
  </clause>

  <clause id="10067">
    <literal><![CDATA[
      K(x \ (y * (x * z)),T(y,x * z)) = L(K(y * z,T(y,x)),z,x)
    ]]></literal>
    <justification jstring="[para(9605(a,1),10065(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9605 10065"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10068">
    <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(10067(a,1),8330(a,1))].">
      <j1 rule="para" parents="10067 8330"/>
    </justification>
  </clause>

  <clause id="10069">
    <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(5888(a,2),10068(a,1,1))].">
      <j1 rule="para" parents="5888 10068"/>
    </justification>
  </clause>

  <clause id="10070">
    <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(7173(a,1),9980(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7173 9980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10071">
    <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,9975,a(flip),b,10070,a),flip(a)].">
      <j1 rule="hyper" parents="320 9975 10070"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10073">
    <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),10071(a,1,2)),flip(a)].">
      <j1 rule="para" parents="107 10071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10074">
    <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),10071(a,1,2,2))].">
      <j1 rule="para" parents="379 10071"/>
    </justification>
  </clause>

  <clause id="10075">
    <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(10073(a,1),9982(a,1,1))].">
      <j1 rule="para" parents="10073 9982"/>
    </justification>
  </clause>

  <clause id="10076">
    <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,7236,a(flip),b,10075,a),flip(a)].">
      <j1 rule="hyper" parents="320 7236 10075"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10077">
    <literal><![CDATA[
      x * (y * (z \ T(z * (y \ (z \ 1)),z))) = (x * K(y \ 1,z)) * (z \ 1)
    ]]></literal>
    <justification jstring="[hyper(286,a,10049,a)].">
      <j1 rule="hyper" parents="286 10049"/>
    </justification>
  </clause>

  <clause id="10078">
    <literal><![CDATA[
      (x * K(y \ 1,z)) * (z \ 1) = x * (K(y \ 1,z) * (z \ 1))
    ]]></literal>
    <justification jstring="[para(5719(a,1),10077(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5719 10077"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10079">
    <literal><![CDATA[
      (x * K(y \ 1,z)) * (z \ 1) = x * (T(z,y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(5131(a,1),10078(a,2,2))].">
      <j1 rule="para" parents="5131 10078"/>
    </justification>
  </clause>

  <clause id="10080">
    <literal><![CDATA[
      (x * K(y,z)) * (z \ 1) = x * (T(z,(1 / y) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(75(a,1),10079(a,1,1,2,1))].">
      <j1 rule="para" parents="75 10079"/>
    </justification>
  </clause>

  <clause id="10081">
    <literal><![CDATA[
      (x * K(y,z)) * (z \ 1) = x * (T(z,y) \ 1)
    ]]></literal>
    <justification jstring="[para(75(a,1),10080(a,2,2,1,2))].">
      <j1 rule="para" parents="75 10080"/>
    </justification>
  </clause>

  <clause id="10082">
    <literal><![CDATA[
      x \ T(x * (y \ 1),y) = T(y,y \ x) \ 1
    ]]></literal>
    <justification jstring="[hyper(6575,a,10081,a)].">
      <j1 rule="hyper" parents="6575 10081"/>
    </justification>
  </clause>

  <clause id="10083">
    <literal><![CDATA[
      (x * K(y,z)) * (z \ 1) = x * (z \ K(y,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,4956,a(flip),b,10081,a),flip(a)].">
      <j1 rule="hyper" parents="320 4956 10081"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10084">
    <literal><![CDATA[
      (x * (y \ 1)) \ (x * (T(y,z) \ 1)) = K(z,y)
    ]]></literal>
    <justification jstring="[hyper(116,a,10081,a(flip),b,6793,a(flip))].">
      <j1 rule="hyper" parents="116 10081 6793"/>
    </justification>
  </clause>

  <clause id="10087">
    <literal><![CDATA[
      (x * K(y,z)) * (T(y,z) \ 1) = x * (y \ 1)
    ]]></literal>
    <justification jstring="[para(6329(a,1),10081(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6329 10081"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10088">
    <literal><![CDATA[
      x \ T(x * (y \ 1),y) = ((y \ x) \ x) \ 1
    ]]></literal>
    <justification jstring="[hyper(320,a,311,a(flip),b,10082,a),flip(a)].">
      <j1 rule="hyper" parents="320 311 10082"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10089">
    <literal><![CDATA[
      (x * (y \ 1)) * K(z,y) = x * (y \ K(z,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,6793,a(flip),b,10083,a)].">
      <j1 rule="hyper" parents="58 6793 10083"/>
    </justification>
  </clause>

  <clause id="10090">
    <literal><![CDATA[
      L(K(x,y),y \ 1,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(5174,a,10084,a)].">
      <j1 rule="hyper" parents="5174 10084"/>
    </justification>
  </clause>

  <clause id="10091">
    <literal><![CDATA[
      L(K((x \ y) \ (z \ 1),z),z \ 1,u) = K(y \ (z \ x),z)
    ]]></literal>
    <justification jstring="[hyper(320,a,9296,a(flip),b,10090,a),flip(a)].">
      <j1 rule="hyper" parents="320 9296 10090"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10092">
    <literal><![CDATA[
      a(x,y \ 1,K(z,y)) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,10090,a,b,1934,a),flip(a)].">
      <j1 rule="hyper" parents="115 10090 1934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10095">
    <literal><![CDATA[
      L(K(x,y),x \ 1,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(5893,a,10092,a)].">
      <j1 rule="hyper" parents="5893 10092"/>
    </justification>
  </clause>

  <clause id="10096">
    <literal><![CDATA[
      a(x,y,K(z,y \ 1)) = 1
    ]]></literal>
    <justification jstring="[hyper(4059,a,10092,a)].">
      <j1 rule="hyper" parents="4059 10092"/>
    </justification>
  </clause>

  <clause id="10097">
    <literal><![CDATA[
      L(K(x \ 1,y),x,z) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(5893,a,10096,a)].">
      <j1 rule="hyper" parents="5893 10096"/>
    </justification>
  </clause>

  <clause id="10098">
    <literal><![CDATA[
      (x * y) * K(z,y \ 1) = x * (y * K(z,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(977,a,10096,a)].">
      <j1 rule="hyper" parents="977 10096"/>
    </justification>
  </clause>

  <clause id="10100">
    <literal><![CDATA[
      L(K(x,y),1 / x,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,4019,a,b,10095,a)].">
      <j1 rule="hyper" parents="58 4019 10095"/>
    </justification>
  </clause>

  <clause id="10101">
    <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(2632(a,1),10100(a,1,2))].">
      <j1 rule="para" parents="2632 10100"/>
    </justification>
  </clause>

  <clause id="10102">
    <literal><![CDATA[
      (x * y) * K(y \ 1,z) = x * (y * K(y \ 1,z))
    ]]></literal>
    <justification jstring="[hyper(119,a,10097,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="119 10097 13"/>
    </justification>
  </clause>

  <clause id="10103">
    <literal><![CDATA[
      (x / (y \ 1)) * K(y,z) = x / (T(y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(117,a,7,a(flip),b,10087,a),flip(a)].">
      <j1 rule="hyper" parents="117 7 10087"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10104">
    <literal><![CDATA[
      (x * K(y * K(z,y),z)) * (y \ 1) = x * ((y * K(z,y)) \ 1)
    ]]></literal>
    <justification jstring="[para(4816(a,1),10087(a,1,2,1))].">
      <j1 rule="para" parents="4816 10087"/>
    </justification>
  </clause>

  <clause id="10105">
    <literal><![CDATA[
      T((x \ 1) * y,x) = (((x \ y) \ y) \ 1) * y
    ]]></literal>
    <justification jstring="[para(10088(a,1),4596(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10088 4596"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10106">
    <literal><![CDATA[
      (x * T(y,z)) * (y \ K(z,y)) = R(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,6795,a(flip),b,10089,a),flip(a)].">
      <j1 rule="hyper" parents="58 6795 10089"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10107">
    <literal><![CDATA[
      L((x / (y \ 1)) / y,z,u) * T(y,w) = L(x,z,u) / (T(y,w) \ 1)
    ]]></literal>
    <justification jstring="[hyper(6858,a,10103,a)].">
      <j1 rule="hyper" parents="6858 10103"/>
    </justification>
  </clause>

  <clause id="10108">
    <literal><![CDATA[
      (x \ (x / (y \ 1))) * x = x / (T(y,x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,5535,a,b,10103,a)].">
      <j1 rule="hyper" parents="58 5535 10103"/>
    </justification>
  </clause>

  <clause id="10109">
    <literal><![CDATA[
      x / (T(y,x) \ 1) = y * ((x / (y \ 1)) / y)
    ]]></literal>
    <justification jstring="[hyper(58,a,5854,a(flip),b,10103,a),flip(a)].">
      <j1 rule="hyper" parents="58 5854 10103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10110">
    <literal><![CDATA[
      (((x \ 1) * y) \ y) \ y = (((x \ y) \ y) \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(58,a,4194,a(flip),b,10105,a)].">
      <j1 rule="hyper" parents="58 4194 10105"/>
    </justification>
  </clause>

  <clause id="10111">
    <literal><![CDATA[
      T(((x / y) \ 1) * x,x / y) = ((y \ x) \ 1) * x
    ]]></literal>
    <justification jstring="[para(75(a,1),10105(a,2,1,1,1))].">
      <j1 rule="para" parents="75 10105"/>
    </justification>
  </clause>

  <clause id="10112">
    <literal><![CDATA[
      x / (y \ K(x,y)) = y * ((x / (y \ 1)) / y)
    ]]></literal>
    <justification jstring="[para(4804(a,1),10109(a,1,2))].">
      <j1 rule="para" parents="4804 10109"/>
    </justification>
  </clause>

  <clause id="10113">
    <literal><![CDATA[
      x \ (y / (x \ K(y,x))) = (y / (x \ 1)) / x
    ]]></literal>
    <justification jstring="[hyper(116,a,10112,a,b,xx)].">
      <j1 rule="hyper" parents="116 10112"/>
    </justification>
  </clause>

  <clause id="10114">
    <literal><![CDATA[
      (x * y) * (x \ K(y,x)) = R(y,x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(569,a,10106,a)].">
      <j1 rule="hyper" parents="569 10106"/>
    </justification>
  </clause>

  <clause id="10115">
    <literal><![CDATA[
      R(x,y,K(z,y \ 1)) = x
    ]]></literal>
    <justification jstring="[hyper(515,a,10098,a)].">
      <j1 rule="hyper" parents="515 10098"/>
    </justification>
  </clause>

  <clause id="10116">
    <literal><![CDATA[
      x / (x * (y * K(z,y \ 1))) = T(x / (x * y),z)
    ]]></literal>
    <justification jstring="[para(10098(a,1),7656(a,1,2))].">
      <j1 rule="para" parents="10098 7656"/>
    </justification>
  </clause>

  <clause id="10118">
    <literal><![CDATA[
      R(x,y \ 1,K(z,y)) = x
    ]]></literal>
    <justification jstring="[para(3150(a,1),10115(a,1,3))].">
      <j1 rule="para" parents="3150 10115"/>
    </justification>
  </clause>

  <clause id="10119">
    <literal><![CDATA[
      R(x,y \ z,K(u,z \ y)) = x
    ]]></literal>
    <justification jstring="[para(6108(a,1),10115(a,1,3))].">
      <j1 rule="para" parents="6108 10115"/>
    </justification>
  </clause>

  <clause id="10120">
    <literal><![CDATA[
      T(x,y) / ((y \ 1) * K(x,y)) = x / (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(6703,a,10118,a)].">
      <j1 rule="hyper" parents="6703 10118"/>
    </justification>
  </clause>

  <clause id="10121">
    <literal><![CDATA[
      R(x,y \ 1,K(z,T(y,u))) = x
    ]]></literal>
    <justification jstring="[para(7160(a,1),10118(a,1,3))].">
      <j1 rule="para" parents="7160 10118"/>
    </justification>
  </clause>

  <clause id="10122">
    <literal><![CDATA[
      x \ (y * K(z,y \ x)) = (x \ y) * K(z,y \ x)
    ]]></literal>
    <justification jstring="[para(10119(a,1),505(a,1,1))].">
      <j1 rule="para" parents="10119 505"/>
    </justification>
  </clause>

  <clause id="10123">
    <literal><![CDATA[
      R(x,(y * K(z,y)) \ 1,K(u,y)) = x
    ]]></literal>
    <justification jstring="[para(4816(a,1),10121(a,1,3,2))].">
      <j1 rule="para" parents="4816 10121"/>
    </justification>
  </clause>

  <clause id="10124">
    <literal><![CDATA[
      R(x,y \ K(y,z),K(u,y)) = x
    ]]></literal>
    <justification jstring="[para(5209(a,1),10123(a,1,2))].">
      <j1 rule="para" parents="5209 10123"/>
    </justification>
  </clause>

  <clause id="10125">
    <literal><![CDATA[
      (x * K(y,z)) / (z \ 1) = x / (z \ K(z,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,6386,a(flip),b,10124,a)].">
      <j1 rule="hyper" parents="58 6386 10124"/>
    </justification>
  </clause>

  <clause id="10126">
    <literal><![CDATA[
      T(x,y) / (T(y,x) \ 1) = x / (y \ 1)
    ]]></literal>
    <justification jstring="[para(4801(a,1),10120(a,1,2))].">
      <j1 rule="para" parents="4801 10120"/>
    </justification>
  </clause>

  <clause id="10127">
    <literal><![CDATA[
      (x / (y \ 1)) \ T(x,y) = T(y,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(188,a,10126,a)].">
      <j1 rule="hyper" parents="188 10126"/>
    </justification>
  </clause>

  <clause id="10128">
    <literal><![CDATA[
      T(x,y) / ((y \ 1) \ x) = T(y,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(58,a,6718,a,b,10127,a)].">
      <j1 rule="hyper" parents="58 6718 10127"/>
    </justification>
  </clause>

  <clause id="10129">
    <literal><![CDATA[
      ((x / y) / (y \ 1)) \ (y \ x) = T(y,y \ x) \ 1
    ]]></literal>
    <justification jstring="[hyper(58,a,6835,a(flip),b,10127,a)].">
      <j1 rule="hyper" parents="58 6835 10127"/>
    </justification>
  </clause>

  <clause id="10130">
    <literal><![CDATA[
      (x \ ((y \ 1) \ x)) * x = (T(y,x) \ 1) \ x
    ]]></literal>
    <justification jstring="[para(10128(a,1),4500(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10128 4500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10132">
    <literal><![CDATA[
      T(x,y) / (y \ 1) = x / (y \ K(y,x))
    ]]></literal>
    <justification jstring="[para(4755(a,2),10125(a,1,1))].">
      <j1 rule="para" parents="4755 10125"/>
    </justification>
  </clause>

  <clause id="10133">
    <literal><![CDATA[
      (T(x,y) / (y \ 1)) \ x = y \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(188,a,10132,a(flip))].">
      <j1 rule="hyper" parents="188 10132"/>
    </justification>
  </clause>

  <clause id="10134">
    <literal><![CDATA[
      x \ (x / (y \ K(y,x))) = (x / (y \ 1)) / x
    ]]></literal>
    <justification jstring="[hyper(116,a,10132,a(flip),b,3915,a(flip))].">
      <j1 rule="hyper" parents="116 10132 3915"/>
    </justification>
  </clause>

  <clause id="10135">
    <literal><![CDATA[
      (x \ K(x,y)) \ y = (x \ 1) \ T(y,x)
    ]]></literal>
    <justification jstring="[para(10133(a,1),6863(a,1,1))].">
      <j1 rule="para" parents="10133 6863"/>
    </justification>
  </clause>

  <clause id="10136">
    <literal><![CDATA[
      (x \ K(x,y)) \ y = (x \ ((x \ 1) \ y)) * x
    ]]></literal>
    <justification jstring="[hyper(320,a,1980,a,b,10135,a),flip(a)].">
      <j1 rule="hyper" parents="320 1980 10135"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10137">
    <literal><![CDATA[
      (x \ K(x,y)) \ y = y * (((x \ 1) \ y) / y)
    ]]></literal>
    <justification jstring="[hyper(320,a,3919,a(flip),b,10135,a),flip(a)].">
      <j1 rule="hyper" parents="320 3919 10135"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10138">
    <literal><![CDATA[
      x \ ((y \ K(y,x)) \ x) = ((y \ 1) \ x) / x
    ]]></literal>
    <justification jstring="[hyper(116,a,10135,a,b,3919,a(flip))].">
      <j1 rule="hyper" parents="116 10135 3919"/>
    </justification>
  </clause>

  <clause id="10139">
    <literal><![CDATA[
      (T(1 / x,y) \ 1) \ y = (y \ (x \ y)) * y
    ]]></literal>
    <justification jstring="[para(75(a,1),10130(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="75 10130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10140">
    <literal><![CDATA[
      x / ((x \ (y \ x)) * x) = T(1 / y,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(197,a,10139,a)].">
      <j1 rule="hyper" parents="197 10139"/>
    </justification>
  </clause>

  <clause id="10141">
    <literal><![CDATA[
      T(1 / (x \ y),y) \ 1 = x \ T(y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,6736,a,b,10140,a),flip(a)].">
      <j1 rule="hyper" parents="58 6736 10140"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10142">
    <literal><![CDATA[
      T(1 / (x / y),x) \ 1 = x / ((x \ y) * x)
    ]]></literal>
    <justification jstring="[para(75(a,1),10140(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="75 10140"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10143">
    <literal><![CDATA[
      (x \ T(y,y \ x)) \ 1 = T((x \ y) \ 1,y)
    ]]></literal>
    <justification jstring="[para(10141(a,1),2165(a,1,1))].">
      <j1 rule="para" parents="10141 2165"/>
    </justification>
  </clause>

  <clause id="10144">
    <literal><![CDATA[
      R(x,y,K(y \ 1,z)) = x
    ]]></literal>
    <justification jstring="[hyper(515,a,10102,a)].">
      <j1 rule="hyper" parents="515 10102"/>
    </justification>
  </clause>

  <clause id="10145">
    <literal><![CDATA[
      R(x,y \ z,K(y / z,u)) = x
    ]]></literal>
    <justification jstring="[para(8000(a,1),10144(a,1,3))].">
      <j1 rule="para" parents="8000 10144"/>
    </justification>
  </clause>

  <clause id="10146">
    <literal><![CDATA[
      x \ (y * K(x / y,z)) = (x \ y) * K(x / y,z)
    ]]></literal>
    <justification jstring="[para(10145(a,1),505(a,1,1))].">
      <j1 rule="para" parents="10145 505"/>
    </justification>
  </clause>

  <clause id="10147">
    <literal><![CDATA[
      ((((x / y) \ 1) * x) \ x) \ x = ((y \ x) \ 1) * x
    ]]></literal>
    <justification jstring="[para(75(a,1),10110(a,2,1,1,1))].">
      <j1 rule="para" parents="75 10110"/>
    </justification>
  </clause>

  <clause id="10148">
    <literal><![CDATA[
      ((x / y) \ 1) * (y * (x / y)) = ((y \ x) \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(58,a,1984,a(flip),b,10111,a)].">
      <j1 rule="hyper" parents="58 1984 10111"/>
    </justification>
  </clause>

  <clause id="10149">
    <literal><![CDATA[
      T(x \ y,z) * ((y \ x) * K(z,x \ y)) = T((x \ y) * (y \ x),z)
    ]]></literal>
    <justification jstring="[hyper(119,a,10122,a(flip),b,5938,a)].">
      <j1 rule="hyper" parents="119 10122 5938"/>
    </justification>
  </clause>

  <clause id="10150">
    <literal><![CDATA[
      (x \ y) / (T(x,x \ y) \ 1) = (y / x) / (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(197,a,10129,a)].">
      <j1 rule="hyper" parents="197 10129"/>
    </justification>
  </clause>

  <clause id="10151">
    <literal><![CDATA[
      (x \ y) * K(x / y,y) = (y * (x / y)) \ y
    ]]></literal>
    <justification jstring="[hyper(58,a,1452,a(flip),b,10146,a),flip(a)].">
      <j1 rule="hyper" parents="58 1452 10146"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10152">
    <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(10148(a,1),6598(a,2,2,1))].">
      <j1 rule="para" parents="10148 6598"/>
    </justification>
  </clause>

  <clause id="10153">
    <literal><![CDATA[
      K(x \ (y * (z \ 1)),z) = K(x \ (z \ y),z)
    ]]></literal>
    <justification jstring="[hyper(58,a,6626,a(flip),b,10091,a)].">
      <j1 rule="hyper" parents="58 6626 10091"/>
    </justification>
  </clause>

  <clause id="10154">
    <literal><![CDATA[
      K(((x \ 1) * y) \ (x \ z),x) = K(y \ T(z,x \ 1),x)
    ]]></literal>
    <justification jstring="[hyper(58,a,9382,a(flip),b,10153,a),flip(a)].">
      <j1 rule="hyper" parents="58 9382 10153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10155">
    <literal><![CDATA[
      K(((x \ 1) * y) \ (x \ z),x) = K(y \ z,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,9421,a(flip),b,10154,a),flip(a)].">
      <j1 rule="hyper" parents="320 9421 10154"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10156">
    <literal><![CDATA[
      K(((x \ 1) * y) \ z,x) = K(y \ (z * x),x)
    ]]></literal>
    <justification jstring="[hyper(7719,a,10155,a)].">
      <j1 rule="hyper" parents="7719 10155"/>
    </justification>
  </clause>

  <clause id="10157">
    <literal><![CDATA[
      K(L(x,y,y \ 1) \ z,y) = K((x * y) \ (z * y),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,8700,a(flip),b,10156,a)].">
      <j1 rule="hyper" parents="58 8700 10156"/>
    </justification>
  </clause>

  <clause id="10158">
    <literal><![CDATA[
      K(L(x,y,y \ 1) \ z,y) = K(x \ z,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,7598,a(flip),b,10157,a),flip(a)].">
      <j1 rule="hyper" parents="320 7598 10157"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10159">
    <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(10158(a,1),5380(a,1,2,1,2))].">
      <j1 rule="para" parents="10158 5380"/>
    </justification>
  </clause>

  <clause id="10160">
    <literal><![CDATA[
      (x * K(y,z)) * (y \ 1) = x * ((y * K(z,y)) \ 1)
    ]]></literal>
    <justification jstring="[para(4970(a,1),10104(a,1,1,2))].">
      <j1 rule="para" parents="4970 10104"/>
    </justification>
  </clause>

  <clause id="10161">
    <literal><![CDATA[
      (x * K(y,z)) * (y \ 1) = x * (K(y,z) * (y \ 1))
    ]]></literal>
    <justification jstring="[para(5398(a,1),10160(a,2,2))].">
      <j1 rule="para" parents="5398 10160"/>
    </justification>
  </clause>

  <clause id="10163">
    <literal><![CDATA[
      L(x \ 1,K(x,y),z) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(479,a,10161,a)].">
      <j1 rule="hyper" parents="479 10161"/>
    </justification>
  </clause>

  <clause id="10164">
    <literal><![CDATA[
      T((x \ y) * (y \ x),z) = (x \ y) * (y \ x)
    ]]></literal>
    <justification jstring="[hyper(5487,a,10149,a),flip(a)].">
      <j1 rule="hyper" parents="5487 10149"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10165">
    <literal><![CDATA[
      K(x,(y \ z) * (z \ y)) = 1
    ]]></literal>
    <justification jstring="[hyper(4825,a,10164,a)].">
      <j1 rule="hyper" parents="4825 10164"/>
    </justification>
  </clause>

  <clause id="10166">
    <literal><![CDATA[
      T(x,(y \ z) * (z \ y)) = x
    ]]></literal>
    <justification jstring="[hyper(49,a,10164,a)].">
      <j1 rule="hyper" parents="49 10164"/>
    </justification>
  </clause>

  <clause id="10167">
    <literal><![CDATA[
      K(x,y * ((z * y) \ z)) = 1
    ]]></literal>
    <justification jstring="[para(4(a,1),10165(a,1,2,1))].">
      <j1 rule="para" parents="4 10165"/>
    </justification>
  </clause>

  <clause id="10168">
    <literal><![CDATA[
      T(x,y * ((z * y) \ z)) = x
    ]]></literal>
    <justification jstring="[para(4(a,1),10166(a,1,2,1))].">
      <j1 rule="para" parents="4 10166"/>
    </justification>
  </clause>

  <clause id="10169">
    <literal><![CDATA[
      T(x * ((y * x) \ y),z) = x * ((y * x) \ y)
    ]]></literal>
    <justification jstring="[hyper(4953,a,10167,a)].">
      <j1 rule="hyper" parents="4953 10167"/>
    </justification>
  </clause>

  <clause id="10170">
    <literal><![CDATA[
      x / (y * ((z * y) \ z)) = (y * ((z * y) \ z)) \ x
    ]]></literal>
    <justification jstring="[hyper(168,a,5016,a,b,10167,a(flip))].">
      <j1 rule="hyper" parents="168 5016 10167"/>
    </justification>
  </clause>

  <clause id="10171">
    <literal><![CDATA[
      x / (y * ((z * y) \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      (y * ((z * y) \ z)) \ x = u
    ]]></literal>
    <justification jstring="[para(10168(a,1),420(a,1))].">
      <j1 rule="para" parents="10168 420"/>
    </justification>
  </clause>

  <clause id="10172">
    <literal><![CDATA[
      T(x * L(x \ 1,x,y),z) = x * ((y * x) \ y)
    ]]></literal>
    <justification jstring="[para(217(a,2),10169(a,1,1,2))].">
      <j1 rule="para" parents="217 10169"/>
    </justification>
  </clause>

  <clause id="10173">
    <literal><![CDATA[
      T(x,y) * ((z * T(x,y)) \ z) = x * ((z * x) \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,9489,a(flip),b,10172,a)].">
      <j1 rule="hyper" parents="58 9489 10172"/>
    </justification>
  </clause>

  <clause id="10174">
    <literal><![CDATA[
      T(x,y) * ((x * y) \ y) = x * ((y * x) \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,5479,a(flip),b,10172,a)].">
      <j1 rule="hyper" parents="58 5479 10172"/>
    </justification>
  </clause>

  <clause id="10177">
    <literal><![CDATA[
      (x * ((y * x) \ y)) \ T(x,z) = 1 / ((y * T(x,z)) \ y)
    ]]></literal>
    <justification jstring="[para(10173(a,1),1848(a,1,1))].">
      <j1 rule="para" parents="10173 1848"/>
    </justification>
  </clause>

  <clause id="10178">
    <literal><![CDATA[
      K(L(x,y,y \ 1) \ z,T(y,u)) = K(x \ z,T(y,u))
    ]]></literal>
    <justification jstring="[hyper(5383,a,10159,a),flip(a)].">
      <j1 rule="hyper" parents="5383 10159"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10179">
    <literal><![CDATA[
      K(((1 / x) * y) \ z,T(x,u)) = K((x \ y) \ z,T(x,u))
    ]]></literal>
    <justification jstring="[para(2815(a,1),10178(a,1,1,1))].">
      <j1 rule="para" parents="2815 10178"/>
    </justification>
  </clause>

  <clause id="10180">
    <literal><![CDATA[
      K(((x \ 1) * y) \ z,T(x,u)) = K((x \ y) \ z,T(x,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,3989,a(flip),b,10179,a)].">
      <j1 rule="hyper" parents="58 3989 10179"/>
    </justification>
  </clause>

  <clause id="10181">
    <literal><![CDATA[
      K(((x \ 1) * y) \ z,T(x,u)) = K(y \ (x * z),T(x,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,7612,a(flip),b,10180,a),flip(a)].">
      <j1 rule="hyper" parents="320 7612 10180"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10182">
    <literal><![CDATA[
      K(x \ (y * z),T(y,x)) = K(((y \ 1) \ z) / x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,9383,a(flip),b,10181,a),flip(a)].">
      <j1 rule="hyper" parents="58 9383 10181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10183">
    <literal><![CDATA[
      K(((x \ 1) \ y) / z,x) = K((x * y) / z,x)
    ]]></literal>
    <justification jstring="[hyper(8061,a,10182,a),flip(a)].">
      <j1 rule="hyper" parents="8061 10182"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10184">
    <literal><![CDATA[
      K(((x \ 1) \ y) / z,x) = K((z / y) \ x,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,6766,a(flip),b,10183,a),flip(a)].">
      <j1 rule="hyper" parents="320 6766 10183"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10185">
    <literal><![CDATA[
      K((x / ((y \ 1) * z)) \ y,y) = K(z / x,y)
    ]]></literal>
    <justification jstring="[para(4(a,1),10184(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4 10184"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10186">
    <literal><![CDATA[
      K(x / (y * ((z \ 1) * x)),z) = K(y \ z,z)
    ]]></literal>
    <justification jstring="[para(6(a,1),10185(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6 10185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10187">
    <literal><![CDATA[
      K(x / (y * ((z \ 1) * x)),(z \ 1) \ 1) = K(y \ z,z)
    ]]></literal>
    <justification jstring="[hyper(3556,a,10186,a)].">
      <j1 rule="hyper" parents="3556 10186"/>
    </justification>
  </clause>

  <clause id="10188">
    <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(9344(a,1),10050(a,2,1))].">
      <j1 rule="para" parents="9344 10050"/>
    </justification>
  </clause>

  <clause id="10189">
    <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,9869,a(flip),b,10188,a),flip(a)].">
      <j1 rule="hyper" parents="320 9869 10188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10190">
    <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(7160(a,1),10189(a,1,1,2))].">
      <j1 rule="para" parents="7160 10189"/>
    </justification>
  </clause>

  <clause id="10191">
    <literal><![CDATA[
      (x * K(y,T(z,u))) * (u * K(z,y)) = (x * K(y,z)) * (K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(7897(a,1),10190(a,1,2))].">
      <j1 rule="para" parents="7897 10190"/>
    </justification>
  </clause>

  <clause id="10192">
    <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(9172(a,2),10191(a,1,1))].">
      <j1 rule="para" parents="9172 10191"/>
    </justification>
  </clause>

  <clause id="10193">
    <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(7832(a,1),10059(a,1,2))].">
      <j1 rule="para" parents="7832 10059"/>
    </justification>
  </clause>

  <clause id="10194">
    <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(9071(a,1),10060(a,1,2))].">
      <j1 rule="para" parents="9071 10060"/>
    </justification>
  </clause>

  <clause id="10195">
    <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(9823(a,1),10061(a,2,2))].">
      <j1 rule="para" parents="9823 10061"/>
    </justification>
  </clause>

  <clause id="10196">
    <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,10195,a),flip(a)].">
      <j1 rule="hyper" parents="320 105 10195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10197">
    <literal><![CDATA[
      L(x \ 1,K(x,T(y,z)),z) * (K(x,y) * z) = (x \ K(x,y)) * z
    ]]></literal>
    <justification jstring="[para(7158(a,2),10196(a,1,1,2))].">
      <j1 rule="para" parents="7158 10196"/>
    </justification>
  </clause>

  <clause id="10198">
    <literal><![CDATA[
      (x \ 1) * (K(x,y) * z) = (x \ K(x,y)) * z
    ]]></literal>
    <justification jstring="[para(10163(a,1),10197(a,1,1))].">
      <j1 rule="para" parents="10163 10197"/>
    </justification>
  </clause>

  <clause id="10199">
    <literal><![CDATA[
      K(x,y) * ((x \ 1) * z) = (x \ K(x,y)) * z
    ]]></literal>
    <justification jstring="[hyper(58,a,6005,a,b,10198,a)].">
      <j1 rule="hyper" parents="58 6005 10198"/>
    </justification>
  </clause>

  <clause id="10200">
    <literal><![CDATA[
      ((x \ 1) * y) / ((x \ K(x,z)) * y) = K(z,x)
    ]]></literal>
    <justification jstring="[para(10198(a,1),6011(a,1,2))].">
      <j1 rule="para" parents="10198 6011"/>
    </justification>
  </clause>

  <clause id="10202">
    <literal><![CDATA[
      L(x,y \ 1,K(y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(3210,a,10199,a)].">
      <j1 rule="hyper" parents="3210 10199"/>
    </justification>
  </clause>

  <clause id="10203">
    <literal><![CDATA[
      L(x,y,K(y \ 1,z)) = x
    ]]></literal>
    <justification jstring="[hyper(58,a,4020,a(flip),b,10202,a)].">
      <j1 rule="hyper" parents="58 4020 10202"/>
    </justification>
  </clause>

  <clause id="10204">
    <literal><![CDATA[
      L(x,T(y,z) \ 1,K(y,u)) = x
    ]]></literal>
    <justification jstring="[para(7888(a,1),10202(a,1,3))].">
      <j1 rule="para" parents="7888 10202"/>
    </justification>
  </clause>

  <clause id="10205">
    <literal><![CDATA[
      L(x,y,K(y \ 1,z)) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(10203(a,1),45(a,2))].">
      <j1 rule="para" parents="10203 45"/>
    </justification>
  </clause>

  <clause id="10206">
    <literal><![CDATA[
      L(x,y \ z,K(y / z,u)) = x
    ]]></literal>
    <justification jstring="[para(8000(a,1),10203(a,1,3))].">
      <j1 rule="para" parents="8000 10203"/>
    </justification>
  </clause>

  <clause id="10207">
    <literal><![CDATA[
      L(x,(y * z) \ z,K(y,u)) = x
    ]]></literal>
    <justification jstring="[para(6(a,1),10206(a,1,3,1))].">
      <j1 rule="para" parents="6 10206"/>
    </justification>
  </clause>

  <clause id="10208">
    <literal><![CDATA[
      R(K(x,y),y \ 1,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,6939,a(flip),b,10200,a)].">
      <j1 rule="hyper" parents="58 6939 10200"/>
    </justification>
  </clause>

  <clause id="10210">
    <literal><![CDATA[
      L(K((x / y) \ x,z),x \ (x / (1 / (1 / y))),u) = K(1 / (x \ (x / y)),z)
    ]]></literal>
    <justification jstring="[para(6266(a,1),10101(a,1,1))].">
      <j1 rule="para" parents="6266 10101"/>
    </justification>
  </clause>

  <clause id="10211">
    <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),10210(a,1,1,1))].">
      <j1 rule="para" parents="75 10210"/>
    </justification>
  </clause>

  <clause id="10213">
    <literal><![CDATA[
      L(K(x,y),1 / (1 / (z \ (z / x))),u) = K(1 / (z \ (z / x)),y)
    ]]></literal>
    <justification jstring="[para(2632(a,2),10211(a,1,2))].">
      <j1 rule="para" parents="2632 10211"/>
    </justification>
  </clause>

  <clause id="10214">
    <literal><![CDATA[
      L(K(x,y),z \ (z / x),u) = K(1 / (z \ (z / x)),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,4021,a(flip),b,10213,a)].">
      <j1 rule="hyper" parents="58 4021 10213"/>
    </justification>
  </clause>

  <clause id="10215">
    <literal><![CDATA[
      L(K(x,y),z \ (z / x),u) = K((z / x) \ z,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,6266,a(flip),b,10214,a),flip(a)].">
      <j1 rule="hyper" parents="320 6266 10214"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10216">
    <literal><![CDATA[
      L(K(x,y),z \ (z / x),u) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,674,a(flip),b,10215,a),flip(a)].">
      <j1 rule="hyper" parents="320 674 10215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10218">
    <literal><![CDATA[
      (x / y) \ (x * (K(y,z) * (x \ (x / y)))) = T(K(y,z),x \ (x / y))
    ]]></literal>
    <justification jstring="[para(10216(a,1),795(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10216 795"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10219">
    <literal><![CDATA[
      (x / y) \ (x * (K(y,z) * (x \ (x / y)))) = T(K(y,z),1 / y)
    ]]></literal>
    <justification jstring="[hyper(320,a,6203,a(flip),b,10218,a),flip(a)].">
      <j1 rule="hyper" parents="320 6203 10218"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10221">
    <literal><![CDATA[
      (x / y) \ (x * (K(y,z) * (x \ (x / y)))) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,1296,a(flip),b,10219,a),flip(a)].">
      <j1 rule="hyper" parents="320 1296 10219"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10222">
    <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(2910(a,1),10193(a,1,2))].">
      <j1 rule="para" parents="2910 10193"/>
    </justification>
  </clause>

  <clause id="10224">
    <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(10222(a,1),5378(a,1,1,2))].">
      <j1 rule="para" parents="10222 5378"/>
    </justification>
  </clause>

  <clause id="10225">
    <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(5202(a,1),10224(a,1,1))].">
      <j1 rule="para" parents="5202 10224"/>
    </justification>
  </clause>

  <clause id="10226">
    <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,7004,a(flip),b,10225,a),flip(a)].">
      <j1 rule="hyper" parents="58 7004 10225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10227">
    <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(10226(a,1),8750(a,2,1))].">
      <j1 rule="para" parents="10226 8750"/>
    </justification>
  </clause>

  <clause id="10228">
    <literal><![CDATA[
      (x * (y \ z)) * (u * (((x * (y \ z)) \ z) / u)) = (x * (u * ((x \ y) / u))) * (y \ z)
    ]]></literal>
    <justification jstring="[para(4623(a,1),4641(a,2,1))].">
      <j1 rule="para" parents="4623 4641"/>
    </justification>
  </clause>

  <clause id="10229">
    <literal><![CDATA[
      ((K(x,y) * z) * (z \ x)) / T(x,y) = a(K(x,y),z,z \ x)
    ]]></literal>
    <justification jstring="[para(9171(a,1),4857(a,1,2))].">
      <j1 rule="para" parents="9171 4857"/>
    </justification>
  </clause>

  <clause id="10231">
    <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(4819(a,1),5185(a,2,2))].">
      <j1 rule="para" parents="4819 5185"/>
    </justification>
  </clause>

  <clause id="10232">
    <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(10231(a,2),482(a,1))].">
      <j1 rule="para" parents="10231 482"/>
    </justification>
  </clause>

  <clause id="10234">
    <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,4597,a,b,6190,a)].">
      <j1 rule="hyper" parents="320 4597 6190"/>
    </justification>
  </clause>

  <clause id="10235">
    <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(6331(a,1),6390(a,2,1))].">
      <j1 rule="para" parents="6331 6390"/>
    </justification>
  </clause>

  <clause id="10236">
    <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,10235,a),flip(a)].">
      <j1 rule="hyper" parents="320 15 10235"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10239">
    <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),10236(a,1,2))].">
      <j1 rule="para" parents="223 10236"/>
    </justification>
  </clause>

  <clause id="10240">
    <literal><![CDATA[
      R(R(x,y / z,z),y,K(z \ y,z)) = R(x,z \ y,z)
    ]]></literal>
    <justification jstring="[para(6725(a,1),10239(a,1,1))].">
      <j1 rule="para" parents="6725 10239"/>
    </justification>
  </clause>

  <clause id="10241">
    <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,9700,a(flip),b,6834,a),flip(a)].">
      <j1 rule="hyper" parents="320 9700 6834"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10242">
    <literal><![CDATA[
      (T(x,y) / z) / K(((z \ 1) / (x / z)) \ 1,y) = T(x / z,K(x,y))
    ]]></literal>
    <justification jstring="[para(4004(a,1),10241(a,1,2))].">
      <j1 rule="para" parents="4004 10241"/>
    </justification>
  </clause>

  <clause id="10243">
    <literal><![CDATA[
      (T(x,y) / z) * K(y,((z \ 1) / (x / z)) \ 1) = T(x / z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(6346,a,10242,a)].">
      <j1 rule="hyper" parents="6346 10242"/>
    </justification>
  </clause>

  <clause id="10244">
    <literal><![CDATA[
      (T(x,y) / z) * K(y,(x / z) / (z \ 1)) = T(x / z,K(x,y))
    ]]></literal>
    <justification jstring="[para(5351(a,1),10243(a,1,2))].">
      <j1 rule="para" parents="5351 10243"/>
    </justification>
  </clause>

  <clause id="10245">
    <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(7158(a,2),10244(a,1,1,1))].">
      <j1 rule="para" parents="7158 10244"/>
    </justification>
  </clause>

  <clause id="10246">
    <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,5055,a,b,6867,a)].">
      <j1 rule="hyper" parents="58 5055 6867"/>
    </justification>
  </clause>

  <clause id="10247">
    <literal><![CDATA[
      x \ K((x * ((y \ 1) / x)) \ 1,z) = (y \ T(y * K(x \ 1,x),z)) / x
    ]]></literal>
    <justification jstring="[para(4009(a,1),10246(a,1,2))].">
      <j1 rule="para" parents="4009 10246"/>
    </justification>
  </clause>

  <clause id="10248">
    <literal><![CDATA[
      x \ K((x * ((y \ 1) / x)) \ 1,z) = ((y \ T(y,z)) * K(x \ 1,x)) / x
    ]]></literal>
    <justification jstring="[para(4652(a,1),10247(a,2,1))].">
      <j1 rule="para" parents="4652 10247"/>
    </justification>
  </clause>

  <clause id="10249">
    <literal><![CDATA[
      x \ K((x * ((y \ 1) / x)) \ 1,z) = (K(y,z) * K(x \ 1,x)) / x
    ]]></literal>
    <justification jstring="[para(4729(a,2),10248(a,2,1,1))].">
      <j1 rule="para" parents="4729 10248"/>
    </justification>
  </clause>

  <clause id="10250">
    <literal><![CDATA[
      K((x * ((y \ 1) / x)) \ 1,z) = x * (K(y,z) / T(x,x \ 1))
    ]]></literal>
    <justification jstring="[hyper(6380,a,10249,a),flip(a)].">
      <j1 rule="hyper" parents="6380 10249"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10251">
    <literal><![CDATA[
      K((x * ((y \ 1) / x)) \ 1,z) = x * (K(y,z) / ((x \ 1) \ 1))
    ]]></literal>
    <justification jstring="[para(106(a,1),10250(a,2,2,2))].">
      <j1 rule="para" parents="106 10250"/>
    </justification>
  </clause>

  <clause id="10252">
    <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(5917(a,1),7732(a,1,1))].">
      <j1 rule="para" parents="5917 7732"/>
    </justification>
  </clause>

  <clause id="10253">
    <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(7078(a,1),7750(a,2,2))].">
      <j1 rule="para" parents="7078 7750"/>
    </justification>
  </clause>

  <clause id="10254">
    <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,7740,a(flip),b,10253,a),flip(a)].">
      <j1 rule="hyper" parents="320 7740 10253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10256">
    <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),8366(a,1,1))].">
      <j1 rule="para" parents="199 8366"/>
    </justification>
  </clause>

  <clause id="10258">
    <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(6335(a,1),10256(a,1,2))].">
      <j1 rule="para" parents="6335 10256"/>
    </justification>
  </clause>

  <clause id="10259">
    <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(10041(a,1),10258(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10041 10258"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10260">
    <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,10259,a),flip(a)].">
      <j1 rule="hyper" parents="320 2 10259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10261">
    <literal><![CDATA[
      K(x,R(y,z,u)) * (y \ R(T(y,x),z,u)) = y \ R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(5147,a,10260,a)].">
      <j1 rule="hyper" parents="5147 10260"/>
    </justification>
  </clause>

  <clause id="10262">
    <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(9074(a,1),10261(a,1,1))].">
      <j1 rule="para" parents="9074 10261"/>
    </justification>
  </clause>

  <clause id="10263">
    <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(7704,a,8653,a)].">
      <j1 rule="hyper" parents="7704 8653"/>
    </justification>
  </clause>

  <clause id="10264">
    <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,9871,a(flip),b,8687,a),flip(a)].">
      <j1 rule="hyper" parents="58 9871 8687"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10265">
    <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,7509,a(flip),b,8710,a),flip(a)].">
      <j1 rule="hyper" parents="58 7509 8710"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10267">
    <literal><![CDATA[
      K(x,L(y,K(x,z) * u,w)) = K(x,(w * u) \ (w * (u * y)))
    ]]></literal>
    <justification jstring="[hyper(58,a,8683,a(flip),b,10265,a),flip(a)].">
      <j1 rule="hyper" parents="58 8683 10265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10269">
    <literal><![CDATA[
      K(x,L(y,K(x,z) * u,w)) = K(x,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(13(a,2),10267(a,2,2))].">
      <j1 rule="para" parents="13 10267"/>
    </justification>
  </clause>

  <clause id="10270">
    <literal><![CDATA[
      K(x,L(y,K(x,z) \ u,w)) = K(x,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(5(a,1),10269(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5 10269"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10271">
    <literal><![CDATA[
      K(L(x,K(y,z) * u,w),y) = (y \ 1) / (y \ K(y,L(x,u,w)))
    ]]></literal>
    <justification jstring="[para(10269(a,1),5138(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10269 5138"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10272">
    <literal><![CDATA[
      K(L(x,K(y,z) * u,w),y) = K(L(x,u,w),y)
    ]]></literal>
    <justification jstring="[hyper(320,a,5138,a(flip),b,10271,a),flip(a)].">
      <j1 rule="hyper" parents="320 5138 10271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10273">
    <literal><![CDATA[
      K(L(x,T(y,z),u),z) = K(L(x,y,u),z)
    ]]></literal>
    <justification jstring="[para(4811(a,1),10272(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4811 10272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10274">
    <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,8418,a(flip),b,8866,a),flip(a)].">
      <j1 rule="hyper" parents="58 8418 8866"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10276">
    <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),10274(a,1,1))].">
      <j1 rule="para" parents="15 10274"/>
    </justification>
  </clause>

  <clause id="10277">
    <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,8296,a,b,10276,a)].">
      <j1 rule="hyper" parents="58 8296 10276"/>
    </justification>
  </clause>

  <clause id="10278">
    <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,9236,a,b,10277,a)].">
      <j1 rule="hyper" parents="58 9236 10277"/>
    </justification>
  </clause>

  <clause id="10279">
    <literal><![CDATA[
      R(K(x,y),z * x,u) = K(R(x,K(w,y) * z,u),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,8850,a(flip),b,10278,a)].">
      <j1 rule="hyper" parents="58 8850 10278"/>
    </justification>
  </clause>

  <clause id="10281">
    <literal><![CDATA[
      K(R(x,K(y,z) * u,w),z) = K(R(x,u,w),z)
    ]]></literal>
    <justification jstring="[hyper(58,a,9234,a(flip),b,10279,a),flip(a)].">
      <j1 rule="hyper" parents="58 9234 10279"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10282">
    <literal><![CDATA[
      T(x,R(y,K(z,x) * u,w)) = 1 / (x \ K(R(y,u,w),x))
    ]]></literal>
    <justification jstring="[para(10281(a,1),4992(a,2,2,2))].">
      <j1 rule="para" parents="10281 4992"/>
    </justification>
  </clause>

  <clause id="10283">
    <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(10282(a,2),4993(a,1))].">
      <j1 rule="para" parents="10282 4993"/>
    </justification>
  </clause>

  <clause id="10284">
    <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,8408,a(flip),b,8883,a),flip(a)].">
      <j1 rule="hyper" parents="58 8408 8883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10286">
    <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),10284(a,1,2))].">
      <j1 rule="para" parents="15 10284"/>
    </justification>
  </clause>

  <clause id="10287">
    <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,9453,a,b,10286,a)].">
      <j1 rule="hyper" parents="58 9453 10286"/>
    </justification>
  </clause>

  <clause id="10288">
    <literal><![CDATA[
      K(x,R(y,K(z,x) * u,w)) = K(x,R(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,9451,a(flip),b,10286,a),flip(a)].">
      <j1 rule="hyper" parents="58 9451 10286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10290">
    <literal><![CDATA[
      K(x,R(y,K(x,z) * u,w)) = K(x,R(y,u,w))
    ]]></literal>
    <justification jstring="[para(5133(a,1),10288(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5133 10288"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10291">
    <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),10290(a,1,2)),flip(a)].">
      <j1 rule="para" parents="560 10290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10292">
    <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,10287,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 10287 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10293">
    <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(5131(a,1),10292(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5131 10292"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10294">
    <literal><![CDATA[
      T(x,R(T(x,y) \ z,u,w)) = T(x,R(x \ z,u,w))
    ]]></literal>
    <justification jstring="[hyper(10283,a,10293,a),flip(a)].">
      <j1 rule="hyper" parents="10283 10293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10296">
    <literal><![CDATA[
      T(x,R(y / T(x,z),u,w)) = T(x,R(x \ y,u,w))
    ]]></literal>
    <justification jstring="[hyper(5290,a,10294,a)].">
      <j1 rule="hyper" parents="5290 10294"/>
    </justification>
  </clause>

  <clause id="10297">
    <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(9520(a,1),8988(a,1,2,2))].">
      <j1 rule="para" parents="9520 8988"/>
    </justification>
  </clause>

  <clause id="10298">
    <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(8257,a,9049,a)].">
      <j1 rule="hyper" parents="8257 9049"/>
    </justification>
  </clause>

  <clause id="10299">
    <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,8625,a(flip),b,10298,a)].">
      <j1 rule="hyper" parents="58 8625 10298"/>
    </justification>
  </clause>

  <clause id="10300">
    <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,9050,a(flip),b,10299,a),flip(a)].">
      <j1 rule="hyper" parents="58 9050 10299"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10301">
    <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,8293,a(flip),b,10300,a),flip(a)].">
      <j1 rule="hyper" parents="320 8293 10300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10302">
    <literal><![CDATA[
      K(K(x * y,x) * T(x,z),u) = K(K(y,x) * T(x,z),u)
    ]]></literal>
    <justification jstring="[para(5471(a,1),10301(a,1,1))].">
      <j1 rule="para" parents="5471 10301"/>
    </justification>
  </clause>

  <clause id="10303">
    <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,9032,a(flip),b,10302,a),flip(a)].">
      <j1 rule="hyper" parents="320 9032 10302"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10304">
    <literal><![CDATA[
      K(x,T(y,T(x * z,u))) = K(x,T(y,T(z,u)))
    ]]></literal>
    <justification jstring="[hyper(9033,a,10303,a)].">
      <j1 rule="hyper" parents="9033 10303"/>
    </justification>
  </clause>

  <clause id="10305">
    <literal><![CDATA[
      K(x,T(x * y,T(y,z))) = K(x,x * y)
    ]]></literal>
    <justification jstring="[para(174(a,1),10304(a,1,2)),flip(a)].">
      <j1 rule="para" parents="174 10304"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10306">
    <literal><![CDATA[
      K(x,T(x * T(y,z),y)) = K(x,x * T(y,z))
    ]]></literal>
    <justification jstring="[para(7909(a,1),10305(a,1,2))].">
      <j1 rule="para" parents="7909 10305"/>
    </justification>
  </clause>

  <clause id="10307">
    <literal><![CDATA[
      K(x,T(T(x * T(y,z),u),y)) = T(K(x,x * T(y,z)),u)
    ]]></literal>
    <justification jstring="[para(10306(a,1),7181(a,2,1))].">
      <j1 rule="para" parents="10306 7181"/>
    </justification>
  </clause>

  <clause id="10308">
    <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(10307(a,2),7708(a,1))].">
      <j1 rule="para" parents="10307 7708"/>
    </justification>
  </clause>

  <clause id="10309">
    <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(9270,a,9273,a),flip(a)].">
      <j1 rule="hyper" parents="9270 9273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10310">
    <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,8626,a(flip),b,10309,a),flip(a)].">
      <j1 rule="hyper" parents="58 8626 10309"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10312">
    <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),9567(a,1,1))].">
      <j1 rule="para" parents="447 9567"/>
    </justification>
  </clause>

  <clause id="10313">
    <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),10228(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="75 10228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10314">
    <literal><![CDATA[
      (x / y) \ T(x * K(y,z),(x / y) \ 1) = T(x * (y / x),z)
    ]]></literal>
    <justification jstring="[para(3925(a,1),10234(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3925 10234"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10315">
    <literal><![CDATA[
      K(x * K(y,z),(x / y) \ 1) = T(x * (y / x),z) / T(y,z)
    ]]></literal>
    <justification jstring="[para(10314(a,1),6191(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10314 6191"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10316">
    <literal><![CDATA[
      K(x * K(y,z),(x / y) \ 1) = K(x,x \ T(y,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,5127,a(flip),b,10315,a),flip(a)].">
      <j1 rule="hyper" parents="320 5127 10315"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10317">
    <literal><![CDATA[
      K(K(x,y) * z,z \ x) = K(z,z \ T(x,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,8616,a(flip),b,10316,a)].">
      <j1 rule="hyper" parents="58 8616 10316"/>
    </justification>
  </clause>

  <clause id="10318">
    <literal><![CDATA[
      ((x \ y) \ R(x \ y,z,x \ y)) * (y / x) = R(y / x,z,x \ y)
    ]]></literal>
    <justification jstring="[para(4776(a,1),10252(a,2,1))].">
      <j1 rule="para" parents="4776 10252"/>
    </justification>
  </clause>

  <clause id="10319">
    <literal><![CDATA[
      a(x \ y,z,x \ y) * (y / x) = R(y / x,z,x \ y)
    ]]></literal>
    <justification jstring="[para(8942(a,1),10318(a,1,1))].">
      <j1 rule="para" parents="8942 10318"/>
    </justification>
  </clause>

  <clause id="10320">
    <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,7733,a,b,10319,a)].">
      <j1 rule="hyper" parents="320 7733 10319"/>
    </justification>
  </clause>

  <clause id="10321">
    <literal><![CDATA[
      a(x / y,z,x / y) = a(y \ x,z,y \ x)
    ]]></literal>
    <justification jstring="[hyper(9684,a,10320,a)].">
      <j1 rule="hyper" parents="9684 10320"/>
    </justification>
  </clause>

  <clause id="10322">
    <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(7132(a,1),10263(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7132 10263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10324">
    <literal><![CDATA[
      K(x,(y * (z * u)) \ ((z * (x \ u)) * x)) = K(x,T(y \ 1,z * (u / x)))
    ]]></literal>
    <justification jstring="[hyper(7711,a,10264,a),flip(a)].">
      <j1 rule="hyper" parents="7711 10264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10325">
    <literal><![CDATA[
      K(x,(y * (z * u)) \ ((z * (x \ u)) * x)) = K(x,T(y \ 1,z * u))
    ]]></literal>
    <justification jstring="[hyper(320,a,9224,a(flip),b,10324,a),flip(a)].">
      <j1 rule="hyper" parents="320 9224 10324"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10326">
    <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),10325(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7 10325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10327">
    <literal><![CDATA[
      K(x,y \ ((z * (x \ u)) * x)) = K(x,y \ (z * u))
    ]]></literal>
    <justification jstring="[hyper(7742,a,10326,a),flip(a)].">
      <j1 rule="hyper" parents="7742 10326"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10328">
    <literal><![CDATA[
      K(x,x \ (y * z)) = K(x,y * (x \ z))
    ]]></literal>
    <justification jstring="[hyper(5036,a,10327,a),flip(a)].">
      <j1 rule="hyper" parents="5036 10327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10329">
    <literal><![CDATA[
      K(x,y \ ((x \ y) * z)) = K(x,x \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,8453,a(flip),b,10327,a),flip(a)].">
      <j1 rule="hyper" parents="58 8453 10327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10330">
    <literal><![CDATA[
      K(x,x \ (y * z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (x \ z)) = u
    ]]></literal>
    <justification jstring="[para(10327(a,1),5036(a,1))].">
      <j1 rule="para" parents="10327 5036"/>
    </justification>
  </clause>

  <clause id="10331">
    <literal><![CDATA[
      T(x,x \ (y * z)) = T(x,y * (x \ z))
    ]]></literal>
    <justification jstring="[hyper(118,a,10328,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 10328 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10332">
    <literal><![CDATA[
      K(x,x \ (y * (x * z))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(4(a,1),10328(a,2,2,2))].">
      <j1 rule="para" parents="4 10328"/>
    </justification>
  </clause>

  <clause id="10333">
    <literal><![CDATA[
      (x * K(y,z * (y \ u))) \ x = K(y \ (z * u),y)
    ]]></literal>
    <justification jstring="[para(10328(a,1),6338(a,1,1,2))].">
      <j1 rule="para" parents="10328 6338"/>
    </justification>
  </clause>

  <clause id="10334">
    <literal><![CDATA[
      K(x,K(y,z * (y \ u))) = K(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[para(10328(a,1),7960(a,1,2))].">
      <j1 rule="para" parents="10328 7960"/>
    </justification>
  </clause>

  <clause id="10335">
    <literal><![CDATA[
      K(x,x \ ((x \ y) \ z)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(5(a,1),10329(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5 10329"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10336">
    <literal><![CDATA[
      T(x,y * (x \ z)) = (x \ (y * z)) \ (y * z)
    ]]></literal>
    <justification jstring="[hyper(427,a,10331,a),flip(a)].">
      <j1 rule="hyper" parents="427 10331"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10337">
    <literal><![CDATA[
      K(x,x \ (y * (z * x))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,8586,a,b,10332,a)].">
      <j1 rule="hyper" parents="58 8586 10332"/>
    </justification>
  </clause>

  <clause id="10338">
    <literal><![CDATA[
      K(x,(x * y) \ z) = K(x,x \ (y \ z))
    ]]></literal>
    <justification jstring="[para(4(a,1),10335(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="4 10335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10339">
    <literal><![CDATA[
      K(x,x \ (y \ (z * x))) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(8448,a,10338,a),flip(a)].">
      <j1 rule="hyper" parents="8448 10338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10340">
    <literal><![CDATA[
      K(x,y \ (x \ z)) = K(x,x \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(7393,a,10338,a)].">
      <j1 rule="hyper" parents="7393 10338"/>
    </justification>
  </clause>

  <clause id="10341">
    <literal><![CDATA[
      K(x,x \ (y \ (x * z))) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(10338(a,1),7391(a,1))].">
      <j1 rule="para" parents="10338 7391"/>
    </justification>
  </clause>

  <clause id="10342">
    <literal><![CDATA[
      K(x,x \ (y \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ (x \ z)) = u
    ]]></literal>
    <justification jstring="[para(10338(a,1),7393(a,1))].">
      <j1 rule="para" parents="10338 7393"/>
    </justification>
  </clause>

  <clause id="10343">
    <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),10339(a,1,2,2,2))].">
      <j1 rule="para" parents="101 10339"/>
    </justification>
  </clause>

  <clause id="10344">
    <literal><![CDATA[
      K(x,y \ (x \ (y * z))) = K(x,x \ z)
    ]]></literal>
    <justification jstring="[para(4(a,1),10340(a,2,2,2))].">
      <j1 rule="para" parents="4 10340"/>
    </justification>
  </clause>

  <clause id="10345">
    <literal><![CDATA[
      L(K(x,x \ y),y,z) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(7597,a,10344,a)].">
      <j1 rule="hyper" parents="7597 10344"/>
    </justification>
  </clause>

  <clause id="10346">
    <literal><![CDATA[
      K(x,y \ (x \ (y * (z * x)))) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,4910,a(flip),b,10344,a),flip(a)].">
      <j1 rule="hyper" parents="320 4910 10344"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10347">
    <literal><![CDATA[
      (x * y) * K(z,z \ y) = x * (z * (y / z))
    ]]></literal>
    <justification jstring="[para(10344(a,1),8537(a,1,2))].">
      <j1 rule="para" parents="10344 8537"/>
    </justification>
  </clause>

  <clause id="10348">
    <literal><![CDATA[
      a(x,y,K(z,z \ y)) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,10345,a,b,1934,a),flip(a)].">
      <j1 rule="hyper" parents="115 10345 1934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10349">
    <literal><![CDATA[
      L(K(x \ y,x),y,z) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(5893,a,10348,a)].">
      <j1 rule="hyper" parents="5893 10348"/>
    </justification>
  </clause>

  <clause id="10350">
    <literal><![CDATA[
      K(x \ (y \ (x * z)),y) = K(y \ z,y)
    ]]></literal>
    <justification jstring="[hyper(8476,a,10349,a)].">
      <j1 rule="hyper" parents="8476 10349"/>
    </justification>
  </clause>

  <clause id="10351">
    <literal><![CDATA[
      K((x * y) \ z,y) = K(y \ (x \ z),y)
    ]]></literal>
    <justification jstring="[hyper(6856,a,10349,a)].">
      <j1 rule="hyper" parents="6856 10349"/>
    </justification>
  </clause>

  <clause id="10353">
    <literal><![CDATA[
      (x * y) * K(z \ y,z) = x * ((z \ y) * z)
    ]]></literal>
    <justification jstring="[hyper(119,a,10349,a(flip),b,463,a)].">
      <j1 rule="hyper" parents="119 10349 463"/>
    </justification>
  </clause>

  <clause id="10354">
    <literal><![CDATA[
      K(x,L(y,x,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(8730,a,10346,a)].">
      <j1 rule="hyper" parents="8730 10346"/>
    </justification>
  </clause>

  <clause id="10355">
    <literal><![CDATA[
      K(L(x,y,z),y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(9028,a,10354,a)].">
      <j1 rule="hyper" parents="9028 10354"/>
    </justification>
  </clause>

  <clause id="10358">
    <literal><![CDATA[
      T(x,L(y,x,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(118,a,10354,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 10354 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10360">
    <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),10354(a,1,2))].">
      <j1 rule="para" parents="501 10354"/>
    </justification>
  </clause>

  <clause id="10362">
    <literal><![CDATA[
      K(L(x,y,z),L(u,x,w)) = L(K(x,u),y * x,z)
    ]]></literal>
    <justification jstring="[para(10354(a,1),6615(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10354 6615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10363">
    <literal><![CDATA[
      (x * (y * z)) * K(z,y) = x * (z * y)
    ]]></literal>
    <justification jstring="[para(10354(a,1),6633(a,1,2))].">
      <j1 rule="para" parents="10354 6633"/>
    </justification>
  </clause>

  <clause id="10364">
    <literal><![CDATA[
      (x * (y * z)) * K(z,y) != u
    ]]></literal>
    <literal><![CDATA[
      x * (z * y) = u
    ]]></literal>
    <justification jstring="[para(10354(a,1),6685(a,1,2))].">
      <j1 rule="para" parents="10354 6685"/>
    </justification>
  </clause>

  <clause id="10365">
    <literal><![CDATA[
      L(K(x,y),T(y,z) * u,w) = K(L(x,y,v5),L(y,u,w))
    ]]></literal>
    <justification jstring="[para(10354(a,1),9957(a,1,1))].">
      <j1 rule="para" parents="10354 9957"/>
    </justification>
  </clause>

  <clause id="10366">
    <literal><![CDATA[
      K(L(x,y,z),y) = K(x,L(y,x,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,10354,a,b,10355,a),flip(a)].">
      <j1 rule="hyper" parents="320 10354 10355"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10369">
    <literal><![CDATA[
      L(x,y,z) * T(y,x) = y * L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(119,a,10358,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 10358 17"/>
    </justification>
  </clause>

  <clause id="10370">
    <literal><![CDATA[
      L(x,y,z) = (z * T(y,x)) \ (z * (T(y,x) * x))
    ]]></literal>
    <justification jstring="[para(10358(a,1),6904(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="10358 6904"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10372">
    <literal><![CDATA[
      K(x,L(y,x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(10366(a,1),7392(a,1))].">
      <j1 rule="para" parents="10366 7392"/>
    </justification>
  </clause>

  <clause id="10374">
    <literal><![CDATA[
      K(x,(y * x) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,x \ (y \ z)) = u
    ]]></literal>
    <justification jstring="[para(298(a,1),10372(a,1,2))].">
      <j1 rule="para" parents="298 10372"/>
    </justification>
  </clause>

  <clause id="10375">
    <literal><![CDATA[
      K(x \ (y \ z),y) = K(y \ (x \ z),y)
    ]]></literal>
    <justification jstring="[para(5(a,1),10350(a,1,1,2,2))].">
      <j1 rule="para" parents="5 10350"/>
    </justification>
  </clause>

  <clause id="10376">
    <literal><![CDATA[
      K(x \ (y \ (z * x)),x) = K(y \ z,x)
    ]]></literal>
    <justification jstring="[hyper(8429,a,10351,a),flip(a)].">
      <j1 rule="hyper" parents="8429 10351"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10377">
    <literal><![CDATA[
      K(x \ (y \ z),x) * z = z * K(z / (y * x),x)
    ]]></literal>
    <justification jstring="[para(10351(a,1),7955(a,1,1))].">
      <j1 rule="para" parents="10351 7955"/>
    </justification>
  </clause>

  <clause id="10378">
    <literal><![CDATA[
      K(x \ (y \ z),x) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ (x \ z),x) = u
    ]]></literal>
    <justification jstring="[para(10351(a,1),8472(a,1))].">
      <j1 rule="para" parents="10351 8472"/>
    </justification>
  </clause>

  <clause id="10379">
    <literal><![CDATA[
      R(x,y * z,K(z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(838,a,10363,a)].">
      <j1 rule="hyper" parents="838 10363"/>
    </justification>
  </clause>

  <clause id="10380">
    <literal><![CDATA[
      (x / (y * z)) * (z * y) = x * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(326,a,10363,a),flip(a)].">
      <j1 rule="hyper" parents="326 10363"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10381">
    <literal><![CDATA[
      K(x,T(y,z * (x * y))) * (z * (y * x)) = z * (x * y)
    ]]></literal>
    <justification jstring="[hyper(119,a,10363,a(flip),b,7921,a)].">
      <j1 rule="hyper" parents="119 10363 7921"/>
    </justification>
  </clause>

  <clause id="10382">
    <literal><![CDATA[
      K(x * (y * z),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x * (z * y),z) = u
    ]]></literal>
    <justification jstring="[para(10363(a,1),7334(a,1,1))].">
      <j1 rule="para" parents="10363 7334"/>
    </justification>
  </clause>

  <clause id="10383">
    <literal><![CDATA[
      R(x,y,T(z,y)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(6898,a,10379,a)].">
      <j1 rule="hyper" parents="6898 10379"/>
    </justification>
  </clause>

  <clause id="10384">
    <literal><![CDATA[
      R(x,y,K(z \ y,z)) = x
    ]]></literal>
    <justification jstring="[para(5(a,1),10379(a,1,2))].">
      <j1 rule="para" parents="5 10379"/>
    </justification>
  </clause>

  <clause id="10385">
    <literal><![CDATA[
      R(x,y / z,z) = R(x,z \ y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,10240,a(flip),b,10384,a),flip(a)].">
      <j1 rule="hyper" parents="58 10240 10384"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10387">
    <literal><![CDATA[
      (x * T(y,z)) / (y * z) = R(x / z,z,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,527,a(flip),b,10383,a)].">
      <j1 rule="hyper" parents="58 527 10383"/>
    </justification>
  </clause>

  <clause id="10388">
    <literal><![CDATA[
      R(x,y,z / y) = R(x,y,y \ z)
    ]]></literal>
    <justification jstring="[para(107(a,1),10383(a,1,3)),flip(a)].">
      <j1 rule="para" parents="107 10383"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10390">
    <literal><![CDATA[
      R(x,y,z) * (z * y) = (x * y) * T(z,y)
    ]]></literal>
    <justification jstring="[para(10383(a,1),516(a,1,1))].">
      <j1 rule="para" parents="10383 516"/>
    </justification>
  </clause>

  <clause id="10392">
    <literal><![CDATA[
      R(x,y,K(z,T(u,y))) = R(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[para(7158(a,2),10383(a,1,3))].">
      <j1 rule="para" parents="7158 10383"/>
    </justification>
  </clause>

  <clause id="10394">
    <literal><![CDATA[
      R(K(x,(y / (z / u)) \ x),u \ z,u) = K(x,z / ((x \ y) * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,8488,a(flip),b,10385,a),flip(a)].">
      <j1 rule="hyper" parents="58 8488 10385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10395">
    <literal><![CDATA[
      R(K(x,(y / z) / u),z \ y,z) = K(x,y / (u * z))
    ]]></literal>
    <justification jstring="[hyper(58,a,6944,a(flip),b,10385,a),flip(a)].">
      <j1 rule="hyper" parents="58 6944 10385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10396">
    <literal><![CDATA[
      R(x / (y / z),z \ y,z) = (x * z) / y
    ]]></literal>
    <justification jstring="[hyper(58,a,525,a(flip),b,10385,a),flip(a)].">
      <j1 rule="hyper" parents="58 525 10385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10399">
    <literal><![CDATA[
      R(x,y \ z,y) * z = (x * (z / y)) * y
    ]]></literal>
    <justification jstring="[para(10385(a,1),508(a,1,1))].">
      <j1 rule="para" parents="10385 508"/>
    </justification>
  </clause>

  <clause id="10400">
    <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(10369(a,1),1414(a,1,2,2))].">
      <j1 rule="para" parents="10369 1414"/>
    </justification>
  </clause>

  <clause id="10401">
    <literal><![CDATA[
      x * K(y \ (z \ u),z) = x * K(z \ (y \ u),z)
    ]]></literal>
    <justification jstring="[hyper(119,a,10375,a,b,4,a)].">
      <j1 rule="hyper" parents="119 10375 4"/>
    </justification>
  </clause>

  <clause id="10402">
    <literal><![CDATA[
      (x * T(y,z)) / (y * z) = (x * y) / (z * y)
    ]]></literal>
    <justification jstring="[hyper(117,a,6331,a(flip),b,10380,a),flip(a)].">
      <j1 rule="hyper" parents="117 6331 10380"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10403">
    <literal><![CDATA[
      R(R(x,y,x) / x,x,z) = (z * R(x,y,x)) / (z * x)
    ]]></literal>
    <justification jstring="[para(7106(a,1),10387(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7106 10387"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10404">
    <literal><![CDATA[
      R(x / ((y * z) / y),z,y) = (x * y) / (y * z)
    ]]></literal>
    <justification jstring="[para(4(a,1),10396(a,1,2))].">
      <j1 rule="para" parents="4 10396"/>
    </justification>
  </clause>

  <clause id="10405">
    <literal><![CDATA[
      K(x,K(y / z,u * z)) = K(x,K(y / z,u * y))
    ]]></literal>
    <justification jstring="[para(75(a,1),10334(a,1,2,2,2))].">
      <j1 rule="para" parents="75 10334"/>
    </justification>
  </clause>

  <clause id="10406">
    <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(10336(a,2),5153(a,1,1))].">
      <j1 rule="para" parents="10336 5153"/>
    </justification>
  </clause>

  <clause id="10409">
    <literal><![CDATA[
      K(x,x \ y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,u * (x \ (u \ y))) = z
    ]]></literal>
    <justification jstring="[para(5(a,1),10330(a,1,2,2))].">
      <j1 rule="para" parents="5 10330"/>
    </justification>
  </clause>

  <clause id="10410">
    <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),10342(a,1,2,2))].">
      <j1 rule="para" parents="17 10342"/>
    </justification>
  </clause>

  <clause id="10411">
    <literal><![CDATA[
      K(L(x,y,z),L(u,x,w)) = K(L(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(320,a,6615,a(flip),b,10362,a),flip(a)].">
      <j1 rule="hyper" parents="320 6615 10362"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10412">
    <literal><![CDATA[
      K(L(x,y,z),(u * x) \ (u * w)) = K(L(x,y,z),x \ w)
    ]]></literal>
    <justification jstring="[hyper(6709,a,10411,a)].">
      <j1 rule="hyper" parents="6709 10411"/>
    </justification>
  </clause>

  <clause id="10413">
    <literal><![CDATA[
      (x * (y * z)) * K(z,L(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      x * (z * y) = w
    ]]></literal>
    <justification jstring="[para(10354(a,2),10364(a,1,2))].">
      <j1 rule="para" parents="10354 10364"/>
    </justification>
  </clause>

  <clause id="10414">
    <literal><![CDATA[
      L(x,T(y,x),z) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,13,a,b,10370,a)].">
      <j1 rule="hyper" parents="320 13 10370"/>
    </justification>
  </clause>

  <clause id="10416">
    <literal><![CDATA[
      L(x,y / x,z) = L(x,x \ y,z)
    ]]></literal>
    <justification jstring="[para(107(a,1),10414(a,1,2)),flip(a)].">
      <j1 rule="para" parents="107 10414"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10420">
    <literal><![CDATA[
      L(x,x \ (y \ z),y) = (y * ((y \ z) / x)) \ z
    ]]></literal>
    <justification jstring="[hyper(58,a,567,a(flip),b,10416,a),flip(a)].">
      <j1 rule="hyper" parents="58 567 10416"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10421">
    <literal><![CDATA[
      L(x,x \ y,z) = (z * (y / x)) \ (z * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,94,a(flip),b,10416,a),flip(a)].">
      <j1 rule="hyper" parents="58 94 10416"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10422">
    <literal><![CDATA[
      x / L(y,y \ (z \ x),z) = z * ((z \ x) / y)
    ]]></literal>
    <justification jstring="[hyper(366,a,10421,a(flip))].">
      <j1 rule="hyper" parents="366 10421"/>
    </justification>
  </clause>

  <clause id="10423">
    <literal><![CDATA[
      K(x,T(L(y,y \ z,u),u * z)) = K(x,(u * z) / (u * (z / y)))
    ]]></literal>
    <justification jstring="[para(10421(a,2),7890(a,1,2,1))].">
      <j1 rule="para" parents="10421 7890"/>
    </justification>
  </clause>

  <clause id="10424">
    <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(10421(a,2),7989(a,1,1,2))].">
      <j1 rule="para" parents="10421 7989"/>
    </justification>
  </clause>

  <clause id="10425">
    <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),10374(a,1,2))].">
      <j1 rule="para" parents="9 10374"/>
    </justification>
  </clause>

  <clause id="10426">
    <literal><![CDATA[
      ((x * y) * z) / (z * y) = R(x * K(y,z),y,z)
    ]]></literal>
    <justification jstring="[para(6471(a,1),10404(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6471 10404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10427">
    <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(7179(a,1),10426(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7179 10426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10428">
    <literal><![CDATA[
      K(x \ (y * z),x) = K(y * (x \ z),x)
    ]]></literal>
    <justification jstring="[hyper(6345,a,10333,a),flip(a)].">
      <j1 rule="hyper" parents="6345 10333"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10429">
    <literal><![CDATA[
      K(x \ (y * z),x) != u
    ]]></literal>
    <literal><![CDATA[
      K(y * (x \ z),x) = u
    ]]></literal>
    <justification jstring="[para(10333(a,1),6345(a,1))].">
      <j1 rule="para" parents="10333 6345"/>
    </justification>
  </clause>

  <clause id="10430">
    <literal><![CDATA[
      K(x * (y \ (x \ z)),y) = K(y \ z,y)
    ]]></literal>
    <justification jstring="[para(5(a,1),10428(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5 10428"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10431">
    <literal><![CDATA[
      K(L(x,y,z),L(y,u,w)) = K(x,L(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,9955,a(flip),b,10365,a),flip(a)].">
      <j1 rule="hyper" parents="58 9955 10365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10432">
    <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(10365(a,2),7392(a,1))].">
      <j1 rule="para" parents="10365 7392"/>
    </justification>
  </clause>

  <clause id="10433">
    <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),10431(a,1,1))].">
      <j1 rule="para" parents="298 10431"/>
    </justification>
  </clause>

  <clause id="10434">
    <literal><![CDATA[
      (x * R(y,z,y)) / (x * y) = R(a(y,z,y),y,x)
    ]]></literal>
    <justification jstring="[para(8944(a,1),10403(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8944 10403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10435">
    <literal><![CDATA[
      R(a(x,y,x),x,z) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(9565,a,10434,a),flip(a)].">
      <j1 rule="hyper" parents="9565 10434"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10437">
    <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,10435,a)].">
      <j1 rule="hyper" parents="58 511 10435"/>
    </justification>
  </clause>

  <clause id="10438">
    <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),10432(a,1,2,1))].">
      <j1 rule="para" parents="104 10432"/>
    </justification>
  </clause>

  <clause id="10439">
    <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),10438(a,1,2))].">
      <j1 rule="para" parents="5 10438"/>
    </justification>
  </clause>

  <clause id="10440">
    <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),10438(a,1,2))].">
      <j1 rule="para" parents="7 10438"/>
    </justification>
  </clause>

  <clause id="10441">
    <literal><![CDATA[
      K(L(x,y,z),u \ (x \ (u * w))) = K(L(x,y,z),x \ w)
    ]]></literal>
    <justification jstring="[hyper(9274,a,10412,a)].">
      <j1 rule="hyper" parents="9274 10412"/>
    </justification>
  </clause>

  <clause id="10443">
    <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),10433(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7 10433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10444">
    <literal><![CDATA[
      K(x \ ((x \ y) \ z),L(x,u,w)) = K(y \ z,L(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(10053,a,10443,a)].">
      <j1 rule="hyper" parents="10053 10443"/>
    </justification>
  </clause>

  <clause id="10445">
    <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),10423(a,1,2))].">
      <j1 rule="para" parents="20 10423"/>
    </justification>
  </clause>

  <clause id="10446">
    <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,9776,a(flip),b,10360,a)].">
      <j1 rule="hyper" parents="58 9776 10360"/>
    </justification>
  </clause>

  <clause id="10447">
    <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,10441,a(flip),b,10446,a),flip(a)].">
      <j1 rule="hyper" parents="58 10441 10446"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10449">
    <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,10447,a,b,4764,a)].">
      <j1 rule="hyper" parents="119 10447 4764"/>
    </justification>
  </clause>

  <clause id="10450">
    <literal><![CDATA[
      x / L(T(y,y \ x),z,u) = L(y,z,u) \ x
    ]]></literal>
    <justification jstring="[para(10449(a,1),4839(a,1,2))].">
      <j1 rule="para" parents="10449 4839"/>
    </justification>
  </clause>

  <clause id="10451">
    <literal><![CDATA[
      x / L(y \ x,z,u) = L(x / y,z,u) \ x
    ]]></literal>
    <justification jstring="[para(643(a,1),10450(a,1,2,1))].">
      <j1 rule="para" parents="643 10450"/>
    </justification>
  </clause>

  <clause id="10453">
    <literal><![CDATA[
      (L(x / y,z,u) \ x) \ x = L(y \ x,z,u)
    ]]></literal>
    <justification jstring="[hyper(188,a,10451,a)].">
      <j1 rule="hyper" parents="188 10451"/>
    </justification>
  </clause>

  <clause id="10455">
    <literal><![CDATA[
      L((x \ y) \ y,z,u) = (L(x,z,u) \ y) \ y
    ]]></literal>
    <justification jstring="[para(72(a,1),10453(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="72 10453"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10459">
    <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(10455(a,2),4799(a,1,1))].">
      <j1 rule="para" parents="10455 4799"/>
    </justification>
  </clause>

  <clause id="10460">
    <literal><![CDATA[
      K(L(x,y,z) \ u,L(x,y,z)) = K(x \ u,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(5028,a,10459,a),flip(a)].">
      <j1 rule="hyper" parents="5028 10459"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10461">
    <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(10378,a,10460,a)].">
      <j1 rule="hyper" parents="10378 10460"/>
    </justification>
  </clause>

  <clause id="10462">
    <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,7470,a(flip),b,10461,a),flip(a)].">
      <j1 rule="hyper" parents="58 7470 10461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10463">
    <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,10444,a(flip),b,10462,a)].">
      <j1 rule="hyper" parents="58 10444 10462"/>
    </justification>
  </clause>

  <clause id="10464">
    <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),10400(a,1,1,1))].">
      <j1 rule="para" parents="105 10400"/>
    </justification>
  </clause>

  <clause id="10465">
    <literal><![CDATA[
      K(L(x,y,z),x * T(y,x)) = K(x,y * L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(1648,a,10464,a),flip(a)].">
      <j1 rule="hyper" parents="1648 10464"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10466">
    <literal><![CDATA[
      K(L(x,y,z),y * x) = K(x,y * L(x,y,z))
    ]]></literal>
    <justification jstring="[para(105(a,1),10465(a,1,2))].">
      <j1 rule="para" parents="105 10465"/>
    </justification>
  </clause>

  <clause id="10467">
    <literal><![CDATA[
      K(x,y * L(x,y,z)) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(8404,a,10466,a),flip(a)].">
      <j1 rule="hyper" parents="8404 10466"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10469">
    <literal><![CDATA[
      L(K(x,x * y),z * x,u) = K(L(x,z,u),y * L(x,y,w))
    ]]></literal>
    <justification jstring="[para(10467(a,1),6615(a,1,1))].">
      <j1 rule="para" parents="10467 6615"/>
    </justification>
  </clause>

  <clause id="10470">
    <literal><![CDATA[
      K(L(x,y,z),u * L(x,u,w)) = K(L(x,y,z),x * u)
    ]]></literal>
    <justification jstring="[hyper(8394,a,10469,a),flip(a)].">
      <j1 rule="hyper" parents="8394 10469"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10471">
    <literal><![CDATA[
      L(K(L(x,y,z),x * y),y,z) = K(x,x * y)
    ]]></literal>
    <justification jstring="[para(10470(a,1),9676(a,1,1))].">
      <j1 rule="para" parents="10470 9676"/>
    </justification>
  </clause>

  <clause id="10472">
    <literal><![CDATA[
      L(K(x,x * y),y,z) = K(x,x * y)
    ]]></literal>
    <justification jstring="[para(8908(a,1),10471(a,1,1))].">
      <j1 rule="para" parents="8908 10471"/>
    </justification>
  </clause>

  <clause id="10474">
    <literal><![CDATA[
      K(x,y \ (z * x)) = K(x,x * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(58,a,9673,a(flip),b,10472,a)].">
      <j1 rule="hyper" parents="58 9673 10472"/>
    </justification>
  </clause>

  <clause id="10475">
    <literal><![CDATA[
      K(x,y \ ((y * z) * x)) = K(x,x * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,9672,a(flip),b,10472,a)].">
      <j1 rule="hyper" parents="58 9672 10472"/>
    </justification>
  </clause>

  <clause id="10476">
    <literal><![CDATA[
      1 / L(K(x,x * y),y,z) = K(x * y,x)
    ]]></literal>
    <justification jstring="[para(10472(a,2),4971(a,1,2))].">
      <j1 rule="para" parents="10472 4971"/>
    </justification>
  </clause>

  <clause id="10478">
    <literal><![CDATA[
      K(x,(y \ z) \ x) = K(x,x * (z \ y))
    ]]></literal>
    <justification jstring="[hyper(6605,a,10474,a)].">
      <j1 rule="hyper" parents="6605 10474"/>
    </justification>
  </clause>

  <clause id="10479">
    <literal><![CDATA[
      K(x,x * ((y * z) \ y)) = K(x,z \ x)
    ]]></literal>
    <justification jstring="[hyper(6588,a,10474,a),flip(a)].">
      <j1 rule="hyper" parents="6588 10474"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10480">
    <literal><![CDATA[
      L(K(x,x * (y \ z)),y \ z,u) = K(x,y \ (z * x))
    ]]></literal>
    <justification jstring="[hyper(320,a,10472,a,b,10474,a)].">
      <j1 rule="hyper" parents="320 10472 10474"/>
    </justification>
  </clause>

  <clause id="10482">
    <literal><![CDATA[
      K(x,y \ ((y * z) * x)) = K(x,z * x)
    ]]></literal>
    <justification jstring="[hyper(320,a,5385,a,b,10475,a),flip(a)].">
      <j1 rule="hyper" parents="320 5385 10475"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10483">
    <literal><![CDATA[
      L(K(x,y * x),y,z) = K(x,y * x)
    ]]></literal>
    <justification jstring="[hyper(58,a,9674,a,b,10482,a)].">
      <j1 rule="hyper" parents="58 9674 10482"/>
    </justification>
  </clause>

  <clause id="10485">
    <literal><![CDATA[
      a(x,y,K(z,y * z)) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,10483,a,b,1934,a),flip(a)].">
      <j1 rule="hyper" parents="115 10483 1934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10486">
    <literal><![CDATA[
      a(x,y,K(y * z,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,10483,a(flip),b,5896,a),flip(a)].">
      <j1 rule="hyper" parents="115 10483 5896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10487">
    <literal><![CDATA[
      L(K(x * y,y),x,z) = K(x * y,y)
    ]]></literal>
    <justification jstring="[hyper(5893,a,10485,a)].">
      <j1 rule="hyper" parents="5893 10485"/>
    </justification>
  </clause>

  <clause id="10488">
    <literal><![CDATA[
      a(x,y,K(z,y \ z)) = 1
    ]]></literal>
    <justification jstring="[para(5(a,1),10486(a,1,3,1))].">
      <j1 rule="para" parents="5 10486"/>
    </justification>
  </clause>

  <clause id="10489">
    <literal><![CDATA[
      L(K(x * y,y),x,z) = K(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,5266,a(flip),b,10487,a),flip(a)].">
      <j1 rule="hyper" parents="320 5266 10487"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10490">
    <literal><![CDATA[
      L(K(x * y,x),y,z) = K(x * y,x)
    ]]></literal>
    <justification jstring="[para(5266(a,1),10489(a,1,1))].">
      <j1 rule="para" parents="5266 10489"/>
    </justification>
  </clause>

  <clause id="10491">
    <literal><![CDATA[
      K((x * (y \ 1)) \ z,y) = K(y * (x \ z),y)
    ]]></literal>
    <justification jstring="[hyper(6857,a,10490,a)].">
      <j1 rule="hyper" parents="6857 10490"/>
    </justification>
  </clause>

  <clause id="10492">
    <literal><![CDATA[
      K(x \ (y * z),z) = K(z * (x \ y),z)
    ]]></literal>
    <justification jstring="[hyper(58,a,9666,a(flip),b,10490,a)].">
      <j1 rule="hyper" parents="58 9666 10490"/>
    </justification>
  </clause>

  <clause id="10493">
    <literal><![CDATA[
      K((x \ y) \ z,x) = K(x * (y \ z),x)
    ]]></literal>
    <justification jstring="[hyper(8430,a,10492,a)].">
      <j1 rule="hyper" parents="8430 10492"/>
    </justification>
  </clause>

  <clause id="10494">
    <literal><![CDATA[
      K(x * ((y * x) \ z),x) = K(y \ z,x)
    ]]></literal>
    <justification jstring="[hyper(8429,a,10492,a),flip(a)].">
      <j1 rule="hyper" parents="8429 10492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10495">
    <literal><![CDATA[
      K((x \ y) \ z,z) = K(z * (y \ x),z)
    ]]></literal>
    <justification jstring="[hyper(6639,a,10492,a)].">
      <j1 rule="hyper" parents="6639 10492"/>
    </justification>
  </clause>

  <clause id="10497">
    <literal><![CDATA[
      K(x * (y \ (x \ z)),x) = K(y \ z,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,7641,a(flip),b,10492,a),flip(a)].">
      <j1 rule="hyper" parents="58 7641 10492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10498">
    <literal><![CDATA[
      K(x,y \ z) * K(x * (y \ z),x) = a(x,(z \ y) \ 1,x)
    ]]></literal>
    <justification jstring="[para(10492(a,1),8950(a,1,2))].">
      <j1 rule="para" parents="10492 8950"/>
    </justification>
  </clause>

  <clause id="10499">
    <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,10463,a(flip),b,10493,a),flip(a)].">
      <j1 rule="hyper" parents="58 10463 10493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10500">
    <literal><![CDATA[
      K((x / y) \ z,y) = K(y * (x \ z),y)
    ]]></literal>
    <justification jstring="[para(7(a,1),10494(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7 10494"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10501">
    <literal><![CDATA[
      1 / ((x * (y \ T(y * z,y))) \ (x * z)) = K(y * z,y)
    ]]></literal>
    <justification jstring="[para(6674(a,2),10476(a,1,2))].">
      <j1 rule="para" parents="6674 10476"/>
    </justification>
  </clause>

  <clause id="10503">
    <literal><![CDATA[
      K((x * (1 / y)) \ z,y) = K(y * (x \ z),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,8649,a,b,10491,a)].">
      <j1 rule="hyper" parents="58 8649 10491"/>
    </justification>
  </clause>

  <clause id="10504">
    <literal><![CDATA[
      K(x,y \ (z * x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,x * (y \ z)) = u
    ]]></literal>
    <justification jstring="[para(10480(a,1),3666(a,1))].">
      <j1 rule="para" parents="10480 3666"/>
    </justification>
  </clause>

  <clause id="10505">
    <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(1412(a,1),10504(a,1,2))].">
      <j1 rule="para" parents="1412 10504"/>
    </justification>
  </clause>

  <clause id="10506">
    <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,7879,a,b,10501,a)].">
      <j1 rule="hyper" parents="320 7879 10501"/>
    </justification>
  </clause>

  <clause id="10508">
    <literal><![CDATA[
      a(x,(y \ z) \ 1,x) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,z \ y,x) = u
    ]]></literal>
    <justification jstring="[para(10498(a,1),8979(a,1))].">
      <j1 rule="para" parents="10498 8979"/>
    </justification>
  </clause>

  <clause id="10509">
    <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,9858,a(flip),b,10499,a),flip(a)].">
      <j1 rule="hyper" parents="320 9858 10499"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10510">
    <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,10509,a),flip(a)].">
      <j1 rule="hyper" parents="320 673 10509"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10511">
    <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),10510(a,1,1,2))].">
      <j1 rule="para" parents="4 10510"/>
    </justification>
  </clause>

  <clause id="10512">
    <literal><![CDATA[
      K((x \ y) \ z,L(x,u,w)) = K(x * (y \ z),L(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,10499,a(flip),b,10511,a)].">
      <j1 rule="hyper" parents="58 10499 10511"/>
    </justification>
  </clause>

  <clause id="10513">
    <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(10511(a,1),5204(a,1,1,2))].">
      <j1 rule="para" parents="10511 5204"/>
    </justification>
  </clause>

  <clause id="10514">
    <literal><![CDATA[
      K((x \ y) \ z,L(x,u,w)) = K((y \ z) * x,L(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(320,a,9593,a,b,10512,a),flip(a)].">
      <j1 rule="hyper" parents="320 9593 10512"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10515">
    <literal><![CDATA[
      K(x \ (y * z),L(y,u,w)) = K((x \ z) * y,L(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(9859,a,10514,a)].">
      <j1 rule="hyper" parents="9859 10514"/>
    </justification>
  </clause>

  <clause id="10516">
    <literal><![CDATA[
      K(x \ (y * z),L(z,u,w)) = K((x \ y) * z,L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,9732,a,b,10515,a)].">
      <j1 rule="hyper" parents="58 9732 10515"/>
    </justification>
  </clause>

  <clause id="10517">
    <literal><![CDATA[
      K(((x \ y) \ z) * u,L(u,z,x)) = K(y \ (x * (u * z)),u)
    ]]></literal>
    <justification jstring="[hyper(58,a,9024,a(flip),b,10515,a),flip(a)].">
      <j1 rule="hyper" parents="58 9024 10515"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10518">
    <literal><![CDATA[
      K((x / y) \ z,L(y,u,w)) = K((x \ z) * y,L(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,9730,a,b,10516,a)].">
      <j1 rule="hyper" parents="58 9730 10516"/>
    </justification>
  </clause>

  <clause id="10519">
    <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(7963(a,2),10506(a,1,1))].">
      <j1 rule="para" parents="7963 10506"/>
    </justification>
  </clause>

  <clause id="10520">
    <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(5517(a,1),10513(a,1,1))].">
      <j1 rule="para" parents="5517 10513"/>
    </justification>
  </clause>

  <clause id="10521">
    <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,10520,a),flip(a)].">
      <j1 rule="hyper" parents="58 20 10520"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10522">
    <literal><![CDATA[
      R(L(x,y,z),u,L(x,y,z)) = L(R(x,u,x),y,z)
    ]]></literal>
    <justification jstring="[para(5204(a,1),10521(a,2,1))].">
      <j1 rule="para" parents="5204 10521"/>
    </justification>
  </clause>

  <clause id="10523">
    <literal><![CDATA[
      R(x,y,L(x,z,u)) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(141,a,10522,a)].">
      <j1 rule="hyper" parents="141 10522"/>
    </justification>
  </clause>

  <clause id="10524">
    <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(10522(a,1),7138(a,1,2))].">
      <j1 rule="para" parents="10522 7138"/>
    </justification>
  </clause>

  <clause id="10525">
    <literal><![CDATA[
      T(x * K(y * x,x),y) = R(x,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,4932,a,b,10523,a)].">
      <j1 rule="hyper" parents="320 4932 10523"/>
    </justification>
  </clause>

  <clause id="10526">
    <literal><![CDATA[
      x * R(y,z,L(y,u,w)) = x * R(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,10523,a,b,4,a)].">
      <j1 rule="hyper" parents="119 10523 4"/>
    </justification>
  </clause>

  <clause id="10528">
    <literal><![CDATA[
      K(x * L(y,z,u),y) = (w * T(y,x)) \ (w * R(y,x,y))
    ]]></literal>
    <justification jstring="[para(10523(a,1),9945(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10523 9945"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10529">
    <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(10523(a,1),10312(a,1,1,2,2))].">
      <j1 rule="para" parents="10523 10312"/>
    </justification>
  </clause>

  <clause id="10530">
    <literal><![CDATA[
      K(x * L(y,z,u),y) = K(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,7328,a(flip),b,10528,a),flip(a)].">
      <j1 rule="hyper" parents="320 7328 10528"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10532">
    <literal><![CDATA[
      K(x * L(y,z,u),y) = K(x,y) * a(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,8968,a,b,10530,a),flip(a)].">
      <j1 rule="hyper" parents="320 8968 10530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10533">
    <literal><![CDATA[
      K(x * (L(x,y,z) \ u),x) = K(u,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,7431,a(flip),b,10530,a),flip(a)].">
      <j1 rule="hyper" parents="58 7431 10530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10534">
    <literal><![CDATA[
      K(x * (y * z),z) = K(z * (x * y),z)
    ]]></literal>
    <justification jstring="[para(90(a,1),10530(a,1,1))].">
      <j1 rule="para" parents="90 10530"/>
    </justification>
  </clause>

  <clause id="10536">
    <literal><![CDATA[
      K(L(x,y,z) \ u,x) = K(x \ u,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,10497,a(flip),b,10533,a)].">
      <j1 rule="hyper" parents="58 10497 10533"/>
    </justification>
  </clause>

  <clause id="10537">
    <literal><![CDATA[
      K(x / L(y,z,u),y) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(8264,a,10536,a)].">
      <j1 rule="hyper" parents="8264 10536"/>
    </justification>
  </clause>

  <clause id="10538">
    <literal><![CDATA[
      K(x \ (y * L(x,z,u)),x) = K(y,x)
    ]]></literal>
    <justification jstring="[para(6(a,1),10537(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6 10537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10539">
    <literal><![CDATA[
      T(x * L(y,z,u),K(x,y)) = x * L(y,z,u)
    ]]></literal>
    <justification jstring="[para(10538(a,1),4724(a,1,2))].">
      <j1 rule="para" parents="10538 4724"/>
    </justification>
  </clause>

  <clause id="10540">
    <literal><![CDATA[
      K(x * (y * z),y) = K(y * (x * z),y)
    ]]></literal>
    <justification jstring="[hyper(10382,a,10534,a)].">
      <j1 rule="hyper" parents="10382 10534"/>
    </justification>
  </clause>

  <clause id="10541">
    <literal><![CDATA[
      a(x,y,L(x,z,u)) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(9967,a,10532,a)].">
      <j1 rule="hyper" parents="9967 10532"/>
    </justification>
  </clause>

  <clause id="10542">
    <literal><![CDATA[
      (x / y) * R(y,z,y) = x * a(y,z,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(10541(a,2),9124(a,2,2))].">
      <j1 rule="para" parents="10541 9124"/>
    </justification>
  </clause>

  <clause id="10544">
    <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),10539(a,1,1,2))].">
      <j1 rule="para" parents="92 10539"/>
    </justification>
  </clause>

  <clause id="10545">
    <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,10526,a,b,10542,a)].">
      <j1 rule="hyper" parents="58 10526 10542"/>
    </justification>
  </clause>

  <clause id="10547">
    <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,9580,a(flip),b,10529,a)].">
      <j1 rule="hyper" parents="58 9580 10529"/>
    </justification>
  </clause>

  <clause id="10549">
    <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),10547(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7 10547"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10550">
    <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(8475,a,10519,a),flip(a)].">
      <j1 rule="hyper" parents="8475 10519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10551">
    <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(4778(a,1),10297(a,1,2))].">
      <j1 rule="para" parents="4778 10297"/>
    </justification>
  </clause>

  <clause id="10552">
    <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(9748(a,1),10551(a,1,2))].">
      <j1 rule="para" parents="9748 10551"/>
    </justification>
  </clause>

  <clause id="10553">
    <literal><![CDATA[
      L(x,y \ R(T(y,z),u,y),y) = x
    ]]></literal>
    <justification jstring="[hyper(341,a,10552,a),flip(a)].">
      <j1 rule="hyper" parents="341 10552"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10555">
    <literal><![CDATA[
      L(x,K(y,z) * a(y,u,y),y) = x
    ]]></literal>
    <justification jstring="[para(8961(a,1),10553(a,1,2))].">
      <j1 rule="para" parents="8961 10553"/>
    </justification>
  </clause>

  <clause id="10556">
    <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(7021(a,1),4381(a,2,1))].">
      <j1 rule="para" parents="7021 4381"/>
    </justification>
  </clause>

  <clause id="10557">
    <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(10556(a,2),327(a,1)),flip(b)].">
      <j1 rule="para" parents="10556 327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10558">
    <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(5357,a,5710,a),flip(a)].">
      <j1 rule="hyper" parents="5357 5710"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10560">
    <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,5427,a(flip),b,10558,a),flip(a)].">
      <j1 rule="hyper" parents="320 5427 10558"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10561">
    <literal><![CDATA[
      K((x / R(1 / y,y,z)) \ 1,y \ 1) = K(z / (x * (y * z)),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(5357,a,10560,a)].">
      <j1 rule="hyper" parents="5357 10560"/>
    </justification>
  </clause>

  <clause id="10562">
    <literal><![CDATA[
      K(R(1 / x,x,y) / z,x \ 1) = K(y / (z * (x * y)),x \ 1)
    ]]></literal>
    <justification jstring="[hyper(5668,a,10561,a)].">
      <j1 rule="hyper" parents="5668 10561"/>
    </justification>
  </clause>

  <clause id="10564">
    <literal><![CDATA[
      K(x \ R(1 / y,y,z),y \ 1) = K(z / (x * (y * z)),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(10038,a,10562,a)].">
      <j1 rule="hyper" parents="10038 10562"/>
    </justification>
  </clause>

  <clause id="10565">
    <literal><![CDATA[
      K(x \ R(y \ 1,y,z),y \ 1) = K(z / (x * (y * z)),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,4002,a(flip),b,10564,a)].">
      <j1 rule="hyper" parents="58 4002 10564"/>
    </justification>
  </clause>

  <clause id="10566">
    <literal><![CDATA[
      K(x / (y * (z * x)),z \ 1) = K(y \ (x / (z * x)),z \ 1)
    ]]></literal>
    <justification jstring="[para(219(a,1),10564(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="219 10564"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10567">
    <literal><![CDATA[
      K(x / (y * (z * x)),z \ 1) = K(y \ ((z * x) \ x),z \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,8662,a(flip),b,10566,a),flip(a)].">
      <j1 rule="hyper" parents="320 8662 10566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10568">
    <literal><![CDATA[
      K(x / (y * ((z \ 1) * x)),(z \ 1) \ 1) = K(y \ (x / ((z \ 1) * x)),z)
    ]]></literal>
    <justification jstring="[hyper(320,a,3554,a(flip),b,10566,a),flip(a)].">
      <j1 rule="hyper" parents="320 3554 10566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10569">
    <literal><![CDATA[
      K(x \ (y / ((z \ 1) * y)),z) = K(x \ z,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,10187,a(flip),b,10568,a),flip(a)].">
      <j1 rule="hyper" parents="58 10187 10568"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10571">
    <literal><![CDATA[
      K(x \ R(y \ 1,y,z),y \ 1) = K(x \ (y \ 1),y \ 1)
    ]]></literal>
    <justification jstring="[para(3087(a,2),10569(a,1,1,2))].">
      <j1 rule="para" parents="3087 10569"/>
    </justification>
  </clause>

  <clause id="10572">
    <literal><![CDATA[
      K(x / (y * (z * x)),z \ 1) = K(y \ (z \ 1),z \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,10565,a(flip),b,10571,a)].">
      <j1 rule="hyper" parents="58 10565 10571"/>
    </justification>
  </clause>

  <clause id="10574">
    <literal><![CDATA[
      K(x \ ((y * z) \ z),y \ 1) = K(x \ (y \ 1),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,10567,a(flip),b,10572,a)].">
      <j1 rule="hyper" parents="58 10567 10572"/>
    </justification>
  </clause>

  <clause id="10576">
    <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(6335(a,1),5762(a,1,1,2))].">
      <j1 rule="para" parents="6335 5762"/>
    </justification>
  </clause>

  <clause id="10577">
    <literal><![CDATA[
      L(T(x,y),x \ (z * K(u,x)),x) = T(L(x,x \ z,x),y)
    ]]></literal>
    <justification jstring="[para(9724(a,1),6393(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9724 6393"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10578">
    <literal><![CDATA[
      L(T(x,y),x \ (K(z,x) * u),x) = T(L(x,x \ u,x),y)
    ]]></literal>
    <justification jstring="[para(7150(a,1),10577(a,1,2,2))].">
      <j1 rule="para" parents="7150 10577"/>
    </justification>
  </clause>

  <clause id="10580">
    <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,10578,a),flip(a)].">
      <j1 rule="hyper" parents="320 20 10578"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10581">
    <literal><![CDATA[
      L(T(x,y),T(x,z) \ u,x) = L(T(x,y),x \ u,x)
    ]]></literal>
    <justification jstring="[para(5106(a,1),10580(a,1,2))].">
      <j1 rule="para" parents="5106 10580"/>
    </justification>
  </clause>

  <clause id="10582">
    <literal><![CDATA[
      L(T(x,y),T(z / T(x,u),x),x) = L(T(x,y),x \ z,x)
    ]]></literal>
    <justification jstring="[para(8338(a,2),10581(a,1,2))].">
      <j1 rule="para" parents="8338 10581"/>
    </justification>
  </clause>

  <clause id="10583">
    <literal><![CDATA[
      L(T(x,y),z / T(x,u),x) = L(T(x,y),x \ z,x)
    ]]></literal>
    <justification jstring="[hyper(7607,a,10582,a)].">
      <j1 rule="hyper" parents="7607 10582"/>
    </justification>
  </clause>

  <clause id="10584">
    <literal><![CDATA[
      R(x,x \ 1,y \ R(y,x \ 1,y)) = x
    ]]></literal>
    <justification jstring="[hyper(320,a,9921,a(flip),b,6574,a),flip(a)].">
      <j1 rule="hyper" parents="320 9921 6574"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10586">
    <literal><![CDATA[
      R(x,x \ 1,a(y,x \ 1,y)) = x
    ]]></literal>
    <justification jstring="[para(8942(a,1),10584(a,1,3))].">
      <j1 rule="para" parents="8942 10584"/>
    </justification>
  </clause>

  <clause id="10587">
    <literal><![CDATA[
      (x \ 1) * a(y,x \ 1,y) = x \ a(y,x \ 1,y)
    ]]></literal>
    <justification jstring="[para(10586(a,1),425(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10586 425"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10588">
    <literal><![CDATA[
      T(x \ a(y,x \ 1,y),y) = y \ T(y * (x \ 1),y)
    ]]></literal>
    <justification jstring="[para(10587(a,1),8975(a,1,1))].">
      <j1 rule="para" parents="10587 8975"/>
    </justification>
  </clause>

  <clause id="10589">
    <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(10588(a,1),2115(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10588 2115"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10590">
    <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(3340(a,1),8113(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3340 8113"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10591">
    <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(3340(a,1),10590(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3340 10590"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10593">
    <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(10591(a,1),640(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10591 640"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10595">
    <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(9217(a,1),8633(a,1,2))].">
      <j1 rule="para" parents="9217 8633"/>
    </justification>
  </clause>

  <clause id="10596">
    <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(7784(a,1),10595(a,1,2))].">
      <j1 rule="para" parents="7784 10595"/>
    </justification>
  </clause>

  <clause id="10598">
    <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(8248(a,1),10596(a,2,1))].">
      <j1 rule="para" parents="8248 10596"/>
    </justification>
  </clause>

  <clause id="10599">
    <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,9981,a(flip),b,10598,a)].">
      <j1 rule="hyper" parents="58 9981 10598"/>
    </justification>
  </clause>

  <clause id="10600">
    <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(9922,a,10599,a)].">
      <j1 rule="hyper" parents="9922 10599"/>
    </justification>
  </clause>

  <clause id="10601">
    <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(10023,a,10600,a)].">
      <j1 rule="hyper" parents="10023 10600"/>
    </justification>
  </clause>

  <clause id="10602">
    <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(7704,a,8798,a),flip(a)].">
      <j1 rule="hyper" parents="7704 8798"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10603">
    <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(5635(a,1),9154(a,1,2))].">
      <j1 rule="para" parents="5635 9154"/>
    </justification>
  </clause>

  <clause id="10604">
    <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,8081,a(flip),b,10603,a),flip(a)].">
      <j1 rule="hyper" parents="320 8081 10603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10606">
    <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),9185(a,1,2,1))].">
      <j1 rule="para" parents="4 9185"/>
    </justification>
  </clause>

  <clause id="10608">
    <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),10606(a,1,2))].">
      <j1 rule="para" parents="13 10606"/>
    </justification>
  </clause>

  <clause id="10609">
    <literal><![CDATA[
      K(L(x,y * z,u),z) = K(x,L(L(z,y,x),x * y,u))
    ]]></literal>
    <justification jstring="[hyper(8443,a,10608,a)].">
      <j1 rule="hyper" parents="8443 10608"/>
    </justification>
  </clause>

  <clause id="10610">
    <literal><![CDATA[
      K(L(x,y * z,u),z) = K(x,L(z,x * y,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,7069,a(flip),b,10609,a),flip(a)].">
      <j1 rule="hyper" parents="320 7069 10609"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10612">
    <literal><![CDATA[
      K(L(x,(x \ y) * z,u),z) = K(x,L(z,y,u))
    ]]></literal>
    <justification jstring="[para(5(a,1),10610(a,2,2,2))].">
      <j1 rule="para" parents="5 10610"/>
    </justification>
  </clause>

  <clause id="10613">
    <literal><![CDATA[
      K(x,L(y * ((z * y) \ z),u,w)) = 1
    ]]></literal>
    <justification jstring="[hyper(58,a,10167,a(flip),b,10612,a),flip(a)].">
      <j1 rule="hyper" parents="58 10167 10612"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10614">
    <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(4331(a,1),10612(a,1,1,2))].">
      <j1 rule="para" parents="4331 10612"/>
    </justification>
  </clause>

  <clause id="10615">
    <literal><![CDATA[
      K(x,y \ K(z,L(x,u,w))) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(10612(a,1),7255(a,1,2,2))].">
      <j1 rule="para" parents="10612 7255"/>
    </justification>
  </clause>

  <clause id="10616">
    <literal><![CDATA[
      K(x,a(y,z,z \ 1) \ 1) = 1
    ]]></literal>
    <justification jstring="[hyper(58,a,6663,a(flip),b,10613,a)].">
      <j1 rule="hyper" parents="58 6663 10613"/>
    </justification>
  </clause>

  <clause id="10618">
    <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,6665,a(flip),b,10615,a),flip(a)].">
      <j1 rule="hyper" parents="58 6665 10615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10619">
    <literal><![CDATA[
      K(x,y \ K(z,L(L(x,u,w),v5,v6))) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(10612(a,1),10615(a,1,2,2))].">
      <j1 rule="para" parents="10612 10615"/>
    </justification>
  </clause>

  <clause id="10620">
    <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),10618(a,1,2,1,1))].">
      <j1 rule="para" parents="20 10618"/>
    </justification>
  </clause>

  <clause id="10621">
    <literal><![CDATA[
      K(x,y \ L(T(x,z),u,w)) = K(x,y \ L(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(6166,a,10620,a)].">
      <j1 rule="hyper" parents="6166 10620"/>
    </justification>
  </clause>

  <clause id="10622">
    <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(1162(a,1),10621(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="1162 10621"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10623">
    <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(1172(a,1),10621(a,1,2,2,1))].">
      <j1 rule="para" parents="1172 10621"/>
    </justification>
  </clause>

  <clause id="10624">
    <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(7138,a,10614,a)].">
      <j1 rule="hyper" parents="7138 10614"/>
    </justification>
  </clause>

  <clause id="10626">
    <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,10273,a(flip),b,10624,a),flip(a)].">
      <j1 rule="hyper" parents="58 10273 10624"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10627">
    <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(10626(a,1),10524(a,1))].">
      <j1 rule="para" parents="10626 10524"/>
    </justification>
  </clause>

  <clause id="10628">
    <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,9366,a)].">
      <j1 rule="hyper" parents="116 105 9366"/>
    </justification>
  </clause>

  <clause id="10629">
    <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(9761,a,10628,a)].">
      <j1 rule="hyper" parents="9761 10628"/>
    </justification>
  </clause>

  <clause id="10630">
    <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(9164,a,10629,a)].">
      <j1 rule="hyper" parents="9164 10629"/>
    </justification>
  </clause>

  <clause id="10631">
    <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),10630(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7 10630"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10632">
    <literal><![CDATA[
      L(K(x,y),T(z,y * x),y * x) = K(x,L(y,x,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,8729,a(flip),b,10631,a),flip(a)].">
      <j1 rule="hyper" parents="320 8729 10631"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10633">
    <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),10632(a,1,2)),flip(a)].">
      <j1 rule="para" parents="224 10632"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10634">
    <literal><![CDATA[
      (x * (y * z)) * K(z,L(y,z,x)) = (y * z) * T(x * K(z,y),y * z)
    ]]></literal>
    <justification jstring="[para(10632(a,1),9366(a,1,2))].">
      <j1 rule="para" parents="10632 9366"/>
    </justification>
  </clause>

  <clause id="10635">
    <literal><![CDATA[
      L(K(x,y),z,y * x) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(10372,a,10633,a),flip(a)].">
      <j1 rule="hyper" parents="10372 10633"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10636">
    <literal><![CDATA[
      L(K(x,y),z,y * x) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(10633(a,1),10372(a,1))].">
      <j1 rule="para" parents="10633 10372"/>
    </justification>
  </clause>

  <clause id="10639">
    <literal><![CDATA[
      K(x,y) * ((y * x) * z) = (y * x) * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(10635(a,1),9882(a,1,1))].">
      <j1 rule="para" parents="10635 9882"/>
    </justification>
  </clause>

  <clause id="10641">
    <literal><![CDATA[
      (x * y) * T(z * K(y,x),x * y) = z * (y * x)
    ]]></literal>
    <justification jstring="[hyper(10413,a,10634,a),flip(a)].">
      <j1 rule="hyper" parents="10413 10634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10642">
    <literal><![CDATA[
      (x * K(y,z)) * (z * y) = x * (y * z)
    ]]></literal>
    <justification jstring="[hyper(284,a,10641,a)].">
      <j1 rule="hyper" parents="284 10641"/>
    </justification>
  </clause>

  <clause id="10643">
    <literal><![CDATA[
      (x * K(y,z)) / (z * y) = (x / (z * y)) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(117,a,10380,a(flip),b,10642,a)].">
      <j1 rule="hyper" parents="117 10380 10642"/>
    </justification>
  </clause>

  <clause id="10644">
    <literal><![CDATA[
      (x / (y * z)) * K(y,z) = x / (z * y)
    ]]></literal>
    <justification jstring="[hyper(117,a,7,a(flip),b,10642,a),flip(a)].">
      <j1 rule="hyper" parents="117 7 10642"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10645">
    <literal><![CDATA[
      ((x * K(y,z)) * z) \ (x * (y * z)) = L(y,z,x * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(116,a,10642,a(flip),b,90,a)].">
      <j1 rule="hyper" parents="116 10642 90"/>
    </justification>
  </clause>

  <clause id="10646">
    <literal><![CDATA[
      (T(x,y) \ 1) * (x * y) = (x \ 1) * (y * x)
    ]]></literal>
    <justification jstring="[para(4801(a,1),10642(a,1,1))].">
      <j1 rule="para" parents="4801 10642"/>
    </justification>
  </clause>

  <clause id="10647">
    <literal><![CDATA[
      (x / y) * K(z,z \ y) = x / ((z \ y) * z)
    ]]></literal>
    <justification jstring="[para(5(a,1),10644(a,1,1,2))].">
      <j1 rule="para" parents="5 10644"/>
    </justification>
  </clause>

  <clause id="10648">
    <literal><![CDATA[
      (x / y) * K(y / z,z) = x / (z * (y / z))
    ]]></literal>
    <justification jstring="[para(7(a,1),10644(a,1,1,2))].">
      <j1 rule="para" parents="7 10644"/>
    </justification>
  </clause>

  <clause id="10649">
    <literal><![CDATA[
      (x / (y * z)) * (z * K(y,z)) = (x / (z * y)) * z
    ]]></literal>
    <justification jstring="[para(10644(a,1),6090(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10644 6090"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10650">
    <literal><![CDATA[
      K(x,y / (z * x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (x * z)) = u
    ]]></literal>
    <justification jstring="[para(10644(a,1),7240(a,1,2))].">
      <j1 rule="para" parents="10644 7240"/>
    </justification>
  </clause>

  <clause id="10651">
    <literal><![CDATA[
      K(x / (y * z),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x / (z * y),y) = u
    ]]></literal>
    <justification jstring="[para(10644(a,1),7334(a,1,1))].">
      <j1 rule="para" parents="10644 7334"/>
    </justification>
  </clause>

  <clause id="10652">
    <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(10646(a,1),6598(a,2,2,2))].">
      <j1 rule="para" parents="10646 6598"/>
    </justification>
  </clause>

  <clause id="10653">
    <literal><![CDATA[
      T(x / ((y \ z) * y),K(y,z)) = K(y,y \ z) * (x / z)
    ]]></literal>
    <justification jstring="[para(10647(a,1),8089(a,1,1))].">
      <j1 rule="para" parents="10647 8089"/>
    </justification>
  </clause>

  <clause id="10654">
    <literal><![CDATA[
      1 / ((x * ((x / y) \ 1)) / x) = x / (x * (y / x))
    ]]></literal>
    <justification jstring="[hyper(58,a,9283,a,b,10648,a)].">
      <j1 rule="hyper" parents="58 9283 10648"/>
    </justification>
  </clause>

  <clause id="10655">
    <literal><![CDATA[
      (x / y) * K(z \ y,z) = x / (z * (y / z))
    ]]></literal>
    <justification jstring="[para(4964(a,1),10648(a,1,2))].">
      <j1 rule="para" parents="4964 10648"/>
    </justification>
  </clause>

  <clause id="10656">
    <literal><![CDATA[
      (x / (y * z)) * ((y * z) / y) = (x / (z * y)) * z
    ]]></literal>
    <justification jstring="[hyper(4899,a,10649,a)].">
      <j1 rule="hyper" parents="4899 10649"/>
    </justification>
  </clause>

  <clause id="10657">
    <literal><![CDATA[
      (x * ((x / y) \ 1)) / x = (x / (x * (y / x))) \ 1
    ]]></literal>
    <justification jstring="[hyper(188,a,10654,a),flip(a)].">
      <j1 rule="hyper" parents="188 10654"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10658">
    <literal><![CDATA[
      x / (x * (((y / x) \ 1) \ 1)) = ((x * ((x / y) \ 1)) / x) \ 1
    ]]></literal>
    <justification jstring="[para(10657(a,2),3081(a,2,1))].">
      <j1 rule="para" parents="10657 3081"/>
    </justification>
  </clause>

  <clause id="10659">
    <literal><![CDATA[
      (x * (y * K(z,y))) \ (x * (z * y)) = L(z,y,x * K(z,y))
    ]]></literal>
    <justification jstring="[para(6090(a,1),10645(a,1,1))].">
      <j1 rule="para" parents="6090 10645"/>
    </justification>
  </clause>

  <clause id="10660">
    <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(9849(a,2),10658(a,2,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9849 10658"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10661">
    <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,3561,a(flip),b,9454,a),flip(a)].">
      <j1 rule="hyper" parents="320 3561 9454"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10662">
    <literal><![CDATA[
      K((x / y) \ z,T(y / x,x / y)) = K(((x / y) \ 1) * z,y / x)
    ]]></literal>
    <justification jstring="[para(650(a,1),10661(a,1,2))].">
      <j1 rule="para" parents="650 10661"/>
    </justification>
  </clause>

  <clause id="10663">
    <literal><![CDATA[
      K(((x / y) \ 1) * z,y / x) = K((x / y) \ z,y / x)
    ]]></literal>
    <justification jstring="[hyper(5781,a,10662,a),flip(a)].">
      <j1 rule="hyper" parents="5781 10662"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10664">
    <literal><![CDATA[
      K(((x / y) \ 1) * z,y / x) = K((y \ x) \ z,y / x)
    ]]></literal>
    <justification jstring="[hyper(320,a,9428,a(flip),b,10663,a),flip(a)].">
      <j1 rule="hyper" parents="320 9428 10663"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10665">
    <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(6927(a,1),9756(a,1,2))].">
      <j1 rule="para" parents="6927 9756"/>
    </justification>
  </clause>

  <clause id="10666">
    <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,9074,a(flip),b,10665,a)].">
      <j1 rule="hyper" parents="58 9074 10665"/>
    </justification>
  </clause>

  <clause id="10667">
    <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),9951(a,1,1))].">
      <j1 rule="para" parents="105 9951"/>
    </justification>
  </clause>

  <clause id="10668">
    <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(10222(a,1),10227(a,1,2,1))].">
      <j1 rule="para" parents="10222 10227"/>
    </justification>
  </clause>

  <clause id="10669">
    <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(5131(a,1),10668(a,1,2))].">
      <j1 rule="para" parents="5131 10668"/>
    </justification>
  </clause>

  <clause id="10671">
    <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(7158(a,2),10262(a,1,2,2,1))].">
      <j1 rule="para" parents="7158 10262"/>
    </justification>
  </clause>

  <clause id="10672">
    <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(7755(a,1),10427(a,1,1,2))].">
      <j1 rule="para" parents="7755 10427"/>
    </justification>
  </clause>

  <clause id="10673">
    <literal><![CDATA[
      x / (y * K(1 / z,z)) = K(z,1 / z) * (x / y)
    ]]></literal>
    <justification jstring="[hyper(3417,a,10576,a)].">
      <j1 rule="hyper" parents="3417 10576"/>
    </justification>
  </clause>

  <clause id="10675">
    <literal><![CDATA[
      K(x,1 / x) * (y / L(x,z,u)) = y / (1 / (1 / L(x,z,u)))
    ]]></literal>
    <justification jstring="[para(5817(a,1),10673(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5817 10673"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10676">
    <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,9599,a(flip),b,10602,a),flip(a)].">
      <j1 rule="hyper" parents="320 9599 10602"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10678">
    <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,7907,a(flip),b,10676,a),flip(a)].">
      <j1 rule="hyper" parents="320 7907 10676"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10679">
    <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(5130(a,1),10671(a,1,2))].">
      <j1 rule="para" parents="5130 10671"/>
    </justification>
  </clause>

  <clause id="10680">
    <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(10679(a,1),39(a,1)),flip(a)].">
      <j1 rule="para" parents="10679 39"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10681">
    <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(1317(a,1),4470(a,1,1))].">
      <j1 rule="para" parents="1317 4470"/>
    </justification>
  </clause>

  <clause id="10682">
    <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(1337(a,1),10681(a,1,2))].">
      <j1 rule="para" parents="1337 10681"/>
    </justification>
  </clause>

  <clause id="10683">
    <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,10682,a),flip(a)].">
      <j1 rule="hyper" parents="691 10682"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10684">
    <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,4667,a,b,10683,a)].">
      <j1 rule="hyper" parents="58 4667 10683"/>
    </justification>
  </clause>

  <clause id="10685">
    <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,10032,a(flip),b,10684,a)].">
      <j1 rule="hyper" parents="58 10032 10684"/>
    </justification>
  </clause>

  <clause id="10686">
    <literal><![CDATA[
      a(x,y,R(T(x,y),z,u)) = a(R(x,z,u),y,x)
    ]]></literal>
    <justification jstring="[hyper(4666,a,10685,a)].">
      <j1 rule="hyper" parents="4666 10685"/>
    </justification>
  </clause>

  <clause id="10687">
    <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(10686(a,1),10033(a,2,1))].">
      <j1 rule="para" parents="10686 10033"/>
    </justification>
  </clause>

  <clause id="10688">
    <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,9976,a(flip),b,10687,a)].">
      <j1 rule="hyper" parents="58 9976 10687"/>
    </justification>
  </clause>

  <clause id="10689">
    <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),5823(a,1,2)),flip(a)].">
      <j1 rule="para" parents="298 5823"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10690">
    <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,6259,a(flip),b,10689,a),flip(a)].">
      <j1 rule="hyper" parents="320 6259 10689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10691">
    <literal><![CDATA[
      K((x \ (y \ z)) \ 1,(y * x) \ z) = K(z \ (y * x),(y * x) \ z)
    ]]></literal>
    <justification jstring="[para(298(a,1),10690(a,1,2))].">
      <j1 rule="para" parents="298 10690"/>
    </justification>
  </clause>

  <clause id="10692">
    <literal><![CDATA[
      K((x \ (y \ z)) \ 1,(y * x) \ z) = K(z \ (y * x),x \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(320,a,6869,a(flip),b,10691,a),flip(a)].">
      <j1 rule="hyper" parents="320 6869 10691"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10693">
    <literal><![CDATA[
      x * K(1 \ (y * x),x \ (y \ 1)) = y \ (((y * x) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(10692(a,1),5736(a,2,2)),flip(a)].">
      <j1 rule="para" parents="10692 5736"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10694">
    <literal><![CDATA[
      x * K(y * x,x \ (y \ 1)) = y \ (((y * x) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(60(a,1),10693(a,1,2,1))].">
      <j1 rule="para" parents="60 10693"/>
    </justification>
  </clause>

  <clause id="10695">
    <literal><![CDATA[
      K((1 / x) * y,y \ ((1 / x) \ 1)) = K(x \ y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(29,a,3365,a(flip),b,10694,a),flip(a)].">
      <j1 rule="hyper" parents="29 3365 10694"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10696">
    <literal><![CDATA[
      K((1 / x) * y,y \ x) = K(x \ y,y \ x)
    ]]></literal>
    <justification jstring="[para(75(a,1),10695(a,1,2,2))].">
      <j1 rule="para" parents="75 10695"/>
    </justification>
  </clause>

  <clause id="10697">
    <literal><![CDATA[
      K((x \ 1) \ y,y \ (x \ 1)) = K(x * y,y \ (x \ 1))
    ]]></literal>
    <justification jstring="[para(72(a,1),10696(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="72 10696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10698">
    <literal><![CDATA[
      ((x \ 1) \ y) \ K(x * y,y \ (x \ 1)) = 1 / ((x \ 1) \ y)
    ]]></literal>
    <justification jstring="[hyper(116,a,10697,a(flip),b,2398,a)].">
      <j1 rule="hyper" parents="116 10697 2398"/>
    </justification>
  </clause>

  <clause id="10699">
    <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(3281(a,1),6072(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3281 6072"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10700">
    <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(6312(a,1),7466(a,2,1))].">
      <j1 rule="para" parents="6312 7466"/>
    </justification>
  </clause>

  <clause id="10701">
    <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(5879(a,1),8899(a,1,1,2))].">
      <j1 rule="para" parents="5879 8899"/>
    </justification>
  </clause>

  <clause id="10702">
    <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,9118,a(flip),b,9138,a),flip(a)].">
      <j1 rule="hyper" parents="320 9118 9138"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10703">
    <literal><![CDATA[
      K(x,T(y / ((z * T(x,u)) * w),v5)) = K(x,T(y / ((z * x) * w),v5))
    ]]></literal>
    <justification jstring="[para(7940(a,1),10702(a,1,2,1,2,1))].">
      <j1 rule="para" parents="7940 10702"/>
    </justification>
  </clause>

  <clause id="10704">
    <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),9690(a,1,2,2,1))].">
      <j1 rule="para" parents="5 9690"/>
    </justification>
  </clause>

  <clause id="10705">
    <literal><![CDATA[
      x \ T(y,((x \ 1) \ (x \ y)) \ z) = x \ T(y,y \ z)
    ]]></literal>
    <justification jstring="[hyper(6417,a,10704,a),flip(a)].">
      <j1 rule="hyper" parents="6417 10704"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10707">
    <literal><![CDATA[
      K(x,y \ T(z,z \ x)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(10705(a,1),8773(a,1,2))].">
      <j1 rule="para" parents="10705 8773"/>
    </justification>
  </clause>

  <clause id="10708">
    <literal><![CDATA[
      T(x,y \ T(z,z \ x)) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(118,a,10707,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 10707 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10709">
    <literal><![CDATA[
      K(x,y \ ((z \ x) \ x)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(106(a,1),10707(a,1,2,2))].">
      <j1 rule="para" parents="106 10707"/>
    </justification>
  </clause>

  <clause id="10710">
    <literal><![CDATA[
      T(x,y \ (x / z)) = T(x,y \ (z \ x))
    ]]></literal>
    <justification jstring="[para(643(a,1),10708(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="643 10708"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10711">
    <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(6490,a,10709,a),flip(a)].">
      <j1 rule="hyper" parents="6490 10709"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10712">
    <literal><![CDATA[
      T((x / (1 / (x \ y))) / x,1 / (y / x)) = (((x / (1 / (x \ y))) / x) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(58,a,9354,a(flip),b,9850,a)].">
      <j1 rule="hyper" parents="58 9354 9850"/>
    </justification>
  </clause>

  <clause id="10713">
    <literal><![CDATA[
      T((x / (1 / (x \ y))) / x,1 / (y / x)) = (1 / ((x / ((x \ y) \ 1)) / x)) \ 1
    ]]></literal>
    <justification jstring="[para(2646(a,2),10712(a,2,1))].">
      <j1 rule="para" parents="2646 10712"/>
    </justification>
  </clause>

  <clause id="10714">
    <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(10713(a,2),583(a,1))].">
      <j1 rule="para" parents="10713 583"/>
    </justification>
  </clause>

  <clause id="10715">
    <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,6335,a(flip),b,10700,a),flip(a)].">
      <j1 rule="hyper" parents="320 6335 10700"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10716">
    <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(8079(a,1),10701(a,1,2))].">
      <j1 rule="para" parents="8079 10701"/>
    </justification>
  </clause>

  <clause id="10717">
    <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(7779(a,1),10716(a,1,2))].">
      <j1 rule="para" parents="7779 10716"/>
    </justification>
  </clause>

  <clause id="10719">
    <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(10717(a,1),7403(a,1,2,2))].">
      <j1 rule="para" parents="10717 7403"/>
    </justification>
  </clause>

  <clause id="10720">
    <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,7627,a(flip),b,10719,a),flip(a)].">
      <j1 rule="hyper" parents="58 7627 10719"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10722">
    <literal><![CDATA[
      K(x,y * (z * (x * (T(T(x,u),u) \ w)))) = K(x,y * (z * w))
    ]]></literal>
    <justification jstring="[hyper(320,a,8425,a(flip),b,10720,a),flip(a)].">
      <j1 rule="hyper" parents="320 8425 10720"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10724">
    <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(6312(a,1),10715(a,1,1,1))].">
      <j1 rule="para" parents="6312 10715"/>
    </justification>
  </clause>

  <clause id="10725">
    <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(2086(a,2),10724(a,1,1))].">
      <j1 rule="para" parents="2086 10724"/>
    </justification>
  </clause>

  <clause id="10726">
    <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(2891(a,1),10725(a,1,1,1,1,2))].">
      <j1 rule="para" parents="2891 10725"/>
    </justification>
  </clause>

  <clause id="10727">
    <literal><![CDATA[
      R((x * y) / x,z,u) * x = (x * (K(w,y) * R(y,z,u))) * K(y,w)
    ]]></literal>
    <justification jstring="[para(9297(a,1),10726(a,1,1,1))].">
      <j1 rule="para" parents="9297 10726"/>
    </justification>
  </clause>

  <clause id="10728">
    <literal><![CDATA[
      (x * (K(y,z) * R(z,u,w))) * K(z,y) = x * R(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(888,a,10727,a),flip(a)].">
      <j1 rule="hyper" parents="888 10727"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10730">
    <literal><![CDATA[
      (x * (R(y,z,u) * K(w,y))) * K(y,w) = x * R(y,z,u)
    ]]></literal>
    <justification jstring="[para(2899(a,2),10728(a,1,1,2))].">
      <j1 rule="para" parents="2899 10728"/>
    </justification>
  </clause>

  <clause id="10731">
    <literal><![CDATA[
      L(K(x,y),R(x,z,u),w) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(6673,a,10730,a)].">
      <j1 rule="hyper" parents="6673 10730"/>
    </justification>
  </clause>

  <clause id="10732">
    <literal><![CDATA[
      a(x,R(y,z,u),K(y,w)) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,10731,a,b,1934,a),flip(a)].">
      <j1 rule="hyper" parents="115 10731 1934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10733">
    <literal><![CDATA[
      K(x,(y \ z) \ R(x,u,w)) = K(x,z \ (y * R(x,u,w)))
    ]]></literal>
    <justification jstring="[hyper(58,a,6584,a(flip),b,10731,a),flip(a)].">
      <j1 rule="hyper" parents="58 6584 10731"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10734">
    <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(5683(a,1),6022(a,1,2))].">
      <j1 rule="para" parents="5683 6022"/>
    </justification>
  </clause>

  <clause id="10735">
    <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(5687(a,1),10734(a,2,3))].">
      <j1 rule="para" parents="5687 10734"/>
    </justification>
  </clause>

  <clause id="10736">
    <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(1694(a,2),6074(a,2,2,1))].">
      <j1 rule="para" parents="1694 6074"/>
    </justification>
  </clause>

  <clause id="10737">
    <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(7784(a,1),6458(a,1,2,2))].">
      <j1 rule="para" parents="7784 6458"/>
    </justification>
  </clause>

  <clause id="10738">
    <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(5485,a,10669,a)].">
      <j1 rule="hyper" parents="5485 10669"/>
    </justification>
  </clause>

  <clause id="10739">
    <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),10736(a,2,2,1,1,2))].">
      <j1 rule="para" parents="61 10736"/>
    </justification>
  </clause>

  <clause id="10740">
    <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),10739(a,2,2))].">
      <j1 rule="para" parents="20 10739"/>
    </justification>
  </clause>

  <clause id="10742">
    <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,10740,a),flip(a)].">
      <j1 rule="hyper" parents="320 668 10740"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10743">
    <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,1446,a(flip),b,10742,a),flip(a)].">
      <j1 rule="hyper" parents="320 1446 10742"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10744">
    <literal><![CDATA[
      (x \ L(x,y,z)) * K(L(x,y,z),u) = x \ L(T(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(3317(a,1),10743(a,1,2))].">
      <j1 rule="para" parents="3317 10743"/>
    </justification>
  </clause>

  <clause id="10745">
    <literal><![CDATA[
      K(x \ L(T(x,y),z,u),x) = K(x \ L(x,z,u),x)
    ]]></literal>
    <justification jstring="[para(10744(a,1),7416(a,1,1))].">
      <j1 rule="para" parents="10744 7416"/>
    </justification>
  </clause>

  <clause id="10746">
    <literal><![CDATA[
      K(x \ L(T(x,y),z,u),x) = 1
    ]]></literal>
    <justification jstring="[hyper(320,a,3521,a(flip),b,10745,a),flip(a)].">
      <j1 rule="hyper" parents="320 3521 10745"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10748">
    <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(7158(a,2),10737(a,2,1,1))].">
      <j1 rule="para" parents="7158 10737"/>
    </justification>
  </clause>

  <clause id="10749">
    <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(8395,a,10738,a)].">
      <j1 rule="hyper" parents="8395 10738"/>
    </justification>
  </clause>

  <clause id="10750">
    <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(7197(a,1),10748(a,2,1))].">
      <j1 rule="para" parents="7197 10748"/>
    </justification>
  </clause>

  <clause id="10751">
    <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,9005,a(flip),b,10750,a),flip(a)].">
      <j1 rule="hyper" parents="320 9005 10750"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10754">
    <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(5996(a,2),10751(a,1,1))].">
      <j1 rule="para" parents="5996 10751"/>
    </justification>
  </clause>

  <clause id="10755">
    <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(7250(a,1),10754(a,1,2,2))].">
      <j1 rule="para" parents="7250 10754"/>
    </justification>
  </clause>

  <clause id="10756">
    <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,10755,a)].">
      <j1 rule="hyper" parents="293 10755"/>
    </justification>
  </clause>

  <clause id="10757">
    <literal><![CDATA[
      K(T(x / y,x) \ x,z) * K(z,y) = K(x,T(x * K(z,y),z))
    ]]></literal>
    <justification jstring="[hyper(5163,a,10756,a)].">
      <j1 rule="hyper" parents="5163 10756"/>
    </justification>
  </clause>

  <clause id="10758">
    <literal><![CDATA[
      K(x,T(y / z,y) \ y) * K(z,x) = K(y,T(y * K(z,x),z))
    ]]></literal>
    <justification jstring="[para(6677(a,1),10757(a,1,1))].">
      <j1 rule="para" parents="6677 10757"/>
    </justification>
  </clause>

  <clause id="10759">
    <literal><![CDATA[
      K(x,T(y / z,y) \ y) * K(z,x) = K(y,y * K(z,x))
    ]]></literal>
    <justification jstring="[hyper(320,a,7588,a(flip),b,10758,a),flip(a)].">
      <j1 rule="hyper" parents="320 7588 10758"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10760">
    <literal><![CDATA[
      K(x * K(y,z),x) = K(x,x * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,6913,a(flip),b,10759,a)].">
      <j1 rule="hyper" parents="58 6913 10759"/>
    </justification>
  </clause>

  <clause id="10761">
    <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(10760(a,1),5665(a,1,1,1,2))].">
      <j1 rule="para" parents="10760 5665"/>
    </justification>
  </clause>

  <clause id="10762">
    <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(4755(a,2),10761(a,1,1,1))].">
      <j1 rule="para" parents="4755 10761"/>
    </justification>
  </clause>

  <clause id="10763">
    <literal><![CDATA[
      R(T(x,K(y,z)),K(z,y),x) = T(x,x * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(5633,a,10762,a)].">
      <j1 rule="hyper" parents="5633 10762"/>
    </justification>
  </clause>

  <clause id="10764">
    <literal><![CDATA[
      T(x,x * K(y,z)) \ T(K(z,y) * x,x) = K(z,T(y,x))
    ]]></literal>
    <justification jstring="[para(10763(a,1),10604(a,1,1))].">
      <j1 rule="para" parents="10763 10604"/>
    </justification>
  </clause>

  <clause id="10765">
    <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(9664(a,1),10764(a,1,1,2,2))].">
      <j1 rule="para" parents="9664 10764"/>
    </justification>
  </clause>

  <clause id="10766">
    <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(5108(a,1),5124(a,1,1))].">
      <j1 rule="para" parents="5108 5124"/>
    </justification>
  </clause>

  <clause id="10767">
    <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(10766(a,1),9316(a,1,2,2))].">
      <j1 rule="para" parents="10766 9316"/>
    </justification>
  </clause>

  <clause id="10768">
    <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,7289,a(flip),b,6819,a),flip(a)].">
      <j1 rule="hyper" parents="320 7289 6819"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10769">
    <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),10768(a,2,1,2))].">
      <j1 rule="para" parents="173 10768"/>
    </justification>
  </clause>

  <clause id="10770">
    <literal><![CDATA[
      L(K(x,y),L(y,z,u),w) = K(x,y)
    ]]></literal>
    <justification jstring="[para(1647(a,1),10769(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1647 10769"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10771">
    <literal><![CDATA[
      K((x \ 1) * L(y,z,u),y) = K(x \ L(y,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(6642,a,10770,a),flip(a)].">
      <j1 rule="hyper" parents="6642 10770"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10772">
    <literal><![CDATA[
      a(x,L(y,z,u),K(w,y)) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,10770,a,b,1934,a),flip(a)].">
      <j1 rule="hyper" parents="115 10770 1934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10773">
    <literal><![CDATA[
      K((x \ y) \ L(z,u,w),z) = K(y \ (x * L(z,u,w)),z)
    ]]></literal>
    <justification jstring="[hyper(58,a,6626,a(flip),b,10770,a),flip(a)].">
      <j1 rule="hyper" parents="58 6626 10770"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10774">
    <literal><![CDATA[
      L(K(x,y),L(x,z,u),w) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(5893,a,10772,a)].">
      <j1 rule="hyper" parents="5893 10772"/>
    </justification>
  </clause>

  <clause id="10775">
    <literal><![CDATA[
      K(x,(y \ z) \ L(x,u,w)) = K(x,z \ (y * L(x,u,w)))
    ]]></literal>
    <justification jstring="[hyper(58,a,6584,a(flip),b,10774,a),flip(a)].">
      <j1 rule="hyper" parents="58 6584 10774"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10776">
    <literal><![CDATA[
      K(x \ L(y,z,u),y) = K(y * (x \ 1),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,10530,a(flip),b,10771,a),flip(a)].">
      <j1 rule="hyper" parents="58 10530 10771"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10778">
    <literal><![CDATA[
      K(x \ L(y,z,u),y) = K(x \ y,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,5363,a(flip),b,10776,a),flip(a)].">
      <j1 rule="hyper" parents="320 5363 10776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10779">
    <literal><![CDATA[
      K(x \ L(y,z,u),y) != w
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,y) = w
    ]]></literal>
    <justification jstring="[para(10776(a,2),5968(a,1))].">
      <j1 rule="para" parents="10776 5968"/>
    </justification>
  </clause>

  <clause id="10780">
    <literal><![CDATA[
      (L(x,y,z) * K((u \ x) \ x,x)) * u = (x \ (L(x,y,z) * u)) * x
    ]]></literal>
    <justification jstring="[para(10778(a,1),9693(a,1,1,2))].">
      <j1 rule="para" parents="10778 9693"/>
    </justification>
  </clause>

  <clause id="10781">
    <literal><![CDATA[
      K(x \ (y * L(z,u,w)),z) = K((y \ x) \ z,z)
    ]]></literal>
    <justification jstring="[hyper(10779,a,10773,a),flip(a)].">
      <j1 rule="hyper" parents="10779 10773"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10783">
    <literal><![CDATA[
      K(x \ (y * L(z,u,w)),z) = K(z * (x \ y),z)
    ]]></literal>
    <justification jstring="[hyper(320,a,10495,a(flip),b,10781,a),flip(a)].">
      <j1 rule="hyper" parents="320 10495 10781"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10784">
    <literal><![CDATA[
      K(x \ (y * L(x,z,u)),x) != w
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = w
    ]]></literal>
    <justification jstring="[para(10781(a,2),6298(a,1))].">
      <j1 rule="para" parents="10781 6298"/>
    </justification>
  </clause>

  <clause id="10785">
    <literal><![CDATA[
      K(x \ (y * (z * x)),x) != u
    ]]></literal>
    <literal><![CDATA[
      K(y * z,x) = u
    ]]></literal>
    <justification jstring="[para(90(a,1),10784(a,1,1,2))].">
      <j1 rule="para" parents="90 10784"/>
    </justification>
  </clause>

  <clause id="10786">
    <literal><![CDATA[
      K(x \ (y * (z * u)),u) = K(u * (x \ (y * z)),u)
    ]]></literal>
    <justification jstring="[para(90(a,1),10783(a,1,1,2))].">
      <j1 rule="para" parents="90 10783"/>
    </justification>
  </clause>

  <clause id="10787">
    <literal><![CDATA[
      K(x \ (y \ (z * (u * y))),y) = K(y * ((x * y) \ (z * u)),y)
    ]]></literal>
    <justification jstring="[hyper(8472,a,10786,a)].">
      <j1 rule="hyper" parents="8472 10786"/>
    </justification>
  </clause>

  <clause id="10788">
    <literal><![CDATA[
      K(x \ (y * (z * u)),z) = K(z * (x \ (y * u)),z)
    ]]></literal>
    <justification jstring="[hyper(58,a,8664,a(flip),b,10786,a)].">
      <j1 rule="hyper" parents="58 8664 10786"/>
    </justification>
  </clause>

  <clause id="10789">
    <literal><![CDATA[
      K(((x \ y) \ z) * u,L(u,z,x)) = K(u * (y \ (x * z)),u)
    ]]></literal>
    <justification jstring="[hyper(58,a,10517,a,b,10788,a)].">
      <j1 rule="hyper" parents="58 10517 10788"/>
    </justification>
  </clause>

  <clause id="10790">
    <literal><![CDATA[
      K(x \ (y \ (z * (u * y))),y) = K(x \ (z * u),y)
    ]]></literal>
    <justification jstring="[hyper(320,a,10494,a(flip),b,10787,a),flip(a)].">
      <j1 rule="hyper" parents="320 10494 10787"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10791">
    <literal><![CDATA[
      K(L(x,y * z,u),y) = K((u * z) \ (u * (z * x)),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,9773,a(flip),b,10790,a)].">
      <j1 rule="hyper" parents="58 9773 10790"/>
    </justification>
  </clause>

  <clause id="10792">
    <literal><![CDATA[
      K(L(x,y * z,u),y) = K(L(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(13(a,2),10791(a,2,1))].">
      <j1 rule="para" parents="13 10791"/>
    </justification>
  </clause>

  <clause id="10793">
    <literal><![CDATA[
      K(L(x,x \ y,z),u) = K(x,L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(10627,a,10792,a),flip(a)].">
      <j1 rule="hyper" parents="10627 10792"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10794">
    <literal><![CDATA[
      L(K(x,y),z,u) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,8906,a(flip),b,10793,a)].">
      <j1 rule="hyper" parents="58 8906 10793"/>
    </justification>
  </clause>

  <clause id="10795">
    <literal><![CDATA[
      K(x,L(y,T(x,z),u)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(6252(a,1),10793(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6252 10793"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10796">
    <literal><![CDATA[
      K(x,(y * T(x,z)) \ u) = K(x,T(x,z) \ (y \ u))
    ]]></literal>
    <justification jstring="[para(298(a,1),10795(a,1,2))].">
      <j1 rule="para" parents="298 10795"/>
    </justification>
  </clause>

  <clause id="10797">
    <literal><![CDATA[
      K(x,L(y / z,z,u)) = K(x,L(y / z,y,u))
    ]]></literal>
    <justification jstring="[hyper(10440,a,10794,a)].">
      <j1 rule="hyper" parents="10440 10794"/>
    </justification>
  </clause>

  <clause id="10798">
    <literal><![CDATA[
      K(x,L(y,y \ z,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(10439,a,10794,a)].">
      <j1 rule="hyper" parents="10439 10794"/>
    </justification>
  </clause>

  <clause id="10799">
    <literal><![CDATA[
      K(x,L(y,z * x,u)) = K(L(x,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(8394,a,10794,a),flip(a)].">
      <j1 rule="hyper" parents="8394 10794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10800">
    <literal><![CDATA[
      K(x,(y * (z \ u)) \ (y * u)) = K(x,L(T(z,u),u,y))
    ]]></literal>
    <justification jstring="[hyper(7262,a,10794,a)].">
      <j1 rule="hyper" parents="7262 10794"/>
    </justification>
  </clause>

  <clause id="10801">
    <literal><![CDATA[
      K(x,(y * ((y \ z) / u)) \ z) = K(x,L(u,y \ z,y))
    ]]></literal>
    <justification jstring="[hyper(6865,a,10794,a)].">
      <j1 rule="hyper" parents="6865 10794"/>
    </justification>
  </clause>

  <clause id="10802">
    <literal><![CDATA[
      K(x,L(y \ z,z,u)) = K(x,(u * y) \ (u * z))
    ]]></literal>
    <justification jstring="[hyper(6708,a,10794,a),flip(a)].">
      <j1 rule="hyper" parents="6708 10794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10803">
    <literal><![CDATA[
      K(L(x,y,z),u) \ 1 = L(K(u,x),y,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,4969,a,b,10794,a)].">
      <j1 rule="hyper" parents="320 4969 10794"/>
    </justification>
  </clause>

  <clause id="10804">
    <literal><![CDATA[
      L(K(x,y \ z),y,u) = K(x,(u * y) \ (u * z))
    ]]></literal>
    <justification jstring="[hyper(320,a,6598,a(flip),b,10794,a),flip(a)].">
      <j1 rule="hyper" parents="320 6598 10794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10806">
    <literal><![CDATA[
      K(x,L(y,z / y,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,6607,a,b,10794,a)].">
      <j1 rule="hyper" parents="58 6607 10794"/>
    </justification>
  </clause>

  <clause id="10807">
    <literal><![CDATA[
      K(x,y) * a(z,u,K(y,x)) = K(x,L(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,5896,a,b,10794,a)].">
      <j1 rule="hyper" parents="58 5896 10794"/>
    </justification>
  </clause>

  <clause id="10808">
    <literal><![CDATA[
      K(x,L(T(y,z),y,u)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,7234,a(flip),b,10794,a),flip(a)].">
      <j1 rule="hyper" parents="58 7234 10794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10809">
    <literal><![CDATA[
      K(x \ y,L(z,y,y \ 1)) = K(((y \ 1) * x) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,6635,a(flip),b,10794,a),flip(a)].">
      <j1 rule="hyper" parents="58 6635 10794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10810">
    <literal><![CDATA[
      K((x \ y) \ z,L(u,z,x)) = K(y \ (x * z),u)
    ]]></literal>
    <justification jstring="[hyper(58,a,6626,a(flip),b,10794,a),flip(a)].">
      <j1 rule="hyper" parents="58 6626 10794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10811">
    <literal><![CDATA[
      K(x,L(y \ z,z,u)) = K(x,L(y \ z,y,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,6587,a(flip),b,10794,a),flip(a)].">
      <j1 rule="hyper" parents="58 6587 10794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10812">
    <literal><![CDATA[
      K(x,L((y \ z) \ u,u,y)) = K(x,z \ (y * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,6584,a(flip),b,10794,a),flip(a)].">
      <j1 rule="hyper" parents="58 6584 10794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10813">
    <literal><![CDATA[
      K(x,L(y \ 1,z,u)) = K(x,L(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,5675,a(flip),b,10794,a),flip(a)].">
      <j1 rule="hyper" parents="58 5675 10794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10814">
    <literal><![CDATA[
      x * K(y,L(z,u \ x,u)) = u * ((u \ x) * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(119,a,10794,a(flip),b,91,a)].">
      <j1 rule="hyper" parents="119 10794 91"/>
    </justification>
  </clause>

  <clause id="10815">
    <literal><![CDATA[
      (x * y) * K(z,L(u,y,x)) = x * (y * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(119,a,10794,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="119 10794 13"/>
    </justification>
  </clause>

  <clause id="10816">
    <literal><![CDATA[
      x \ K(y,L(z,x \ 1,x)) = (x \ 1) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(116,a,10794,a(flip),b,257,a)].">
      <j1 rule="hyper" parents="116 10794 257"/>
    </justification>
  </clause>

  <clause id="10818">
    <literal><![CDATA[
      L(K(x,y \ (z \ u)),y,z) = K(x,(z * y) \ u)
    ]]></literal>
    <justification jstring="[para(298(a,1),10794(a,2,2))].">
      <j1 rule="para" parents="298 10794"/>
    </justification>
  </clause>

  <clause id="10819">
    <literal><![CDATA[
      L(K(x,(y \ z) \ u),y \ z,y) = K(x,z \ (y * u))
    ]]></literal>
    <justification jstring="[para(490(a,1),10794(a,2,2))].">
      <j1 rule="para" parents="490 10794"/>
    </justification>
  </clause>

  <clause id="10820">
    <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(10794(a,1),469(a,1,2,2))].">
      <j1 rule="para" parents="10794 469"/>
    </justification>
  </clause>

  <clause id="10821">
    <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(10794(a,1),1421(a,1,2,1))].">
      <j1 rule="para" parents="10794 1421"/>
    </justification>
  </clause>

  <clause id="10822">
    <literal><![CDATA[
      K(x,L(y,z,u)) * a(u,z,K(x,y)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(10794(a,1),1934(a,1,1))].">
      <j1 rule="para" parents="10794 1934"/>
    </justification>
  </clause>

  <clause id="10823">
    <literal><![CDATA[
      K(x,L(y,z,u)) * K(y,x) = a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[para(10794(a,1),5890(a,1,1))].">
      <j1 rule="para" parents="10794 5890"/>
    </justification>
  </clause>

  <clause id="10824">
    <literal><![CDATA[
      K(x,y) * K(y,L(x,z,u)) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[para(10794(a,1),5892(a,1,2))].">
      <j1 rule="para" parents="10794 5892"/>
    </justification>
  </clause>

  <clause id="10825">
    <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(10794(a,1),5899(a,1,2))].">
      <j1 rule="para" parents="10794 5899"/>
    </justification>
  </clause>

  <clause id="10826">
    <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(10794(a,1),5900(a,1,1))].">
      <j1 rule="para" parents="10794 5900"/>
    </justification>
  </clause>

  <clause id="10827">
    <literal><![CDATA[
      a(x,y,K(z,u)) * K(z,L(u,y,x)) = K(z,u)
    ]]></literal>
    <justification jstring="[para(10794(a,1),5953(a,1,2))].">
      <j1 rule="para" parents="10794 5953"/>
    </justification>
  </clause>

  <clause id="10828">
    <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(10794(a,1),6856(a,1))].">
      <j1 rule="para" parents="10794 6856"/>
    </justification>
  </clause>

  <clause id="10829">
    <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(10794(a,1),6864(a,1))].">
      <j1 rule="para" parents="10794 6864"/>
    </justification>
  </clause>

  <clause id="10830">
    <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(10794(a,1),6865(a,1))].">
      <j1 rule="para" parents="10794 6865"/>
    </justification>
  </clause>

  <clause id="10831">
    <literal><![CDATA[
      L(K(x,K(y,z)),u,w) = K(x,K(z,L(y,u,w)))
    ]]></literal>
    <justification jstring="[para(10794(a,1),7833(a,2,2))].">
      <j1 rule="para" parents="10794 7833"/>
    </justification>
  </clause>

  <clause id="10832">
    <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(10794(a,1),8611(a,1,2))].">
      <j1 rule="para" parents="10794 8611"/>
    </justification>
  </clause>

  <clause id="10833">
    <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(4414(a,2),10798(a,1,2,2))].">
      <j1 rule="para" parents="4414 10798"/>
    </justification>
  </clause>

  <clause id="10834">
    <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(10798(a,1),10424(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10798 10424"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10835">
    <literal><![CDATA[
      K(x,K(y,L(z,u * y,w))) = K(x,K(z,L(y,u,w)))
    ]]></literal>
    <justification jstring="[para(10799(a,2),7797(a,1,2))].">
      <j1 rule="para" parents="10799 7797"/>
    </justification>
  </clause>

  <clause id="10836">
    <literal><![CDATA[
      L(K(x,y),z,u) = K(L(x,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(34,a,5750,a,b,10803,a)].">
      <j1 rule="hyper" parents="34 5750 10803"/>
    </justification>
  </clause>

  <clause id="10837">
    <literal><![CDATA[
      L(K(x,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(10803(a,1),4985(a,1))].">
      <j1 rule="para" parents="10803 4985"/>
    </justification>
  </clause>

  <clause id="10838">
    <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(10803(a,1),4986(a,1))].">
      <j1 rule="para" parents="10803 4986"/>
    </justification>
  </clause>

  <clause id="10839">
    <literal><![CDATA[
      L(K(x,K(y,z)),u,w) = K(y,K(z,L(x,u,w)))
    ]]></literal>
    <justification jstring="[hyper(320,a,7784,a,b,10836,a),flip(a)].">
      <j1 rule="hyper" parents="320 7784 10836"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10840">
    <literal><![CDATA[
      K(L(x,y,z),u) = K(x,L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,10794,a(flip),b,10836,a),flip(a)].">
      <j1 rule="hyper" parents="58 10794 10836"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10841">
    <literal><![CDATA[
      L(K((x \ 1) \ y,z),x \ 1,x) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(489(a,1),10836(a,2,1))].">
      <j1 rule="para" parents="489 10836"/>
    </justification>
  </clause>

  <clause id="10842">
    <literal><![CDATA[
      K(L(x,y,z),u) * a(z,y,K(x,u)) = K(x,u)
    ]]></literal>
    <justification jstring="[para(10836(a,1),1934(a,1,1))].">
      <j1 rule="para" parents="10836 1934"/>
    </justification>
  </clause>

  <clause id="10843">
    <literal><![CDATA[
      K(L(K(x,y),z,u),w) = K(w,K(y,L(x,z,u)))
    ]]></literal>
    <justification jstring="[para(10836(a,2),5621(a,1,1))].">
      <j1 rule="para" parents="10836 5621"/>
    </justification>
  </clause>

  <clause id="10844">
    <literal><![CDATA[
      K(x,y) * K(L(y,z,u),x) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[para(10836(a,1),5892(a,1,2))].">
      <j1 rule="para" parents="10836 5892"/>
    </justification>
  </clause>

  <clause id="10845">
    <literal><![CDATA[
      K(L(K(x,y),z,u),w) = K(y,K(w,L(x,z,u)))
    ]]></literal>
    <justification jstring="[para(10836(a,2),7780(a,1,1))].">
      <j1 rule="para" parents="10836 7780"/>
    </justification>
  </clause>

  <clause id="10846">
    <literal><![CDATA[
      K(x,L(K(y,z),u,w)) = K(x,K(z,L(y,u,w)))
    ]]></literal>
    <justification jstring="[para(10836(a,2),7797(a,1,2))].">
      <j1 rule="para" parents="10836 7797"/>
    </justification>
  </clause>

  <clause id="10847">
    <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(10836(a,2),7821(a,1))].">
      <j1 rule="para" parents="10836 7821"/>
    </justification>
  </clause>

  <clause id="10848">
    <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(10836(a,2),7831(a,1,2))].">
      <j1 rule="para" parents="10836 7831"/>
    </justification>
  </clause>

  <clause id="10849">
    <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(10836(a,2),8046(a,1,1))].">
      <j1 rule="para" parents="10836 8046"/>
    </justification>
  </clause>

  <clause id="10850">
    <literal><![CDATA[
      K(x,L(y,z * x,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,10799,a,b,10840,a)].">
      <j1 rule="hyper" parents="58 10799 10840"/>
    </justification>
  </clause>

  <clause id="10851">
    <literal><![CDATA[
      L(x,y,z) \ L(T(x,u),y,z) = K(x,L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,4764,a,b,10840,a)].">
      <j1 rule="hyper" parents="58 4764 10840"/>
    </justification>
  </clause>

  <clause id="10852">
    <literal><![CDATA[
      K(x,L(y,z,u)) * (K(y,L(x,z,u)) * w) = w
    ]]></literal>
    <justification jstring="[hyper(118,a,10840,a(flip),b,5142,a),flip(a)].">
      <j1 rule="hyper" parents="118 10840 5142"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10853">
    <literal><![CDATA[
      K(x \ (y \ z),L(u,x,y)) = K((y * x) \ z,u)
    ]]></literal>
    <justification jstring="[para(298(a,1),10840(a,1,1)),flip(a)].">
      <j1 rule="para" parents="298 10840"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10854">
    <literal><![CDATA[
      K((x \ 1) \ y,L(z,x \ 1,x)) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(489(a,1),10840(a,1,1)),flip(a)].">
      <j1 rule="para" parents="489 10840"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10855">
    <literal><![CDATA[
      K(x \ T(y,z),L(u,x,z)) = K((z * x) \ (y * z),u)
    ]]></literal>
    <justification jstring="[para(450(a,1),10840(a,1,1)),flip(a)].">
      <j1 rule="para" parents="450 10840"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10856">
    <literal><![CDATA[
      K(a(x,y,z) \ u,L(w,a(x,y,z),x * (y * z))) = K(((x * y) * z) \ ((x * (y * z)) * u),w)
    ]]></literal>
    <justification jstring="[para(692(a,1),10840(a,1,1)),flip(a)].">
      <j1 rule="para" parents="692 10840"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10857">
    <literal><![CDATA[
      K(x,L(y,z,u)) * L(x,z,u) = L(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(10840(a,1),4844(a,1,1))].">
      <j1 rule="para" parents="10840 4844"/>
    </justification>
  </clause>

  <clause id="10858">
    <literal><![CDATA[
      ((x * y) * K(z,L(u,y,x))) \ (x * (y * T(z,u))) = L(z,y,x)
    ]]></literal>
    <justification jstring="[para(10840(a,1),6235(a,1,1,2))].">
      <j1 rule="para" parents="10840 6235"/>
    </justification>
  </clause>

  <clause id="10859">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w))) = K(z,K(x,L(y,u,w)))
    ]]></literal>
    <justification jstring="[para(10840(a,1),7784(a,1,2))].">
      <j1 rule="para" parents="10840 7784"/>
    </justification>
  </clause>

  <clause id="10860">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w))) = K(x,K(z,L(y,u,w)))
    ]]></literal>
    <justification jstring="[para(10840(a,1),7797(a,1,2))].">
      <j1 rule="para" parents="10840 7797"/>
    </justification>
  </clause>

  <clause id="10861">
    <literal><![CDATA[
      x * K(y,K(z,L(x,u,w))) = T(x,K(y,L(z,u,w)))
    ]]></literal>
    <justification jstring="[para(10840(a,1),7794(a,1,2,2))].">
      <j1 rule="para" parents="10840 7794"/>
    </justification>
  </clause>

  <clause id="10862">
    <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(10840(a,1),7831(a,1,2))].">
      <j1 rule="para" parents="10840 7831"/>
    </justification>
  </clause>

  <clause id="10863">
    <literal><![CDATA[
      K(x,L(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(K(x,y),z,u) = w
    ]]></literal>
    <justification jstring="[para(10806(a,1),6614(a,1))].">
      <j1 rule="para" parents="10806 6614"/>
    </justification>
  </clause>

  <clause id="10864">
    <literal><![CDATA[
      K(x \ y,L(z,y,u)) = K(x \ y,L(z,x,u))
    ]]></literal>
    <justification jstring="[para(5(a,1),10850(a,1,2,2))].">
      <j1 rule="para" parents="5 10850"/>
    </justification>
  </clause>

  <clause id="10865">
    <literal><![CDATA[
      K(x,L(y,z / x,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(7(a,1),10850(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7 10850"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10866">
    <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(5896(a,2),10837(a,1))].">
      <j1 rule="para" parents="5896 10837"/>
    </justification>
  </clause>

  <clause id="10867">
    <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(6587(a,1),10837(a,1))].">
      <j1 rule="para" parents="6587 10837"/>
    </justification>
  </clause>

  <clause id="10868">
    <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(6606(a,2),10837(a,1))].">
      <j1 rule="para" parents="6606 10837"/>
    </justification>
  </clause>

  <clause id="10869">
    <literal><![CDATA[
      (x * (y * K(z,u))) \ (x * y) != w
    ]]></literal>
    <literal><![CDATA[
      K(u,L(z,y,x)) = w
    ]]></literal>
    <justification jstring="[para(6671(a,2),10837(a,1))].">
      <j1 rule="para" parents="6671 10837"/>
    </justification>
  </clause>

  <clause id="10870">
    <literal><![CDATA[
      K(L(x,y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(u,y,z)) = w
    ]]></literal>
    <justification jstring="[para(10836(a,1),10837(a,1))].">
      <j1 rule="para" parents="10836 10837"/>
    </justification>
  </clause>

  <clause id="10871">
    <literal><![CDATA[
      K(L(x,y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(K(x,u),y,z) = w
    ]]></literal>
    <justification jstring="[para(10840(a,2),10863(a,1))].">
      <j1 rule="para" parents="10840 10863"/>
    </justification>
  </clause>

  <clause id="10872">
    <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(7784(a,2),10871(a,1))].">
      <j1 rule="para" parents="7784 10871"/>
    </justification>
  </clause>

  <clause id="10873">
    <literal><![CDATA[
      a(x,y,K(z,u)) * K(u,z) = K(u,L(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(58,a,7406,a(flip),b,10807,a)].">
      <j1 rule="hyper" parents="58 7406 10807"/>
    </justification>
  </clause>

  <clause id="10874">
    <literal><![CDATA[
      K(x,L(T(y,z) \ u,u,z)) = K(x,(y * z) \ (z * u))
    ]]></literal>
    <justification jstring="[para(496(a,1),10811(a,2,2))].">
      <j1 rule="para" parents="496 10811"/>
    </justification>
  </clause>

  <clause id="10875">
    <literal><![CDATA[
      a(x,y * z,K(z,u)) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(6612,a,10823,a)].">
      <j1 rule="hyper" parents="6612 10823"/>
    </justification>
  </clause>

  <clause id="10876">
    <literal><![CDATA[
      T(x,L(y,z,u)) * K(y,x) = x * a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(119,a,10823,a(flip),b,4777,a),flip(a)].">
      <j1 rule="hyper" parents="119 10823 4777"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10877">
    <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(10823(a,1),2005(a,1))].">
      <j1 rule="para" parents="10823 2005"/>
    </justification>
  </clause>

  <clause id="10878">
    <literal><![CDATA[
      K(x,L(y,z,u)) * K(y,x) = a(u,z * x,K(y,x))
    ]]></literal>
    <justification jstring="[para(10850(a,1),10823(a,1,1))].">
      <j1 rule="para" parents="10850 10823"/>
    </justification>
  </clause>

  <clause id="10879">
    <literal><![CDATA[
      a(x,y * z,K(u,K(w,z))) = a(x,y,K(z,K(u,w)))
    ]]></literal>
    <justification jstring="[para(7784(a,2),10875(a,1,3))].">
      <j1 rule="para" parents="7784 10875"/>
    </justification>
  </clause>

  <clause id="10880">
    <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(10824(a,1),2009(a,1))].">
      <j1 rule="para" parents="10824 2009"/>
    </justification>
  </clause>

  <clause id="10881">
    <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,9031,a,b,10831,a)].">
      <j1 rule="hyper" parents="58 9031 10831"/>
    </justification>
  </clause>

  <clause id="10882">
    <literal><![CDATA[
      K(x,L(K(y,z),u,w)) = K(x,K(y,L(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(58,a,7833,a(flip),b,10831,a)].">
      <j1 rule="hyper" parents="58 7833 10831"/>
    </justification>
  </clause>

  <clause id="10883">
    <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,10839,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="119 10839 13"/>
    </justification>
  </clause>

  <clause id="10884">
    <literal><![CDATA[
      L(K(x,K(y,y * z)),u,w) = K(x,K(z * x,L(y,u,w)))
    ]]></literal>
    <justification jstring="[para(8033(a,1),10839(a,1,1))].">
      <j1 rule="para" parents="8033 10839"/>
    </justification>
  </clause>

  <clause id="10885">
    <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(10842(a,1),5155(a,2,2))].">
      <j1 rule="para" parents="10842 5155"/>
    </justification>
  </clause>

  <clause id="10886">
    <literal><![CDATA[
      a(x,y * z,K(u,z)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(6621,a,10844,a)].">
      <j1 rule="hyper" parents="6621 10844"/>
    </justification>
  </clause>

  <clause id="10887">
    <literal><![CDATA[
      T(x,L(y,z,u)) \ T(x,y) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(5672,a,10844,a)].">
      <j1 rule="hyper" parents="5672 10844"/>
    </justification>
  </clause>

  <clause id="10888">
    <literal><![CDATA[
      (x * y) / T(x,L(y,z,u)) = y * a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[para(10844(a,1),6369(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10844 6369"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10889">
    <literal><![CDATA[
      a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y * u,K(z,u)) = w
    ]]></literal>
    <justification jstring="[para(10844(a,1),6621(a,1))].">
      <j1 rule="para" parents="10844 6621"/>
    </justification>
  </clause>

  <clause id="10890">
    <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(10843(a,1),10844(a,1,2))].">
      <j1 rule="para" parents="10843 10844"/>
    </justification>
  </clause>

  <clause id="10891">
    <literal><![CDATA[
      x / T(x / y,L(y,z,u)) = y * a(u,z,K(y \ x,y))
    ]]></literal>
    <justification jstring="[para(10886(a,1),9679(a,2,2))].">
      <j1 rule="para" parents="10886 9679"/>
    </justification>
  </clause>

  <clause id="10892">
    <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,10062,a,b,10845,a)].">
      <j1 rule="hyper" parents="58 10062 10845"/>
    </justification>
  </clause>

  <clause id="10893">
    <literal><![CDATA[
      K(x,1 / L(K(y,z),u,w)) = K(x,K(y,L(z,u,w)))
    ]]></literal>
    <justification jstring="[para(5751(a,2),10846(a,1,2))].">
      <j1 rule="para" parents="5751 10846"/>
    </justification>
  </clause>

  <clause id="10894">
    <literal><![CDATA[
      K(x,K(y,L(z,z,u))) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[para(6102(a,1),10846(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6102 10846"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10895">
    <literal><![CDATA[
      K(x,K(y / z,L(u,y,w))) = K(x,K(u,L(y / z,z,w)))
    ]]></literal>
    <justification jstring="[para(9026(a,1),10846(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9026 10846"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10896">
    <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,10852,a(flip),b,5261,a),flip(a)].">
      <j1 rule="hyper" parents="119 10852 5261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10897">
    <literal><![CDATA[
      K(x,K(y,L(z \ 1,u,w))) = K(y,K(z,L(x,u,w)))
    ]]></literal>
    <justification jstring="[hyper(8203,a,10859,a),flip(a)].">
      <j1 rule="hyper" parents="8203 10859"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10898">
    <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(10859(a,2),4766(a,1,2))].">
      <j1 rule="para" parents="10859 4766"/>
    </justification>
  </clause>

  <clause id="10899">
    <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(10420(a,1),10864(a,2,2))].">
      <j1 rule="para" parents="10420 10864"/>
    </justification>
  </clause>

  <clause id="10900">
    <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(5601(a,1),10802(a,2,2,2))].">
      <j1 rule="para" parents="5601 10802"/>
    </justification>
  </clause>

  <clause id="10901">
    <literal><![CDATA[
      K(x,(y * z) \ (y * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(z \ u,z,y)) = w
    ]]></literal>
    <justification jstring="[para(10804(a,1),10837(a,1))].">
      <j1 rule="para" parents="10804 10837"/>
    </justification>
  </clause>

  <clause id="10902">
    <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(406(a,1),10812(a,1,2,1,1))].">
      <j1 rule="para" parents="406 10812"/>
    </justification>
  </clause>

  <clause id="10903">
    <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),10815(a,1,2,2))].">
      <j1 rule="para" parents="25 10815"/>
    </justification>
  </clause>

  <clause id="10904">
    <literal><![CDATA[
      (x * y) * z != x * (y * K(u,w))
    ]]></literal>
    <literal><![CDATA[
      K(u,L(w,y,x)) = z
    ]]></literal>
    <justification jstring="[para(10815(a,1),38(a,1)),flip(a)].">
      <j1 rule="para" parents="10815 38"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10905">
    <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(10815(a,1),322(a,1)),flip(b)].">
      <j1 rule="para" parents="10815 322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10906">
    <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(7208(a,1),10815(a,2,2))].">
      <j1 rule="para" parents="7208 10815"/>
    </justification>
  </clause>

  <clause id="10907">
    <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(10815(a,1),7557(a,2,2,1))].">
      <j1 rule="para" parents="10815 7557"/>
    </justification>
  </clause>

  <clause id="10908">
    <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(10815(a,1),8858(a,2,2,1))].">
      <j1 rule="para" parents="10815 8858"/>
    </justification>
  </clause>

  <clause id="10909">
    <literal><![CDATA[
      (x * y) * K(z,K(u,L(w,y,x))) = x * (y * K(z,K(u,w)))
    ]]></literal>
    <justification jstring="[para(10794(a,1),10815(a,1,2,2))].">
      <j1 rule="para" parents="10794 10815"/>
    </justification>
  </clause>

  <clause id="10910">
    <literal><![CDATA[
      (x * (y / z)) * K(z,L(u,y,x)) = x * ((y / z) * K(z,u))
    ]]></literal>
    <justification jstring="[para(10865(a,1),10815(a,1,2))].">
      <j1 rule="para" parents="10865 10815"/>
    </justification>
  </clause>

  <clause id="10911">
    <literal><![CDATA[
      K(x,L(T(y,z),z \ 1,z)) = z * (K(x,y) * (z \ 1))
    ]]></literal>
    <justification jstring="[hyper(119,a,8239,a(flip),b,10816,a),flip(a)].">
      <j1 rule="hyper" parents="119 8239 10816"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10912">
    <literal><![CDATA[
      L(K((x \ 1) \ (y \ z),y),x \ 1,x) = K(y \ (x * z),y)
    ]]></literal>
    <justification jstring="[hyper(320,a,10428,a,b,10841,a),flip(a)].">
      <j1 rule="hyper" parents="320 10428 10841"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10913">
    <literal><![CDATA[
      K(x,L(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(L(x,z,u),y) = w
    ]]></literal>
    <justification jstring="[para(10851(a,1),5031(a,1))].">
      <j1 rule="para" parents="10851 5031"/>
    </justification>
  </clause>

  <clause id="10914">
    <literal><![CDATA[
      K((x * ((y \ 1) \ 1)) \ z,u) = K(y \ (x \ z),L(u,y,x))
    ]]></literal>
    <justification jstring="[hyper(320,a,3994,a,b,10853,a)].">
      <j1 rule="hyper" parents="320 3994 10853"/>
    </justification>
  </clause>

  <clause id="10915">
    <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(10853(a,2),7799(a,1,2))].">
      <j1 rule="para" parents="10853 7799"/>
    </justification>
  </clause>

  <clause id="10916">
    <literal><![CDATA[
      K((x \ 1) \ y,x * z) = K(x * y,(x \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(489(a,1),10854(a,1,2))].">
      <j1 rule="para" parents="489 10854"/>
    </justification>
  </clause>

  <clause id="10917">
    <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(10857(a,1),8592(a,1,2,2))].">
      <j1 rule="para" parents="10857 8592"/>
    </justification>
  </clause>

  <clause id="10919">
    <literal><![CDATA[
      K(x,(y * T(x,z)) \ u) = K(x,x \ (y \ u))
    ]]></literal>
    <justification jstring="[hyper(320,a,7278,a(flip),b,10796,a),flip(a)].">
      <j1 rule="hyper" parents="320 7278 10796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10921">
    <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),10835(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="298 10835"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10922">
    <literal><![CDATA[
      x * ((x \ y) * K(y,z)) = T(y,L(z,x \ y,x))
    ]]></literal>
    <justification jstring="[hyper(9506,a,10876,a)].">
      <j1 rule="hyper" parents="9506 10876"/>
    </justification>
  </clause>

  <clause id="10923">
    <literal><![CDATA[
      T(x * K(y,x),L(y,z,u)) = x * a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(7237,a,10876,a)].">
      <j1 rule="hyper" parents="7237 10876"/>
    </justification>
  </clause>

  <clause id="10924">
    <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(4468(a,1),10888(a,1,1))].">
      <j1 rule="para" parents="4468 10888"/>
    </justification>
  </clause>

  <clause id="10925">
    <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,10882,a,b,10893,a),flip(a)].">
      <j1 rule="hyper" parents="320 10882 10893"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10926">
    <literal><![CDATA[
      K(x * y,(x \ 1) \ (x \ z)) = K((x \ 1) \ y,z)
    ]]></literal>
    <justification jstring="[para(5(a,1),10916(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5 10916"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10927">
    <literal><![CDATA[
      T(x * a(y,z,K(u,x)),u) = T(x,L(u,z,y))
    ]]></literal>
    <justification jstring="[para(10923(a,1),4870(a,1,1))].">
      <j1 rule="para" parents="10923 4870"/>
    </justification>
  </clause>

  <clause id="10928">
    <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(10923(a,1),4936(a,1,1))].">
      <j1 rule="para" parents="10923 4936"/>
    </justification>
  </clause>

  <clause id="10929">
    <literal><![CDATA[
      K((x \ 1) \ (x \ y),z) = K(y,(x \ 1) \ (x \ z))
    ]]></literal>
    <justification jstring="[para(5(a,1),10926(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5 10926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10930">
    <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(6241(a,1),10800(a,1,2,1))].">
      <j1 rule="para" parents="6241 10800"/>
    </justification>
  </clause>

  <clause id="10931">
    <literal><![CDATA[
      K(((x \ y) / z) \ y,L(z,x \ y,x)) = K(((x \ y) / z) \ y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,9043,a(flip),b,10801,a),flip(a)].">
      <j1 rule="hyper" parents="58 9043 10801"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10932">
    <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,10929,a(flip),b,10809,a)].">
      <j1 rule="hyper" parents="58 10929 10809"/>
    </justification>
  </clause>

  <clause id="10933">
    <literal><![CDATA[
      x \ (y * K(z,y \ (x * u))) = (x \ y) * K(z,(x \ y) \ u)
    ]]></literal>
    <justification jstring="[para(10819(a,1),474(a,1,2,2))].">
      <j1 rule="para" parents="10819 474"/>
    </justification>
  </clause>

  <clause id="10934">
    <literal><![CDATA[
      a(x,y * z,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,K(z,u)) = w
    ]]></literal>
    <justification jstring="[para(6611(a,1),10825(a,1))].">
      <j1 rule="para" parents="6611 10825"/>
    </justification>
  </clause>

  <clause id="10935">
    <literal><![CDATA[
      a(x,y * z,K(u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(10878(a,1),10826(a,1))].">
      <j1 rule="para" parents="10878 10826"/>
    </justification>
  </clause>

  <clause id="10936">
    <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(7779(a,1),10847(a,1,1))].">
      <j1 rule="para" parents="7779 10847"/>
    </justification>
  </clause>

  <clause id="10937">
    <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(10846(a,2),10862(a,1))].">
      <j1 rule="para" parents="10846 10862"/>
    </justification>
  </clause>

  <clause id="10938">
    <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(4196(a,1),10874(a,2,2,1))].">
      <j1 rule="para" parents="4196 10874"/>
    </justification>
  </clause>

  <clause id="10939">
    <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,9369,a(flip),b,10881,a)].">
      <j1 rule="hyper" parents="58 9369 10881"/>
    </justification>
  </clause>

  <clause id="10940">
    <literal><![CDATA[
      K(x,K(y * z,L(y,u,w))) = K(x,K(z * x,L(y,u,w)))
    ]]></literal>
    <justification jstring="[hyper(10936,a,10884,a)].">
      <j1 rule="hyper" parents="10936 10884"/>
    </justification>
  </clause>

  <clause id="10941">
    <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(10891(a,1),9459(a,2,2))].">
      <j1 rule="para" parents="10891 9459"/>
    </justification>
  </clause>

  <clause id="10942">
    <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),10895(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="497 10895"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10943">
    <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(10802(a,2),10901(a,1))].">
      <j1 rule="para" parents="10802 10901"/>
    </justification>
  </clause>

  <clause id="10944">
    <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,7969,a(flip),b,10940,a),flip(a)].">
      <j1 rule="hyper" parents="320 7969 10940"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10945">
    <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(10909(a,1),10898(a,1))].">
      <j1 rule="para" parents="10909 10898"/>
    </justification>
  </clause>

  <clause id="10946">
    <literal><![CDATA[
      L(K((x \ y) \ z,y),x \ 1,x) = K(y \ (x * z),y)
    ]]></literal>
    <justification jstring="[para(8297(a,1),10912(a,1,1))].">
      <j1 rule="para" parents="8297 10912"/>
    </justification>
  </clause>

  <clause id="10947">
    <literal><![CDATA[
      K(x \ (y \ z),L(u,x,y)) != w
    ]]></literal>
    <literal><![CDATA[
      K((y * x) \ z,u) = w
    ]]></literal>
    <justification jstring="[para(10864(a,1),10828(a,1))].">
      <j1 rule="para" parents="10864 10828"/>
    </justification>
  </clause>

  <clause id="10948">
    <literal><![CDATA[
      L(K(x \ (y \ z),u),x,y) != w
    ]]></literal>
    <literal><![CDATA[
      K((y * x) \ z,u) = w
    ]]></literal>
    <justification jstring="[para(10794(a,2),10947(a,1))].">
      <j1 rule="para" parents="10794 10947"/>
    </justification>
  </clause>

  <clause id="10949">
    <literal><![CDATA[
      K((x * ((y \ 1) \ 1)) \ z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K((x * y) \ z,u) = w
    ]]></literal>
    <justification jstring="[para(10914(a,2),10947(a,1))].">
      <j1 rule="para" parents="10914 10947"/>
    </justification>
  </clause>

  <clause id="10950">
    <literal><![CDATA[
      (x * (y * K(z,u))) \ (x * (y * T(z,u))) = L(z,y,x)
    ]]></literal>
    <justification jstring="[para(10815(a,1),10858(a,1,1))].">
      <j1 rule="para" parents="10815 10858"/>
    </justification>
  </clause>

  <clause id="10951">
    <literal><![CDATA[
      L(x,y * K(x,z),u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(6240,a,10950,a)].">
      <j1 rule="hyper" parents="6240 10950"/>
    </justification>
  </clause>

  <clause id="10952">
    <literal><![CDATA[
      L(x,y,z) = (z * (y * K(x,y))) \ (z * (x * y))
    ]]></literal>
    <justification jstring="[para(105(a,1),10950(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="105 10950"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10953">
    <literal><![CDATA[
      L(x,y \ T(z,x),u) = L(x,y \ z,u)
    ]]></literal>
    <justification jstring="[para(6567(a,1),10951(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6567 10951"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10955">
    <literal><![CDATA[
      L(x,K(x,y) * z,u) = L(x,z,u)
    ]]></literal>
    <justification jstring="[para(7179(a,1),10951(a,1,2))].">
      <j1 rule="para" parents="7179 10951"/>
    </justification>
  </clause>

  <clause id="10956">
    <literal><![CDATA[
      L(x,T(y,x) \ z,u) = L(x,y \ z,u)
    ]]></literal>
    <justification jstring="[para(7298(a,1),10951(a,1,2))].">
      <j1 rule="para" parents="7298 10951"/>
    </justification>
  </clause>

  <clause id="10959">
    <literal><![CDATA[
      L(T(x,y),K(x,z) * u,w) = L(T(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(7888(a,1),10955(a,1,2,1))].">
      <j1 rule="para" parents="7888 10955"/>
    </justification>
  </clause>

  <clause id="10960">
    <literal><![CDATA[
      T(x,y) * L(y,z \ x,z) = z * ((z \ T(x,y)) * y)
    ]]></literal>
    <justification jstring="[hyper(119,a,10953,a(flip),b,91,a)].">
      <j1 rule="hyper" parents="119 10953 91"/>
    </justification>
  </clause>

  <clause id="10962">
    <literal><![CDATA[
      L(T(x,y),z / x,u) = L(T(x,y),x \ z,u)
    ]]></literal>
    <justification jstring="[para(4859(a,1),10959(a,1,2))].">
      <j1 rule="para" parents="4859 10959"/>
    </justification>
  </clause>

  <clause id="10963">
    <literal><![CDATA[
      L(T(x,y),T(x,z) \ u,w) = L(T(x,y),x \ u,w)
    ]]></literal>
    <justification jstring="[para(5081(a,1),10959(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5081 10959"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10965">
    <literal><![CDATA[
      L(x,y,z * K(x,y)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,10659,a(flip),b,10952,a)].">
      <j1 rule="hyper" parents="320 10659 10952"/>
    </justification>
  </clause>

  <clause id="10968">
    <literal><![CDATA[
      K(x,L(T(y,z),y \ u,w)) = K(x,L(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(10963(a,1),10798(a,1,2))].">
      <j1 rule="para" parents="10963 10798"/>
    </justification>
  </clause>

  <clause id="10969">
    <literal><![CDATA[
      K(x,(y * z) / (y * (z / u))) = K(x,L(T(u,y * z),z,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,10445,a(flip),b,10968,a)].">
      <j1 rule="hyper" parents="58 10445 10968"/>
    </justification>
  </clause>

  <clause id="10970">
    <literal><![CDATA[
      K(x,L(T(y,z),u / y,w)) = K(x,L(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(10962(a,2),10968(a,1,2))].">
      <j1 rule="para" parents="10962 10968"/>
    </justification>
  </clause>

  <clause id="10971">
    <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),10970(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6 10970"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10972">
    <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(10890(a,1),5640(a,1))].">
      <j1 rule="para" parents="10890 5640"/>
    </justification>
  </clause>

  <clause id="10973">
    <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(10849,a,10892,a)].">
      <j1 rule="hyper" parents="10849 10892"/>
    </justification>
  </clause>

  <clause id="10974">
    <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,10897,a(flip),b,10939,a),flip(a)].">
      <j1 rule="hyper" parents="320 10897 10939"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10975">
    <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(9729(a,1),10974(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9729 10974"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10976">
    <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(9595(a,1),10973(a,1,2))].">
      <j1 rule="para" parents="9595 10973"/>
    </justification>
  </clause>

  <clause id="10977">
    <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(5889(a,1),10832(a,1,1))].">
      <j1 rule="para" parents="5889 10832"/>
    </justification>
  </clause>

  <clause id="10978">
    <literal><![CDATA[
      K(((x \ y) \ y) * z,L(z,x \ y,x)) = K(((x \ y) / z) \ y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,10518,a(flip),b,10931,a)].">
      <j1 rule="hyper" parents="58 10518 10931"/>
    </justification>
  </clause>

  <clause id="10979">
    <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,6668,a(flip),b,10977,a),flip(a)].">
      <j1 rule="hyper" parents="320 6668 10977"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10980">
    <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(7851,a,10979,a)].">
      <j1 rule="hyper" parents="7851 10979"/>
    </justification>
  </clause>

  <clause id="10981">
    <literal><![CDATA[
      (x \ (L(x,y,z) * u)) * x = (L(x,y,z) * K(u,x)) * u
    ]]></literal>
    <justification jstring="[para(6293(a,1),10780(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6293 10780"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10982">
    <literal><![CDATA[
      (x \ (L(x,y,z) * u)) * x = L(x,y,z) * T(u,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,6196,a(flip),b,10981,a),flip(a)].">
      <j1 rule="hyper" parents="320 6196 10981"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10983">
    <literal><![CDATA[
      (L(x,y,z) * (x \ u)) * x = L(x,y,z) * T(u,x)
    ]]></literal>
    <justification jstring="[para(1406(a,1),10982(a,1,1))].">
      <j1 rule="para" parents="1406 10982"/>
    </justification>
  </clause>

  <clause id="10984">
    <literal><![CDATA[
      (x / y) \ (L(y,z,u) * (y \ x)) = x \ (L(y,z,u) * T(x,y))
    ]]></literal>
    <justification jstring="[para(10983(a,1),9851(a,2,2))].">
      <j1 rule="para" parents="10983 9851"/>
    </justification>
  </clause>

  <clause id="10985">
    <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,6197,a,b,10984,a),flip(a)].">
      <j1 rule="hyper" parents="320 6197 10984"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10986">
    <literal><![CDATA[
      (x * (y / z)) * K(u,L(T(z,w),y,x)) = x * (y / T(z,T(u,w)))
    ]]></literal>
    <justification jstring="[para(10970(a,1),10906(a,1,2))].">
      <j1 rule="para" parents="10970 10906"/>
    </justification>
  </clause>

  <clause id="10987">
    <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(9864(a,1),10921(a,1,2))].">
      <j1 rule="para" parents="9864 10921"/>
    </justification>
  </clause>

  <clause id="10988">
    <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,10976,a(flip),b,10987,a)].">
      <j1 rule="hyper" parents="58 10976 10987"/>
    </justification>
  </clause>

  <clause id="10989">
    <literal><![CDATA[
      K(x,K(y,(z * (u * y)) \ w)) = K(y,K(x,(z * u) \ w))
    ]]></literal>
    <justification jstring="[hyper(10915,a,10988,a),flip(a)].">
      <j1 rule="hyper" parents="10915 10988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10990">
    <literal><![CDATA[
      K(x,K(y,(z * (u * x)) \ w)) = K(x,K(y,(z * u) \ w))
    ]]></literal>
    <justification jstring="[hyper(7781,a,10989,a)].">
      <j1 rule="hyper" parents="7781 10989"/>
    </justification>
  </clause>

  <clause id="10991">
    <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,9758,a(flip),b,10990,a)].">
      <j1 rule="hyper" parents="58 9758 10990"/>
    </justification>
  </clause>

  <clause id="10992">
    <literal><![CDATA[
      K(x,K(y,a(z,x,T(u,x)))) = 1
    ]]></literal>
    <justification jstring="[hyper(320,a,9495,a(flip),b,10991,a),flip(a)].">
      <j1 rule="hyper" parents="320 9495 10991"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10994">
    <literal><![CDATA[
      K(x,K(y,a(z,x,u))) = 1
    ]]></literal>
    <justification jstring="[para(224(a,1),10992(a,1,2,2,3))].">
      <j1 rule="para" parents="224 10992"/>
    </justification>
  </clause>

  <clause id="10996">
    <literal><![CDATA[
      T(a(x,y,z),K(u,y)) = a(x,y,z) * 1
    ]]></literal>
    <justification jstring="[para(10994(a,1),7757(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10994 7757"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10997">
    <literal><![CDATA[
      T(a(x,y,z),K(u,y)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,3,a(flip),b,10996,a),flip(a)].">
      <j1 rule="hyper" parents="320 3 10996"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10998">
    <literal><![CDATA[
      T(a(x,y \ z,u),K(y,z)) = a(x,y \ z,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,8032,a(flip),b,10997,a)].">
      <j1 rule="hyper" parents="58 8032 10997"/>
    </justification>
  </clause>

  <clause id="10999">
    <literal><![CDATA[
      a(x,y \ z,u) * K(y,z) = K(y,z) * a(x,y \ z,u)
    ]]></literal>
    <justification jstring="[hyper(119,a,10998,a(flip),b,17,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 10998 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11000">
    <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(3693(a,1),10902(a,1,2))].">
      <j1 rule="para" parents="3693 10902"/>
    </justification>
  </clause>

  <clause id="11001">
    <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(4969(a,1),10975(a,2,1))].">
      <j1 rule="para" parents="4969 10975"/>
    </justification>
  </clause>

  <clause id="11002">
    <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,7755,a(flip),b,11001,a),flip(a)].">
      <j1 rule="hyper" parents="320 7755 11001"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11003">
    <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(11002(a,2),8195(a,1))].">
      <j1 rule="para" parents="11002 8195"/>
    </justification>
  </clause>

  <clause id="11004">
    <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(5130(a,1),10821(a,1,2))].">
      <j1 rule="para" parents="5130 10821"/>
    </justification>
  </clause>

  <clause id="11005">
    <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(10840(a,1),11004(a,1,2,1))].">
      <j1 rule="para" parents="10840 11004"/>
    </justification>
  </clause>

  <clause id="11006">
    <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(4781(a,1),11005(a,1,2))].">
      <j1 rule="para" parents="4781 11005"/>
    </justification>
  </clause>

  <clause id="11007">
    <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(10876(a,1),11006(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10876 11006"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11008">
    <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(10969(a,1),10834(a,1,2))].">
      <j1 rule="para" parents="10969 10834"/>
    </justification>
  </clause>

  <clause id="11009">
    <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,10986,a(flip),b,11008,a),flip(a)].">
      <j1 rule="hyper" parents="58 10986 11008"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11010">
    <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,10514,a(flip),b,10899,a),flip(a)].">
      <j1 rule="hyper" parents="58 10514 10899"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11011">
    <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(10985(a,1),10941(a,1,2))].">
      <j1 rule="para" parents="10985 10941"/>
    </justification>
  </clause>

  <clause id="11012">
    <literal><![CDATA[
      x \ (x * a(y,z,K(x \ u,x))) = K(L(x,z,y),u) * K(u,x)
    ]]></literal>
    <justification jstring="[hyper(7587,a,11011,a),flip(a)].">
      <j1 rule="hyper" parents="7587 11011"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11013">
    <literal><![CDATA[
      x \ (x * a(y,z,K(x \ u,x))) = K(x,L(u,z,y)) * K(u,x)
    ]]></literal>
    <justification jstring="[para(10840(a,1),11012(a,2,1))].">
      <j1 rule="para" parents="10840 11012"/>
    </justification>
  </clause>

  <clause id="11014">
    <literal><![CDATA[
      x * a(y,z,K(x \ u,x)) = x * a(y,z,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(10885,a,11013,a),flip(a)].">
      <j1 rule="hyper" parents="10885 11013"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11015">
    <literal><![CDATA[
      x \ (x * a(y,z,K(x \ u,x))) = a(y,z,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(320,a,10823,a(flip),b,11013,a),flip(a)].">
      <j1 rule="hyper" parents="320 10823 11013"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11016">
    <literal><![CDATA[
      a(x,y,K(z \ u,z)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(278,a,11014,a),flip(a)].">
      <j1 rule="hyper" parents="278 11014"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11019">
    <literal><![CDATA[
      a(x,y,K(z * u,z)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[para(4(a,1),11016(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="4 11016"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11020">
    <literal><![CDATA[
      a(x,y,K(z * u,u)) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[para(4963(a,1),11016(a,1,3)),flip(a)].">
      <j1 rule="para" parents="4963 11016"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11021">
    <literal><![CDATA[
      a(x,y,K(z,u \ z)) = a(x,y,K(u,u \ z))
    ]]></literal>
    <justification jstring="[para(4965(a,1),11016(a,1,3)),flip(a)].">
      <j1 rule="para" parents="4965 11016"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11022">
    <literal><![CDATA[
      a(x,y,K(z \ 1,u)) = a(x,y,K(z \ u,u))
    ]]></literal>
    <justification jstring="[para(5438(a,1),11016(a,1,3))].">
      <j1 rule="para" parents="5438 11016"/>
    </justification>
  </clause>

  <clause id="11023">
    <literal><![CDATA[
      a(x,y,K(z \ (u * w),w)) = a(x,y,K(z \ u,w))
    ]]></literal>
    <justification jstring="[para(10376(a,1),11016(a,1,3)),flip(a)].">
      <j1 rule="para" parents="10376 11016"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11024">
    <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(11019(a,2),9913(a,1,1))].">
      <j1 rule="para" parents="11019 9913"/>
    </justification>
  </clause>

  <clause id="11025">
    <literal><![CDATA[
      a(x,y,K(x * z,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(320,a,7037,a(flip),b,11020,a),flip(a)].">
      <j1 rule="hyper" parents="320 7037 11020"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11026">
    <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(11020(a,1),11007(a,2,2,2))].">
      <j1 rule="para" parents="11020 11007"/>
    </justification>
  </clause>

  <clause id="11027">
    <literal><![CDATA[
      L(K(x * y,y),z,x) = K(x * y,y)
    ]]></literal>
    <justification jstring="[hyper(47,a,11025,a)].">
      <j1 rule="hyper" parents="47 11025"/>
    </justification>
  </clause>

  <clause id="11028">
    <literal><![CDATA[
      x * (y * K(x * z,T(z,x * y))) = K(x * z,z) * (x * y)
    ]]></literal>
    <justification jstring="[para(11027(a,1),7185(a,2,1))].">
      <j1 rule="para" parents="11027 7185"/>
    </justification>
  </clause>

  <clause id="11029">
    <literal><![CDATA[
      a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,K(u \ z,u)) = w
    ]]></literal>
    <justification jstring="[para(11015(a,1),287(a,1)),flip(b)].">
      <j1 rule="para" parents="11015 287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11030">
    <literal><![CDATA[
      a(x,y,K(z,z * u)) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(9916,a,11024,a)].">
      <j1 rule="hyper" parents="9916 11024"/>
    </justification>
  </clause>

  <clause id="11031">
    <literal><![CDATA[
      a(x,y,K(z,z \ u)) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[para(5(a,1),11030(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="5 11030"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11032">
    <literal><![CDATA[
      a(x,y,K(z,u * z)) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[para(5385(a,2),11030(a,1,3))].">
      <j1 rule="para" parents="5385 11030"/>
    </justification>
  </clause>

  <clause id="11033">
    <literal><![CDATA[
      a(x,y,K(z,u \ z)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,11021,a,b,11031,a)].">
      <j1 rule="hyper" parents="58 11021 11031"/>
    </justification>
  </clause>

  <clause id="11034">
    <literal><![CDATA[
      a(x,y,K(z \ u,u)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[para(5196(a,1),11033(a,1,3)),flip(a)].">
      <j1 rule="para" parents="5196 11033"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11035">
    <literal><![CDATA[
      a(x,y,K(z \ 1,u)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,11022,a,b,11034,a)].">
      <j1 rule="hyper" parents="58 11022 11034"/>
    </justification>
  </clause>

  <clause id="11036">
    <literal><![CDATA[
      a(x,y,K(z \ u,w)) = a(x,y,K(w,u \ z))
    ]]></literal>
    <justification jstring="[para(6259(a,1),11035(a,1,3))].">
      <j1 rule="para" parents="6259 11035"/>
    </justification>
  </clause>

  <clause id="11037">
    <literal><![CDATA[
      x * (y * K(x * z,T(z,y))) = K(x * z,z) * (x * y)
    ]]></literal>
    <justification jstring="[para(8471(a,1),11028(a,1,2,2))].">
      <j1 rule="para" parents="8471 11028"/>
    </justification>
  </clause>

  <clause id="11038">
    <literal><![CDATA[
      K(x * y,y) * (x * z) = x * (K(x * y,y) * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,7301,a(flip),b,11037,a),flip(a)].">
      <j1 rule="hyper" parents="58 7301 11037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11039">
    <literal><![CDATA[
      x * (K(x * y,y) * (K(y,x) * z)) = a(y,x,y) * (x * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,9576,a(flip),b,11038,a),flip(a)].">
      <j1 rule="hyper" parents="58 9576 11038"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11040">
    <literal><![CDATA[
      a(x,y,x) * (y * z) = y * (a(x,y,x) * z)
    ]]></literal>
    <justification jstring="[para(9574(a,1),11039(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9574 11039"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11041">
    <literal><![CDATA[
      x * (a(y,x,y) * (x \ z)) = a(y,x,y) * z
    ]]></literal>
    <justification jstring="[hyper(342,a,11040,a),flip(a)].">
      <j1 rule="hyper" parents="342 11040"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11042">
    <literal><![CDATA[
      K((x \ (y \ z)) \ u,(y * ((y \ z) / x)) \ z) = K(x * (z \ (y * u)),x)
    ]]></literal>
    <justification jstring="[hyper(320,a,10789,a(flip),b,11010,a),flip(a)].">
      <j1 rule="hyper" parents="320 10789 11010"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11043">
    <literal><![CDATA[
      K((x \ (y \ z)) \ u,L(x,y \ z,y)) = K(x * (z \ (y * u)),x)
    ]]></literal>
    <justification jstring="[hyper(10868,a,11042,a)].">
      <j1 rule="hyper" parents="10868 11042"/>
    </justification>
  </clause>

  <clause id="11044">
    <literal><![CDATA[
      K(((x \ y) \ z) * u,L(u,x \ y,x)) = K(u * (y \ (x * z)),u)
    ]]></literal>
    <justification jstring="[hyper(58,a,10514,a(flip),b,11043,a)].">
      <j1 rule="hyper" parents="58 10514 11043"/>
    </justification>
  </clause>

  <clause id="11045">
    <literal><![CDATA[
      K(((x \ y) / z) \ y,z) = K(z * (y \ (x * y)),z)
    ]]></literal>
    <justification jstring="[hyper(58,a,10978,a(flip),b,11044,a)].">
      <j1 rule="hyper" parents="58 10978 11044"/>
    </justification>
  </clause>

  <clause id="11046">
    <literal><![CDATA[
      K(((x \ y) / z) \ y,z) = K(z * T(x,y),z)
    ]]></literal>
    <justification jstring="[para(17(a,2),11045(a,2,1,2))].">
      <j1 rule="para" parents="17 11045"/>
    </justification>
  </clause>

  <clause id="11047">
    <literal><![CDATA[
      K(x * ((y \ z) \ z),x) = K(x * T(y,z),x)
    ]]></literal>
    <justification jstring="[hyper(58,a,10500,a(flip),b,11046,a)].">
      <j1 rule="hyper" parents="58 10500 11046"/>
    </justification>
  </clause>

  <clause id="11048">
    <literal><![CDATA[
      K(x,x * ((y \ z) \ z)) = u / (K(x * T(y,z),x) * u)
    ]]></literal>
    <justification jstring="[para(11047(a,1),5142(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11047 5142"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11049">
    <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(11047(a,1),10764(a,1,1,2,2))].">
      <j1 rule="para" parents="11047 10764"/>
    </justification>
  </clause>

  <clause id="11050">
    <literal><![CDATA[
      K(x,x * ((y \ z) \ z)) = K(x,x * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,5142,a(flip),b,11048,a),flip(a)].">
      <j1 rule="hyper" parents="320 5142 11048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11051">
    <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,5099,a(flip),b,11026,a),flip(a)].">
      <j1 rule="hyper" parents="320 5099 11026"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11052">
    <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(1694(a,2),10932(a,1,2))].">
      <j1 rule="para" parents="1694 10932"/>
    </justification>
  </clause>

  <clause id="11053">
    <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(6798(a,1),6878(a,1,2,2))].">
      <j1 rule="para" parents="6798 6878"/>
    </justification>
  </clause>

  <clause id="11054">
    <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(9496(a,1),6938(a,1,1))].">
      <j1 rule="para" parents="9496 6938"/>
    </justification>
  </clause>

  <clause id="11055">
    <literal><![CDATA[
      R(T(K(x,y),R(K(y,x),z,u) * w),z,u) \ w = w / R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(6930(a,1),11054(a,2,2))].">
      <j1 rule="para" parents="6930 11054"/>
    </justification>
  </clause>

  <clause id="11056">
    <literal><![CDATA[
      R(T(K(x,y),z),u,w) \ z = z / R(K(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(7682(a,1),11055(a,1,1,1))].">
      <j1 rule="para" parents="7682 11055"/>
    </justification>
  </clause>

  <clause id="11057">
    <literal><![CDATA[
      x / (x / R(K(y,z),u,w)) = R(T(K(y,z),x),u,w)
    ]]></literal>
    <justification jstring="[hyper(197,a,11056,a)].">
      <j1 rule="hyper" parents="197 11056"/>
    </justification>
  </clause>

  <clause id="11059">
    <literal><![CDATA[
      (R(K(x,y),z,u) \ w) \ w = R(T(K(x,y),w),z,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,9501,a(flip),b,11057,a)].">
      <j1 rule="hyper" parents="58 9501 11057"/>
    </justification>
  </clause>

  <clause id="11060">
    <literal><![CDATA[
      ((K(x,y) * z) * u) \ (z * u) = R(T(K(y,x),z * u),z,u)
    ]]></literal>
    <justification jstring="[para(6933(a,1),11059(a,1,1))].">
      <j1 rule="para" parents="6933 11059"/>
    </justification>
  </clause>

  <clause id="11061">
    <literal><![CDATA[
      ((K(x,y) * z) * u) \ (z * u) = R(K(y,T(x,z * u)),z,u)
    ]]></literal>
    <justification jstring="[para(7158(a,2),11060(a,2,1))].">
      <j1 rule="para" parents="7158 11060"/>
    </justification>
  </clause>

  <clause id="11062">
    <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(8312(a,1),11061(a,2,1))].">
      <j1 rule="para" parents="8312 11061"/>
    </justification>
  </clause>

  <clause id="11063">
    <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(6321(a,1),7655(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6321 7655"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11064">
    <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,7747,a(flip),b,11063,a),flip(a)].">
      <j1 rule="hyper" parents="320 7747 11063"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11065">
    <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(7614(a,1),11064(a,2,1))].">
      <j1 rule="para" parents="7614 11064"/>
    </justification>
  </clause>

  <clause id="11066">
    <literal><![CDATA[
      T(x,T(y / T(y / z,u),w)) = T(x,T(T(z \ y,u) \ y,w))
    ]]></literal>
    <justification jstring="[para(11065(a,1),8315(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11065 8315"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11067">
    <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(4778(a,1),8801(a,1,1))].">
      <j1 rule="para" parents="4778 8801"/>
    </justification>
  </clause>

  <clause id="11068">
    <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,11067,a),flip(a)].">
      <j1 rule="hyper" parents="691 11067"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11069">
    <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(11067(a,1),691(a,1))].">
      <j1 rule="para" parents="11067 691"/>
    </justification>
  </clause>

  <clause id="11070">
    <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(5081(a,1),11068(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5081 11068"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11071">
    <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(5130(a,1),9001(a,1,1,1))].">
      <j1 rule="para" parents="5130 9001"/>
    </justification>
  </clause>

  <clause id="11072">
    <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(10027(a,1),9014(a,1,1))].">
      <j1 rule="para" parents="10027 9014"/>
    </justification>
  </clause>

  <clause id="11073">
    <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),9189(a,2,1))].">
      <j1 rule="para" parents="7 9189"/>
    </justification>
  </clause>

  <clause id="11074">
    <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,6366,a,b,11073,a)].">
      <j1 rule="hyper" parents="320 6366 11073"/>
    </justification>
  </clause>

  <clause id="11075">
    <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(10251(a,2),9469(a,2,2,2))].">
      <j1 rule="para" parents="10251 9469"/>
    </justification>
  </clause>

  <clause id="11076">
    <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,5340,a(flip),b,9808,a),flip(a)].">
      <j1 rule="hyper" parents="320 5340 9808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11077">
    <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(10006(a,1),10014(a,2,2,1,1))].">
      <j1 rule="para" parents="10006 10014"/>
    </justification>
  </clause>

  <clause id="11078">
    <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(4969(a,1),11077(a,2,2,1))].">
      <j1 rule="para" parents="4969 11077"/>
    </justification>
  </clause>

  <clause id="11080">
    <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(4969(a,1),11078(a,1,1,2,1))].">
      <j1 rule="para" parents="4969 11078"/>
    </justification>
  </clause>

  <clause id="11081">
    <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,6027,a(flip),b,11080,a)].">
      <j1 rule="hyper" parents="58 6027 11080"/>
    </justification>
  </clause>

  <clause id="11082">
    <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(11080(a,1),507(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="11080 507"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11083">
    <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(11080(a,2),9904(a,1,1))].">
      <j1 rule="para" parents="11080 9904"/>
    </justification>
  </clause>

  <clause id="11085">
    <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(7755(a,1),11083(a,1,1,1,2,1))].">
      <j1 rule="para" parents="7755 11083"/>
    </justification>
  </clause>

  <clause id="11086">
    <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),10313(a,2,2,2,1,1,2))].">
      <j1 rule="para" parents="75 10313"/>
    </justification>
  </clause>

  <clause id="11087">
    <literal><![CDATA[
      (x * (y * ((x \ (z / u)) / y))) * u = (x * u) * (y * (((x * u) \ z) / y))
    ]]></literal>
    <justification jstring="[hyper(586,a,11086,a)].">
      <j1 rule="hyper" parents="586 11086"/>
    </justification>
  </clause>

  <clause id="11090">
    <literal><![CDATA[
      ((x * y) * (z * (((x * y) \ u) / z))) / u = K(z,u / ((x * z) * y))
    ]]></literal>
    <justification jstring="[para(11087(a,1),10039(a,1,1))].">
      <j1 rule="para" parents="11087 10039"/>
    </justification>
  </clause>

  <clause id="11091">
    <literal><![CDATA[
      K(x,y / ((z * u) * x)) = K(x,y / ((z * x) * u))
    ]]></literal>
    <justification jstring="[hyper(5912,a,11090,a)].">
      <j1 rule="hyper" parents="5912 11090"/>
    </justification>
  </clause>

  <clause id="11092">
    <literal><![CDATA[
      K(x,y / ((z * x) * u)) = K(x,y / (x * (z * u)))
    ]]></literal>
    <justification jstring="[hyper(10650,a,11091,a),flip(a)].">
      <j1 rule="hyper" parents="10650 11091"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11093">
    <literal><![CDATA[
      K(x,y / ((z * y) * x)) = K(x,1 / (z * x))
    ]]></literal>
    <justification jstring="[hyper(320,a,5353,a(flip),b,11091,a),flip(a)].">
      <j1 rule="hyper" parents="320 5353 11091"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11094">
    <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),11091(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="105 11091"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11095">
    <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),11091(a,1,2))].">
      <j1 rule="para" parents="102 11091"/>
    </justification>
  </clause>

  <clause id="11096">
    <literal><![CDATA[
      K(x,y / ((z * y) * x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,1 / (z * x)) = u
    ]]></literal>
    <justification jstring="[para(11091(a,2),5498(a,1))].">
      <j1 rule="para" parents="11091 5498"/>
    </justification>
  </clause>

  <clause id="11097">
    <literal><![CDATA[
      K(x,1 / ((y / z) * x)) = K(x,z / (y * x))
    ]]></literal>
    <justification jstring="[para(7(a,1),11093(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="7 11093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11098">
    <literal><![CDATA[
      K(x,((y * x) * z) / (x * (y * (y \ z)))) = L(K(x,y),z,y * x)
    ]]></literal>
    <justification jstring="[hyper(9888,a,11092,a),flip(a)].">
      <j1 rule="hyper" parents="9888 11092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11099">
    <literal><![CDATA[
      K(x,y / ((x * z) * u)) = K(x,y / (x * (z * u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,8878,a(flip),b,11092,a)].">
      <j1 rule="hyper" parents="58 8878 11092"/>
    </justification>
  </clause>

  <clause id="11100">
    <literal><![CDATA[
      K(x,(y * x) / ((z * x) * u)) = K(x,y / (z * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,7098,a(flip),b,11095,a),flip(a)].">
      <j1 rule="hyper" parents="58 7098 11095"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11102">
    <literal><![CDATA[
      L(K(x,y),z,y * x) = K(x,((y * x) * z) / (x * z))
    ]]></literal>
    <justification jstring="[para(5(a,1),11098(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="5 11098"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11103">
    <literal><![CDATA[
      L(K(x,y),z,y * x) = K(x,R(y,x,z))
    ]]></literal>
    <justification jstring="[para(15(a,2),11102(a,2,2))].">
      <j1 rule="para" parents="15 11102"/>
    </justification>
  </clause>

  <clause id="11105">
    <literal><![CDATA[
      K(x,R(y,x,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(10636,a,11103,a),flip(a)].">
      <j1 rule="hyper" parents="10636 11103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11106">
    <literal><![CDATA[
      R(K(x,y),z,T(y * x,z)) = K(x,R(y,x,z))
    ]]></literal>
    <justification jstring="[hyper(9892,a,11103,a)].">
      <j1 rule="hyper" parents="9892 11103"/>
    </justification>
  </clause>

  <clause id="11107">
    <literal><![CDATA[
      K(x,R(y,x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(11103(a,1),10636(a,1))].">
      <j1 rule="para" parents="11103 10636"/>
    </justification>
  </clause>

  <clause id="11108">
    <literal><![CDATA[
      R(K(x \ y,x),y,z) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(9246,a,11105,a)].">
      <j1 rule="hyper" parents="9246 11105"/>
    </justification>
  </clause>

  <clause id="11110">
    <literal><![CDATA[
      T(x,R(y,x,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(118,a,11105,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 11105 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11111">
    <literal><![CDATA[
      K(x,y / (z * x)) = K(x,x \ (y / z))
    ]]></literal>
    <justification jstring="[hyper(58,a,9643,a(flip),b,11105,a)].">
      <j1 rule="hyper" parents="58 9643 11105"/>
    </justification>
  </clause>

  <clause id="11113">
    <literal><![CDATA[
      K(x,R(R(y,x,z),u,w)) = K(x,R(y,u,w))
    ]]></literal>
    <justification jstring="[para(26(a,1),11105(a,1,2))].">
      <j1 rule="para" parents="26 11105"/>
    </justification>
  </clause>

  <clause id="11114">
    <literal><![CDATA[
      K(1 / x,y / (1 / x)) = K(1 / x,y * x)
    ]]></literal>
    <justification jstring="[para(522(a,1),11105(a,1,2)),flip(a)].">
      <j1 rule="para" parents="522 11105"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11117">
    <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),11110(a,1,2))].">
      <j1 rule="para" parents="533 11110"/>
    </justification>
  </clause>

  <clause id="11118">
    <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(611(a,1),11107(a,1,2))].">
      <j1 rule="para" parents="611 11107"/>
    </justification>
  </clause>

  <clause id="11119">
    <literal><![CDATA[
      ((x * y) * z) \ ((y * x) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,T(x,z)) = u
    ]]></literal>
    <justification jstring="[para(9363(a,2),11107(a,1))].">
      <j1 rule="para" parents="9363 11107"/>
    </justification>
  </clause>

  <clause id="11120">
    <literal><![CDATA[
      K(x / (y * z),y) = K(y \ (x / z),y)
    ]]></literal>
    <justification jstring="[hyper(5973,a,11108,a)].">
      <j1 rule="hyper" parents="5973 11108"/>
    </justification>
  </clause>

  <clause id="11121">
    <literal><![CDATA[
      K(x,y / (x * z)) = K(x,x \ (y / z))
    ]]></literal>
    <justification jstring="[hyper(10650,a,11111,a)].">
      <j1 rule="hyper" parents="10650 11111"/>
    </justification>
  </clause>

  <clause id="11123">
    <literal><![CDATA[
      K(x,y / ((z * x) * u)) = K(x,x \ (y / (z * u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,11091,a(flip),b,11111,a)].">
      <j1 rule="hyper" parents="58 11091 11111"/>
    </justification>
  </clause>

  <clause id="11124">
    <literal><![CDATA[
      K(x,x \ ((x * y) / z)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(58,a,8503,a(flip),b,11111,a),flip(a)].">
      <j1 rule="hyper" parents="58 8503 11111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11125">
    <literal><![CDATA[
      K(x / (y * z),z) = K(z \ (x / y),z)
    ]]></literal>
    <justification jstring="[hyper(10651,a,11120,a)].">
      <j1 rule="hyper" parents="10651 11120"/>
    </justification>
  </clause>

  <clause id="11126">
    <literal><![CDATA[
      K((x \ y) / z,x) = K(x \ (y / z),x)
    ]]></literal>
    <justification jstring="[hyper(8744,a,11120,a)].">
      <j1 rule="hyper" parents="8744 11120"/>
    </justification>
  </clause>

  <clause id="11127">
    <literal><![CDATA[
      K(x,y / ((x * z) * u)) = K(x,x \ (y / (z * u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,11099,a,b,11121,a)].">
      <j1 rule="hyper" parents="58 11099 11121"/>
    </justification>
  </clause>

  <clause id="11128">
    <literal><![CDATA[
      K(x,x \ ((y \ 1) \ (x * z))) = K(x,z / T(y \ 1,y * (x * z)))
    ]]></literal>
    <justification jstring="[para(4368(a,1),11124(a,1,2,2))].">
      <j1 rule="para" parents="4368 11124"/>
    </justification>
  </clause>

  <clause id="11129">
    <literal><![CDATA[
      K(x \ (y \ z),x) * z = z * K(x \ (z / y),x)
    ]]></literal>
    <justification jstring="[para(11125(a,1),10377(a,2,2))].">
      <j1 rule="para" parents="11125 10377"/>
    </justification>
  </clause>

  <clause id="11130">
    <literal><![CDATA[
      K(x \ (y / z),x) * z = z * K(z \ (x \ y),x)
    ]]></literal>
    <justification jstring="[para(11126(a,1),7287(a,1,1))].">
      <j1 rule="para" parents="11126 7287"/>
    </justification>
  </clause>

  <clause id="11131">
    <literal><![CDATA[
      R(K(x,R(y,x,z)),(y * x) * z,u) = K(x,R(y,x * z,u))
    ]]></literal>
    <justification jstring="[hyper(9247,a,11113,a)].">
      <j1 rule="hyper" parents="9247 11113"/>
    </justification>
  </clause>

  <clause id="11132">
    <literal><![CDATA[
      K(x,R(y,x,z)) * ((y * x) * z) = (K(x,y) * z) * T(y * x,z)
    ]]></literal>
    <justification jstring="[para(11106(a,1),516(a,1,1))].">
      <j1 rule="para" parents="11106 516"/>
    </justification>
  </clause>

  <clause id="11133">
    <literal><![CDATA[
      K(x,y * K(1 / y,z * y)) = T(K(x,y),z / (1 / y))
    ]]></literal>
    <justification jstring="[para(11114(a,1),9638(a,1,2,2))].">
      <j1 rule="para" parents="11114 9638"/>
    </justification>
  </clause>

  <clause id="11134">
    <literal><![CDATA[
      K(x,x \ (y / ((x \ z) * u))) = K(x,y / (z * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,8879,a(flip),b,11123,a),flip(a)].">
      <j1 rule="hyper" parents="58 8879 11123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11135">
    <literal><![CDATA[
      T(x,y / ((x * z) * u)) = T(x,x \ (y / (z * u)))
    ]]></literal>
    <justification jstring="[hyper(118,a,11127,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 11127 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11136">
    <literal><![CDATA[
      K(x \ (y / z),T(x,z)) = K(z \ (x \ y),x)
    ]]></literal>
    <justification jstring="[hyper(7305,a,11130,a)].">
      <j1 rule="hyper" parents="7305 11130"/>
    </justification>
  </clause>

  <clause id="11137">
    <literal><![CDATA[
      K(x \ (y / z),T(x,y)) = K(z \ (x \ y),x)
    ]]></literal>
    <justification jstring="[hyper(58,a,8467,a(flip),b,11136,a)].">
      <j1 rule="hyper" parents="58 8467 11136"/>
    </justification>
  </clause>

  <clause id="11138">
    <literal><![CDATA[
      K(T(x,y),x \ (y / z)) = (u * K(z \ (x \ y),x)) \ u
    ]]></literal>
    <justification jstring="[para(11137(a,1),6338(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="11137 6338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11139">
    <literal><![CDATA[
      K(x,(x * y) / (z * u)) = K(x,y / ((x \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,11124,a(flip),b,11134,a),flip(a)].">
      <j1 rule="hyper" parents="58 11124 11134"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11140">
    <literal><![CDATA[
      K(x,y / ((x \ z) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,((z * u) / y) \ x) = w
    ]]></literal>
    <justification jstring="[para(11139(a,1),6964(a,1))].">
      <j1 rule="para" parents="11139 6964"/>
    </justification>
  </clause>

  <clause id="11141">
    <literal><![CDATA[
      T(K(x,y),z / (1 / y)) = T(K(x,y),z * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,9638,a(flip),b,11133,a),flip(a)].">
      <j1 rule="hyper" parents="58 9638 11133"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11142">
    <literal><![CDATA[
      T(K(x,y),z * y) = K(x,1 / (z / (z / (1 / y))))
    ]]></literal>
    <justification jstring="[hyper(58,a,9639,a(flip),b,11141,a),flip(a)].">
      <j1 rule="hyper" parents="58 9639 11141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11143">
    <literal><![CDATA[
      K(x,1 / (y / (y / (1 / z)))) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,6218,a(flip),b,11142,a),flip(a)].">
      <j1 rule="hyper" parents="58 6218 11142"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11144">
    <literal><![CDATA[
      K(T(x,y),x \ (y / z)) = K(x,z \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(320,a,6338,a(flip),b,11138,a),flip(a)].">
      <j1 rule="hyper" parents="320 6338 11138"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11145">
    <literal><![CDATA[
      K(x,T(x \ (y / z),y)) = K(x,z \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(7704,a,11144,a)].">
      <j1 rule="hyper" parents="7704 11144"/>
    </justification>
  </clause>

  <clause id="11146">
    <literal><![CDATA[
      K(x,(y \ z) \ (x \ z)) = K(x,T(x \ y,z))
    ]]></literal>
    <justification jstring="[para(72(a,1),11145(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="72 11145"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11147">
    <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,8426,a,b,11146,a)].">
      <j1 rule="hyper" parents="58 8426 11146"/>
    </justification>
  </clause>

  <clause id="11148">
    <literal><![CDATA[
      R(K(x,y),(y * x) * z,u) = K(x,R(y,x * z,u))
    ]]></literal>
    <justification jstring="[para(11105(a,1),11131(a,1,1))].">
      <j1 rule="para" parents="11105 11131"/>
    </justification>
  </clause>

  <clause id="11150">
    <literal><![CDATA[
      (K(x,y) * z) * T(y * x,z) = (y * (K(x,y) * x)) * z
    ]]></literal>
    <justification jstring="[hyper(6984,a,11132,a),flip(a)].">
      <j1 rule="hyper" parents="6984 11132"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11151">
    <literal><![CDATA[
      (K(x,y) * z) * T(y * x,z) = (x * y) * z
    ]]></literal>
    <justification jstring="[para(4847(a,1),11150(a,2,1))].">
      <j1 rule="para" parents="4847 11150"/>
    </justification>
  </clause>

  <clause id="11152">
    <literal><![CDATA[
      (x * y) * (K(y,x) * z) = (y * x) * z
    ]]></literal>
    <justification jstring="[hyper(8777,a,11151,a)].">
      <j1 rule="hyper" parents="8777 11151"/>
    </justification>
  </clause>

  <clause id="11153">
    <literal><![CDATA[
      (x * y) \ ((y * x) * z) = K(y,x) * z
    ]]></literal>
    <justification jstring="[hyper(116,a,11151,a(flip),b,8776,a(flip))].">
      <j1 rule="hyper" parents="116 11151 8776"/>
    </justification>
  </clause>

  <clause id="11154">
    <literal><![CDATA[
      L(x,K(y,z),z * y) = x
    ]]></literal>
    <justification jstring="[hyper(830,a,11152,a)].">
      <j1 rule="hyper" parents="830 11152"/>
    </justification>
  </clause>

  <clause id="11155">
    <literal><![CDATA[
      ((x \ y) * x) \ (y * z) = K(x,x \ y) * z
    ]]></literal>
    <justification jstring="[hyper(116,a,148,a(flip),b,11152,a)].">
      <j1 rule="hyper" parents="116 148 11152"/>
    </justification>
  </clause>

  <clause id="11156">
    <literal><![CDATA[
      K(x,y) * ((x * y) \ z) = (y * x) \ z
    ]]></literal>
    <justification jstring="[hyper(116,a,5,a(flip),b,11152,a),flip(a)].">
      <j1 rule="hyper" parents="116 5 11152"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11157">
    <literal><![CDATA[
      K(x,y) * ((y * x) * z) = (x * y) * z
    ]]></literal>
    <justification jstring="[hyper(58,a,10639,a,b,11152,a)].">
      <j1 rule="hyper" parents="58 10639 11152"/>
    </justification>
  </clause>

  <clause id="11158">
    <literal><![CDATA[
      K(x,y) \ ((x * y) * z) = (y * x) * z
    ]]></literal>
    <justification jstring="[hyper(116,a,11152,a(flip),b,10639,a)].">
      <j1 rule="hyper" parents="116 11152 10639"/>
    </justification>
  </clause>

  <clause id="11160">
    <literal><![CDATA[
      (x * y) * (1 / T(x,y)) = (y * x) * (1 / x)
    ]]></literal>
    <justification jstring="[para(5176(a,1),11152(a,1,2))].">
      <j1 rule="para" parents="5176 11152"/>
    </justification>
  </clause>

  <clause id="11161">
    <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(11152(a,1),7917(a,1,1,1))].">
      <j1 rule="para" parents="11152 7917"/>
    </justification>
  </clause>

  <clause id="11162">
    <literal><![CDATA[
      (K(x,y) * z) * (K(y,T(x,z)) * u) = (z * K(x,y)) * (K(y,x) * u)
    ]]></literal>
    <justification jstring="[para(7190(a,1),11152(a,1,2))].">
      <j1 rule="para" parents="7190 11152"/>
    </justification>
  </clause>

  <clause id="11163">
    <literal><![CDATA[
      L(x,K(y \ z,y),z) = x
    ]]></literal>
    <justification jstring="[para(5(a,1),11154(a,1,3))].">
      <j1 rule="para" parents="5 11154"/>
    </justification>
  </clause>

  <clause id="11164">
    <literal><![CDATA[
      L(x,K(y,y \ z),z) = x
    ]]></literal>
    <justification jstring="[para(4965(a,1),11163(a,1,2))].">
      <j1 rule="para" parents="4965 11163"/>
    </justification>
  </clause>

  <clause id="11165">
    <literal><![CDATA[
      (x * (y / x)) \ (y * z) = K(x \ y,x) * z
    ]]></literal>
    <justification jstring="[hyper(58,a,5767,a(flip),b,11164,a)].">
      <j1 rule="hyper" parents="58 5767 11164"/>
    </justification>
  </clause>

  <clause id="11166">
    <literal><![CDATA[
      T(x,y) * ((x * y) \ z) = x * ((y * x) \ z)
    ]]></literal>
    <justification jstring="[hyper(119,a,11156,a(flip),b,5175,a)].">
      <j1 rule="hyper" parents="119 11156 5175"/>
    </justification>
  </clause>

  <clause id="11167">
    <literal><![CDATA[
      ((x * y) / x) \ ((y * x) \ z) = y \ ((x * y) \ z)
    ]]></literal>
    <justification jstring="[hyper(116,a,11156,a(flip),b,5448,a)].">
      <j1 rule="hyper" parents="116 11156 5448"/>
    </justification>
  </clause>

  <clause id="11168">
    <literal><![CDATA[
      ((x * y) \ z) * L(u,(y * x) \ z,K(y,x)) = K(y,x) * (((y * x) \ z) * u)
    ]]></literal>
    <justification jstring="[para(11156(a,1),90(a,1,1))].">
      <j1 rule="para" parents="11156 90"/>
    </justification>
  </clause>

  <clause id="11169">
    <literal><![CDATA[
      T(x,y) * ((x * y) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      x * ((y * x) \ z) = u
    ]]></literal>
    <justification jstring="[para(11156(a,1),5262(a,1,2))].">
      <j1 rule="para" parents="11156 5262"/>
    </justification>
  </clause>

  <clause id="11170">
    <literal><![CDATA[
      T((x * y) \ z,K(y,x)) = ((y * x) \ z) * K(y,x)
    ]]></literal>
    <justification jstring="[para(11156(a,1),6340(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11156 6340"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11171">
    <literal><![CDATA[
      K(x,y * ((z * x) \ u)) = K(x,y * ((x * z) \ u))
    ]]></literal>
    <justification jstring="[para(11156(a,1),7279(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11156 7279"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11172">
    <literal><![CDATA[
      L(x,y * z,K(z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(5005,a,11157,a)].">
      <j1 rule="hyper" parents="5005 11157"/>
    </justification>
  </clause>

  <clause id="11173">
    <literal><![CDATA[
      (x * y) \ (K(x,y) * z) = (y * x) \ z
    ]]></literal>
    <justification jstring="[hyper(599,a,11157,a)].">
      <j1 rule="hyper" parents="599 11157"/>
    </justification>
  </clause>

  <clause id="11174">
    <literal><![CDATA[
      (x * y) * ((y * x) \ z) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(342,a,11157,a),flip(a)].">
      <j1 rule="hyper" parents="342 11157"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11175">
    <literal><![CDATA[
      K(x \ y,x) * (y * z) = ((x \ y) * x) * z
    ]]></literal>
    <justification jstring="[para(5(a,1),11157(a,1,2,1))].">
      <j1 rule="para" parents="5 11157"/>
    </justification>
  </clause>

  <clause id="11176">
    <literal><![CDATA[
      K(x,(x * y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * x) * z) = u
    ]]></literal>
    <justification jstring="[para(11157(a,1),7360(a,1,2))].">
      <j1 rule="para" parents="11157 7360"/>
    </justification>
  </clause>

  <clause id="11177">
    <literal><![CDATA[
      K(x,y \ ((x * z) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ ((z * x) * u)) = w
    ]]></literal>
    <justification jstring="[para(11157(a,1),8592(a,1,2,2))].">
      <j1 rule="para" parents="11157 8592"/>
    </justification>
  </clause>

  <clause id="11178">
    <literal><![CDATA[
      K(x \ ((y * z) * u),z) = K(x \ ((z * y) * u),z)
    ]]></literal>
    <justification jstring="[para(11157(a,1),8654(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="11157 8654"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11180">
    <literal><![CDATA[
      L(x,T(y,z),z) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(6833,a,11172,a)].">
      <j1 rule="hyper" parents="6833 11172"/>
    </justification>
  </clause>

  <clause id="11181">
    <literal><![CDATA[
      L(x,y,z) = (y * z) \ (z * (T(y,z) * x))
    ]]></literal>
    <justification jstring="[hyper(58,a,6831,a(flip),b,11172,a),flip(a)].">
      <j1 rule="hyper" parents="58 6831 11172"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11182">
    <literal><![CDATA[
      (x * y) * L(z,x,y) = y * (T(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(119,a,11172,a(flip),b,6831,a(flip))].">
      <j1 rule="hyper" parents="119 11172 6831"/>
    </justification>
  </clause>

  <clause id="11183">
    <literal><![CDATA[
      L(x,y * z,K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(11172(a,1),45(a,2))].">
      <j1 rule="para" parents="11172 45"/>
    </justification>
  </clause>

  <clause id="11184">
    <literal><![CDATA[
      L(x,T(y,z) * z,K(z,y)) = x
    ]]></literal>
    <justification jstring="[para(4908(a,1),11172(a,1,3))].">
      <j1 rule="para" parents="4908 11172"/>
    </justification>
  </clause>

  <clause id="11185">
    <literal><![CDATA[
      L(L(x,y,z),u * w,K(w,u)) = L(x,T(y,z),z)
    ]]></literal>
    <justification jstring="[hyper(320,a,11172,a,b,11180,a)].">
      <j1 rule="hyper" parents="320 11172 11180"/>
    </justification>
  </clause>

  <clause id="11186">
    <literal><![CDATA[
      L(x \ y,x,x \ z) = z \ ((z / x) * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,7001,a(flip),b,11180,a),flip(a)].">
      <j1 rule="hyper" parents="58 7001 11180"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11187">
    <literal><![CDATA[
      L(x,(y \ z) \ z,y \ z) = L(x,y,y \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,1614,a(flip),b,11180,a)].">
      <j1 rule="hyper" parents="58 1614 11180"/>
    </justification>
  </clause>

  <clause id="11188">
    <literal><![CDATA[
      L(T(x,y) \ z,x,y) = (x * y) \ (y * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,496,a(flip),b,11180,a),flip(a)].">
      <j1 rule="hyper" parents="58 496 11180"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11189">
    <literal><![CDATA[
      L(x,y / z,z) = L(x,z \ y,z)
    ]]></literal>
    <justification jstring="[para(107(a,1),11180(a,1,2)),flip(a)].">
      <j1 rule="para" parents="107 11180"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11193">
    <literal><![CDATA[
      L(x,y,T(z,y)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(10232,a,11184,a),flip(a)].">
      <j1 rule="hyper" parents="10232 11184"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11194">
    <literal><![CDATA[
      L(x,y,T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(11184(a,1),10232(a,1))].">
      <j1 rule="para" parents="11184 10232"/>
    </justification>
  </clause>

  <clause id="11195">
    <literal><![CDATA[
      L(x,y \ z,(y \ z) \ z) = L(x,y \ z,y)
    ]]></literal>
    <justification jstring="[hyper(2113,a,11193,a)].">
      <j1 rule="hyper" parents="2113 11193"/>
    </justification>
  </clause>

  <clause id="11196">
    <literal><![CDATA[
      L(x,y,z / y) = L(x,y,y \ z)
    ]]></literal>
    <justification jstring="[para(107(a,1),11193(a,1,3)),flip(a)].">
      <j1 rule="para" parents="107 11193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11198">
    <literal><![CDATA[
      L(x,y,z \ K(y,z \ 1)) = L(x,y,z \ 1)
    ]]></literal>
    <justification jstring="[para(4880(a,1),11193(a,1,3)),flip(a)].">
      <j1 rule="para" parents="4880 11193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11199">
    <literal><![CDATA[
      L(x,T(y,z),z) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(6832(a,1),11183(a,1))].">
      <j1 rule="para" parents="6832 11183"/>
    </justification>
  </clause>

  <clause id="11202">
    <literal><![CDATA[
      x \ ((x / y) * (y * z)) = L(z,y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,93,a,b,11196,a)].">
      <j1 rule="hyper" parents="58 93 11196"/>
    </justification>
  </clause>

  <clause id="11203">
    <literal><![CDATA[
      L(T(x,y),y,y \ z) = z \ ((z / y) * (x * y))
    ]]></literal>
    <justification jstring="[hyper(58,a,696,a(flip),b,11196,a),flip(a)].">
      <j1 rule="hyper" parents="58 696 11196"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11204">
    <literal><![CDATA[
      x * L(y,z,z \ x) = (x / z) * (z * y)
    ]]></literal>
    <justification jstring="[hyper(119,a,11196,a(flip),b,93,a)].">
      <j1 rule="hyper" parents="119 11196 93"/>
    </justification>
  </clause>

  <clause id="11205">
    <literal><![CDATA[
      (x / y) * (y * T(z,x)) = L(z,y,y \ x) * x
    ]]></literal>
    <justification jstring="[para(11196(a,1),753(a,2,1))].">
      <j1 rule="para" parents="11196 753"/>
    </justification>
  </clause>

  <clause id="11206">
    <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(6125(a,1),11199(a,1,2))].">
      <j1 rule="para" parents="6125 11199"/>
    </justification>
  </clause>

  <clause id="11207">
    <literal><![CDATA[
      (x * y) \ (T(x,y) * z) = (y * x) \ (x * z)
    ]]></literal>
    <justification jstring="[para(4781(a,1),11173(a,1,2))].">
      <j1 rule="para" parents="4781 11173"/>
    </justification>
  </clause>

  <clause id="11208">
    <literal><![CDATA[
      (x * y) \ (R(y,z,u) * T(x,y)) = (y * x) \ (R(y,z,u) * x)
    ]]></literal>
    <justification jstring="[para(5876(a,1),11173(a,1,2))].">
      <j1 rule="para" parents="5876 11173"/>
    </justification>
  </clause>

  <clause id="11209">
    <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,4322,a,b,11174,a)].">
      <j1 rule="hyper" parents="320 4322 11174"/>
    </justification>
  </clause>

  <clause id="11210">
    <literal><![CDATA[
      (x * y) * K(z,L(u,x,y)) = y * (T(x,y) * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(10838,a,11181,a)].">
      <j1 rule="hyper" parents="10838 11181"/>
    </justification>
  </clause>

  <clause id="11212">
    <literal><![CDATA[
      (x * (T(y,x) * z)) / L(z,y,x) = y * x
    ]]></literal>
    <justification jstring="[hyper(197,a,11181,a(flip))].">
      <j1 rule="hyper" parents="197 11181"/>
    </justification>
  </clause>

  <clause id="11213">
    <literal><![CDATA[
      (K(x,y) * z) \ (z * (K(x,T(y,z)) * u)) = L(u,K(x,y),z)
    ]]></literal>
    <justification jstring="[para(7158(a,2),11181(a,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="7158 11181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11214">
    <literal><![CDATA[
      L(T(x,y) \ z,T(x,y),T(x,y) \ y) = y \ ((T(y,x) / x) * z)
    ]]></literal>
    <justification jstring="[para(4246(a,2),11186(a,2,2,1))].">
      <j1 rule="para" parents="4246 11186"/>
    </justification>
  </clause>

  <clause id="11215">
    <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(6338(a,1),11186(a,1,3))].">
      <j1 rule="para" parents="6338 11186"/>
    </justification>
  </clause>

  <clause id="11216">
    <literal><![CDATA[
      x * K(y,L(z,u,u \ x)) = (x / u) * (u * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(119,a,10794,a(flip),b,11202,a)].">
      <j1 rule="hyper" parents="119 10794 11202"/>
    </justification>
  </clause>

  <clause id="11217">
    <literal><![CDATA[
      ((x / y) * (y * z)) \ K(x,L(z,y,y \ x)) = (L(z,y,y \ x) * x) \ 1
    ]]></literal>
    <justification jstring="[para(11204(a,1),5569(a,1,1))].">
      <j1 rule="para" parents="11204 5569"/>
    </justification>
  </clause>

  <clause id="11218">
    <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(1709(a,1),11160(a,2,1))].">
      <j1 rule="para" parents="1709 11160"/>
    </justification>
  </clause>

  <clause id="11220">
    <literal><![CDATA[
      K(x \ y,x) * (y \ z) = (x * (y / x)) \ z
    ]]></literal>
    <justification jstring="[para(5(a,1),11165(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5 11165"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11221">
    <literal><![CDATA[
      T(x,y) * ((x * y) \ z) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (x * ((y * x) \ z)) = w
    ]]></literal>
    <justification jstring="[para(11166(a,2),536(a,1))].">
      <j1 rule="para" parents="11166 536"/>
    </justification>
  </clause>

  <clause id="11222">
    <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(7862(a,1),11166(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7862 11166"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11223">
    <literal><![CDATA[
      K(x,(((x \ y) * x) * z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * z) \ u) = w
    ]]></literal>
    <justification jstring="[para(11175(a,1),8591(a,1,2,1))].">
      <j1 rule="para" parents="11175 8591"/>
    </justification>
  </clause>

  <clause id="11224">
    <literal><![CDATA[
      K((x * T(y,x * y)) \ z,x * y) * (z * u) = (((x * y) \ z) * (x * y)) * u
    ]]></literal>
    <justification jstring="[para(8648(a,2),11175(a,1,1))].">
      <j1 rule="para" parents="8648 11175"/>
    </justification>
  </clause>

  <clause id="11225">
    <literal><![CDATA[
      K(x,L(y,T(z,u),u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(11185(a,1),7506(a,1,2))].">
      <j1 rule="para" parents="11185 7506"/>
    </justification>
  </clause>

  <clause id="11226">
    <literal><![CDATA[
      K(x,L(y,z / u,u)) = K(x,L(y,u \ z,u))
    ]]></literal>
    <justification jstring="[para(107(a,1),11225(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="107 11225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11227">
    <literal><![CDATA[
      L(x,y,x) \ (T(x * y,x) \ z) = x \ ((y * x) \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,9728,a,b,11167,a)].">
      <j1 rule="hyper" parents="58 9728 11167"/>
    </justification>
  </clause>

  <clause id="11228">
    <literal><![CDATA[
      L(x,y,T((y * x) \ z,K(x,y))) = L(x,y,(x * y) \ z)
    ]]></literal>
    <justification jstring="[para(11170(a,2),10965(a,1,3))].">
      <j1 rule="para" parents="11170 10965"/>
    </justification>
  </clause>

  <clause id="11229">
    <literal><![CDATA[
      (x / y) * (y * K(z,T(u,y))) = x * K(z,x \ ((x / y) * (u * y)))
    ]]></literal>
    <justification jstring="[para(11203(a,1),11216(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11203 11216"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11230">
    <literal><![CDATA[
      a(x,y,x) * (T(x * y,x) \ z) = (y * x) \ z
    ]]></literal>
    <justification jstring="[hyper(9570,a,11227,a)].">
      <j1 rule="hyper" parents="9570 11227"/>
    </justification>
  </clause>

  <clause id="11231">
    <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),11208(a,2,2))].">
      <j1 rule="para" parents="101 11208"/>
    </justification>
  </clause>

  <clause id="11232">
    <literal><![CDATA[
      K(x,y / T(z \ 1,z * (x * y))) = K(x,(z \ 1) \ y)
    ]]></literal>
    <justification jstring="[hyper(10341,a,11128,a),flip(a)].">
      <j1 rule="hyper" parents="10341 11128"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11233">
    <literal><![CDATA[
      x * K(y,x \ ((x / z) * (u * z))) = (x / z) * (K(y,u) * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,7301,a(flip),b,11229,a),flip(a)].">
      <j1 rule="hyper" parents="58 7301 11229"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11234">
    <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,11117,a)].">
      <j1 rule="hyper" parents="58 22 11117"/>
    </justification>
  </clause>

  <clause id="11235">
    <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(3770(a,1),11147(a,2,2))].">
      <j1 rule="para" parents="3770 11147"/>
    </justification>
  </clause>

  <clause id="11236">
    <literal><![CDATA[
      K(x,y) * (((x * y) \ y) * z) = ((y * x) \ y) * z
    ]]></literal>
    <justification jstring="[para(10207(a,1),11168(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10207 11168"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11237">
    <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(7997(a,1),11215(a,2,2,1))].">
      <j1 rule="para" parents="7997 11215"/>
    </justification>
  </clause>

  <clause id="11238">
    <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,11231,a)].">
      <j1 rule="hyper" parents="119 9 11231"/>
    </justification>
  </clause>

  <clause id="11239">
    <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,4253,a(flip),b,11234,a),flip(a)].">
      <j1 rule="hyper" parents="320 4253 11234"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11240">
    <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,8637,a(flip),b,11235,a),flip(a)].">
      <j1 rule="hyper" parents="320 8637 11235"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11241">
    <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,8227,a(flip),b,11240,a),flip(a)].">
      <j1 rule="hyper" parents="320 8227 11240"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11242">
    <literal><![CDATA[
      K(x,T(x \ y,z)) = K(x,x \ T(y,z))
    ]]></literal>
    <justification jstring="[hyper(10372,a,11241,a),flip(a)].">
      <j1 rule="hyper" parents="10372 11241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11243">
    <literal><![CDATA[
      K(x,L(x \ T(y,z),x,u)) = K(x,T(x \ y,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,10354,a,b,11242,a)].">
      <j1 rule="hyper" parents="320 10354 11242"/>
    </justification>
  </clause>

  <clause id="11244">
    <literal><![CDATA[
      K(K(x,y) * z,z \ x) = K(z,T(z \ x,y))
    ]]></literal>
    <justification jstring="[hyper(320,a,10317,a,b,11242,a)].">
      <j1 rule="hyper" parents="320 10317 11242"/>
    </justification>
  </clause>

  <clause id="11245">
    <literal><![CDATA[
      T((x \ y) * x,z) \ T(y,z) = K(x,T(x \ y,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,4620,a,b,11242,a)].">
      <j1 rule="hyper" parents="320 4620 11242"/>
    </justification>
  </clause>

  <clause id="11246">
    <literal><![CDATA[
      K(x,y \ (x \ (z * y))) = K(x,T(x \ z,y))
    ]]></literal>
    <justification jstring="[hyper(10410,a,11242,a(flip))].">
      <j1 rule="hyper" parents="10410 11242"/>
    </justification>
  </clause>

  <clause id="11247">
    <literal><![CDATA[
      K(x,x \ T(x * y,z)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(4(a,1),11242(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4 11242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11248">
    <literal><![CDATA[
      K(x,T(y,z) / x) = K(x,T(y / x,z))
    ]]></literal>
    <justification jstring="[para(4573(a,1),11247(a,1,2))].">
      <j1 rule="para" parents="4573 11247"/>
    </justification>
  </clause>

  <clause id="11249">
    <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(2728(a,1),11248(a,2,2,1))].">
      <j1 rule="para" parents="2728 11248"/>
    </justification>
  </clause>

  <clause id="11250">
    <literal><![CDATA[
      K(x,T(x \ y,z)) * (K(y,z) * x) = T(K(y,z) * x,x \ y)
    ]]></literal>
    <justification jstring="[para(11244(a,1),4770(a,2,1)),flip(a)].">
      <j1 rule="para" parents="11244 4770"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11251">
    <literal><![CDATA[
      K(x,T(x \ y,y \ (x * z))) = K(x,(y \ (x * z)) \ z)
    ]]></literal>
    <justification jstring="[para(66(a,1),11246(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="66 11246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11252">
    <literal><![CDATA[
      K(x,L(x \ T(y,z),x,u)) = K(x,T(x \ y,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(320,a,8227,a,b,11243,a),flip(a)].">
      <j1 rule="hyper" parents="320 8227 11243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11253">
    <literal><![CDATA[
      T(x,y) * K(z \ x,T(z,y)) = T((z \ x) * z,y)
    ]]></literal>
    <justification jstring="[hyper(34,a,7203,a,b,11245,a)].">
      <j1 rule="hyper" parents="34 7203 11245"/>
    </justification>
  </clause>

  <clause id="11254">
    <literal><![CDATA[
      T(x,y) * K(z \ x,T(z,y)) = (z \ T(x,y)) * z
    ]]></literal>
    <justification jstring="[hyper(320,a,4597,a(flip),b,11253,a),flip(a)].">
      <j1 rule="hyper" parents="320 4597 11253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11255">
    <literal><![CDATA[
      K(x \ T(y,z),x) = K(x \ y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(29,a,302,a,b,11254,a)].">
      <j1 rule="hyper" parents="29 302 11254"/>
    </justification>
  </clause>

  <clause id="11257">
    <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(11252(a,2),8271(a,1))].">
      <j1 rule="para" parents="11252 8271"/>
    </justification>
  </clause>

  <clause id="11258">
    <literal><![CDATA[
      K(x,T(x \ y,y \ z)) = K(x,(y \ (x * z)) \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,9318,a(flip),b,11251,a)].">
      <j1 rule="hyper" parents="58 9318 11251"/>
    </justification>
  </clause>

  <clause id="11259">
    <literal><![CDATA[
      K(x,(y \ (x * z)) \ z) = K(x,T(x \ y,z))
    ]]></literal>
    <justification jstring="[hyper(8751,a,11258,a),flip(a)].">
      <j1 rule="hyper" parents="8751 11258"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11260">
    <literal><![CDATA[
      K(x,x \ T(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(x \ y,z)) = u
    ]]></literal>
    <justification jstring="[para(2459(a,1),11257(a,1,2))].">
      <j1 rule="para" parents="2459 11257"/>
    </justification>
  </clause>

  <clause id="11261">
    <literal><![CDATA[
      K(K(x,y) * z,z \ x) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,T(z \ x,y)) = u
    ]]></literal>
    <justification jstring="[para(10317(a,2),11260(a,1))].">
      <j1 rule="para" parents="10317 11260"/>
    </justification>
  </clause>

  <clause id="11262">
    <literal><![CDATA[
      T(K(x,y) * z,z \ x) = T(z,z \ x) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(9343,a,11250,a),flip(a)].">
      <j1 rule="hyper" parents="9343 11250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11263">
    <literal><![CDATA[
      (x \ y) * T(K(y,z) * x,x \ y) = (y / x) * (x * K(y,z))
    ]]></literal>
    <justification jstring="[para(11262(a,2),4564(a,1,2))].">
      <j1 rule="para" parents="11262 4564"/>
    </justification>
  </clause>

  <clause id="11264">
    <literal><![CDATA[
      (K(x,y) * z) * (z \ x) = (x / z) * (z * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(284,a,11263,a)].">
      <j1 rule="hyper" parents="284 11263"/>
    </justification>
  </clause>

  <clause id="11265">
    <literal><![CDATA[
      ((x / y) * (y * K(x,z))) / T(x,z) = a(K(x,z),y,y \ x)
    ]]></literal>
    <justification jstring="[para(11264(a,1),10229(a,1,1))].">
      <j1 rule="para" parents="11264 10229"/>
    </justification>
  </clause>

  <clause id="11266">
    <literal><![CDATA[
      ((x / y) * (y * K(z,x))) \ ((z * x) / z) = T(a(K(x,z),y,y \ x),x)
    ]]></literal>
    <justification jstring="[para(11265(a,1),11074(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11265 11074"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11267">
    <literal><![CDATA[
      K(x \ 1,T(y * x,z)) = K(x \ 1,T(y,z) * x)
    ]]></literal>
    <justification jstring="[para(2729(a,1),11249(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2729 11249"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11268">
    <literal><![CDATA[
      ((x / y) * (y * K(z,x))) \ ((z * x) / z) = a(K(x,z),y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(320,a,9168,a(flip),b,11266,a),flip(a)].">
      <j1 rule="hyper" parents="320 9168 11266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11269">
    <literal><![CDATA[
      a(K(x,y),z,z \ x) = a(x / z,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(58,a,4935,a(flip),b,11268,a),flip(a)].">
      <j1 rule="hyper" parents="58 4935 11268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11270">
    <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),11269(a,2,1))].">
      <j1 rule="para" parents="6 11269"/>
    </justification>
  </clause>

  <clause id="11271">
    <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),11270(a,1,3))].">
      <j1 rule="para" parents="17 11270"/>
    </justification>
  </clause>

  <clause id="11272">
    <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(11271(a,1),4856(a,1,2))].">
      <j1 rule="para" parents="11271 4856"/>
    </justification>
  </clause>

  <clause id="11273">
    <literal><![CDATA[
      (K(x * y,z) * y) * T(x,y) = x * (y * K(x * y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,5941,a(flip),b,11272,a),flip(a)].">
      <j1 rule="hyper" parents="58 5941 11272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11274">
    <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(11273(a,2),38(a,1))].">
      <j1 rule="para" parents="11273 38"/>
    </justification>
  </clause>

  <clause id="11275">
    <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,11239,a),flip(a)].">
      <j1 rule="hyper" parents="320 22 11239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11276">
    <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(11135(a,1),11275(a,1,1))].">
      <j1 rule="para" parents="11135 11275"/>
    </justification>
  </clause>

  <clause id="11277">
    <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),11276(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6 11276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11278">
    <literal><![CDATA[
      R(T(x,x \ y),z,u) = (R(x,z,u) \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(601,a,11277,a),flip(a)].">
      <j1 rule="hyper" parents="601 11277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11280">
    <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(11277(a,1),5227(a,1,2,1))].">
      <j1 rule="para" parents="11277 5227"/>
    </justification>
  </clause>

  <clause id="11281">
    <literal><![CDATA[
      R((x \ y) \ y,z,u) = (R(x,z,u) \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(58,a,828,a(flip),b,11278,a)].">
      <j1 rule="hyper" parents="58 828 11278"/>
    </justification>
  </clause>

  <clause id="11282">
    <literal><![CDATA[
      (R(x,y,z) \ (x * u)) \ (x * u) = R(T(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(4(a,1),11278(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4 11278"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11283">
    <literal><![CDATA[
      (R(x / y,z,u) \ x) \ x = R(y \ x,z,u)
    ]]></literal>
    <justification jstring="[para(643(a,1),11278(a,1,1)),flip(a)].">
      <j1 rule="para" parents="643 11278"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11287">
    <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(5525(a,1),11281(a,2,1))].">
      <j1 rule="para" parents="5525 11281"/>
    </justification>
  </clause>

  <clause id="11289">
    <literal><![CDATA[
      K(x,R(x / y,z,u) \ w) = K(x,R(y \ x,z,u) \ w)
    ]]></literal>
    <justification jstring="[para(11283(a,1),6842(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11283 6842"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11290">
    <literal><![CDATA[
      R(T(x,R(x,y,z) * u),y,z) = (x * u) \ (x * (R(x,y,z) * u))
    ]]></literal>
    <justification jstring="[para(1315(a,1),11282(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1315 11282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11291">
    <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,11290,a),flip(a)].">
      <j1 rule="hyper" parents="320 232 11290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11292">
    <literal><![CDATA[
      T(x,R(x,y,z) * u) = T(x,x * u)
    ]]></literal>
    <justification jstring="[hyper(972,a,11291,a),flip(a)].">
      <j1 rule="hyper" parents="972 11291"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11293">
    <literal><![CDATA[
      T(x,x * (R(x,y,z) \ u)) = T(x,u)
    ]]></literal>
    <justification jstring="[para(5(a,1),11292(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5 11292"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11295">
    <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(11292(a,1),4807(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="11292 4807"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11296">
    <literal><![CDATA[
      T(x,x * ((x \ y) * z)) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(505(a,1),11293(a,1,2,2))].">
      <j1 rule="para" parents="505 11293"/>
    </justification>
  </clause>

  <clause id="11297">
    <literal><![CDATA[
      T(x,y * K(x \ y,z)) = T(x,x * T(x \ y,z))
    ]]></literal>
    <justification jstring="[para(4755(a,2),11296(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4755 11296"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11298">
    <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,4807,a(flip),b,11295,a),flip(a)].">
      <j1 rule="hyper" parents="320 4807 11295"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11299">
    <literal><![CDATA[
      K(x * R(y,z,u),R(y,z,u)) = K(y * x,R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(7419,a,11298,a)].">
      <j1 rule="hyper" parents="7419 11298"/>
    </justification>
  </clause>

  <clause id="11300">
    <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,9867,a,b,11299,a),flip(a)].">
      <j1 rule="hyper" parents="320 9867 11299"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11301">
    <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(11300(a,1),10525(a,1,1,2))].">
      <j1 rule="para" parents="11300 10525"/>
    </justification>
  </clause>

  <clause id="11302">
    <literal><![CDATA[
      K((L(x,y,x) * y) \ z,y * x) * (z * u) = (((y * x) \ z) * (y * x)) * u
    ]]></literal>
    <justification jstring="[para(4319(a,1),11224(a,1,1,1,1))].">
      <j1 rule="para" parents="4319 11224"/>
    </justification>
  </clause>

  <clause id="11303">
    <literal><![CDATA[
      K(R(x,y,z) \ u,R(x,y,z)) = K(x \ u,R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(5940,a,11280,a),flip(a)].">
      <j1 rule="hyper" parents="5940 11280"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11305">
    <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(11303(a,1),4721(a,1,1,2))].">
      <j1 rule="para" parents="11303 4721"/>
    </justification>
  </clause>

  <clause id="11306">
    <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(5518(a,1),11301(a,1,1))].">
      <j1 rule="para" parents="5518 11301"/>
    </justification>
  </clause>

  <clause id="11307">
    <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(5266(a,1),11306(a,1,1,1,2))].">
      <j1 rule="para" parents="5266 11306"/>
    </justification>
  </clause>

  <clause id="11308">
    <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,11307,a)].">
      <j1 rule="hyper" parents="58 22 11307"/>
    </justification>
  </clause>

  <clause id="11309">
    <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(5204(a,1),11308(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5204 11308"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11310">
    <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,10523,a(flip),b,11309,a)].">
      <j1 rule="hyper" parents="58 10523 11309"/>
    </justification>
  </clause>

  <clause id="11311">
    <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(11309(a,1),10545(a,1,2))].">
      <j1 rule="para" parents="11309 10545"/>
    </justification>
  </clause>

  <clause id="11312">
    <literal><![CDATA[
      R(x,y,R(x,z,u)) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(144,a,11310,a)].">
      <j1 rule="hyper" parents="144 11310"/>
    </justification>
  </clause>

  <clause id="11313">
    <literal><![CDATA[
      (R(x,y,R(x,z,u)) * z) * u = R(R(x,y,x),z,u) * (z * u)
    ]]></literal>
    <justification jstring="[para(11310(a,1),514(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11310 514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11315">
    <literal><![CDATA[
      K(x,R(y,z,R(y,u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[para(11312(a,2),7078(a,1,2))].">
      <j1 rule="para" parents="11312 7078"/>
    </justification>
  </clause>

  <clause id="11316">
    <literal><![CDATA[
      K(T(x,y),T(z,y)) = K(x,R(z,u,R(T(z,y),w,v5)))
    ]]></literal>
    <justification jstring="[hyper(8067,a,11315,a),flip(a)].">
      <j1 rule="hyper" parents="8067 11315"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11317">
    <literal><![CDATA[
      K(x,R(y,z,R(T(y,u),w,v5))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(8056,a,11316,a),flip(a)].">
      <j1 rule="hyper" parents="8056 11316"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11319">
    <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(11317(a,1),10261(a,1,1))].">
      <j1 rule="para" parents="11317 10261"/>
    </justification>
  </clause>

  <clause id="11320">
    <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,11313,a),flip(a)].">
      <j1 rule="hyper" parents="320 101 11313"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11321">
    <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(10226(a,1),11320(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10226 11320"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11322">
    <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(5180,a,11319,a)].">
      <j1 rule="hyper" parents="5180 11319"/>
    </justification>
  </clause>

  <clause id="11323">
    <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(10226(a,1),11319(a,1,2,2))].">
      <j1 rule="para" parents="10226 11319"/>
    </justification>
  </clause>

  <clause id="11324">
    <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(9973,a,11322,a)].">
      <j1 rule="hyper" parents="9973 11322"/>
    </justification>
  </clause>

  <clause id="11325">
    <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(11322(a,1),9973(a,1))].">
      <j1 rule="para" parents="11322 9973"/>
    </justification>
  </clause>

  <clause id="11326">
    <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(9977(a,1),11323(a,1,2))].">
      <j1 rule="para" parents="9977 11323"/>
    </justification>
  </clause>

  <clause id="11327">
    <literal><![CDATA[
      x \ R(x,y,R(T(x,z),u,w)) = a(x,y,R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(5149,a,11326,a),flip(a)].">
      <j1 rule="hyper" parents="5149 11326"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11328">
    <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(11326(a,1),5148(a,1)),flip(b)].">
      <j1 rule="para" parents="11326 5148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11329">
    <literal><![CDATA[
      a(T(x,y),z,R(T(x,y),u,w)) = a(x,z,R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(11325,a,11327,a)].">
      <j1 rule="hyper" parents="11325 11327"/>
    </justification>
  </clause>

  <clause id="11332">
    <literal><![CDATA[
      a(R(x,y,z),u,x) \ 1 = a(x,u,R(x,y,z)) \ 1
    ]]></literal>
    <justification jstring="[para(11329(a,1),10688(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11329 10688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11333">
    <literal><![CDATA[
      a(R(x,y,z),u,x) = a(x,u,R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(43,a,11332,a)].">
      <j1 rule="hyper" parents="43 11332"/>
    </justification>
  </clause>

  <clause id="11335">
    <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,6844,a,b,11333,a)].">
      <j1 rule="hyper" parents="320 6844 11333"/>
    </justification>
  </clause>

  <clause id="11337">
    <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(11324(a,2),11328(a,1))].">
      <j1 rule="para" parents="11324 11328"/>
    </justification>
  </clause>

  <clause id="11338">
    <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,7160,a(flip),b,11094,a),flip(a)].">
      <j1 rule="hyper" parents="320 7160 11094"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11339">
    <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,6084,a(flip),b,11287,a),flip(a)].">
      <j1 rule="hyper" parents="320 6084 11287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11340">
    <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(6082(a,1),11339(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6082 11339"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11341">
    <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(11340(a,1),9129(a,1,2))].">
      <j1 rule="para" parents="11340 9129"/>
    </justification>
  </clause>

  <clause id="11342">
    <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(5518(a,1),11305(a,1,1))].">
      <j1 rule="para" parents="5518 11305"/>
    </justification>
  </clause>

  <clause id="11343">
    <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,11342,a)].">
      <j1 rule="hyper" parents="58 22 11342"/>
    </justification>
  </clause>

  <clause id="11344">
    <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(4721(a,1),11343(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4721 11343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11345">
    <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,11344,a),flip(a)].">
      <j1 rule="hyper" parents="320 24 11344"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11346">
    <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(11345(a,1),1354(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="11345 1354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11347">
    <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,7744,a(flip),b,11338,a),flip(a)].">
      <j1 rule="hyper" parents="320 7744 11338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11348">
    <literal><![CDATA[
      K(x,T(y / ((z * T(x,z * u)) * u),z * u)) = K(x,(z * u) \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(7704,a,11347,a)].">
      <j1 rule="hyper" parents="7704 11347"/>
    </justification>
  </clause>

  <clause id="11349">
    <literal><![CDATA[
      K(x,T(y / ((z * x) * u),z * u)) = K(x,(z * u) \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(58,a,10703,a(flip),b,11348,a)].">
      <j1 rule="hyper" parents="58 10703 11348"/>
    </justification>
  </clause>

  <clause id="11351">
    <literal><![CDATA[
      K(x,((y * x) * z) \ u) = K(x,(y * z) \ (x \ u))
    ]]></literal>
    <justification jstring="[hyper(58,a,9210,a(flip),b,11349,a)].">
      <j1 rule="hyper" parents="58 9210 11349"/>
    </justification>
  </clause>

  <clause id="11352">
    <literal><![CDATA[
      K(x,((x \ y) * z) \ (x \ u)) = K(x,(y * z) \ u)
    ]]></literal>
    <justification jstring="[hyper(11223,a,11351,a),flip(a)].">
      <j1 rule="hyper" parents="11223 11351"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11353">
    <literal><![CDATA[
      K(x,((y * x) * (y \ 1)) \ z) = K(x,x \ z)
    ]]></literal>
    <justification jstring="[para(163(a,1),11351(a,2,2))].">
      <j1 rule="para" parents="163 11351"/>
    </justification>
  </clause>

  <clause id="11354">
    <literal><![CDATA[
      K(x,a(x,y,y \ 1) \ z) = K(x,x \ (x * z))
    ]]></literal>
    <justification jstring="[hyper(58,a,9697,a(flip),b,11353,a)].">
      <j1 rule="hyper" parents="58 9697 11353"/>
    </justification>
  </clause>

  <clause id="11356">
    <literal><![CDATA[
      K(x,a(x,y,y \ 1) \ z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(4(a,1),11354(a,2,2))].">
      <j1 rule="para" parents="4 11354"/>
    </justification>
  </clause>

  <clause id="11357">
    <literal><![CDATA[
      K(x,y \ R(x,z,z \ 1)) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,9325,a(flip),b,11356,a),flip(a)].">
      <j1 rule="hyper" parents="58 9325 11356"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11358">
    <literal><![CDATA[
      K(x,y \ ((z * x) * (z \ 1))) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[hyper(8593,a,11357,a)].">
      <j1 rule="hyper" parents="8593 11357"/>
    </justification>
  </clause>

  <clause id="11360">
    <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,9503,a(flip),b,11358,a)].">
      <j1 rule="hyper" parents="58 9503 11358"/>
    </justification>
  </clause>

  <clause id="11361">
    <literal><![CDATA[
      K(x,((x \ y) * z) \ 1) = K(x,(y * z) \ x)
    ]]></literal>
    <justification jstring="[para(61(a,1),11352(a,1,2,2))].">
      <j1 rule="para" parents="61 11352"/>
    </justification>
  </clause>

  <clause id="11362">
    <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,11218,a)].">
      <j1 rule="hyper" parents="568 11218"/>
    </justification>
  </clause>

  <clause id="11364">
    <literal><![CDATA[
      (x / (1 / y)) * (1 / T(y,(x / (1 / y)) / y)) = (T(x,y) / (1 / y)) * (1 / y)
    ]]></literal>
    <justification jstring="[para(4253(a,2),11362(a,1,2,2))].">
      <j1 rule="para" parents="4253 11362"/>
    </justification>
  </clause>

  <clause id="11365">
    <literal><![CDATA[
      (T(x,y) / (1 / y)) * (1 / y) = (x / (1 / y)) * (1 / T(y,x))
    ]]></literal>
    <justification jstring="[para(6225(a,1),11364(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6225 11364"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11366">
    <literal><![CDATA[
      T(x,y) / (1 / T(y,x)) = x / (1 / y)
    ]]></literal>
    <justification jstring="[hyper(413,a,11365,a)].">
      <j1 rule="hyper" parents="413 11365"/>
    </justification>
  </clause>

  <clause id="11367">
    <literal><![CDATA[
      T(x,y / x) / (1 / (x \ y)) = x / (1 / (y / x))
    ]]></literal>
    <justification jstring="[para(107(a,1),11366(a,1,2,2))].">
      <j1 rule="para" parents="107 11366"/>
    </justification>
  </clause>

  <clause id="11368">
    <literal><![CDATA[
      (x / (1 / (x \ y))) / x = x \ (x / (1 / (y / x)))
    ]]></literal>
    <justification jstring="[para(11367(a,1),4295(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11367 4295"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11369">
    <literal><![CDATA[
      T((x / (1 / (x \ y))) / x,1 / (y / x)) = x \ (x / ((y / x) \ 1))
    ]]></literal>
    <justification jstring="[para(11368(a,2),2647(a,1,1))].">
      <j1 rule="para" parents="11368 2647"/>
    </justification>
  </clause>

  <clause id="11370">
    <literal><![CDATA[
      x * ((x / ((x \ y) \ 1)) / x) = x / ((y / x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(10714,a,11369,a)].">
      <j1 rule="hyper" parents="10714 11369"/>
    </justification>
  </clause>

  <clause id="11371">
    <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,10722,a(flip),b,11053,a)].">
      <j1 rule="hyper" parents="58 10722 11053"/>
    </justification>
  </clause>

  <clause id="11372">
    <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(8608(a,1),11371(a,1,2,2))].">
      <j1 rule="para" parents="8608 11371"/>
    </justification>
  </clause>

  <clause id="11373">
    <literal><![CDATA[
      K(x,y * ((z \ 1) \ K(u,x))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,7579,a(flip),b,11372,a),flip(a)].">
      <j1 rule="hyper" parents="58 7579 11372"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11375">
    <literal><![CDATA[
      K(x,y * (z \ K(u,x))) = K(x,y * (z \ 1))
    ]]></literal>
    <justification jstring="[hyper(58,a,5577,a(flip),b,11373,a)].">
      <j1 rule="hyper" parents="58 5577 11373"/>
    </justification>
  </clause>

  <clause id="11376">
    <literal><![CDATA[
      K((x * (y \ 1)) \ 1,K(z,u)) = K(z,K(u,x * (y \ K(w,u))))
    ]]></literal>
    <justification jstring="[para(11375(a,2),8185(a,2,2))].">
      <j1 rule="para" parents="11375 8185"/>
    </justification>
  </clause>

  <clause id="11377">
    <literal><![CDATA[
      K(x,K(y,z * (u \ K(w,y)))) = K(x,K(y,z * (u \ 1)))
    ]]></literal>
    <justification jstring="[hyper(8198,a,11376,a),flip(a)].">
      <j1 rule="hyper" parents="8198 11376"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11378">
    <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(7251(a,1),11377(a,1,2))].">
      <j1 rule="para" parents="7251 11377"/>
    </justification>
  </clause>

  <clause id="11379">
    <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),11378(a,2,2,2))].">
      <j1 rule="para" parents="261 11378"/>
    </justification>
  </clause>

  <clause id="11380">
    <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,9073,a,b,11379,a)].">
      <j1 rule="hyper" parents="58 9073 11379"/>
    </justification>
  </clause>

  <clause id="11381">
    <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,7779,a,b,11380,a),flip(a)].">
      <j1 rule="hyper" parents="320 7779 11380"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11382">
    <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(4513(a,1),11062(a,1,1))].">
      <j1 rule="para" parents="4513 11062"/>
    </justification>
  </clause>

  <clause id="11383">
    <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(2410(a,1),11071(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="2410 11071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11384">
    <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(6340(a,1),11383(a,2,1))].">
      <j1 rule="para" parents="6340 11383"/>
    </justification>
  </clause>

  <clause id="11385">
    <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,8835,a,b,11384,a),flip(a)].">
      <j1 rule="hyper" parents="320 8835 11384"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11386">
    <literal><![CDATA[
      (K(x,y) \ z) * (K(x,y) * K(u,x)) = T(z * K(u,x),K(x,y))
    ]]></literal>
    <justification jstring="[para(2413(a,1),11385(a,1,1,1))].">
      <j1 rule="para" parents="2413 11385"/>
    </justification>
  </clause>

  <clause id="11387">
    <literal><![CDATA[
      (K(x,y) * z) * (K(y,x) * K(u,y)) = T(z * K(u,y),K(y,x))
    ]]></literal>
    <justification jstring="[para(5130(a,1),11386(a,1,1))].">
      <j1 rule="para" parents="5130 11386"/>
    </justification>
  </clause>

  <clause id="11388">
    <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,10034,a(flip),b,11387,a),flip(a)].">
      <j1 rule="hyper" parents="58 10034 11387"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11389">
    <literal><![CDATA[
      x * K(K(y,z) * K(z,u),x) = T(T(x,K(z,u)),K(z,y))
    ]]></literal>
    <justification jstring="[para(7839(a,1),11388(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7839 11388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11390">
    <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,10016,a(flip),b,11072,a),flip(a)].">
      <j1 rule="hyper" parents="58 10016 11072"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11391">
    <literal><![CDATA[
      K(x,y * K(((z \ 1) \ 1) \ K(u,x),(z \ 1) \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,7244,a(flip),b,11075,a),flip(a)].">
      <j1 rule="hyper" parents="320 7244 11075"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11393">
    <literal><![CDATA[
      K(x,y * K(z \ K(u,x),z)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(3131(a,1),11391(a,1,2,2))].">
      <j1 rule="para" parents="3131 11391"/>
    </justification>
  </clause>

  <clause id="11395">
    <literal><![CDATA[
      K(x,y * (K(z,x) / u)) = K(x,y * (u \ K(z,x)))
    ]]></literal>
    <justification jstring="[para(6475(a,1),11393(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6475 11393"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11396">
    <literal><![CDATA[
      K(x,y * (K(z,x) / u)) = K(x,y * (u \ 1))
    ]]></literal>
    <justification jstring="[hyper(320,a,11375,a(flip),b,11395,a),flip(a)].">
      <j1 rule="hyper" parents="320 11375 11395"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11398">
    <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),11076(a,2,2,1,2))].">
      <j1 rule="para" parents="72 11076"/>
    </justification>
  </clause>

  <clause id="11400">
    <literal><![CDATA[
      K(x,((1 / (K(y,x \ z) / y)) * z) \ (u * x)) = K(x,(((z \ x) \ 1) * y) \ u)
    ]]></literal>
    <justification jstring="[para(6108(a,1),11398(a,1,2,1,1,2,1))].">
      <j1 rule="para" parents="6108 11398"/>
    </justification>
  </clause>

  <clause id="11401">
    <literal><![CDATA[
      K(x,(((y \ x) \ 1) * z) \ u) = K(x,((x \ y) * z) \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,9811,a(flip),b,11400,a),flip(a)].">
      <j1 rule="hyper" parents="58 9811 11400"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11402">
    <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(4432(a,1),11341(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4432 11341"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11403">
    <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(7897(a,1),11382(a,1,1,2))].">
      <j1 rule="para" parents="7897 11382"/>
    </justification>
  </clause>

  <clause id="11404">
    <literal><![CDATA[
      R(K(x,L(y,z,L(y,u,w))),L(y,u,w),z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(8760,a,11403,a),flip(a)].">
      <j1 rule="hyper" parents="8760 11403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11405">
    <literal><![CDATA[
      R(K(x,y),L(y,z,u),w) = K(x,y)
    ]]></literal>
    <justification jstring="[para(8797(a,1),11404(a,1,1))].">
      <j1 rule="para" parents="8797 11404"/>
    </justification>
  </clause>

  <clause id="11406">
    <literal><![CDATA[
      K((L(x,y,z) * u) / w,x) = K(L(x,y,z) / (w / u),x)
    ]]></literal>
    <justification jstring="[hyper(58,a,6764,a(flip),b,11405,a)].">
      <j1 rule="hyper" parents="58 6764 11405"/>
    </justification>
  </clause>

  <clause id="11408">
    <literal><![CDATA[
      K((L(x,y,z) * u) / w,x) = K((w / u) \ L(x,y,z),x)
    ]]></literal>
    <justification jstring="[hyper(320,a,6289,a(flip),b,11406,a),flip(a)].">
      <j1 rule="hyper" parents="320 6289 11406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11409">
    <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,10678,a,b,11408,a)].">
      <j1 rule="hyper" parents="58 10678 11408"/>
    </justification>
  </clause>

  <clause id="11410">
    <literal><![CDATA[
      K(x / (L(y,z,u) \ w),y) = K((w / x) \ L(y,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(8263,a,11409,a)].">
      <j1 rule="hyper" parents="8263 11409"/>
    </justification>
  </clause>

  <clause id="11411">
    <literal><![CDATA[
      K(x / (L(y,z,u) \ w),y) = K((w / x) \ y,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,10778,a(flip),b,11410,a),flip(a)].">
      <j1 rule="hyper" parents="320 10778 11410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11413">
    <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(7160(a,1),11390(a,2,2,1))].">
      <j1 rule="para" parents="7160 11390"/>
    </justification>
  </clause>

  <clause id="11414">
    <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),11413(a,2,2))].">
      <j1 rule="para" parents="3 11413"/>
    </justification>
  </clause>

  <clause id="11415">
    <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(4331(a,1),4341(a,2,2,1,1))].">
      <j1 rule="para" parents="4331 4341"/>
    </justification>
  </clause>

  <clause id="11416">
    <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,11415,a)].">
      <j1 rule="hyper" parents="123 11415"/>
    </justification>
  </clause>

  <clause id="11417">
    <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(4885(a,1),5008(a,1,1,1,1))].">
      <j1 rule="para" parents="4885 5008"/>
    </justification>
  </clause>

  <clause id="11418">
    <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(6850(a,1),11417(a,1,1))].">
      <j1 rule="para" parents="6850 11417"/>
    </justification>
  </clause>

  <clause id="11419">
    <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,5390,a(flip),b,11418,a),flip(a)].">
      <j1 rule="hyper" parents="320 5390 11418"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11420">
    <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),11419(a,1,1,2))].">
      <j1 rule="para" parents="25 11419"/>
    </justification>
  </clause>

  <clause id="11421">
    <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,7945,a(flip),b,11420,a)].">
      <j1 rule="hyper" parents="58 7945 11420"/>
    </justification>
  </clause>

  <clause id="11422">
    <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,8247,a(flip),b,11421,a)].">
      <j1 rule="hyper" parents="58 8247 11421"/>
    </justification>
  </clause>

  <clause id="11423">
    <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(11422(a,1),5113(a,1,2,2))].">
      <j1 rule="para" parents="11422 5113"/>
    </justification>
  </clause>

  <clause id="11424">
    <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(7264(a,1),11423(a,1,1))].">
      <j1 rule="para" parents="7264 11423"/>
    </justification>
  </clause>

  <clause id="11425">
    <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(4779(a,1),6915(a,2,2))].">
      <j1 rule="para" parents="4779 6915"/>
    </justification>
  </clause>

  <clause id="11426">
    <literal><![CDATA[
      L(K((x \ 1) \ (x \ y),z),x \ y,T(x,x \ y)) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,6202,a(flip),b,11425,a),flip(a)].">
      <j1 rule="hyper" parents="320 6202 11425"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11428">
    <literal><![CDATA[
      L(K((x \ 1) \ (x \ y),z),y / x,x) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,4571,a(flip),b,11426,a)].">
      <j1 rule="hyper" parents="58 4571 11426"/>
    </justification>
  </clause>

  <clause id="11429">
    <literal><![CDATA[
      K((x \ 1) \ (x \ y),L(z,y / x,x)) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(10837,a,11428,a)].">
      <j1 rule="hyper" parents="10837 11428"/>
    </justification>
  </clause>

  <clause id="11430">
    <literal><![CDATA[
      K(x,(y \ 1) \ (y \ L(z,x / y,y))) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,10929,a(flip),b,11429,a)].">
      <j1 rule="hyper" parents="58 10929 11429"/>
    </justification>
  </clause>

  <clause id="11431">
    <literal><![CDATA[
      K(x,L((y \ 1) \ (y \ z),x / y,y)) = K(x,z)
    ]]></literal>
    <justification jstring="[para(1694(a,2),11430(a,1,2))].">
      <j1 rule="para" parents="1694 11430"/>
    </justification>
  </clause>

  <clause id="11432">
    <literal><![CDATA[
      K(x,L((y \ 1) \ (y \ z),y \ x,y)) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,11226,a(flip),b,11431,a)].">
      <j1 rule="hyper" parents="58 11226 11431"/>
    </justification>
  </clause>

  <clause id="11433">
    <literal><![CDATA[
      K(R(x \ y,z,u),w \ (y / x)) = K(R(x \ y,z,u),w \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(5527,a,8701,a),flip(a)].">
      <j1 rule="hyper" parents="5527 8701"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11434">
    <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(4929(a,1),11433(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4929 11433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11435">
    <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(1766(a,2),8977(a,1,2,2))].">
      <j1 rule="para" parents="1766 8977"/>
    </justification>
  </clause>

  <clause id="11436">
    <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(3562(a,1),9793(a,1,1))].">
      <j1 rule="para" parents="3562 9793"/>
    </justification>
  </clause>

  <clause id="11437">
    <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),9837(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6 9837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11439">
    <literal><![CDATA[
      (K(x,y) * K(z,y)) * u = K(z,y) * (K(x,y) * u)
    ]]></literal>
    <justification jstring="[para(10024(a,1),11437(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10024 11437"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11441">
    <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(11439(a,1),5699(a,1,2,2))].">
      <j1 rule="para" parents="11439 5699"/>
    </justification>
  </clause>

  <clause id="11442">
    <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(5161(a,1),11441(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5161 11441"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11443">
    <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,5103,a(flip),b,11442,a),flip(a)].">
      <j1 rule="hyper" parents="320 5103 11442"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11445">
    <literal><![CDATA[
      L(x,T(y,z) \ ((u * y) / u),T(y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(320,a,5133,a(flip),b,11443,a),flip(a)].">
      <j1 rule="hyper" parents="320 5133 11443"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11447">
    <literal><![CDATA[
      L(x,K(y,z) * K(u,z),T(z,u)) = x
    ]]></literal>
    <justification jstring="[para(5698(a,1),11445(a,1,2))].">
      <j1 rule="para" parents="5698 11445"/>
    </justification>
  </clause>

  <clause id="11448">
    <literal><![CDATA[
      L(x,K(y,z) * K(u,z),T(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(11447(a,1),45(a,2))].">
      <j1 rule="para" parents="11447 45"/>
    </justification>
  </clause>

  <clause id="11449">
    <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(8956(a,1),10437(a,1,1,1))].">
      <j1 rule="para" parents="8956 10437"/>
    </justification>
  </clause>

  <clause id="11450">
    <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),11449(a,1,1))].">
      <j1 rule="para" parents="514 11449"/>
    </justification>
  </clause>

  <clause id="11451">
    <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(11312(a,1),11450(a,1,1,1,1))].">
      <j1 rule="para" parents="11312 11450"/>
    </justification>
  </clause>

  <clause id="11452">
    <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(11451(a,1),9563(a,1))].">
      <j1 rule="para" parents="11451 9563"/>
    </justification>
  </clause>

  <clause id="11454">
    <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,1354,a(flip),b,11346,a),flip(a)].">
      <j1 rule="hyper" parents="320 1354 11346"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11455">
    <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),11454(a,2,3))].">
      <j1 rule="para" parents="22 11454"/>
    </justification>
  </clause>

  <clause id="11456">
    <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),11435(a,1,2)),flip(a)].">
      <j1 rule="para" parents="90 11435"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11457">
    <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(10664(a,1),11436(a,1,1))].">
      <j1 rule="para" parents="10664 11436"/>
    </justification>
  </clause>

  <clause id="11458">
    <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(5427(a,1),11457(a,1,2))].">
      <j1 rule="para" parents="5427 11457"/>
    </justification>
  </clause>

  <clause id="11459">
    <literal><![CDATA[
      K((x \ y) \ z,x / y) * K(x / y,z) = a((y / x) \ 1,z,(y / x) \ 1)
    ]]></literal>
    <justification jstring="[para(8250(a,1),11458(a,1,2))].">
      <j1 rule="para" parents="8250 11458"/>
    </justification>
  </clause>

  <clause id="11460">
    <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(1193(a,1),5844(a,2,1))].">
      <j1 rule="para" parents="1193 5844"/>
    </justification>
  </clause>

  <clause id="11461">
    <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,11460,a(flip),b,5845,a),flip(a)].">
      <j1 rule="hyper" parents="58 11460 5845"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11462">
    <literal><![CDATA[
      T(x \ L(x,y,z),u * x) = T(x \ L(x,y,z),x * u)
    ]]></literal>
    <justification jstring="[para(1193(a,1),11461(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1193 11461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11463">
    <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(3635(a,2),6026(a,1,1))].">
      <j1 rule="para" parents="3635 6026"/>
    </justification>
  </clause>

  <clause id="11464">
    <literal><![CDATA[
      x \ ((x / ((y * z) / y)) * ((z \ 1) * ((y * z) / y))) = T(x \ (x / z),(y * z) / y)
    ]]></literal>
    <justification jstring="[para(4758(a,1),6399(a,1,2,2,1))].">
      <j1 rule="para" parents="4758 6399"/>
    </justification>
  </clause>

  <clause id="11466">
    <literal><![CDATA[
      x \ ((x / ((y * z) / y)) * ((T(z,y) \ 1) * z)) = T(x \ (x / z),(y * z) / y)
    ]]></literal>
    <justification jstring="[para(5657(a,1),11464(a,1,2,2))].">
      <j1 rule="para" parents="5657 11464"/>
    </justification>
  </clause>

  <clause id="11467">
    <literal><![CDATA[
      (1 / ((x * y) / x)) * ((T(y,x) \ 1) * y) = T(1 \ (1 / y),(x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(165,a,11466,a)].">
      <j1 rule="hyper" parents="165 11466"/>
    </justification>
  </clause>

  <clause id="11468">
    <literal><![CDATA[
      (1 / ((x * y) / x)) * ((T(y,x) \ 1) * y) = T(1 / y,(x * y) / x)
    ]]></literal>
    <justification jstring="[para(60(a,1),11467(a,2,1))].">
      <j1 rule="para" parents="60 11467"/>
    </justification>
  </clause>

  <clause id="11469">
    <literal><![CDATA[
      (1 / ((x * y) / x)) \ (y \ 1) = (T(y,x) \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(116,a,5206,a(flip),b,11468,a)].">
      <j1 rule="hyper" parents="116 5206 11468"/>
    </justification>
  </clause>

  <clause id="11470">
    <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,8882,a(flip),b,7016,a),flip(a)].">
      <j1 rule="hyper" parents="58 8882 7016"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11472">
    <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(6127(a,1),7566(a,2,1))].">
      <j1 rule="para" parents="6127 7566"/>
    </justification>
  </clause>

  <clause id="11473">
    <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),11472(a,2,1,2))].">
      <j1 rule="para" parents="75 11472"/>
    </justification>
  </clause>

  <clause id="11475">
    <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,7520,a,b,11473,a),flip(a)].">
      <j1 rule="hyper" parents="320 7520 11473"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11476">
    <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,7618,a(flip),b,11475,a),flip(a)].">
      <j1 rule="hyper" parents="320 7618 11475"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11477">
    <literal><![CDATA[
      x / (T(y,z) \ R(x,y \ 1,y)) = T((x * (1 / y)) \ x,z)
    ]]></literal>
    <justification jstring="[para(11476(a,1),7657(a,1,2))].">
      <j1 rule="para" parents="11476 7657"/>
    </justification>
  </clause>

  <clause id="11478">
    <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(11050(a,1),11049(a,1,2,1,1))].">
      <j1 rule="para" parents="11050 11049"/>
    </justification>
  </clause>

  <clause id="11479">
    <literal><![CDATA[
      K(x,T(x * ((y \ z) \ z),u)) = K(x,T(x * T(y,z),u))
    ]]></literal>
    <justification jstring="[hyper(58,a,10764,a(flip),b,11478,a),flip(a)].">
      <j1 rule="hyper" parents="58 10764 11478"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11480">
    <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(4540(a,1),4377(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4540 4377"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11481">
    <literal><![CDATA[
      T(x / T(y,x),z) * T(y,y * T(y \ x,z)) = y * T(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(10557,a,11480,a),flip(a)].">
      <j1 rule="hyper" parents="10557 11480"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11482">
    <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(5472(a,1),5269(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5472 5269"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11483">
    <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(4969(a,1),11482(a,2,1,2))].">
      <j1 rule="para" parents="4969 11482"/>
    </justification>
  </clause>

  <clause id="11485">
    <literal><![CDATA[
      (x * K(y,x)) * (T(x,z) * (x \ K(x,y))) = T(x,z)
    ]]></literal>
    <justification jstring="[para(6329(a,1),11483(a,2,1))].">
      <j1 rule="para" parents="6329 11483"/>
    </justification>
  </clause>

  <clause id="11486">
    <literal><![CDATA[
      T(x,y) / (T(x,y) * (x \ K(x,z))) = x * K(z,x)
    ]]></literal>
    <justification jstring="[hyper(131,a,11485,a)].">
      <j1 rule="hyper" parents="131 11485"/>
    </justification>
  </clause>

  <clause id="11487">
    <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(11486(a,1),3085(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="11486 3085"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11488">
    <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(5824(a,1),11487(a,2,1))].">
      <j1 rule="para" parents="5824 11487"/>
    </justification>
  </clause>

  <clause id="11489">
    <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(5613(a,1),11488(a,1,2,2))].">
      <j1 rule="para" parents="5613 11488"/>
    </justification>
  </clause>

  <clause id="11490">
    <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(8029(a,1),11489(a,1,2))].">
      <j1 rule="para" parents="8029 11489"/>
    </justification>
  </clause>

  <clause id="11491">
    <literal><![CDATA[
      ((x \ 1) \ K(y,x)) \ T(x,z) = T(x,z) * T(x \ K(x,y),x)
    ]]></literal>
    <justification jstring="[para(8134(a,1),11490(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8134 11490"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11492">
    <literal><![CDATA[
      ((x \ 1) \ K(y,x)) \ T(x,z) = (x \ K(x,y)) * T(x,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,8346,a(flip),b,11491,a),flip(a)].">
      <j1 rule="hyper" parents="320 8346 11491"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11494">
    <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(11492(a,1),6124(a,1,2,1))].">
      <j1 rule="para" parents="11492 6124"/>
    </justification>
  </clause>

  <clause id="11495">
    <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(11492(a,2),10698(a,1,2,1))].">
      <j1 rule="para" parents="11492 10698"/>
    </justification>
  </clause>

  <clause id="11496">
    <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),8370(a,1,1,1))].">
      <j1 rule="para" parents="198 8370"/>
    </justification>
  </clause>

  <clause id="11497">
    <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),11496(a,1,2,2,1,1)),flip(a)].">
      <j1 rule="para" parents="198 11496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11498">
    <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),11497(a,2,2,3,1))].">
      <j1 rule="para" parents="198 11497"/>
    </justification>
  </clause>

  <clause id="11499">
    <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),8516(a,1,1)),flip(a)].">
      <j1 rule="para" parents="232 8516"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11500">
    <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(10007(a,1),11499(a,2,1))].">
      <j1 rule="para" parents="10007 11499"/>
    </justification>
  </clause>

  <clause id="11501">
    <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,7832,a,b,11500,a),flip(a)].">
      <j1 rule="hyper" parents="320 7832 11500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11503">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(y,u)) = T(x,K(u,y) * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(8927,a,11501,a)].">
      <j1 rule="hyper" parents="8927 11501"/>
    </justification>
  </clause>

  <clause id="11504">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(z,u)) = T(x,K(y,z) * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(7849,a,11503,a)].">
      <j1 rule="hyper" parents="7849 11503"/>
    </justification>
  </clause>

  <clause id="11506">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(y,u)) = T(x,K(y,z) * K(u,y))
    ]]></literal>
    <justification jstring="[para(2003(a,2),11503(a,2,2))].">
      <j1 rule="para" parents="2003 11503"/>
    </justification>
  </clause>

  <clause id="11507">
    <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(11503(a,1),9711(a,1,1))].">
      <j1 rule="para" parents="11503 9711"/>
    </justification>
  </clause>

  <clause id="11508">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(z,u)) = T(x,K(z,u) * K(y,z))
    ]]></literal>
    <justification jstring="[para(2003(a,2),11504(a,2,2))].">
      <j1 rule="para" parents="2003 11504"/>
    </justification>
  </clause>

  <clause id="11509">
    <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(11504(a,1),7848(a,1))].">
      <j1 rule="para" parents="11504 7848"/>
    </justification>
  </clause>

  <clause id="11510">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(y,u)) = T(x,K(y,u) * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(434,a,11506,a)].">
      <j1 rule="hyper" parents="434 11506"/>
    </justification>
  </clause>

  <clause id="11511">
    <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,11389,a,b,11506,a)].">
      <j1 rule="hyper" parents="58 11389 11506"/>
    </justification>
  </clause>

  <clause id="11512">
    <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,9078,a,b,11506,a)].">
      <j1 rule="hyper" parents="58 9078 11506"/>
    </justification>
  </clause>

  <clause id="11513">
    <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(9232(a,1),11508(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9232 11508"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11514">
    <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(11508(a,1),10058(a,2,1))].">
      <j1 rule="para" parents="11508 10058"/>
    </justification>
  </clause>

  <clause id="11515">
    <literal><![CDATA[
      T(x,K(y,z) * K(u,y)) = T(x,K(y,u) * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,11506,a(flip),b,11510,a)].">
      <j1 rule="hyper" parents="58 11506 11510"/>
    </justification>
  </clause>

  <clause id="11516">
    <literal><![CDATA[
      x * K(x,K(y,z) * K(u,y)) = T(x,K(y,u) * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(4858,a,11515,a)].">
      <j1 rule="hyper" parents="4858 11515"/>
    </justification>
  </clause>

  <clause id="11517">
    <literal><![CDATA[
      x * K(K(y,z) * K(u,y),x) = T(x,K(y,z) * K(u,y))
    ]]></literal>
    <justification jstring="[para(2003(a,2),11511(a,1,2,1))].">
      <j1 rule="para" parents="2003 11511"/>
    </justification>
  </clause>

  <clause id="11518">
    <literal><![CDATA[
      K(K(x,y) * K(y,z),u) = K(u,K(y,x) * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(29,a,11511,a,b,11516,a)].">
      <j1 rule="hyper" parents="29 11511 11516"/>
    </justification>
  </clause>

  <clause id="11519">
    <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(11516(a,1),4766(a,1))].">
      <j1 rule="para" parents="11516 4766"/>
    </justification>
  </clause>

  <clause id="11520">
    <literal><![CDATA[
      K(K(x,y) * K(z,x),u) = K(u,K(x,z) * K(y,x))
    ]]></literal>
    <justification jstring="[para(2003(a,2),11518(a,1,1))].">
      <j1 rule="para" parents="2003 11518"/>
    </justification>
  </clause>

  <clause id="11521">
    <literal><![CDATA[
      K(K(x,y) * K(z,x),u) = K(u,K(y,x) * K(x,z))
    ]]></literal>
    <justification jstring="[para(2003(a,1),11520(a,2,2))].">
      <j1 rule="para" parents="2003 11520"/>
    </justification>
  </clause>

  <clause id="11522">
    <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,11521,a,b,4795,a(flip))].">
      <j1 rule="hyper" parents="117 11521 4795"/>
    </justification>
  </clause>

  <clause id="11523">
    <literal><![CDATA[
      K(K(x,y) * K(z,x),u) = K(u,K(x,y) * K(z,x))
    ]]></literal>
    <justification jstring="[hyper(29,a,4755,a(flip),b,11517,a),flip(a)].">
      <j1 rule="hyper" parents="29 4755 11517"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11524">
    <literal><![CDATA[
      K(x,K(y,z) * K(u,y)) = K(x,K(z,y) * K(y,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,11521,a(flip),b,11523,a),flip(a)].">
      <j1 rule="hyper" parents="58 11521 11523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11525">
    <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(11506(a,2),11519(a,1))].">
      <j1 rule="para" parents="11506 11519"/>
    </justification>
  </clause>

  <clause id="11526">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,K(y,u)) = K(K(z,y) * K(y,u),x)
    ]]></literal>
    <justification jstring="[hyper(4827,a,11507,a),flip(a)].">
      <j1 rule="hyper" parents="4827 11507"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11527">
    <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,11518,a(flip),b,11526,a),flip(a)].">
      <j1 rule="hyper" parents="320 11518 11526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11528">
    <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(6946(a,1),11526(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6946 11526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11529">
    <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,11523,a,b,11527,a),flip(a)].">
      <j1 rule="hyper" parents="320 11523 11527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11530">
    <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,9842,a,b,11527,a)].">
      <j1 rule="hyper" parents="58 9842 11527"/>
    </justification>
  </clause>

  <clause id="11531">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,K(z,u)) = K(x,K(z,y) * K(u,z))
    ]]></literal>
    <justification jstring="[para(7797(a,1),11527(a,1,1))].">
      <j1 rule="para" parents="7797 11527"/>
    </justification>
  </clause>

  <clause id="11532">
    <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,11524,a(flip),b,11531,a),flip(a)].">
      <j1 rule="hyper" parents="320 11524 11531"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11533">
    <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,11504,a(flip),b,11512,a),flip(a)].">
      <j1 rule="hyper" parents="58 11504 11512"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11534">
    <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,4730,a,b,11514,a),flip(a)].">
      <j1 rule="hyper" parents="320 4730 11514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11535">
    <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(5130(a,1),11534(a,1,2))].">
      <j1 rule="para" parents="5130 11534"/>
    </justification>
  </clause>

  <clause id="11536">
    <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,11523,a(flip),b,11535,a),flip(a)].">
      <j1 rule="hyper" parents="320 11523 11535"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11537">
    <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(11519,a,11533,a)].">
      <j1 rule="hyper" parents="11519 11533"/>
    </justification>
  </clause>

  <clause id="11538">
    <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,4755,a(flip),b,11537,a)].">
      <j1 rule="hyper" parents="320 4755 11537"/>
    </justification>
  </clause>

  <clause id="11539">
    <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(9076(a,1),11513(a,2,1))].">
      <j1 rule="para" parents="9076 11513"/>
    </justification>
  </clause>

  <clause id="11540">
    <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,4755,a(flip),b,11538,a)].">
      <j1 rule="hyper" parents="29 4755 11538"/>
    </justification>
  </clause>

  <clause id="11541">
    <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,11510,a(flip),b,11539,a),flip(a)].">
      <j1 rule="hyper" parents="320 11510 11539"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11542">
    <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(9232(a,1),11541(a,1,2,2))].">
      <j1 rule="para" parents="9232 11541"/>
    </justification>
  </clause>

  <clause id="11543">
    <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,11515,a,b,11542,a)].">
      <j1 rule="hyper" parents="320 11515 11542"/>
    </justification>
  </clause>

  <clause id="11544">
    <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,9016,a(flip),b,11522,a)].">
      <j1 rule="hyper" parents="58 9016 11522"/>
    </justification>
  </clause>

  <clause id="11545">
    <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(7779(a,1),11530(a,1,2,2,2))].">
      <j1 rule="para" parents="7779 11530"/>
    </justification>
  </clause>

  <clause id="11546">
    <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,6560,a(flip),b,11544,a)].">
      <j1 rule="hyper" parents="58 6560 11544"/>
    </justification>
  </clause>

  <clause id="11547">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,K(z,u)) = K(z,K(x,y) * K(u,x))
    ]]></literal>
    <justification jstring="[hyper(5412,a,11545,a)].">
      <j1 rule="hyper" parents="5412 11545"/>
    </justification>
  </clause>

  <clause id="11548">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y,K(z,u)) = K(z,K(y,x) * K(u,y))
    ]]></literal>
    <justification jstring="[para(7779(a,1),11547(a,1,1))].">
      <j1 rule="para" parents="7779 11547"/>
    </justification>
  </clause>

  <clause id="11549">
    <literal><![CDATA[
      1 / T(K(x,y) * K(y,z),u) = 1 * T(K(y,x) * K(z,y),u)
    ]]></literal>
    <justification jstring="[para(2001(a,1),11546(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2001 11546"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11550">
    <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,11549,a),flip(a)].">
      <j1 rule="hyper" parents="320 2 11549"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11552">
    <literal><![CDATA[
      1 / T(K(x,y) * K(y,z),u) = T(K(z,y) * K(y,x),u)
    ]]></literal>
    <justification jstring="[para(2003(a,1),11550(a,2,1))].">
      <j1 rule="para" parents="2003 11550"/>
    </justification>
  </clause>

  <clause id="11553">
    <literal><![CDATA[
      1 / T(K(x,y) * K(z,x),u) = T(K(y,x) * K(x,z),u)
    ]]></literal>
    <justification jstring="[para(2003(a,2),11552(a,1,2,1))].">
      <j1 rule="para" parents="2003 11552"/>
    </justification>
  </clause>

  <clause id="11554">
    <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(11553(a,1),267(a,1,1)),flip(b)].">
      <j1 rule="para" parents="11553 267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11555">
    <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(9072(a,1),11528(a,2,2))].">
      <j1 rule="para" parents="9072 11528"/>
    </justification>
  </clause>

  <clause id="11556">
    <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,11526,a(flip),b,11555,a),flip(a)].">
      <j1 rule="hyper" parents="320 11526 11555"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11557">
    <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(6946(a,1),11556(a,1,1,2))].">
      <j1 rule="para" parents="6946 11556"/>
    </justification>
  </clause>

  <clause id="11558">
    <literal><![CDATA[
      (x \ 1) * (R(K(y,x),x \ K(x,z),u) * u) = (K(y,x) * (x \ 1)) * u
    ]]></literal>
    <justification jstring="[para(6012(a,1),8851(a,2,1,1))].">
      <j1 rule="para" parents="6012 8851"/>
    </justification>
  </clause>

  <clause id="11559">
    <literal><![CDATA[
      (x \ 1) * (R(K(y,x),x \ K(x,z),u) * u) = (T(x,y) \ 1) * u
    ]]></literal>
    <justification jstring="[para(5131(a,1),11558(a,2,1))].">
      <j1 rule="para" parents="5131 11558"/>
    </justification>
  </clause>

  <clause id="11561">
    <literal><![CDATA[
      (x \ 1) * (R(K(y,x),x \ 1,z) * z) = (T(x,y) \ 1) * z
    ]]></literal>
    <justification jstring="[para(166(a,1),11559(a,1,2,1,2,2))].">
      <j1 rule="para" parents="166 11559"/>
    </justification>
  </clause>

  <clause id="11562">
    <literal><![CDATA[
      (x \ 1) * (K(y,x) * z) = (T(x,y) \ 1) * z
    ]]></literal>
    <justification jstring="[para(10208(a,1),11561(a,1,2,1))].">
      <j1 rule="para" parents="10208 11561"/>
    </justification>
  </clause>

  <clause id="11563">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) \ 1) * z) = L(z,x \ 1,x)
    ]]></literal>
    <justification jstring="[para(11562(a,1),6014(a,1,2))].">
      <j1 rule="para" parents="11562 6014"/>
    </justification>
  </clause>

  <clause id="11565">
    <literal><![CDATA[
      L(x,T(y,z) \ 1,y) = L(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,4533,a(flip),b,11563,a)].">
      <j1 rule="hyper" parents="58 4533 11563"/>
    </justification>
  </clause>

  <clause id="11567">
    <literal><![CDATA[
      L(x,((y \ z) \ z) \ 1,(y \ z) \ z) = L(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,4699,a(flip),b,11565,a)].">
      <j1 rule="hyper" parents="58 4699 11565"/>
    </justification>
  </clause>

  <clause id="11570">
    <literal><![CDATA[
      K(x,L(y,z \ 1,z) \ z) = K(x,((((z \ x) \ x) \ 1) * y) \ 1)
    ]]></literal>
    <justification jstring="[para(11567(a,1),10711(a,1,2,1))].">
      <j1 rule="para" parents="11567 10711"/>
    </justification>
  </clause>

  <clause id="11571">
    <literal><![CDATA[
      K(x,((((y \ x) \ x) \ 1) * z) \ 1) = K(x,((y \ 1) * z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(6490,a,11570,a),flip(a)].">
      <j1 rule="hyper" parents="6490 11570"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11573">
    <literal><![CDATA[
      K(x,((x \ (y \ x)) * z) \ 1) = K(x,((y \ 1) * z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,11401,a(flip),b,11571,a)].">
      <j1 rule="hyper" parents="58 11401 11571"/>
    </justification>
  </clause>

  <clause id="11574">
    <literal><![CDATA[
      K(x,((y \ 1) * z) \ 1) = K(x,((y \ x) * z) \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,11361,a(flip),b,11573,a),flip(a)].">
      <j1 rule="hyper" parents="58 11361 11573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11575">
    <literal><![CDATA[
      K(x,((y \ x) * (y / z)) \ x) = L(K(x,z),y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,6662,a(flip),b,11574,a),flip(a)].">
      <j1 rule="hyper" parents="58 6662 11574"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11576">
    <literal><![CDATA[
      L(K(x,y),z,z \ 1) = L(K(x,y),z,z \ x)
    ]]></literal>
    <justification jstring="[hyper(9336,a,11575,a),flip(a)].">
      <j1 rule="hyper" parents="9336 11575"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11577">
    <literal><![CDATA[
      L(K(x,y),z,z \ x) = K(x,L(y,z,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(10837,a,11576,a),flip(a)].">
      <j1 rule="hyper" parents="10837 11576"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11578">
    <literal><![CDATA[
      K(x,L(y,z,z \ 1)) = K(x,L(y,z,z \ x))
    ]]></literal>
    <justification jstring="[hyper(10837,a,11577,a),flip(a)].">
      <j1 rule="hyper" parents="10837 11577"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11579">
    <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(11577(a,1),10837(a,1))].">
      <j1 rule="para" parents="11577 10837"/>
    </justification>
  </clause>

  <clause id="11580">
    <literal><![CDATA[
      K(x,L(y,z \ x,(z \ x) \ 1)) = K(x,L(y,z \ x,z))
    ]]></literal>
    <justification jstring="[para(11195(a,1),11578(a,2,2))].">
      <j1 rule="para" parents="11195 11578"/>
    </justification>
  </clause>

  <clause id="11581">
    <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,11052,a(flip),b,11580,a),flip(a)].">
      <j1 rule="hyper" parents="58 11052 11580"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11582">
    <literal><![CDATA[
      K((((x \ y) \ 1) * (x \ 1)) \ 1,z) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,11432,a(flip),b,11581,a),flip(a)].">
      <j1 rule="hyper" parents="58 11432 11581"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11583">
    <literal><![CDATA[
      K(((((x \ 1) \ y) \ 1) * x) \ 1,z) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(10949,a,11582,a)].">
      <j1 rule="hyper" parents="10949 11582"/>
    </justification>
  </clause>

  <clause id="11585">
    <literal><![CDATA[
      (1 / (x \ y)) * (x \ T(y,z)) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,6042,a(flip),b,11582,a)].">
      <j1 rule="hyper" parents="58 6042 11582"/>
    </justification>
  </clause>

  <clause id="11587">
    <literal><![CDATA[
      (1 / x) * (y \ T(y * x,z)) = K(y * x,z)
    ]]></literal>
    <justification jstring="[para(4(a,1),11585(a,1,1,2))].">
      <j1 rule="para" parents="4 11585"/>
    </justification>
  </clause>

  <clause id="11588">
    <literal><![CDATA[
      T(x,y) / ((1 / z) \ x) = K(x,y) / z
    ]]></literal>
    <justification jstring="[para(11583(a,1),6914(a,2,1))].">
      <j1 rule="para" parents="11583 6914"/>
    </justification>
  </clause>

  <clause id="11589">
    <literal><![CDATA[
      T(x,y) / ((1 / y) \ x) = 1 / T(y,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,4803,a(flip),b,11588,a),flip(a)].">
      <j1 rule="hyper" parents="320 4803 11588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11590">
    <literal><![CDATA[
      (K(x,y) / z) \ T(x,y) = (1 / z) \ x
    ]]></literal>
    <justification jstring="[hyper(188,a,11588,a)].">
      <j1 rule="hyper" parents="188 11588"/>
    </justification>
  </clause>

  <clause id="11591">
    <literal><![CDATA[
      (1 / (x \ K(y,z))) \ y = x \ T(y,z)
    ]]></literal>
    <justification jstring="[hyper(31,a,180,a,b,11588,a),flip(a)].">
      <j1 rule="hyper" parents="31 180 11588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11593">
    <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(10172(a,1),11589(a,2,2))].">
      <j1 rule="para" parents="10172 11589"/>
    </justification>
  </clause>

  <clause id="11594">
    <literal><![CDATA[
      T(x,y) / ((1 / z) \ x) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) / z = u
    ]]></literal>
    <justification jstring="[para(11590(a,1),330(a,1,2)),flip(b)].">
      <j1 rule="para" parents="11590 330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11595">
    <literal><![CDATA[
      K(x,((y \ 1) * (z \ 1)) \ 1) = 1 / K(z * y,x)
    ]]></literal>
    <justification jstring="[para(11587(a,1),6043(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11587 6043"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11596">
    <literal><![CDATA[
      K(x,((y \ 1) * (z \ 1)) \ 1) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(320,a,4971,a(flip),b,11595,a),flip(a)].">
      <j1 rule="hyper" parents="320 4971 11595"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11597">
    <literal><![CDATA[
      (1 / x) \ K(y,z * x) = x * K(y,(z \ 1) \ x)
    ]]></literal>
    <justification jstring="[para(11596(a,1),6661(a,1,2))].">
      <j1 rule="para" parents="11596 6661"/>
    </justification>
  </clause>

  <clause id="11598">
    <literal><![CDATA[
      x * K(y,((z / x) \ 1) \ x) = (1 / x) \ K(y,z)
    ]]></literal>
    <justification jstring="[para(7(a,1),11597(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7 11597"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11599">
    <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(6652(a,1),11593(a,1,1))].">
      <j1 rule="para" parents="6652 11593"/>
    </justification>
  </clause>

  <clause id="11600">
    <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(9483(a,1),10924(a,1,2))].">
      <j1 rule="para" parents="9483 10924"/>
    </justification>
  </clause>

  <clause id="11601">
    <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(4359(a,1),11600(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4359 11600"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11602">
    <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),11601(a,2,2))].">
      <j1 rule="para" parents="18 11601"/>
    </justification>
  </clause>

  <clause id="11603">
    <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,7564,a(flip),b,11602,a),flip(a)].">
      <j1 rule="hyper" parents="320 7564 11602"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11604">
    <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(10840(a,1),11603(a,2,1))].">
      <j1 rule="para" parents="10840 11603"/>
    </justification>
  </clause>

  <clause id="11605">
    <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,7067,a(flip),b,11604,a),flip(a)].">
      <j1 rule="hyper" parents="320 7067 11604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11606">
    <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(7157(a,1),11605(a,1,2,3))].">
      <j1 rule="para" parents="7157 11605"/>
    </justification>
  </clause>

  <clause id="11607">
    <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(4261(a,1),11606(a,1,2,3))].">
      <j1 rule="para" parents="4261 11606"/>
    </justification>
  </clause>

  <clause id="11608">
    <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,11051,a,b,11607,a)].">
      <j1 rule="hyper" parents="58 11051 11607"/>
    </justification>
  </clause>

  <clause id="11609">
    <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(10794(a,1),11608(a,1,1))].">
      <j1 rule="para" parents="10794 11608"/>
    </justification>
  </clause>

  <clause id="11610">
    <literal><![CDATA[
      L(T(x,L(y,z,u)),y,x) = K(y * x,L(x,z,u)) \ x
    ]]></literal>
    <justification jstring="[para(2890(a,1),11609(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2890 11609"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11611">
    <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,5130,a(flip),b,11610,a),flip(a)].">
      <j1 rule="hyper" parents="320 5130 11610"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11612">
    <literal><![CDATA[
      L(T(x,L(y,z,u)),y,x) = K(x,L(y * x,z,u)) * x
    ]]></literal>
    <justification jstring="[para(10840(a,1),11611(a,2,1))].">
      <j1 rule="para" parents="10840 11611"/>
    </justification>
  </clause>

  <clause id="11613">
    <literal><![CDATA[
      L(T(x,L(y,z,u)),y,x) = T(x,L(y * x,z,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,4770,a,b,11612,a),flip(a)].">
      <j1 rule="hyper" parents="320 4770 11612"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11614">
    <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,10928,a,b,11613,a)].">
      <j1 rule="hyper" parents="58 10928 11613"/>
    </justification>
  </clause>

  <clause id="11615">
    <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),11434(a,2,1,1))].">
      <j1 rule="para" parents="4 11434"/>
    </justification>
  </clause>

  <clause id="11616">
    <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,9474,a(flip),b,11615,a),flip(a)].">
      <j1 rule="hyper" parents="320 9474 11615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11618">
    <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),11616(a,1,1,1))].">
      <j1 rule="para" parents="4 11616"/>
    </justification>
  </clause>

  <clause id="11619">
    <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),11618(a,1,2,2))].">
      <j1 rule="para" parents="4 11618"/>
    </justification>
  </clause>

  <clause id="11620">
    <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(4823(a,1),11619(a,1,2,1,3))].">
      <j1 rule="para" parents="4823 11619"/>
    </justification>
  </clause>

  <clause id="11621">
    <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,5684,a(flip),b,5391,a),flip(a)].">
      <j1 rule="hyper" parents="320 5684 5391"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11622">
    <literal><![CDATA[
      ((x * y) * K(T(z,(1 / y) \ x),x * y)) / y = x * K(z,(x \ (1 / y)) \ 1)
    ]]></literal>
    <justification jstring="[para(4752(a,1),11621(a,1,1))].">
      <j1 rule="para" parents="4752 11621"/>
    </justification>
  </clause>

  <clause id="11623">
    <literal><![CDATA[
      ((x * y) * K(z,x * y)) / y = x * K(z,(x \ (1 / y)) \ 1)
    ]]></literal>
    <justification jstring="[para(7218(a,1),11622(a,1,1,2))].">
      <j1 rule="para" parents="7218 11622"/>
    </justification>
  </clause>

  <clause id="11624">
    <literal><![CDATA[
      ((x * y) * K(z,x * y)) / y = x * K(z,(1 / y) \ x)
    ]]></literal>
    <justification jstring="[para(6108(a,1),11623(a,2,2))].">
      <j1 rule="para" parents="6108 11623"/>
    </justification>
  </clause>

  <clause id="11625">
    <literal><![CDATA[
      ((x * y) * K(z,x * y)) / y = x * K(z,(y \ 1) \ x)
    ]]></literal>
    <justification jstring="[para(5323(a,1),11624(a,2,2))].">
      <j1 rule="para" parents="5323 11624"/>
    </justification>
  </clause>

  <clause id="11626">
    <literal><![CDATA[
      (x * K(y,(z \ 1) \ x)) * z = (x * z) * K(y,x * z)
    ]]></literal>
    <justification jstring="[hyper(133,a,11625,a)].">
      <j1 rule="hyper" parents="133 11625"/>
    </justification>
  </clause>

  <clause id="11627">
    <literal><![CDATA[
      (x \ y) * K(z,(x \ 1) \ (x \ y)) = x \ (y * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(30,a,5697,a(flip),b,11626,a),flip(a)].">
      <j1 rule="hyper" parents="30 5697 11626"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11628">
    <literal><![CDATA[
      (x \ y) \ (x \ (y * K(z,y))) = K(z,(x \ 1) \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(123,a,11627,a)].">
      <j1 rule="hyper" parents="123 11627"/>
    </justification>
  </clause>

  <clause id="11629">
    <literal><![CDATA[
      (x \ K(y,z)) \ (x \ K(y,T(z,u))) = K(u,(x \ 1) \ (x \ K(y,z)))
    ]]></literal>
    <justification jstring="[para(7836(a,1),11628(a,1,2,2))].">
      <j1 rule="para" parents="7836 11628"/>
    </justification>
  </clause>

  <clause id="11630">
    <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(6999(a,1),7000(a,2,2,1,1))].">
      <j1 rule="para" parents="6999 7000"/>
    </justification>
  </clause>

  <clause id="11631">
    <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),11630(a,2,2,1))].">
      <j1 rule="para" parents="75 11630"/>
    </justification>
  </clause>

  <clause id="11633">
    <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,5915,a(flip),b,11631,a),flip(a)].">
      <j1 rule="hyper" parents="320 5915 11631"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11634">
    <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),11633(a,1,1,2,1))].">
      <j1 rule="para" parents="75 11633"/>
    </justification>
  </clause>

  <clause id="11635">
    <literal><![CDATA[
      T(x \ R(x,y,z),R(x,u,w) \ x) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(5915(a,1),11634(a,1,1))].">
      <j1 rule="para" parents="5915 11634"/>
    </justification>
  </clause>

  <clause id="11636">
    <literal><![CDATA[
      ((x \ R(x,y,z)) \ 1) \ 1 = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(6178,a,11635,a)].">
      <j1 rule="hyper" parents="6178 11635"/>
    </justification>
  </clause>

  <clause id="11637">
    <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(11636(a,1),11463(a,1,1,1))].">
      <j1 rule="para" parents="11636 11463"/>
    </justification>
  </clause>

  <clause id="11638">
    <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(791,a,11637,a)].">
      <j1 rule="hyper" parents="791 11637"/>
    </justification>
  </clause>

  <clause id="11639">
    <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),11638(a,1,1,2))].">
      <j1 rule="para" parents="101 11638"/>
    </justification>
  </clause>

  <clause id="11640">
    <literal><![CDATA[
      (((x * (y * z)) \ ((x * y) * z)) \ 1) \ 1 = T(a(x,y,z),x)
    ]]></literal>
    <justification jstring="[para(9(a,2),11639(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 11639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11641">
    <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(7755(a,1),9290(a,2,1))].">
      <j1 rule="para" parents="7755 9290"/>
    </justification>
  </clause>

  <clause id="11642">
    <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,3836,a(flip),b,9361,a),flip(a)].">
      <j1 rule="hyper" parents="58 3836 9361"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11644">
    <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,3641,a(flip),b,11642,a),flip(a)].">
      <j1 rule="hyper" parents="320 3641 11642"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11645">
    <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(2180(a,1),11644(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2180 11644"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11647">
    <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(9986,a,10031,a)].">
      <j1 rule="hyper" parents="9986 10031"/>
    </justification>
  </clause>

  <clause id="11648">
    <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(11069,a,11647,a)].">
      <j1 rule="hyper" parents="11069 11647"/>
    </justification>
  </clause>

  <clause id="11650">
    <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(9959(a,1),11648(a,2,2,2))].">
      <j1 rule="para" parents="9959 11648"/>
    </justification>
  </clause>

  <clause id="11651">
    <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),11650(a,2,2,2,1))].">
      <j1 rule="para" parents="5 11650"/>
    </justification>
  </clause>

  <clause id="11652">
    <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),11651(a,2,2))].">
      <j1 rule="para" parents="4 11651"/>
    </justification>
  </clause>

  <clause id="11654">
    <literal><![CDATA[
      a(T(x,y),z,R(x,u,w)) = a(x,z,R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(320,a,9972,a(flip),b,11652,a),flip(a)].">
      <j1 rule="hyper" parents="320 9972 11652"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11655">
    <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,11070,a(flip),b,11654,a),flip(a)].">
      <j1 rule="hyper" parents="58 11070 11654"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11657">
    <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,7081,a(flip),b,10622,a),flip(a)].">
      <j1 rule="hyper" parents="320 7081 10622"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11659">
    <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(11657(a,2),10917(a,1))].">
      <j1 rule="para" parents="11657 10917"/>
    </justification>
  </clause>

  <clause id="11660">
    <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(8723(a,1),10765(a,1,2,1,1))].">
      <j1 rule="para" parents="8723 10765"/>
    </justification>
  </clause>

  <clause id="11661">
    <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,8520,a(flip),b,11641,a),flip(a)].">
      <j1 rule="hyper" parents="320 8520 11641"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11662">
    <literal><![CDATA[
      K(x,T((y * (x \ z)) \ u,w)) = K(x,T((y * z) \ (u * x),w))
    ]]></literal>
    <justification jstring="[hyper(58,a,10764,a(flip),b,11660,a),flip(a)].">
      <j1 rule="hyper" parents="58 10764 11660"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11663">
    <literal><![CDATA[
      K(x,T((y * z) \ (u * x),y * z)) = K(x,u / (y * (x \ z)))
    ]]></literal>
    <justification jstring="[hyper(9229,a,11662,a),flip(a)].">
      <j1 rule="hyper" parents="9229 11662"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11664">
    <literal><![CDATA[
      K(x,(y * x) / (z * u)) = K(x,y / (z * (x \ u)))
    ]]></literal>
    <justification jstring="[hyper(8060,a,11663,a)].">
      <j1 rule="hyper" parents="8060 11663"/>
    </justification>
  </clause>

  <clause id="11665">
    <literal><![CDATA[
      K(x,y / (z * (x \ u))) = K(x,((z * u) / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(8497,a,11664,a),flip(a)].">
      <j1 rule="hyper" parents="8497 11664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11666">
    <literal><![CDATA[
      R(K(x,((y * z) / (u / w)) \ x),w \ u,w) = K(x,u / ((y * (x \ z)) * w))
    ]]></literal>
    <justification jstring="[para(11665(a,1),10395(a,1,1))].">
      <j1 rule="para" parents="11665 10395"/>
    </justification>
  </clause>

  <clause id="11667">
    <literal><![CDATA[
      K(x,y / ((x \ (z * u)) * w)) = K(x,y / ((z * (x \ u)) * w))
    ]]></literal>
    <justification jstring="[hyper(58,a,10394,a(flip),b,11666,a)].">
      <j1 rule="hyper" parents="58 10394 11666"/>
    </justification>
  </clause>

  <clause id="11668">
    <literal><![CDATA[
      K(x,y / ((z * (x \ u)) * w)) = K(x,(((z * u) * w) / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(11140,a,11667,a),flip(a)].">
      <j1 rule="hyper" parents="11140 11667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11669">
    <literal><![CDATA[
      K(x,(((y * z) * u) / (z * u)) \ x) = R(K(x,y \ x),z,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,7017,a(flip),b,11668,a),flip(a)].">
      <j1 rule="hyper" parents="58 7017 11668"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11670">
    <literal><![CDATA[
      R(K(x,y \ x),z,u) = K(x,R(y,z,u) \ x)
    ]]></literal>
    <justification jstring="[para(15(a,2),11669(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="15 11669"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11671">
    <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),11670(a,2,2,1))].">
      <j1 rule="para" parents="531 11670"/>
    </justification>
  </clause>

  <clause id="11672">
    <literal><![CDATA[
      K(x,R(y \ x,z,u) \ x) = R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(5196(a,1),11670(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5196 11670"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11673">
    <literal><![CDATA[
      K(x,R(y \ 1,z,u) \ x) = R(K(x,x * y),z,u)
    ]]></literal>
    <justification jstring="[para(5422(a,1),11670(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5422 11670"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11674">
    <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(11289(a,1),11670(a,1,1))].">
      <j1 rule="para" parents="11289 11670"/>
    </justification>
  </clause>

  <clause id="11675">
    <literal><![CDATA[
      K(x,R(1 / y,z,u) \ x) = R(K(x,x * y),z,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,5344,a,b,11673,a)].">
      <j1 rule="hyper" parents="58 5344 11673"/>
    </justification>
  </clause>

  <clause id="11676">
    <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(11672(a,1),11674(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11672 11674"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11677">
    <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(5344(a,1),11671(a,1,1))].">
      <j1 rule="para" parents="5344 11671"/>
    </justification>
  </clause>

  <clause id="11678">
    <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),4221(a,1,1,2))].">
      <j1 rule="para" parents="75 4221"/>
    </justification>
  </clause>

  <clause id="11679">
    <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),11678(a,1,1))].">
      <j1 rule="para" parents="20 11678"/>
    </justification>
  </clause>

  <clause id="11680">
    <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(2821(a,1),11679(a,1,1))].">
      <j1 rule="para" parents="2821 11679"/>
    </justification>
  </clause>

  <clause id="11681">
    <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),11680(a,1,2,2,2))].">
      <j1 rule="para" parents="75 11680"/>
    </justification>
  </clause>

  <clause id="11682">
    <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),11681(a,1,2,2))].">
      <j1 rule="para" parents="20 11681"/>
    </justification>
  </clause>

  <clause id="11683">
    <literal><![CDATA[
      ((1 / x) * (y * x)) \ ((1 / x) \ ((1 / x) * (y * x))) = L(y,x,x \ 1) \ (x * y)
    ]]></literal>
    <justification jstring="[para(2821(a,1),11682(a,1,2,2))].">
      <j1 rule="para" parents="2821 11682"/>
    </justification>
  </clause>

  <clause id="11684">
    <literal><![CDATA[
      ((1 / x) * (y * x)) \ (y * x) = L(y,x,x \ 1) \ (x * y)
    ]]></literal>
    <justification jstring="[para(4(a,1),11683(a,1,2))].">
      <j1 rule="para" parents="4 11683"/>
    </justification>
  </clause>

  <clause id="11686">
    <literal><![CDATA[
      1 / R(T(x,y),x \ 1,y * x) = (L(y,x,x \ 1) \ (x * y)) \ 1
    ]]></literal>
    <justification jstring="[para(11684(a,1),4174(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11684 4174"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11687">
    <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,11686,a)].">
      <j1 rule="hyper" parents="188 11686"/>
    </justification>
  </clause>

  <clause id="11688">
    <literal><![CDATA[
      ((x \ 1) * (x * y)) \ (x * y) = R(T(x,y),x \ 1,y * x)
    ]]></literal>
    <justification jstring="[hyper(58,a,2829,a(flip),b,11687,a)].">
      <j1 rule="hyper" parents="58 2829 11687"/>
    </justification>
  </clause>

  <clause id="11689">
    <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(7352(a,1),5971(a,1,3))].">
      <j1 rule="para" parents="7352 5971"/>
    </justification>
  </clause>

  <clause id="11691">
    <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(8820(a,1),8533(a,1,1))].">
      <j1 rule="para" parents="8820 8533"/>
    </justification>
  </clause>

  <clause id="11692">
    <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(9989(a,1),9007(a,2,2))].">
      <j1 rule="para" parents="9989 9007"/>
    </justification>
  </clause>

  <clause id="11693">
    <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(5130(a,1),9264(a,1,1,2,2))].">
      <j1 rule="para" parents="5130 9264"/>
    </justification>
  </clause>

  <clause id="11694">
    <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,7793,a(flip),b,10767,a),flip(a)].">
      <j1 rule="hyper" parents="58 7793 10767"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11695">
    <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(7781,a,11694,a)].">
      <j1 rule="hyper" parents="7781 11694"/>
    </justification>
  </clause>

  <clause id="11697">
    <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(8670(a,1),11695(a,1,2))].">
      <j1 rule="para" parents="8670 11695"/>
    </justification>
  </clause>

  <clause id="11698">
    <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,9305,a(flip),b,11697,a)].">
      <j1 rule="hyper" parents="58 9305 11697"/>
    </justification>
  </clause>

  <clause id="11699">
    <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(9070(a,1),11085(a,1,1,1,2))].">
      <j1 rule="para" parents="9070 11085"/>
    </justification>
  </clause>

  <clause id="11700">
    <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(6800(a,1),11335(a,1,1,2))].">
      <j1 rule="para" parents="6800 11335"/>
    </justification>
  </clause>

  <clause id="11701">
    <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(635(a,1),11700(a,1,1))].">
      <j1 rule="para" parents="635 11700"/>
    </justification>
  </clause>

  <clause id="11702">
    <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),11701(a,1,2)),flip(a)].">
      <j1 rule="para" parents="238 11701"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11703">
    <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,1354,a(flip),b,11702,a),flip(a)].">
      <j1 rule="hyper" parents="320 1354 11702"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11704">
    <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),11703(a,2,3))].">
      <j1 rule="para" parents="22 11703"/>
    </justification>
  </clause>

  <clause id="11705">
    <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,11333,a(flip),b,11704,a)].">
      <j1 rule="hyper" parents="58 11333 11704"/>
    </justification>
  </clause>

  <clause id="11706">
    <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(11337,a,11705,a)].">
      <j1 rule="hyper" parents="11337 11705"/>
    </justification>
  </clause>

  <clause id="11708">
    <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,11655,a(flip),b,11706,a),flip(a)].">
      <j1 rule="hyper" parents="58 11655 11706"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11710">
    <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,11455,a,b,11708,a)].">
      <j1 rule="hyper" parents="58 11455 11708"/>
    </justification>
  </clause>

  <clause id="11711">
    <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(9493,a,11710,a)].">
      <j1 rule="hyper" parents="9493 11710"/>
    </justification>
  </clause>

  <clause id="11712">
    <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(11711(a,1),11402(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11711 11402"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11713">
    <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),11712(a,2,2,2))].">
      <j1 rule="para" parents="17 11712"/>
    </justification>
  </clause>

  <clause id="11714">
    <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(10074(a,1),11713(a,2,2))].">
      <j1 rule="para" parents="10074 11713"/>
    </justification>
  </clause>

  <clause id="11715">
    <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,11311,a(flip),b,11714,a)].">
      <j1 rule="hyper" parents="58 11311 11714"/>
    </justification>
  </clause>

  <clause id="11716">
    <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),11715(a,1,2,3))].">
      <j1 rule="para" parents="372 11715"/>
    </justification>
  </clause>

  <clause id="11717">
    <literal><![CDATA[
      a(R(x,y,z),u,R(x,y,z)) = a(x,u,R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(9545,a,11716,a)].">
      <j1 rule="hyper" parents="9545 11716"/>
    </justification>
  </clause>

  <clause id="11718">
    <literal><![CDATA[
      R(a(x,y,x),x * z,u) = a(x,y,R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(11452,a,11717,a)].">
      <j1 rule="hyper" parents="11452 11717"/>
    </justification>
  </clause>

  <clause id="11719">
    <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,11711,a(flip),b,11717,a),flip(a)].">
      <j1 rule="hyper" parents="58 11711 11717"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11720">
    <literal><![CDATA[
      a(x,y,R(x,x \ z,u)) = R(a(x,y,x),z,u)
    ]]></literal>
    <justification jstring="[para(5(a,1),11718(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5 11718"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11721">
    <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,11720,a(flip),b,9983,a),flip(a)].">
      <j1 rule="hyper" parents="119 11720 9983"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11722">
    <literal><![CDATA[
      R(x,y,R(x,x \ z,u)) = x * R(a(x,y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(119,a,11720,a(flip),b,9972,a),flip(a)].">
      <j1 rule="hyper" parents="119 11720 9972"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11723">
    <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,10226,a(flip),b,11722,a),flip(a)].">
      <j1 rule="hyper" parents="58 10226 11722"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11724">
    <literal><![CDATA[
      a(x,x \ y,R(x,z,u)) * K(x,y) = K(x,R(x,z,u) \ y)
    ]]></literal>
    <justification jstring="[para(11719(a,1),10076(a,1,1))].">
      <j1 rule="para" parents="11719 10076"/>
    </justification>
  </clause>

  <clause id="11725">
    <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,10999,a(flip),b,11724,a)].">
      <j1 rule="hyper" parents="58 10999 11724"/>
    </justification>
  </clause>

  <clause id="11726">
    <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(9367(a,1),11723(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9367 11723"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11727">
    <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,11721,a,b,11726,a),flip(a)].">
      <j1 rule="hyper" parents="320 11721 11726"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11729">
    <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(11727(a,1),11321(a,2,1,1))].">
      <j1 rule="para" parents="11727 11321"/>
    </justification>
  </clause>

  <clause id="11730">
    <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(7078(a,1),11691(a,1,2))].">
      <j1 rule="para" parents="7078 11691"/>
    </justification>
  </clause>

  <clause id="11732">
    <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(10746(a,1),11730(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10746 11730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11733">
    <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,11732,a),flip(a)].">
      <j1 rule="hyper" parents="320 3 11732"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11735">
    <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,10254,a(flip),b,11733,a),flip(a)].">
      <j1 rule="hyper" parents="58 10254 11733"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11736">
    <literal><![CDATA[
      R(T(x,y),z,x) \ T(x,y) = x \ L(x,z,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,7476,a(flip),b,11735,a),flip(a)].">
      <j1 rule="hyper" parents="320 7476 11735"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11737">
    <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(9326(a,1),11692(a,2,2))].">
      <j1 rule="para" parents="9326 11692"/>
    </justification>
  </clause>

  <clause id="11738">
    <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,6722,a(flip),b,11737,a),flip(a)].">
      <j1 rule="hyper" parents="320 6722 11737"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11739">
    <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(7796(a,1),11738(a,2,1))].">
      <j1 rule="para" parents="7796 11738"/>
    </justification>
  </clause>

  <clause id="11740">
    <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(8127(a,1),11739(a,2,2))].">
      <j1 rule="para" parents="8127 11739"/>
    </justification>
  </clause>

  <clause id="11741">
    <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,11532,a(flip),b,11740,a),flip(a)].">
      <j1 rule="hyper" parents="320 11532 11740"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11743">
    <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(9003(a,1),11741(a,1,2))].">
      <j1 rule="para" parents="9003 11741"/>
    </justification>
  </clause>

  <clause id="11745">
    <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(11743(a,1),11414(a,1,2))].">
      <j1 rule="para" parents="11743 11414"/>
    </justification>
  </clause>

  <clause id="11746">
    <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(5102(a,1),11693(a,1,1,2))].">
      <j1 rule="para" parents="5102 11693"/>
    </justification>
  </clause>

  <clause id="11747">
    <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(10270(a,1),11746(a,1,2))].">
      <j1 rule="para" parents="10270 11746"/>
    </justification>
  </clause>

  <clause id="11748">
    <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(9020(a,1),11747(a,1,2))].">
      <j1 rule="para" parents="9020 11747"/>
    </justification>
  </clause>

  <clause id="11750">
    <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(5130(a,1),11748(a,2,2,1,1))].">
      <j1 rule="para" parents="5130 11748"/>
    </justification>
  </clause>

  <clause id="11751">
    <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(7839(a,1),11750(a,2,2,1))].">
      <j1 rule="para" parents="7839 11750"/>
    </justification>
  </clause>

  <clause id="11752">
    <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(7640(a,2),11751(a,2,2))].">
      <j1 rule="para" parents="7640 11751"/>
    </justification>
  </clause>

  <clause id="11753">
    <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),11752(a,2,2,1))].">
      <j1 rule="para" parents="7 11752"/>
    </justification>
  </clause>

  <clause id="11754">
    <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(11753(a,1),5984(a,1,1,2))].">
      <j1 rule="para" parents="11753 5984"/>
    </justification>
  </clause>

  <clause id="11755">
    <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(11548(a,1),11699(a,1,1,1))].">
      <j1 rule="para" parents="11548 11699"/>
    </justification>
  </clause>

  <clause id="11756">
    <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(3585(a,1),6073(a,1,1))].">
      <j1 rule="para" parents="3585 6073"/>
    </justification>
  </clause>

  <clause id="11757">
    <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(3585(a,1),11756(a,1,2,1,1))].">
      <j1 rule="para" parents="3585 11756"/>
    </justification>
  </clause>

  <clause id="11758">
    <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(6053(a,1),11757(a,1,2,1))].">
      <j1 rule="para" parents="6053 11757"/>
    </justification>
  </clause>

  <clause id="11759">
    <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,10699,a(flip),b,11758,a),flip(a)].">
      <j1 rule="hyper" parents="320 10699 11758"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11760">
    <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(11759(a,1),427(a,1,2))].">
      <j1 rule="para" parents="11759 427"/>
    </justification>
  </clause>

  <clause id="11761">
    <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),6809(a,2,2,1,2))].">
      <j1 rule="para" parents="5 6809"/>
    </justification>
  </clause>

  <clause id="11762">
    <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,11761,a),flip(a)].">
      <j1 rule="hyper" parents="320 237 11761"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11763">
    <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),11762(a,1,2))].">
      <j1 rule="para" parents="237 11762"/>
    </justification>
  </clause>

  <clause id="11764">
    <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(5130(a,1),11763(a,1,2,2))].">
      <j1 rule="para" parents="5130 11763"/>
    </justification>
  </clause>

  <clause id="11765">
    <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(5147,a,11764,a),flip(a)].">
      <j1 rule="hyper" parents="5147 11764"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11766">
    <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,3281,a(flip),b,11764,a),flip(a)].">
      <j1 rule="hyper" parents="320 3281 11764"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11767">
    <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(11765(a,2),5148(a,1,2)),flip(b)].">
      <j1 rule="para" parents="11765 5148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11768">
    <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(7031(a,1),11222(a,2,2,1))].">
      <j1 rule="para" parents="7031 11222"/>
    </justification>
  </clause>

  <clause id="11769">
    <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(8992(a,1),11768(a,2,2,1,2))].">
      <j1 rule="para" parents="8992 11768"/>
    </justification>
  </clause>

  <clause id="11770">
    <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(6534(a,1),9896(a,1,1,1))].">
      <j1 rule="para" parents="6534 9896"/>
    </justification>
  </clause>

  <clause id="11771">
    <literal><![CDATA[
      L((x \ y) \ y,T(x,y) \ y,(x \ y) \ y) = T(x,x * (y / T(x,y)))
    ]]></literal>
    <justification jstring="[para(4247(a,1),11770(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4247 11770"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11772">
    <literal><![CDATA[
      L((x \ y) \ y,T(x,y) \ y,(x \ y) \ y) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,7383,a(flip),b,11771,a),flip(a)].">
      <j1 rule="hyper" parents="320 7383 11771"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11774">
    <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,10593,a),flip(a)].">
      <j1 rule="hyper" parents="320 514 10593"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11775">
    <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(2111,a,11774,a)].">
      <j1 rule="hyper" parents="2111 11774"/>
    </justification>
  </clause>

  <clause id="11776">
    <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(5143(a,1),11775(a,1,1,2,1))].">
      <j1 rule="para" parents="5143 11775"/>
    </justification>
  </clause>

  <clause id="11777">
    <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(5559(a,1),11776(a,1,1,2,1))].">
      <j1 rule="para" parents="5559 11776"/>
    </justification>
  </clause>

  <clause id="11778">
    <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(7919(a,1),11777(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7919 11777"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11779">
    <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,4422,a(flip),b,11778,a),flip(a)].">
      <j1 rule="hyper" parents="58 4422 11778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11781">
    <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(11779(a,1),1328(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="11779 1328"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11782">
    <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(5130(a,1),11781(a,1,1))].">
      <j1 rule="para" parents="5130 11781"/>
    </justification>
  </clause>

  <clause id="11783">
    <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(9926(a,1),11782(a,1,1))].">
      <j1 rule="para" parents="9926 11782"/>
    </justification>
  </clause>

  <clause id="11784">
    <literal><![CDATA[
      R(K(x,y),R(T(x,z),u,w),v5) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(332,a,11783,a),flip(a)].">
      <j1 rule="hyper" parents="332 11783"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11787">
    <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,6942,a(flip),b,11784,a)].">
      <j1 rule="hyper" parents="58 6942 11784"/>
    </justification>
  </clause>

  <clause id="11788">
    <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,7263,a(flip),b,11787,a),flip(a)].">
      <j1 rule="hyper" parents="320 7263 11787"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11789">
    <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,7428,a(flip),b,11788,a),flip(a)].">
      <j1 rule="hyper" parents="58 7428 11788"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11790">
    <literal><![CDATA[
      K(x,R(x,y,z) * (u \ 1)) = K(x,u \ R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(8410,a,11789,a),flip(a)].">
      <j1 rule="hyper" parents="8410 11789"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11792">
    <literal><![CDATA[
      K(x,y \ R(T(x,z),u,w)) = K(x,y \ R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,11789,a,b,11790,a)].">
      <j1 rule="hyper" parents="58 11789 11790"/>
    </justification>
  </clause>

  <clause id="11793">
    <literal><![CDATA[
      K(x,R(T(x,y),z,u) / w) = K(x,w \ R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(8291,a,11792,a)].">
      <j1 rule="hyper" parents="8291 11792"/>
    </justification>
  </clause>

  <clause id="11795">
    <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,7081,a(flip),b,10623,a),flip(a)].">
      <j1 rule="hyper" parents="58 7081 10623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11797">
    <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(4969(a,1),11766(a,2,1,2,1))].">
      <j1 rule="para" parents="4969 11766"/>
    </justification>
  </clause>

  <clause id="11798">
    <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(5892(a,1),11797(a,2,1))].">
      <j1 rule="para" parents="5892 11797"/>
    </justification>
  </clause>

  <clause id="11799">
    <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(5750(a,1),11798(a,1,2,2,2,1))].">
      <j1 rule="para" parents="5750 11798"/>
    </justification>
  </clause>

  <clause id="11800">
    <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(11767,a,11799,a)].">
      <j1 rule="hyper" parents="11767 11799"/>
    </justification>
  </clause>

  <clause id="11801">
    <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,10735,a(flip),b,11800,a)].">
      <j1 rule="hyper" parents="58 10735 11800"/>
    </justification>
  </clause>

  <clause id="11802">
    <literal><![CDATA[
      a(x,y,K(z,L(u,w,v5))) = L(a(x,y,K(z,u)),w,v5)
    ]]></literal>
    <justification jstring="[para(10794(a,1),11801(a,1,3))].">
      <j1 rule="para" parents="10794 11801"/>
    </justification>
  </clause>

  <clause id="11803">
    <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,11802,a),flip(a)].">
      <j1 rule="hyper" parents="320 146 11802"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11805">
    <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),11803(a,1,3,2))].">
      <j1 rule="para" parents="298 11803"/>
    </justification>
  </clause>

  <clause id="11806">
    <literal><![CDATA[
      a(x,y,K((z \ u) \ w,v5)) = a(x,y,K(u \ (z * w),v5))
    ]]></literal>
    <justification jstring="[para(10810(a,1),11803(a,1,3)),flip(a)].">
      <j1 rule="para" parents="10810 11803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11807">
    <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(8923(a,1),8929(a,1,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="8923 8929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11808">
    <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),11807(a,2,1,2,1))].">
      <j1 rule="para" parents="4 11807"/>
    </justification>
  </clause>

  <clause id="11810">
    <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(8923(a,1),11808(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8923 11808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11811">
    <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(2007(a,1),11810(a,2,2))].">
      <j1 rule="para" parents="2007 11810"/>
    </justification>
  </clause>

  <clause id="11812">
    <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,9707,a,b,11811,a)].">
      <j1 rule="hyper" parents="58 9707 11811"/>
    </justification>
  </clause>

  <clause id="11813">
    <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,11812,a),flip(a)].">
      <j1 rule="hyper" parents="328 11812"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11814">
    <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(5140(a,1),11812(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5140 11812"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11815">
    <literal><![CDATA[
      x / a(K(y,z),u,u \ 1) = x * a(K(z,y),u,u \ 1)
    ]]></literal>
    <justification jstring="[para(5140(a,1),11814(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5140 11814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11816">
    <literal><![CDATA[
      a(K(x,y),z,z \ 1) \ 1 = a(K(y,x),z,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(3961,a,11815,a)].">
      <j1 rule="hyper" parents="3961 11815"/>
    </justification>
  </clause>

  <clause id="11817">
    <literal><![CDATA[
      K(x,a(K(y,z),u,u \ 1)) = 1
    ]]></literal>
    <justification jstring="[para(11816(a,1),10616(a,1,2))].">
      <j1 rule="para" parents="11816 10616"/>
    </justification>
  </clause>

  <clause id="11818">
    <literal><![CDATA[
      T(x,a(K(y,z),u,u \ 1)) = x
    ]]></literal>
    <justification jstring="[hyper(51,a,11817,a)].">
      <j1 rule="hyper" parents="51 11817"/>
    </justification>
  </clause>

  <clause id="11819">
    <literal><![CDATA[
      T(x,a(K(y,z),u \ 1,u)) = x
    ]]></literal>
    <justification jstring="[para(3694(a,1),11818(a,1,2))].">
      <j1 rule="para" parents="3694 11818"/>
    </justification>
  </clause>

  <clause id="11820">
    <literal><![CDATA[
      T(a(K(x,y),z \ 1,z),u) = a(K(x,y),z \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(49,a,11819,a)].">
      <j1 rule="hyper" parents="49 11819"/>
    </justification>
  </clause>

  <clause id="11821">
    <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,3670,a,b,11820,a),flip(a)].">
      <j1 rule="hyper" parents="320 3670 11820"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11822">
    <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(5145(a,2),11821(a,1,1))].">
      <j1 rule="para" parents="5145 11821"/>
    </justification>
  </clause>

  <clause id="11823">
    <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,9899,a,b,11822,a)].">
      <j1 rule="hyper" parents="58 9899 11822"/>
    </justification>
  </clause>

  <clause id="11824">
    <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,7190,a,b,11823,a)].">
      <j1 rule="hyper" parents="58 7190 11823"/>
    </justification>
  </clause>

  <clause id="11825">
    <literal><![CDATA[
      K(x,K(y,R(z,u \ 1,u))) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(10680,a,11824,a)].">
      <j1 rule="hyper" parents="10680 11824"/>
    </justification>
  </clause>

  <clause id="11826">
    <literal><![CDATA[
      K(x,K(y,R(z,u,u \ 1))) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[para(2613(a,1),11825(a,1,2,2))].">
      <j1 rule="para" parents="2613 11825"/>
    </justification>
  </clause>

  <clause id="11827">
    <literal><![CDATA[
      K(x,K(y,R(z,u,u \ 1))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,7797,a,b,11826,a),flip(a)].">
      <j1 rule="hyper" parents="320 7797 11826"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11828">
    <literal><![CDATA[
      K(x,K(y,R(z,u,u \ K(w,x)))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,11381,a,b,11826,a)].">
      <j1 rule="hyper" parents="58 11381 11826"/>
    </justification>
  </clause>

  <clause id="11829">
    <literal><![CDATA[
      K(x,K(y,z * (u \ 1))) = K(x,K(y,z / u))
    ]]></literal>
    <justification jstring="[para(523(a,1),11827(a,1,2,2))].">
      <j1 rule="para" parents="523 11827"/>
    </justification>
  </clause>

  <clause id="11830">
    <literal><![CDATA[
      T(x,K(y,z * (u \ 1))) = T(x,K(y,z / u))
    ]]></literal>
    <justification jstring="[hyper(118,a,11829,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 11829 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11831">
    <literal><![CDATA[
      K(x,K(y,z / (1 / u))) = K(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[para(75(a,1),11829(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="75 11829"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11832">
    <literal><![CDATA[
      K(x,K(y,z / (u \ 1))) = K(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[para(5312(a,1),11829(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5312 11829"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11833">
    <literal><![CDATA[
      K(x,K(y,z * (1 / u))) = K(x,K(y,z / u))
    ]]></literal>
    <justification jstring="[para(5315(a,2),11829(a,1,2))].">
      <j1 rule="para" parents="5315 11829"/>
    </justification>
  </clause>

  <clause id="11834">
    <literal><![CDATA[
      T(T(x,y),K(y,z / u)) = T(x,T(y,(z * (u \ 1)) \ 1))
    ]]></literal>
    <justification jstring="[hyper(8209,a,11830,a),flip(a)].">
      <j1 rule="hyper" parents="8209 11830"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11835">
    <literal><![CDATA[
      T(x,K(y,z * (x \ 1))) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,8035,a(flip),b,11830,a),flip(a)].">
      <j1 rule="hyper" parents="320 8035 11830"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11836">
    <literal><![CDATA[
      T(x \ 1,K(y,z * x)) = T(x \ 1,K(y,z))
    ]]></literal>
    <justification jstring="[para(5312(a,1),11835(a,1,2))].">
      <j1 rule="para" parents="5312 11835"/>
    </justification>
  </clause>

  <clause id="11837">
    <literal><![CDATA[
      K(x,K(y,(1 / z) / u)) = K(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(8268,a,11831,a)].">
      <j1 rule="hyper" parents="8268 11831"/>
    </justification>
  </clause>

  <clause id="11838">
    <literal><![CDATA[
      K(x,K(y,(z \ 1) / u)) = K(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(8268,a,11832,a)].">
      <j1 rule="hyper" parents="8268 11832"/>
    </justification>
  </clause>

  <clause id="11839">
    <literal><![CDATA[
      K(x,K(y / (z \ 1),u)) = K(x,K(u,y * z))
    ]]></literal>
    <justification jstring="[hyper(7831,a,11832,a)].">
      <j1 rule="hyper" parents="7831 11832"/>
    </justification>
  </clause>

  <clause id="11840">
    <literal><![CDATA[
      K(x,K(T(y,z),z * u)) = K(x,K(y,(u \ 1) \ z))
    ]]></literal>
    <justification jstring="[para(7146(a,1),11832(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7146 11832"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11841">
    <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(11836(a,1),4994(a,1,1))].">
      <j1 rule="para" parents="11836 4994"/>
    </justification>
  </clause>

  <clause id="11842">
    <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(11837(a,1),10879(a,1,3))].">
      <j1 rule="para" parents="11837 10879"/>
    </justification>
  </clause>

  <clause id="11843">
    <literal><![CDATA[
      K(x,K(y,(z \ 1) / (u / z))) = K(x,K(y,u))
    ]]></literal>
    <justification jstring="[para(7(a,1),11838(a,2,2,2))].">
      <j1 rule="para" parents="7 11838"/>
    </justification>
  </clause>

  <clause id="11844">
    <literal><![CDATA[
      K(x,K(y / (z \ 1),u)) = K(x,K(y * z,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,7797,a,b,11839,a),flip(a)].">
      <j1 rule="hyper" parents="320 7797 11839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11845">
    <literal><![CDATA[
      K(x,K(y,(z \ 1) / (u / z))) = K(y,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(7781,a,11843,a)].">
      <j1 rule="hyper" parents="7781 11843"/>
    </justification>
  </clause>

  <clause id="11846">
    <literal><![CDATA[
      K(x,K(y * z,L(u,z \ 1,z))) = K(u,K(x,T(z * y,z)))
    ]]></literal>
    <justification jstring="[hyper(11003,a,11844,a),flip(a)].">
      <j1 rule="hyper" parents="11003 11844"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11847">
    <literal><![CDATA[
      K(x,K(y / (z \ 1),u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(u,y * z)) = w
    ]]></literal>
    <justification jstring="[para(11844(a,2),7831(a,1))].">
      <j1 rule="para" parents="11844 7831"/>
    </justification>
  </clause>

  <clause id="11848">
    <literal><![CDATA[
      K(x,(T(y,z) / u) / (y / u)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,8205,a(flip),b,11845,a)].">
      <j1 rule="hyper" parents="58 8205 11845"/>
    </justification>
  </clause>

  <clause id="11850">
    <literal><![CDATA[
      K(x,K(y,z)) * (z / u) = T(z,K(x,y)) / u
    ]]></literal>
    <justification jstring="[para(11848(a,1),9619(a,1,1))].">
      <j1 rule="para" parents="11848 9619"/>
    </justification>
  </clause>

  <clause id="11851">
    <literal><![CDATA[
      R(K(x,K(y,z)),z / u,u) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[para(11848(a,1),9881(a,1,1))].">
      <j1 rule="para" parents="11848 9881"/>
    </justification>
  </clause>

  <clause id="11852">
    <literal><![CDATA[
      R(K(x,K(y,z)),y / u,u) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(7797(a,1),11851(a,1,1))].">
      <j1 rule="para" parents="7797 11851"/>
    </justification>
  </clause>

  <clause id="11854">
    <literal><![CDATA[
      K(x,K(y,R(z,x / u,u))) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,9071,a(flip),b,11852,a)].">
      <j1 rule="hyper" parents="58 9071 11852"/>
    </justification>
  </clause>

  <clause id="11855">
    <literal><![CDATA[
      K(x,K(y,R(z,u,u \ x))) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[para(72(a,1),11854(a,1,2,2,2))].">
      <j1 rule="para" parents="72 11854"/>
    </justification>
  </clause>

  <clause id="11856">
    <literal><![CDATA[
      K(x,K(y,z)) * (T(z,K(x,y)) / u) = z / u
    ]]></literal>
    <justification jstring="[hyper(7827,a,11850,a)].">
      <j1 rule="hyper" parents="7827 11850"/>
    </justification>
  </clause>

  <clause id="11857">
    <literal><![CDATA[
      T(x,K(y,z)) / (u \ x) = K(y,K(z,x)) * u
    ]]></literal>
    <justification jstring="[para(72(a,1),11850(a,1,2)),flip(a)].">
      <j1 rule="para" parents="72 11850"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11859">
    <literal><![CDATA[
      K(x,K(y,z)) * (T(x,K(z,y)) / u) = x / u
    ]]></literal>
    <justification jstring="[para(7753(a,1),11856(a,1,1))].">
      <j1 rule="para" parents="7753 11856"/>
    </justification>
  </clause>

  <clause id="11860">
    <literal><![CDATA[
      T(x,K(y,z)) / (u \ x) = K(x,K(y,z)) * u
    ]]></literal>
    <justification jstring="[para(7784(a,1),11857(a,2,1))].">
      <j1 rule="para" parents="7784 11857"/>
    </justification>
  </clause>

  <clause id="11861">
    <literal><![CDATA[
      K((T(x,y) / z) / (x / z),u) = K(x,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(9621,a,11859,a)].">
      <j1 rule="hyper" parents="9621 11859"/>
    </justification>
  </clause>

  <clause id="11862">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) \ T(x,K(y,z)) = u \ x
    ]]></literal>
    <justification jstring="[hyper(188,a,11860,a)].">
      <j1 rule="hyper" parents="188 11860"/>
    </justification>
  </clause>

  <clause id="11863">
    <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(11462(a,1),11861(a,1,1,1,1))].">
      <j1 rule="para" parents="11462 11861"/>
    </justification>
  </clause>

  <clause id="11864">
    <literal><![CDATA[
      L(x \ y,x,K(y,K(z,u))) = x \ y
    ]]></literal>
    <justification jstring="[hyper(4855,a,11862,a)].">
      <j1 rule="hyper" parents="4855 11862"/>
    </justification>
  </clause>

  <clause id="11865">
    <literal><![CDATA[
      a(K(x,K(y,z)),u,u \ x) = 1
    ]]></literal>
    <justification jstring="[hyper(48,a,11864,a)].">
      <j1 rule="hyper" parents="48 11864"/>
    </justification>
  </clause>

  <clause id="11866">
    <literal><![CDATA[
      a(K(x * y,K(z,u)),x,y) = 1
    ]]></literal>
    <justification jstring="[para(4(a,1),11865(a,1,3))].">
      <j1 rule="para" parents="4 11865"/>
    </justification>
  </clause>

  <clause id="11867">
    <literal><![CDATA[
      a(K(K(x,y),z),u,u \ z) = 1
    ]]></literal>
    <justification jstring="[para(5621(a,2),11865(a,1,1))].">
      <j1 rule="para" parents="5621 11865"/>
    </justification>
  </clause>

  <clause id="11868">
    <literal><![CDATA[
      a(K(x,K(y,z * u)),z,u) = 1
    ]]></literal>
    <justification jstring="[para(7753(a,1),11866(a,1,1))].">
      <j1 rule="para" parents="7753 11866"/>
    </justification>
  </clause>

  <clause id="11869">
    <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,7805,a,b,11867,a),flip(a)].">
      <j1 rule="hyper" parents="320 7805 11867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11871">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) * (u \ K(w,z)) = K(w,z) * K(z,K(x,y))
    ]]></literal>
    <justification jstring="[para(11828(a,1),10194(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11828 10194"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11872">
    <literal><![CDATA[
      K(x,K(y,T(z * u,z))) = K(x,K(y,(u \ 1) \ z))
    ]]></literal>
    <justification jstring="[para(7160(a,1),11840(a,1,2))].">
      <j1 rule="para" parents="7160 11840"/>
    </justification>
  </clause>

  <clause id="11873">
    <literal><![CDATA[
      T(x,T(y,(z * (u \ 1)) \ 1)) = T(x,T(y,z / u))
    ]]></literal>
    <justification jstring="[hyper(7703,a,11834,a),flip(a)].">
      <j1 rule="hyper" parents="7703 11834"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11874">
    <literal><![CDATA[
      T(x,T(y,z * (u \ 1))) = T(x,T(y,z / u))
    ]]></literal>
    <justification jstring="[hyper(8221,a,11873,a)].">
      <j1 rule="hyper" parents="8221 11873"/>
    </justification>
  </clause>

  <clause id="11875">
    <literal><![CDATA[
      T(x,T(y,z * (u \ 1))) = x * K(x,T(y,z / u))
    ]]></literal>
    <justification jstring="[hyper(320,a,4755,a(flip),b,11874,a),flip(a)].">
      <j1 rule="hyper" parents="320 4755 11874"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11876">
    <literal><![CDATA[
      K(x,T(y,z * (u \ 1))) = K(x,T(y,z / u))
    ]]></literal>
    <justification jstring="[hyper(4837,a,11875,a)].">
      <j1 rule="hyper" parents="4837 11875"/>
    </justification>
  </clause>

  <clause id="11877">
    <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(11876(a,1),11360(a,1,1))].">
      <j1 rule="para" parents="11876 11360"/>
    </justification>
  </clause>

  <clause id="11878">
    <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),11846(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7 11846"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11879">
    <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(11855(a,1),11869(a,2,2))].">
      <j1 rule="para" parents="11855 11869"/>
    </justification>
  </clause>

  <clause id="11880">
    <literal><![CDATA[
      K(x,K(y,T(z * (u / z),z))) = K(x,K(u,L(y,z \ 1,z)))
    ]]></literal>
    <justification jstring="[hyper(7781,a,11878,a)].">
      <j1 rule="hyper" parents="7781 11878"/>
    </justification>
  </clause>

  <clause id="11881">
    <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,11872,a(flip),b,11880,a)].">
      <j1 rule="hyper" parents="58 11872 11880"/>
    </justification>
  </clause>

  <clause id="11882">
    <literal><![CDATA[
      (x / y) \ T(x,K(z,u)) = y * K(z,K(x,L(u,y \ 1,y)))
    ]]></literal>
    <justification jstring="[para(11881(a,1),8827(a,2,2))].">
      <j1 rule="para" parents="11881 8827"/>
    </justification>
  </clause>

  <clause id="11883">
    <literal><![CDATA[
      (x / y) \ T(x,K(z,u)) = y * K(x,K(z,L(u,y \ 1,y)))
    ]]></literal>
    <justification jstring="[para(7779(a,1),11882(a,2,2))].">
      <j1 rule="para" parents="7779 11882"/>
    </justification>
  </clause>

  <clause id="11884">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) * (u \ K(y,z)) = T(K(y,z),x)
    ]]></literal>
    <justification jstring="[hyper(320,a,7790,a(flip),b,11871,a),flip(a)].">
      <j1 rule="hyper" parents="320 7790 11871"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11886">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) * (u \ K(x,y)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(7784(a,2),11884(a,1,1,1))].">
      <j1 rule="para" parents="7784 11884"/>
    </justification>
  </clause>

  <clause id="11887">
    <literal><![CDATA[
      K(x,T(y,z)) / (u \ K(x,y)) = K(x,K(y,z)) * u
    ]]></literal>
    <justification jstring="[hyper(117,a,7158,a,b,11886,a)].">
      <j1 rule="hyper" parents="117 7158 11886"/>
    </justification>
  </clause>

  <clause id="11888">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(x,y) / u) = K(x,T(y,z)) / u
    ]]></literal>
    <justification jstring="[para(75(a,1),11887(a,1,2)),flip(a)].">
      <j1 rule="para" parents="75 11887"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11889">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(x,T(y,z)) / u) = K(x,y) / u
    ]]></literal>
    <justification jstring="[hyper(7827,a,11888,a)].">
      <j1 rule="hyper" parents="7827 11888"/>
    </justification>
  </clause>

  <clause id="11890">
    <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(11889(a,1),6351(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11889 6351"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11891">
    <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(7755(a,2),11890(a,2,2))].">
      <j1 rule="para" parents="7755 11890"/>
    </justification>
  </clause>

  <clause id="11892">
    <literal><![CDATA[
      K(x,(K(y,z) / u) / (u \ 1)) = K(y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(29,a,10245,a,b,11891,a)].">
      <j1 rule="hyper" parents="29 10245 11891"/>
    </justification>
  </clause>

  <clause id="11894">
    <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(7784(a,2),11879(a,2,2))].">
      <j1 rule="para" parents="7784 11879"/>
    </justification>
  </clause>

  <clause id="11895">
    <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(5621(a,1),11894(a,1,1))].">
      <j1 rule="para" parents="5621 11894"/>
    </justification>
  </clause>

  <clause id="11896">
    <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,11527,a(flip),b,11895,a)].">
      <j1 rule="hyper" parents="320 11527 11895"/>
    </justification>
  </clause>

  <clause id="11897">
    <literal><![CDATA[
      K(x,K(y,R(z,u,u \ x)) * K(z,y)) = 1
    ]]></literal>
    <justification jstring="[hyper(320,a,11868,a(flip),b,11896,a),flip(a)].">
      <j1 rule="hyper" parents="320 11868 11896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11898">
    <literal><![CDATA[
      K(x,K(y,z) * K(z,R(y,u,u \ x))) = 1
    ]]></literal>
    <justification jstring="[hyper(58,a,11540,a(flip),b,11897,a)].">
      <j1 rule="hyper" parents="58 11540 11897"/>
    </justification>
  </clause>

  <clause id="11899">
    <literal><![CDATA[
      K(x * y,K(z,u) * K(u,R(z,x,y))) = 1
    ]]></literal>
    <justification jstring="[para(4(a,1),11898(a,1,2,2,2,3))].">
      <j1 rule="para" parents="4 11898"/>
    </justification>
  </clause>

  <clause id="11900">
    <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(7943(a,1),11877(a,1,1,2))].">
      <j1 rule="para" parents="7943 11877"/>
    </justification>
  </clause>

  <clause id="11901">
    <literal><![CDATA[
      K(x,((y \ (z * x)) * (z \ 1)) \ x) = R(K(x,y),z * x,z \ 1)
    ]]></literal>
    <justification jstring="[para(5190(a,1),11900(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5190 11900"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11902">
    <literal><![CDATA[
      K(x,((y \ (z * x)) * (z \ 1)) \ x) = K(R(x,z,z \ 1),y)
    ]]></literal>
    <justification jstring="[hyper(320,a,9234,a(flip),b,11901,a),flip(a)].">
      <j1 rule="hyper" parents="320 9234 11901"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11904">
    <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),11902(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="505 11902"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11905">
    <literal><![CDATA[
      R(K(R(x,y,y \ 1),z),y,x) = K(x,(((z \ y) * x) * (y \ 1)) \ x)
    ]]></literal>
    <justification jstring="[hyper(9246,a,11904,a)].">
      <j1 rule="hyper" parents="9246 11904"/>
    </justification>
  </clause>

  <clause id="11906">
    <literal><![CDATA[
      K(x,(((y \ z) * x) * (z \ 1)) \ x) = K(R(x,z,z \ 1),y)
    ]]></literal>
    <justification jstring="[hyper(7101,a,11905,a)].">
      <j1 rule="hyper" parents="7101 11905"/>
    </justification>
  </clause>

  <clause id="11907">
    <literal><![CDATA[
      K(x,((y \ z) * (z \ 1)) \ (x \ x)) = K(R(x,z,z \ 1),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,11351,a(flip),b,11906,a)].">
      <j1 rule="hyper" parents="58 11351 11906"/>
    </justification>
  </clause>

  <clause id="11909">
    <literal><![CDATA[
      K(x,((y \ z) * (z \ 1)) \ 1) = K(R(x,z,z \ 1),y)
    ]]></literal>
    <justification jstring="[para(61(a,1),11907(a,1,2,2))].">
      <j1 rule="para" parents="61 11907"/>
    </justification>
  </clause>

  <clause id="11910">
    <literal><![CDATA[
      R(K(x,y),z,z \ 1) = K(R(x,z,z \ 1),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,6975,a(flip),b,11909,a)].">
      <j1 rule="hyper" parents="58 6975 11909"/>
    </justification>
  </clause>

  <clause id="11912">
    <literal><![CDATA[
      R(K(x,y),z,z \ 1) \ 1 = K(y,R(x,z,z \ 1))
    ]]></literal>
    <justification jstring="[para(11910(a,2),4969(a,1,1))].">
      <j1 rule="para" parents="11910 4969"/>
    </justification>
  </clause>

  <clause id="11913">
    <literal><![CDATA[
      R(K(x,y),z,z \ 1) = K(x,R(y,z,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(6935,a,11912,a)].">
      <j1 rule="hyper" parents="6935 11912"/>
    </justification>
  </clause>

  <clause id="11914">
    <literal><![CDATA[
      K(x,(y * z) * (z \ 1)) = R(K(x,y),z,z \ 1)
    ]]></literal>
    <justification jstring="[para(261(a,2),11913(a,2,2)),flip(a)].">
      <j1 rule="para" parents="261 11913"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11915">
    <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(5177(a,2),11863(a,1,1))].">
      <j1 rule="para" parents="5177 11863"/>
    </justification>
  </clause>

  <clause id="11916">
    <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(8045,a,11915,a)].">
      <j1 rule="hyper" parents="8045 11915"/>
    </justification>
  </clause>

  <clause id="11917">
    <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(11847,a,11916,a)].">
      <j1 rule="hyper" parents="11847 11916"/>
    </justification>
  </clause>

  <clause id="11918">
    <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),11917(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7 11917"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11919">
    <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(11918(a,1),7774(a,1))].">
      <j1 rule="para" parents="11918 7774"/>
    </justification>
  </clause>

  <clause id="11920">
    <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(3090(a,1),9292(a,2,1,2))].">
      <j1 rule="para" parents="3090 9292"/>
    </justification>
  </clause>

  <clause id="11921">
    <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(442(a,1),11920(a,1,1,2,2))].">
      <j1 rule="para" parents="442 11920"/>
    </justification>
  </clause>

  <clause id="11922">
    <literal><![CDATA[
      K(x * T((y * z) \ z,y),y \ 1) = K(x * R(y \ 1,y,z),y \ 1)
    ]]></literal>
    <justification jstring="[para(2754(a,1),11921(a,1,1,2))].">
      <j1 rule="para" parents="2754 11921"/>
    </justification>
  </clause>

  <clause id="11923">
    <literal><![CDATA[
      K(x * R(y \ 1,y,z),y \ 1) = K(x * ((y * z) \ z),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,3998,a(flip),b,11922,a),flip(a)].">
      <j1 rule="hyper" parents="58 3998 11922"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11924">
    <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(7755(a,1),11841(a,1,2,1,2))].">
      <j1 rule="para" parents="7755 11841"/>
    </justification>
  </clause>

  <clause id="11925">
    <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(8166(a,1),11924(a,1,2,1,2))].">
      <j1 rule="para" parents="8166 11924"/>
    </justification>
  </clause>

  <clause id="11926">
    <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(7788(a,1),11925(a,1,2,1,2))].">
      <j1 rule="para" parents="7788 11925"/>
    </justification>
  </clause>

  <clause id="11927">
    <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(7967(a,1),11926(a,1,2,1,2))].">
      <j1 rule="para" parents="7967 11926"/>
    </justification>
  </clause>

  <clause id="11928">
    <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(4733(a,2),11927(a,1,2,1))].">
      <j1 rule="para" parents="4733 11927"/>
    </justification>
  </clause>

  <clause id="11929">
    <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(5671,a,11928,a)].">
      <j1 rule="hyper" parents="5671 11928"/>
    </justification>
  </clause>

  <clause id="11930">
    <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(8196(a,1),11929(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8196 11929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11931">
    <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(1446(a,1),11930(a,2,2))].">
      <j1 rule="para" parents="1446 11930"/>
    </justification>
  </clause>

  <clause id="11932">
    <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,7826,a(flip),b,11931,a),flip(a)].">
      <j1 rule="hyper" parents="320 7826 11931"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11933">
    <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),6716(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4 6716"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11934">
    <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,7165,a(flip),b,11933,a),flip(a)].">
      <j1 rule="hyper" parents="320 7165 11933"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11936">
    <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,9207,a(flip),b,11934,a),flip(a)].">
      <j1 rule="hyper" parents="320 9207 11934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11937">
    <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(7704,a,11936,a)].">
      <j1 rule="hyper" parents="7704 11936"/>
    </justification>
  </clause>

  <clause id="11938">
    <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,9227,a(flip),b,11937,a)].">
      <j1 rule="hyper" parents="58 9227 11937"/>
    </justification>
  </clause>

  <clause id="11939">
    <literal><![CDATA[
      K(x,T((R(x,y,z) \ u) \ w,w)) = K(x,(R(x,y,z) * w) / u)
    ]]></literal>
    <justification jstring="[hyper(9212,a,11938,a)].">
      <j1 rule="hyper" parents="9212 11938"/>
    </justification>
  </clause>

  <clause id="11940">
    <literal><![CDATA[
      K(x,(R(x,y,z) * u) / w) = K(x,u / (R(x,y,z) \ w))
    ]]></literal>
    <justification jstring="[hyper(8290,a,11939,a),flip(a)].">
      <j1 rule="hyper" parents="8290 11939"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11942">
    <literal><![CDATA[
      K(x,R(x,y,z) / (u / w)) = K(x,w / (R(x,y,z) \ u))
    ]]></literal>
    <justification jstring="[hyper(10045,a,11940,a)].">
      <j1 rule="hyper" parents="10045 11940"/>
    </justification>
  </clause>

  <clause id="11943">
    <literal><![CDATA[
      K(x,y / (R(x,z,u) \ w)) = K(x,(w / y) \ R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(6508,a,11942,a),flip(a)].">
      <j1 rule="hyper" parents="6508 11942"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11944">
    <literal><![CDATA[
      K(x,(y * R(x,z,u)) / w) = K(x,(w / y) \ R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,9061,a,b,11943,a)].">
      <j1 rule="hyper" parents="58 9061 11943"/>
    </justification>
  </clause>

  <clause id="11945">
    <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,11470,a,b,11944,a)].">
      <j1 rule="hyper" parents="58 11470 11944"/>
    </justification>
  </clause>

  <clause id="11946">
    <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),11945(a,2,2,1))].">
      <j1 rule="para" parents="15 11945"/>
    </justification>
  </clause>

  <clause id="11947">
    <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,9257,a(flip),b,11946,a),flip(a)].">
      <j1 rule="hyper" parents="58 9257 11946"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11949">
    <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(5130(a,1),9755(a,1,1,1))].">
      <j1 rule="para" parents="5130 9755"/>
    </justification>
  </clause>

  <clause id="11950">
    <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(7153(a,1),10938(a,1,2,1,1))].">
      <j1 rule="para" parents="7153 10938"/>
    </justification>
  </clause>

  <clause id="11951">
    <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(11080(a,1),11949(a,1,1))].">
      <j1 rule="para" parents="11080 11949"/>
    </justification>
  </clause>

  <clause id="11952">
    <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,6141,a(flip),b,11951,a)].">
      <j1 rule="hyper" parents="58 6141 11951"/>
    </justification>
  </clause>

  <clause id="11954">
    <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,11557,a(flip),b,11952,a)].">
      <j1 rule="hyper" parents="58 11557 11952"/>
    </justification>
  </clause>

  <clause id="11955">
    <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,11536,a(flip),b,11954,a),flip(a)].">
      <j1 rule="hyper" parents="58 11536 11954"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11956">
    <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,11540,a(flip),b,11955,a),flip(a)].">
      <j1 rule="hyper" parents="320 11540 11955"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11957">
    <literal><![CDATA[
      K(a(K(x,y),z,u),((z * u) \ K(y,x)) \ 1) = 1
    ]]></literal>
    <justification jstring="[hyper(320,a,11899,a(flip),b,11956,a),flip(a)].">
      <j1 rule="hyper" parents="320 11899 11956"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11959">
    <literal><![CDATA[
      K(a(K(x,y),z,u),K(x,y) * (z * u)) = 1
    ]]></literal>
    <justification jstring="[hyper(58,a,6141,a(flip),b,11957,a)].">
      <j1 rule="hyper" parents="58 6141 11957"/>
    </justification>
  </clause>

  <clause id="11960">
    <literal><![CDATA[
      1 * (((K(x,y) * z) * u) / (K(x,y) * (z * u))) = a(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(11959(a,1),4999(a,1,1))].">
      <j1 rule="para" parents="11959 4999"/>
    </justification>
  </clause>

  <clause id="11961">
    <literal><![CDATA[
      1 * (K(x,y) * R(K(y,x),z,u)) = a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(11081(a,1),11960(a,1,2))].">
      <j1 rule="para" parents="11081 11960"/>
    </justification>
  </clause>

  <clause id="11962">
    <literal><![CDATA[
      K(x,y) * R(K(y,x),z,u) = a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(120,a,11961,a)].">
      <j1 rule="hyper" parents="120 11961"/>
    </justification>
  </clause>

  <clause id="11963">
    <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(7796(a,1),11961(a,1,2,1))].">
      <j1 rule="para" parents="7796 11961"/>
    </justification>
  </clause>

  <clause id="11964">
    <literal><![CDATA[
      K(x,y) * a(K(x,y),z,u) = R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(5147,a,11962,a)].">
      <j1 rule="hyper" parents="5147 11962"/>
    </justification>
  </clause>

  <clause id="11965">
    <literal><![CDATA[
      R(K(x,y),z,u) * K(y,x) = a(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(2013,a,11962,a)].">
      <j1 rule="hyper" parents="2013 11962"/>
    </justification>
  </clause>

  <clause id="11966">
    <literal><![CDATA[
      K(x \ 1,y) * K(y,R(x,z,u) \ 1) = a(K(y,x \ 1),z,u)
    ]]></literal>
    <justification jstring="[para(6921(a,1),11962(a,1,2))].">
      <j1 rule="para" parents="6921 11962"/>
    </justification>
  </clause>

  <clause id="11967">
    <literal><![CDATA[
      K(x,y) * K(y,R(x,z,u)) = a(K(y,x),z * x,u)
    ]]></literal>
    <justification jstring="[para(9240(a,1),11962(a,1,2))].">
      <j1 rule="para" parents="9240 11962"/>
    </justification>
  </clause>

  <clause id="11968">
    <literal><![CDATA[
      K(x,y) * (R(K(y,x),z,u) * w) = a(K(y,x),z,u) * w
    ]]></literal>
    <justification jstring="[para(11962(a,1),9904(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11962 9904"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11969">
    <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(11962(a,1),11543(a,2,2))].">
      <j1 rule="para" parents="11962 11543"/>
    </justification>
  </clause>

  <clause id="11970">
    <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(11962(a,1),11557(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11962 11557"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11972">
    <literal><![CDATA[
      (x * a(K(y,z),u,w)) * (K(y,z) * R(K(z,y),u,w)) = x
    ]]></literal>
    <justification jstring="[para(11962(a,1),11813(a,1,1,2))].">
      <j1 rule="para" parents="11962 11813"/>
    </justification>
  </clause>

  <clause id="11973">
    <literal><![CDATA[
      a(K(x,y),K(z,y),u) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,10024,a(flip),b,11964,a),flip(a)].">
      <j1 rule="hyper" parents="115 10024 11964"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11974">
    <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(11964(a,1),10192(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11964 10192"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11975">
    <literal><![CDATA[
      L(x,K(y,z),K(u,z)) = x
    ]]></literal>
    <justification jstring="[hyper(47,a,11973,a)].">
      <j1 rule="hyper" parents="47 11973"/>
    </justification>
  </clause>

  <clause id="11976">
    <literal><![CDATA[
      (K(x,y) * K(z,y)) \ u = K(y,z) * (K(y,x) * u)
    ]]></literal>
    <justification jstring="[hyper(58,a,5766,a(flip),b,11975,a)].">
      <j1 rule="hyper" parents="58 5766 11975"/>
    </justification>
  </clause>

  <clause id="11977">
    <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(11965(a,1),9770(a,2,2))].">
      <j1 rule="para" parents="11965 9770"/>
    </justification>
  </clause>

  <clause id="11978">
    <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,9013,a,b,11976,a)].">
      <j1 rule="hyper" parents="58 9013 11976"/>
    </justification>
  </clause>

  <clause id="11979">
    <literal><![CDATA[
      K(x,y) * (a(K(x,y),z,u) * w) = R(K(x,y),z,u) * w
    ]]></literal>
    <justification jstring="[hyper(5147,a,11968,a)].">
      <j1 rule="hyper" parents="5147 11968"/>
    </justification>
  </clause>

  <clause id="11982">
    <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,11518,a(flip),b,11970,a)].">
      <j1 rule="hyper" parents="58 11518 11970"/>
    </justification>
  </clause>

  <clause id="11983">
    <literal><![CDATA[
      (x * a(K(y,z),u,w)) * a(K(z,y),u,w) = x
    ]]></literal>
    <justification jstring="[para(11962(a,1),11972(a,1,2))].">
      <j1 rule="para" parents="11962 11972"/>
    </justification>
  </clause>

  <clause id="11985">
    <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,11983,a)].">
      <j1 rule="hyper" parents="116 106 11983"/>
    </justification>
  </clause>

  <clause id="11986">
    <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,9121,a(flip),b,11979,a)].">
      <j1 rule="hyper" parents="58 9121 11979"/>
    </justification>
  </clause>

  <clause id="11987">
    <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(11982(a,1),11755(a,1,1,1))].">
      <j1 rule="para" parents="11982 11755"/>
    </justification>
  </clause>

  <clause id="11988">
    <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(9071(a,1),11963(a,1,2,2))].">
      <j1 rule="para" parents="9071 11963"/>
    </justification>
  </clause>

  <clause id="11989">
    <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),11978(a,2,2))].">
      <j1 rule="para" parents="3 11978"/>
    </justification>
  </clause>

  <clause id="11990">
    <literal><![CDATA[
      K(K(x,y) * K(x,z),K(z,x) * K(y,x)) = 1
    ]]></literal>
    <justification jstring="[hyper(50,a,11989,a)].">
      <j1 rule="hyper" parents="50 11989"/>
    </justification>
  </clause>

  <clause id="11991">
    <literal><![CDATA[
      K(K(x,y) * K(x,z),(K(x,y) * K(x,z)) \ 1) = 1
    ]]></literal>
    <justification jstring="[para(9012(a,2),11990(a,1,2))].">
      <j1 rule="para" parents="9012 11990"/>
    </justification>
  </clause>

  <clause id="11992">
    <literal><![CDATA[
      K((K(x,y) * K(x,z)) \ 1,K(x,y) * K(x,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,11991,a,b,4973,a),flip(a)].">
      <j1 rule="hyper" parents="115 11991 4973"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11993">
    <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(11992(a,1),3047(a,1,1,2))].">
      <j1 rule="para" parents="11992 3047"/>
    </justification>
  </clause>

  <clause id="11994">
    <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(11548(a,1),11988(a,1,2))].">
      <j1 rule="para" parents="11548 11988"/>
    </justification>
  </clause>

  <clause id="11995">
    <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(9167(a,1),11986(a,1,2))].">
      <j1 rule="para" parents="9167 11986"/>
    </justification>
  </clause>

  <clause id="11996">
    <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(5041,a,11995,a)].">
      <j1 rule="hyper" parents="5041 11995"/>
    </justification>
  </clause>

  <clause id="11997">
    <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,9764,a,b,11996,a),flip(a)].">
      <j1 rule="hyper" parents="320 9764 11996"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11998">
    <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,11977,a(flip),b,11974,a),flip(a)].">
      <j1 rule="hyper" parents="320 11977 11974"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11999">
    <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),11987(a,1,1)),flip(a)].">
      <j1 rule="para" parents="383 11987"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12000">
    <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,9173,a(flip),b,11999,a),flip(a)].">
      <j1 rule="hyper" parents="320 9173 11999"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12001">
    <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(7755(a,1),12000(a,1,2,1,1))].">
      <j1 rule="para" parents="7755 12000"/>
    </justification>
  </clause>

  <clause id="12002">
    <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(9070(a,1),12001(a,1,2,1))].">
      <j1 rule="para" parents="9070 12001"/>
    </justification>
  </clause>

  <clause id="12003">
    <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(4770(a,2),12002(a,1,2))].">
      <j1 rule="para" parents="4770 12002"/>
    </justification>
  </clause>

  <clause id="12004">
    <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,9079,a,b,12003,a)].">
      <j1 rule="hyper" parents="58 9079 12003"/>
    </justification>
  </clause>

  <clause id="12005">
    <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(7786(a,1),12004(a,1,1))].">
      <j1 rule="para" parents="7786 12004"/>
    </justification>
  </clause>

  <clause id="12006">
    <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(11525,a,12005,a)].">
      <j1 rule="hyper" parents="11525 12005"/>
    </justification>
  </clause>

  <clause id="12007">
    <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,11969,a(flip),b,12006,a),flip(a)].">
      <j1 rule="hyper" parents="58 11969 12006"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12008">
    <literal><![CDATA[
      K(a(K(x,y),z,u),w) = K(x,a(K(w,y),z,u))
    ]]></literal>
    <justification jstring="[hyper(29,a,4755,a(flip),b,12007,a),flip(a)].">
      <j1 rule="hyper" parents="29 4755 12007"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12009">
    <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,11982,a,b,12008,a)].">
      <j1 rule="hyper" parents="58 11982 12008"/>
    </justification>
  </clause>

  <clause id="12010">
    <literal><![CDATA[
      1 * K(x,a(K(y,z),u,w)) = a(K(z,K(x,y)),u,w)
    ]]></literal>
    <justification jstring="[para(12009(a,1),11994(a,1,2))].">
      <j1 rule="para" parents="12009 11994"/>
    </justification>
  </clause>

  <clause id="12011">
    <literal><![CDATA[
      a(K(x,K(y,z)),u,w) = K(y,a(K(z,x),u,w))
    ]]></literal>
    <justification jstring="[hyper(120,a,12010,a),flip(a)].">
      <j1 rule="hyper" parents="120 12010"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12012">
    <literal><![CDATA[
      a(K(x,K(y,z)),u,w) = K(a(K(y,x),u,w),z)
    ]]></literal>
    <justification jstring="[hyper(320,a,12008,a,b,12011,a),flip(a)].">
      <j1 rule="hyper" parents="320 12008 12011"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12013">
    <literal><![CDATA[
      a(K(x,K(y,z)),u,w) = K(x,a(K(z,y),u,w))
    ]]></literal>
    <justification jstring="[para(7779(a,1),12011(a,1,1))].">
      <j1 rule="para" parents="7779 12011"/>
    </justification>
  </clause>

  <clause id="12014">
    <literal><![CDATA[
      a(K(x,K(y,z)),u,w) = K(a(K(x,y),u,w),z)
    ]]></literal>
    <justification jstring="[para(7779(a,1),12012(a,1,1))].">
      <j1 rule="para" parents="7779 12012"/>
    </justification>
  </clause>

  <clause id="12015">
    <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),11993(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3 11993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12016">
    <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(9011(a,1),12015(a,2,3))].">
      <j1 rule="para" parents="9011 12015"/>
    </justification>
  </clause>

  <clause id="12017">
    <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(9011(a,1),12016(a,1,1))].">
      <j1 rule="para" parents="9011 12016"/>
    </justification>
  </clause>

  <clause id="12018">
    <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,5791,a(flip),b,5384,a),flip(a)].">
      <j1 rule="hyper" parents="58 5791 5384"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12020">
    <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,5988,a(flip),b,12018,a)].">
      <j1 rule="hyper" parents="58 5988 12018"/>
    </justification>
  </clause>

  <clause id="12021">
    <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,10048,a(flip),b,12020,a)].">
      <j1 rule="hyper" parents="58 10048 12020"/>
    </justification>
  </clause>

  <clause id="12022">
    <literal><![CDATA[
      K((x \ 1) \ (y / (z * y)),z \ 1) = K(x * (y / (z * y)),z \ 1)
    ]]></literal>
    <justification jstring="[para(6(a,1),12021(a,1,2,1))].">
      <j1 rule="para" parents="6 12021"/>
    </justification>
  </clause>

  <clause id="12023">
    <literal><![CDATA[
      K((x \ 1) \ ((y * z) \ z),y \ 1) = K(x * (z / (y * z)),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,8662,a(flip),b,12022,a)].">
      <j1 rule="hyper" parents="58 8662 12022"/>
    </justification>
  </clause>

  <clause id="12024">
    <literal><![CDATA[
      K((x \ 1) \ ((y * z) \ z),y \ 1) = K(x * ((y * z) \ z),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,7574,a(flip),b,12023,a),flip(a)].">
      <j1 rule="hyper" parents="320 7574 12023"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12025">
    <literal><![CDATA[
      K((x \ 1) \ (y \ 1),y \ 1) = K(x * ((y * z) \ z),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,10574,a(flip),b,12024,a)].">
      <j1 rule="hyper" parents="58 10574 12024"/>
    </justification>
  </clause>

  <clause id="12026">
    <literal><![CDATA[
      K(x * ((y * z) \ z),y \ 1) = K(x * (y \ 1),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(7435,a,12025,a),flip(a)].">
      <j1 rule="hyper" parents="7435 12025"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12028">
    <literal><![CDATA[
      K(x * ((y * z) \ z),y \ 1) = K(y \ x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,6543,a(flip),b,12026,a),flip(a)].">
      <j1 rule="hyper" parents="320 6543 12026"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12029">
    <literal><![CDATA[
      K(x * R(y \ 1,y,z),y \ 1) = K(y \ x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,11923,a,b,12028,a)].">
      <j1 rule="hyper" parents="58 11923 12028"/>
    </justification>
  </clause>

  <clause id="12031">
    <literal><![CDATA[
      T(K(x \ y,x \ 1) / x,y) = R(1 / x,y,z / (x * z))
    ]]></literal>
    <justification jstring="[para(12029(a,1),9919(a,1,1,1))].">
      <j1 rule="para" parents="12029 9919"/>
    </justification>
  </clause>

  <clause id="12032">
    <literal><![CDATA[
      R(1 / x,y,z / (x * z)) = R(1 / x,y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,6544,a(flip),b,12031,a),flip(a)].">
      <j1 rule="hyper" parents="58 6544 12031"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12034">
    <literal><![CDATA[
      R(1 / (x / y),z,(x / y) \ 1) = R(1 / (x / y),z,y / x)
    ]]></literal>
    <justification jstring="[para(7(a,1),12032(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="7 12032"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12035">
    <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(12034(a,1),9561(a,2,2))].">
      <j1 rule="para" parents="12034 9561"/>
    </justification>
  </clause>

  <clause id="12036">
    <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,1215,a(flip),b,12035,a),flip(a)].">
      <j1 rule="hyper" parents="320 1215 12035"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12037">
    <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,1705,a(flip),b,12036,a),flip(a)].">
      <j1 rule="hyper" parents="320 1705 12036"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12038">
    <literal><![CDATA[
      T(a(1 / (x / y),z,1 / (x / y)),u) = (x * R(x \ y,z,x \ y)) / y
    ]]></literal>
    <justification jstring="[para(9615(a,1),12037(a,2,1,2))].">
      <j1 rule="para" parents="9615 12037"/>
    </justification>
  </clause>

  <clause id="12039">
    <literal><![CDATA[
      T(a(1 / (x / y),z,1 / (x / y)),u) = a(x \ y,z,x \ y)
    ]]></literal>
    <justification jstring="[hyper(320,a,9564,a(flip),b,12038,a),flip(a)].">
      <j1 rule="hyper" parents="320 9564 12038"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12040">
    <literal><![CDATA[
      T(a(1 / (x / y),z,(x / y) \ 1),u) = a(x \ y,z,x \ y)
    ]]></literal>
    <justification jstring="[para(4048(a,1),12039(a,1,1))].">
      <j1 rule="para" parents="4048 12039"/>
    </justification>
  </clause>

  <clause id="12041">
    <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(6790(a,1),6401(a,2,1))].">
      <j1 rule="para" parents="6790 6401"/>
    </justification>
  </clause>

  <clause id="12042">
    <literal><![CDATA[
      (1 / ((x * y) / x)) \ T(1 / y,(x * y) / x) = (1 / y) * (1 / (1 / ((x * y) / x)))
    ]]></literal>
    <justification jstring="[para(2960(a,1),12041(a,1,2))].">
      <j1 rule="para" parents="2960 12041"/>
    </justification>
  </clause>

  <clause id="12043">
    <literal><![CDATA[
      (1 / x) * (1 / (1 / ((y * x) / y))) = (1 / ((y * x) / y)) \ (x \ 1)
    ]]></literal>
    <justification jstring="[para(5206(a,1),12042(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5206 12042"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12044">
    <literal><![CDATA[
      (1 / x) * (1 / (1 / ((y * x) / y))) = (T(x,y) \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(320,a,11469,a(flip),b,12043,a),flip(a)].">
      <j1 rule="hyper" parents="320 11469 12043"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12046">
    <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(5045(a,1),5360(a,1,1))].">
      <j1 rule="para" parents="5045 5360"/>
    </justification>
  </clause>

  <clause id="12047">
    <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(5045(a,1),12046(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="5045 12046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12048">
    <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(4969(a,1),12047(a,2,2,1))].">
      <j1 rule="para" parents="4969 12047"/>
    </justification>
  </clause>

  <clause id="12049">
    <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(6921(a,1),12048(a,2,2))].">
      <j1 rule="para" parents="6921 12048"/>
    </justification>
  </clause>

  <clause id="12050">
    <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(4746(a,1),12049(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4746 12049"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12051">
    <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(6921(a,1),12050(a,2,1,2))].">
      <j1 rule="para" parents="6921 12050"/>
    </justification>
  </clause>

  <clause id="12052">
    <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,11966,a(flip),b,12051,a),flip(a)].">
      <j1 rule="hyper" parents="58 11966 12051"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12053">
    <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),2249(a,1,2,1))].">
      <j1 rule="para" parents="7 2249"/>
    </justification>
  </clause>

  <clause id="12054">
    <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),12053(a,1,2))].">
      <j1 rule="para" parents="69 12053"/>
    </justification>
  </clause>

  <clause id="12056">
    <literal><![CDATA[
      (x / (x * L(x \ 1,y,z))) / x = 1 / (x * L(x \ 1,y,z))
    ]]></literal>
    <justification jstring="[hyper(343,a,12054,a),flip(a)].">
      <j1 rule="hyper" parents="343 12054"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12059">
    <literal><![CDATA[
      (L(1 / x,y,z) \ 1) / x = 1 / (x * L(x \ 1,y,z))
    ]]></literal>
    <justification jstring="[para(3230(a,1),12056(a,1,1))].">
      <j1 rule="para" parents="3230 12056"/>
    </justification>
  </clause>

  <clause id="12060">
    <literal><![CDATA[
      1 / (x * L(x \ 1,y,z)) = x \ (L(1 / x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,6056,a(flip),b,12059,a),flip(a)].">
      <j1 rule="hyper" parents="58 6056 12059"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12061">
    <literal><![CDATA[
      1 / (x * L(x \ 1,y,z)) = L(x \ 1,y,z) \ (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,3588,a,b,12060,a),flip(a)].">
      <j1 rule="hyper" parents="320 3588 12060"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12062">
    <literal><![CDATA[
      1 / ((x \ 1) * L((x \ 1) \ 1,y,z)) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(320,a,3590,a(flip),b,12061,a),flip(a)].">
      <j1 rule="hyper" parents="320 3590 12061"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12063">
    <literal><![CDATA[
      (1 / (x * L(x \ 1,y,z))) \ (L(x \ 1,y,z) \ 1) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(12061(a,2),6055(a,1,1))].">
      <j1 rule="para" parents="12061 6055"/>
    </justification>
  </clause>

  <clause id="12064">
    <literal><![CDATA[
      1 / (x \ L(x,y,z)) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[para(1193(a,1),12062(a,1,2))].">
      <j1 rule="para" parents="1193 12062"/>
    </justification>
  </clause>

  <clause id="12065">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ 1 = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(188,a,12064,a)].">
      <j1 rule="hyper" parents="188 12064"/>
    </justification>
  </clause>

  <clause id="12066">
    <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(12064(a,1),4743(a,2,1)),flip(a)].">
      <j1 rule="para" parents="12064 4743"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12067">
    <literal><![CDATA[
      1 / (L(x,y,z) \ x) = (L(x,y,z) \ x) \ 1
    ]]></literal>
    <justification jstring="[hyper(320,a,3584,a,b,12065,a)].">
      <j1 rule="hyper" parents="320 3584 12065"/>
    </justification>
  </clause>

  <clause id="12068">
    <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(1931(a,1),12065(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1931 12065"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12069">
    <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(12068(a,1),3518(a,1,1))].">
      <j1 rule="para" parents="12068 3518"/>
    </justification>
  </clause>

  <clause id="12070">
    <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,7797,a,b,12066,a),flip(a)].">
      <j1 rule="hyper" parents="320 7797 12066"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12071">
    <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(12066(a,2),7831(a,1))].">
      <j1 rule="para" parents="12066 7831"/>
    </justification>
  </clause>

  <clause id="12072">
    <literal><![CDATA[
      (((x * y) \ x) \ 1) / ((y \ 1) \ 1) = 1 / (y * ((x * y) \ x))
    ]]></literal>
    <justification jstring="[para(12063(a,1),11599(a,1,2))].">
      <j1 rule="para" parents="12063 11599"/>
    </justification>
  </clause>

  <clause id="12073">
    <literal><![CDATA[
      1 / (x * ((y * x) \ y)) = x \ (1 / ((y * x) \ y))
    ]]></literal>
    <justification jstring="[hyper(58,a,6060,a(flip),b,12072,a),flip(a)].">
      <j1 rule="hyper" parents="58 6060 12072"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12074">
    <literal><![CDATA[
      (1 / ((x * y) \ x)) / y = 1 / (y * ((x * y) \ x))
    ]]></literal>
    <justification jstring="[hyper(58,a,3842,a(flip),b,12072,a)].">
      <j1 rule="hyper" parents="58 3842 12072"/>
    </justification>
  </clause>

  <clause id="12075">
    <literal><![CDATA[
      (x * ((y * x) \ y)) \ 1 = x \ (1 / ((y * x) \ y))
    ]]></literal>
    <justification jstring="[hyper(10171,a,12073,a)].">
      <j1 rule="hyper" parents="10171 12073"/>
    </justification>
  </clause>

  <clause id="12076">
    <literal><![CDATA[
      (1 / ((x * y) \ x)) / y = (y * ((x * y) \ x)) \ 1
    ]]></literal>
    <justification jstring="[hyper(320,a,10170,a(flip),b,12074,a),flip(a)].">
      <j1 rule="hyper" parents="320 10170 12074"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12077">
    <literal><![CDATA[
      ((x * ((y * x) \ y)) \ 1) \ (1 / ((y * x) \ y)) = x
    ]]></literal>
    <justification jstring="[hyper(188,a,12076,a)].">
      <j1 rule="hyper" parents="188 12076"/>
    </justification>
  </clause>

  <clause id="12078">
    <literal><![CDATA[
      ((x * ((y * x) \ y)) \ 1) * T(x,z) = T(x,z) / (x * ((y * x) \ y))
    ]]></literal>
    <justification jstring="[para(12077(a,1),4640(a,1,2,1))].">
      <j1 rule="para" parents="12077 4640"/>
    </justification>
  </clause>

  <clause id="12079">
    <literal><![CDATA[
      ((x * ((y * x) \ y)) \ 1) * T(x,z) = (x * ((y * x) \ y)) \ T(x,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,10170,a(flip),b,12078,a),flip(a)].">
      <j1 rule="hyper" parents="320 10170 12078"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12080">
    <literal><![CDATA[
      (x \ (1 / ((y * x) \ y))) * T(x,z) = (x * ((y * x) \ y)) \ T(x,z)
    ]]></literal>
    <justification jstring="[para(12075(a,1),12079(a,1,1))].">
      <j1 rule="para" parents="12075 12079"/>
    </justification>
  </clause>

  <clause id="12081">
    <literal><![CDATA[
      T((1 / ((x * y) \ x)) * K(y,z),y) = (y * ((x * y) \ x)) \ T(y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,9769,a,b,12080,a)].">
      <j1 rule="hyper" parents="58 9769 12080"/>
    </justification>
  </clause>

  <clause id="12082">
    <literal><![CDATA[
      T(T(1 / ((x * y) \ x),z),y) = (y * ((x * y) \ x)) \ T(y,z)
    ]]></literal>
    <justification jstring="[para(6265(a,1),12081(a,1,1))].">
      <j1 rule="para" parents="6265 12081"/>
    </justification>
  </clause>

  <clause id="12083">
    <literal><![CDATA[
      (x * ((y * x) \ y)) \ T(x,z) = T(1 / ((y * x) \ y),z)
    ]]></literal>
    <justification jstring="[hyper(58,a,871,a(flip),b,12082,a),flip(a)].">
      <j1 rule="hyper" parents="58 871 12082"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12084">
    <literal><![CDATA[
      1 / ((x * T(y,z)) \ x) = T(1 / ((x * y) \ x),z)
    ]]></literal>
    <justification jstring="[hyper(58,a,10177,a(flip),b,12083,a)].">
      <j1 rule="hyper" parents="58 10177 12083"/>
    </justification>
  </clause>

  <clause id="12085">
    <literal><![CDATA[
      T(1 / ((x * y) \ x),z) \ 1 = (x * T(y,z)) \ x
    ]]></literal>
    <justification jstring="[hyper(188,a,12084,a)].">
      <j1 rule="hyper" parents="188 12084"/>
    </justification>
  </clause>

  <clause id="12086">
    <literal><![CDATA[
      T(((x * y) \ x) \ 1,z) = ((x * T(y,z)) \ x) \ 1
    ]]></literal>
    <justification jstring="[para(12085(a,1),2165(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12085 2165"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12087">
    <literal><![CDATA[
      K(x,T(((y * z) \ y) \ 1,u) \ x) = K(x,1 \ (((y * T(z,u)) \ y) * x))
    ]]></literal>
    <justification jstring="[para(12086(a,2),6589(a,1,2,1))].">
      <j1 rule="para" parents="12086 6589"/>
    </justification>
  </clause>

  <clause id="12088">
    <literal><![CDATA[
      K(x,T((((y * z) \ y) \ 1) \ x,u)) = K(x,1 \ (((y * T(z,u)) \ y) * x))
    ]]></literal>
    <justification jstring="[hyper(8735,a,12087,a)].">
      <j1 rule="hyper" parents="8735 12087"/>
    </justification>
  </clause>

  <clause id="12089">
    <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(7158(a,2),8840(a,2,2))].">
      <j1 rule="para" parents="7158 8840"/>
    </justification>
  </clause>

  <clause id="12090">
    <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(8761(a,1),9969(a,1,1,2))].">
      <j1 rule="para" parents="8761 9969"/>
    </justification>
  </clause>

  <clause id="12092">
    <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(8762(a,1),12090(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8762 12090"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12093">
    <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,5949,a(flip),b,12092,a),flip(a)].">
      <j1 rule="hyper" parents="58 5949 12092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12095">
    <literal><![CDATA[
      L(x,y,L(x,z,u)) = (a(x,y,x) * K(x,w)) \ T(x,w)
    ]]></literal>
    <justification jstring="[para(10541(a,1),12093(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10541 12093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12097">
    <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(7669(a,1),12089(a,2,2))].">
      <j1 rule="para" parents="7669 12089"/>
    </justification>
  </clause>

  <clause id="12098">
    <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,7230,a(flip),b,12097,a),flip(a)].">
      <j1 rule="hyper" parents="320 7230 12097"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12100">
    <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,7464,a(flip),b,12098,a),flip(a)].">
      <j1 rule="hyper" parents="320 7464 12098"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12101">
    <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,7301,a(flip),b,12100,a),flip(a)].">
      <j1 rule="hyper" parents="320 7301 12100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12102">
    <literal><![CDATA[
      (x * K(y,z * x)) / K(y,z) = K(y,z * x) * (K(z,y) * x)
    ]]></literal>
    <justification jstring="[para(7878(a,1),12101(a,1,2))].">
      <j1 rule="para" parents="7878 12101"/>
    </justification>
  </clause>

  <clause id="12103">
    <literal><![CDATA[
      (x * K(y,z * x)) * K(z,y) = K(y,z * x) * (K(z,y) * x)
    ]]></literal>
    <justification jstring="[hyper(6346,a,12102,a)].">
      <j1 rule="hyper" parents="6346 12102"/>
    </justification>
  </clause>

  <clause id="12105">
    <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(12103(a,1),9004(a,1))].">
      <j1 rule="para" parents="12103 9004"/>
    </justification>
  </clause>

  <clause id="12106">
    <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),1937(a,1,1))].">
      <j1 rule="para" parents="145 1937"/>
    </justification>
  </clause>

  <clause id="12107">
    <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,12106,a),flip(a)].">
      <j1 rule="hyper" parents="58 145 12106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12110">
    <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(10846(a,1),6699(a,1,1))].">
      <j1 rule="para" parents="10846 6699"/>
    </justification>
  </clause>

  <clause id="12111">
    <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(6443(a,1),10028(a,1,2,1))].">
      <j1 rule="para" parents="6443 10028"/>
    </justification>
  </clause>

  <clause id="12112">
    <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(3935(a,1),12111(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3935 12111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12113">
    <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(8112(a,1),12112(a,2,2))].">
      <j1 rule="para" parents="8112 12112"/>
    </justification>
  </clause>

  <clause id="12114">
    <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),12113(a,2,2,1))].">
      <j1 rule="para" parents="4 12113"/>
    </justification>
  </clause>

  <clause id="12115">
    <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(11688(a,1),12114(a,1,1,2))].">
      <j1 rule="para" parents="11688 12114"/>
    </justification>
  </clause>

  <clause id="12116">
    <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(8719(a,1),12115(a,1,1))].">
      <j1 rule="para" parents="8719 12115"/>
    </justification>
  </clause>

  <clause id="12118">
    <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(11688(a,1),12116(a,1,2,1))].">
      <j1 rule="para" parents="11688 12116"/>
    </justification>
  </clause>

  <clause id="12119">
    <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(5318(a,1),12118(a,1,2))].">
      <j1 rule="para" parents="5318 12118"/>
    </justification>
  </clause>

  <clause id="12120">
    <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(7545(a,1),12119(a,1,2))].">
      <j1 rule="para" parents="7545 12119"/>
    </justification>
  </clause>

  <clause id="12121">
    <literal><![CDATA[
      (x * y) / (y * T(x,z)) = T(K(z,x),y) * K(x,y)
    ]]></literal>
    <justification jstring="[para(6754(a,1),12120(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6754 12120"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12122">
    <literal><![CDATA[
      (x * y) / (y * T(x,z)) = T(K(z,x) * K(x,y),y)
    ]]></literal>
    <justification jstring="[hyper(320,a,7637,a,b,12121,a),flip(a)].">
      <j1 rule="hyper" parents="320 7637 12121"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12124">
    <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(9023(a,1),12110(a,1,1,2))].">
      <j1 rule="para" parents="9023 12110"/>
    </justification>
  </clause>

  <clause id="12125">
    <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(7779(a,1),12124(a,1,1))].">
      <j1 rule="para" parents="7779 12124"/>
    </justification>
  </clause>

  <clause id="12127">
    <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(7575(a,1),12125(a,1,1,2))].">
      <j1 rule="para" parents="7575 12125"/>
    </justification>
  </clause>

  <clause id="12128">
    <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),12127(a,1,1,2,1,2))].">
      <j1 rule="para" parents="4 12127"/>
    </justification>
  </clause>

  <clause id="12130">
    <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(7784(a,1),12128(a,1,1))].">
      <j1 rule="para" parents="7784 12128"/>
    </justification>
  </clause>

  <clause id="12131">
    <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(7870(a,1),12130(a,1,1))].">
      <j1 rule="para" parents="7870 12130"/>
    </justification>
  </clause>

  <clause id="12132">
    <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(7867(a,1),12131(a,1,1))].">
      <j1 rule="para" parents="7867 12131"/>
    </justification>
  </clause>

  <clause id="12133">
    <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(7779(a,1),12132(a,1,1))].">
      <j1 rule="para" parents="7779 12132"/>
    </justification>
  </clause>

  <clause id="12134">
    <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(9757(a,1),12133(a,1,2))].">
      <j1 rule="para" parents="9757 12133"/>
    </justification>
  </clause>

  <clause id="12135">
    <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(6670,a,12134,a)].">
      <j1 rule="hyper" parents="6670 12134"/>
    </justification>
  </clause>

  <clause id="12136">
    <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(7160(a,1),12135(a,1,2,1))].">
      <j1 rule="para" parents="7160 12135"/>
    </justification>
  </clause>

  <clause id="12137">
    <literal><![CDATA[
      L(K(x * y,T(y,z)),x,z) = K(y * x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(29,a,10550,a(flip),b,12136,a),flip(a)].">
      <j1 rule="hyper" parents="29 10550 12136"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12138">
    <literal><![CDATA[
      K((x / (x * y)) \ z,z) = K(z * y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(10069,a,12137,a)].">
      <j1 rule="hyper" parents="10069 12137"/>
    </justification>
  </clause>

  <clause id="12140">
    <literal><![CDATA[
      K(x * (y \ z),T(x,y)) = K((y / z) \ x,x)
    ]]></literal>
    <justification jstring="[para(5(a,1),12138(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5 12138"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12141">
    <literal><![CDATA[
      K((x \ y) * z,T(z,x)) = K((x / y) \ z,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,5888,a,b,12140,a)].">
      <j1 rule="hyper" parents="58 5888 12140"/>
    </justification>
  </clause>

  <clause id="12142">
    <literal><![CDATA[
      K(x / y,z) * a(z,y \ x,z) = K((y / x) \ z,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,9653,a,b,12141,a)].">
      <j1 rule="hyper" parents="58 9653 12141"/>
    </justification>
  </clause>

  <clause id="12143">
    <literal><![CDATA[
      K(x,y / z) * K((z / y) \ x,x) = a(x,z \ y,x)
    ]]></literal>
    <justification jstring="[hyper(5147,a,12142,a)].">
      <j1 rule="hyper" parents="5147 12142"/>
    </justification>
  </clause>

  <clause id="12144">
    <literal><![CDATA[
      T(x,(y / z) \ x) \ T(x,z / y) = a(x,y \ z,x)
    ]]></literal>
    <justification jstring="[hyper(5672,a,12143,a)].">
      <j1 rule="hyper" parents="5672 12143"/>
    </justification>
  </clause>

  <clause id="12145">
    <literal><![CDATA[
      T(x,(y / z) \ x) \ T(x,(y / z) \ 1) = a(x,y \ z,x)
    ]]></literal>
    <justification jstring="[para(4456(a,2),12144(a,1,2))].">
      <j1 rule="para" parents="4456 12144"/>
    </justification>
  </clause>

  <clause id="12146">
    <literal><![CDATA[
      T(x,(y / z) \ x) \ ((x \ ((y / z) \ x)) \ ((y / z) \ x)) = a(x,y \ z,x)
    ]]></literal>
    <justification jstring="[para(4179(a,2),12145(a,1,2))].">
      <j1 rule="para" parents="4179 12145"/>
    </justification>
  </clause>

  <clause id="12147">
    <literal><![CDATA[
      a(x,(y / z) \ 1,x) = a(x,y \ z,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,8987,a(flip),b,12146,a)].">
      <j1 rule="hyper" parents="58 8987 12146"/>
    </justification>
  </clause>

  <clause id="12148">
    <literal><![CDATA[
      a(x,(y * z) \ z,x) = a(x,y \ 1,x)
    ]]></literal>
    <justification jstring="[para(6(a,1),12147(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6 12147"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12150">
    <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(8815(a,1),6019(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8815 6019"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12151">
    <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,7604,a,b,12150,a),flip(a)].">
      <j1 rule="hyper" parents="320 7604 12150"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12153">
    <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(4781(a,1),12151(a,2,1))].">
      <j1 rule="para" parents="4781 12151"/>
    </justification>
  </clause>

  <clause id="12154">
    <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,9810,a(flip),b,12153,a),flip(a)].">
      <j1 rule="hyper" parents="320 9810 12153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12155">
    <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(4315(a,2),12154(a,1,2))].">
      <j1 rule="para" parents="4315 12154"/>
    </justification>
  </clause>

  <clause id="12156">
    <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(8811(a,1),12155(a,1,2,1))].">
      <j1 rule="para" parents="8811 12155"/>
    </justification>
  </clause>

  <clause id="12157">
    <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(4307(a,2),12156(a,1,2,1))].">
      <j1 rule="para" parents="4307 12156"/>
    </justification>
  </clause>

  <clause id="12159">
    <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(8815(a,1),6020(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8815 6020"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12160">
    <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,7604,a,b,12159,a),flip(a)].">
      <j1 rule="hyper" parents="320 7604 12159"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12162">
    <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(4781(a,1),12160(a,2,1))].">
      <j1 rule="para" parents="4781 12160"/>
    </justification>
  </clause>

  <clause id="12163">
    <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(8961(a,1),8989(a,1,2))].">
      <j1 rule="para" parents="8961 8989"/>
    </justification>
  </clause>

  <clause id="12164">
    <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(8643(a,1),11494(a,1,1,1))].">
      <j1 rule="para" parents="8643 11494"/>
    </justification>
  </clause>

  <clause id="12165">
    <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(5613(a,1),11495(a,1,1,1))].">
      <j1 rule="para" parents="5613 11495"/>
    </justification>
  </clause>

  <clause id="12166">
    <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),12163(a,1,3)),flip(a)].">
      <j1 rule="para" parents="212 12163"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12167">
    <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,10555,a(flip),b,12166,a),flip(a)].">
      <j1 rule="hyper" parents="320 10555 12166"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12169">
    <literal><![CDATA[
      (K(x,y) * a(x,z,x)) \ u = R(T(x,y),z,x) \ (x * u)
    ]]></literal>
    <justification jstring="[hyper(58,a,4552,a(flip),b,12167,a),flip(a)].">
      <j1 rule="hyper" parents="58 4552 12167"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12170">
    <literal><![CDATA[
      (K(x,y) * a(x,z,x)) \ u = x * (R(T(x,y),z,x) \ u)
    ]]></literal>
    <justification jstring="[hyper(320,a,1914,a(flip),b,12169,a),flip(a)].">
      <j1 rule="hyper" parents="320 1914 12169"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12171">
    <literal><![CDATA[
      (a(x,y,x) * K(x,z)) \ u = x * (R(T(x,z),y,x) \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,9544,a,b,12170,a)].">
      <j1 rule="hyper" parents="58 9544 12170"/>
    </justification>
  </clause>

  <clause id="12172">
    <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,12095,a,b,12171,a)].">
      <j1 rule="hyper" parents="58 12095 12171"/>
    </justification>
  </clause>

  <clause id="12173">
    <literal><![CDATA[
      L(x,y,L(x,z,u)) = x * (x \ L(x,y,x))
    ]]></literal>
    <justification jstring="[para(11736(a,1),12172(a,2,2))].">
      <j1 rule="para" parents="11736 12172"/>
    </justification>
  </clause>

  <clause id="12174">
    <literal><![CDATA[
      L(x,y,L(x,z,u)) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,5,a(flip),b,12173,a),flip(a)].">
      <j1 rule="hyper" parents="320 5 12173"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12176">
    <literal><![CDATA[
      L(L(x,y,z),u,L(x,w,v5)) = L(L(x,u,x),y,z)
    ]]></literal>
    <justification jstring="[para(12174(a,1),25(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12174 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12177">
    <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(12176(a,1),10019(a,1,1,2))].">
      <j1 rule="para" parents="12176 10019"/>
    </justification>
  </clause>

  <clause id="12178">
    <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(11492(a,1),12165(a,1,1))].">
      <j1 rule="para" parents="11492 12165"/>
    </justification>
  </clause>

  <clause id="12179">
    <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(11492(a,1),12178(a,1,2,1))].">
      <j1 rule="para" parents="11492 12178"/>
    </justification>
  </clause>

  <clause id="12180">
    <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(5613(a,1),12179(a,1,2,2,2))].">
      <j1 rule="para" parents="5613 12179"/>
    </justification>
  </clause>

  <clause id="12181">
    <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(10588(a,1),10589(a,2,2,1,1))].">
      <j1 rule="para" parents="10588 10589"/>
    </justification>
  </clause>

  <clause id="12182">
    <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,1697,a(flip),b,12181,a),flip(a)].">
      <j1 rule="hyper" parents="320 1697 12181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12183">
    <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(2045(a,1),12182(a,2,2))].">
      <j1 rule="para" parents="2045 12182"/>
    </justification>
  </clause>

  <clause id="12184">
    <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(916(a,1),12183(a,2,2,1))].">
      <j1 rule="para" parents="916 12183"/>
    </justification>
  </clause>

  <clause id="12185">
    <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(1207(a,1),12184(a,2,2,1,2))].">
      <j1 rule="para" parents="1207 12184"/>
    </justification>
  </clause>

  <clause id="12186">
    <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(1697(a,1),12185(a,1,1))].">
      <j1 rule="para" parents="1697 12185"/>
    </justification>
  </clause>

  <clause id="12187">
    <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,9341,a(flip),b,9616,a),flip(a)].">
      <j1 rule="hyper" parents="320 9341 9616"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12188">
    <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,7784,a(flip),b,12187,a),flip(a)].">
      <j1 rule="hyper" parents="320 7784 12187"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12190">
    <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(2673(a,1),9509(a,1,1,1,2))].">
      <j1 rule="para" parents="2673 9509"/>
    </justification>
  </clause>

  <clause id="12191">
    <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,11082,a),flip(a)].">
      <j1 rule="hyper" parents="320 4 11082"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12193">
    <literal><![CDATA[
      L(x,K(y,z),K(u,y) * R(K(y,u),w,v5)) = x
    ]]></literal>
    <justification jstring="[para(11080(a,1),12191(a,1,3))].">
      <j1 rule="para" parents="11080 12191"/>
    </justification>
  </clause>

  <clause id="12195">
    <literal><![CDATA[
      L(x,K(y,z),a(K(y,u),w,v5)) = x
    ]]></literal>
    <justification jstring="[para(11962(a,1),12193(a,1,3))].">
      <j1 rule="para" parents="11962 12193"/>
    </justification>
  </clause>

  <clause id="12196">
    <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(1338,a,12195,a),flip(a)].">
      <j1 rule="hyper" parents="1338 12195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12197">
    <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,11998,a(flip),b,12196,a),flip(a)].">
      <j1 rule="hyper" parents="58 11998 12196"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12198">
    <literal><![CDATA[
      a(K(x,T(y,z)),u,w) * z = z * a(K(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(5133(a,1),12197(a,1,2))].">
      <j1 rule="para" parents="5133 12197"/>
    </justification>
  </clause>

  <clause id="12199">
    <literal><![CDATA[
      x * a(K(y,T(z,x)),u,w) = a(K(y,z),u,w) * x
    ]]></literal>
    <justification jstring="[para(7883(a,1),12198(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7883 12198"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12200">
    <literal><![CDATA[
      a(K(x,T(y,z)),u,w) = T(a(K(x,y),u,w),z)
    ]]></literal>
    <justification jstring="[hyper(240,a,12199,a),flip(a)].">
      <j1 rule="hyper" parents="240 12199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12201">
    <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(10794(a,1),11754(a,1,2,2))].">
      <j1 rule="para" parents="10794 11754"/>
    </justification>
  </clause>

  <clause id="12203">
    <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(3771(a,1),12190(a,1,1,1))].">
      <j1 rule="para" parents="3771 12190"/>
    </justification>
  </clause>

  <clause id="12204">
    <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),12203(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="104 12203"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12208">
    <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(2673(a,1),12204(a,2,1,3,2))].">
      <j1 rule="para" parents="2673 12204"/>
    </justification>
  </clause>

  <clause id="12209">
    <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),12208(a,2,1,3))].">
      <j1 rule="para" parents="4 12208"/>
    </justification>
  </clause>

  <clause id="12213">
    <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(3410(a,1),12209(a,2,1))].">
      <j1 rule="para" parents="3410 12209"/>
    </justification>
  </clause>

  <clause id="12214">
    <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),12213(a,1,1,1,1,2))].">
      <j1 rule="para" parents="72 12213"/>
    </justification>
  </clause>

  <clause id="12216">
    <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(2673(a,1),12214(a,1,1,2))].">
      <j1 rule="para" parents="2673 12214"/>
    </justification>
  </clause>

  <clause id="12217">
    <literal><![CDATA[
      K(((x \ y) * (y \ x)) \ y,z) = K(R(y,y \ x,x \ y),z)
    ]]></literal>
    <justification jstring="[hyper(58,a,4006,a(flip),b,12216,a)].">
      <j1 rule="hyper" parents="58 4006 12216"/>
    </justification>
  </clause>

  <clause id="12219">
    <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),12217(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="17 12217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12220">
    <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(10174(a,1),12219(a,2,1,1))].">
      <j1 rule="para" parents="10174 12219"/>
    </justification>
  </clause>

  <clause id="12221">
    <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,7260,a(flip),b,12220,a),flip(a)].">
      <j1 rule="hyper" parents="320 7260 12220"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12222">
    <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),12221(a,1,1,3))].">
      <j1 rule="para" parents="17 12221"/>
    </justification>
  </clause>

  <clause id="12223">
    <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(7160(a,1),12222(a,2,1))].">
      <j1 rule="para" parents="7160 12222"/>
    </justification>
  </clause>

  <clause id="12224">
    <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,6745,a(flip),b,12223,a)].">
      <j1 rule="hyper" parents="58 6745 12223"/>
    </justification>
  </clause>

  <clause id="12225">
    <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(12224(a,1),6536(a,2,2))].">
      <j1 rule="para" parents="12224 6536"/>
    </justification>
  </clause>

  <clause id="12226">
    <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,12225,a),flip(a)].">
      <j1 rule="hyper" parents="320 90 12225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12227">
    <literal><![CDATA[
      (K(x * y,z) * ((x * y) / x)) * x = x * (K(y * x,z) * y)
    ]]></literal>
    <justification jstring="[hyper(320,a,7301,a(flip),b,12226,a),flip(a)].">
      <j1 rule="hyper" parents="320 7301 12226"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12228">
    <literal><![CDATA[
      (K(x * y,z) * y) * T(x,y) = x * (K(y * x,z) * y)
    ]]></literal>
    <justification jstring="[hyper(6491,a,12227,a)].">
      <j1 rule="hyper" parents="6491 12227"/>
    </justification>
  </clause>

  <clause id="12229">
    <literal><![CDATA[
      K(x * y,z) * x = x * K(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(11274,a,12228,a),flip(a)].">
      <j1 rule="hyper" parents="11274 12228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12230">
    <literal><![CDATA[
      K(x * y,T(z,y)) = K(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(7983,a,12229,a),flip(a)].">
      <j1 rule="hyper" parents="7983 12229"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12231">
    <literal><![CDATA[
      K(x * y,T(z,x)) = K(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(7305,a,12229,a)].">
      <j1 rule="hyper" parents="7305 12229"/>
    </justification>
  </clause>

  <clause id="12232">
    <literal><![CDATA[
      K(x * (y \ 1),T(z,y)) = K((y \ 1) * x,z)
    ]]></literal>
    <justification jstring="[hyper(30,a,8241,a,b,12229,a)].">
      <j1 rule="hyper" parents="30 8241 12229"/>
    </justification>
  </clause>

  <clause id="12233">
    <literal><![CDATA[
      K((x \ 1) * y,T(z,x)) = K(y * (x \ 1),z)
    ]]></literal>
    <justification jstring="[hyper(30,a,8239,a(flip),b,12229,a),flip(a)].">
      <j1 rule="hyper" parents="30 8239 12229"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12235">
    <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(12229(a,1),9870(a,1,2,2))].">
      <j1 rule="para" parents="12229 9870"/>
    </justification>
  </clause>

  <clause id="12236">
    <literal><![CDATA[
      K((x \ y) * x,z) = K(y,T(z,x \ y))
    ]]></literal>
    <justification jstring="[para(5(a,1),12230(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5 12230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12237">
    <literal><![CDATA[
      K(x * (y / x),z) = K(y,T(z,x))
    ]]></literal>
    <justification jstring="[para(7(a,1),12230(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7 12230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12239">
    <literal><![CDATA[
      K(x * y,T(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y * x,z) = u
    ]]></literal>
    <justification jstring="[para(12230(a,1),8007(a,1))].">
      <j1 rule="para" parents="12230 8007"/>
    </justification>
  </clause>

  <clause id="12240">
    <literal><![CDATA[
      K((x * y) * (z / (y * x)),u) = K(z * K(x,y),T(u,x * y))
    ]]></literal>
    <justification jstring="[para(10380(a,1),12230(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10380 12230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12241">
    <literal><![CDATA[
      K(x * y,(z * x) \ x) = K(y * x,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(8432,a,12231,a)].">
      <j1 rule="hyper" parents="8432 12231"/>
    </justification>
  </clause>

  <clause id="12243">
    <literal><![CDATA[
      K((x \ y) * x,z) = K(y,T(z,x))
    ]]></literal>
    <justification jstring="[para(5(a,1),12231(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5 12231"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12244">
    <literal><![CDATA[
      K(x * y,T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y * x,z) = u
    ]]></literal>
    <justification jstring="[para(12231(a,1),8007(a,1))].">
      <j1 rule="para" parents="12231 8007"/>
    </justification>
  </clause>

  <clause id="12245">
    <literal><![CDATA[
      K(T(x,y) * y,z) = K(x * y,T(z,x))
    ]]></literal>
    <justification jstring="[para(4092(a,2),12237(a,1,1))].">
      <j1 rule="para" parents="4092 12237"/>
    </justification>
  </clause>

  <clause id="12246">
    <literal><![CDATA[
      K(x * K((x \ y) \ 1,z),T(u,y)) = K(y * T(x / y,z),u)
    ]]></literal>
    <justification jstring="[para(5542(a,1),12237(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5542 12237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12247">
    <literal><![CDATA[
      K(x * K(y \ x,z),T(u,y)) = K(y * T(x / y,z),u)
    ]]></literal>
    <justification jstring="[para(6279(a,1),12237(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6279 12237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12248">
    <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(12237(a,1),8374(a,1,1,2))].">
      <j1 rule="para" parents="12237 8374"/>
    </justification>
  </clause>

  <clause id="12249">
    <literal><![CDATA[
      T(x,(y \ z) * y) = x / K(z,T(x,y))
    ]]></literal>
    <justification jstring="[para(12243(a,1),4805(a,2,2))].">
      <j1 rule="para" parents="12243 4805"/>
    </justification>
  </clause>

  <clause id="12250">
    <literal><![CDATA[
      K((x \ y) * x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,T(z,x)) = u
    ]]></literal>
    <justification jstring="[para(12236(a,2),8252(a,1))].">
      <j1 rule="para" parents="12236 8252"/>
    </justification>
  </clause>

  <clause id="12251">
    <literal><![CDATA[
      K(T(x,y) * y,z) = K(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,12231,a(flip),b,12245,a),flip(a)].">
      <j1 rule="hyper" parents="320 12231 12245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12252">
    <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,12251,a(flip),b,4896,a)].">
      <j1 rule="hyper" parents="119 12251 4896"/>
    </justification>
  </clause>

  <clause id="12253">
    <literal><![CDATA[
      T(x,(y \ z) * y) = T(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(320,a,7221,a(flip),b,12249,a),flip(a)].">
      <j1 rule="hyper" parents="320 7221 12249"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12254">
    <literal><![CDATA[
      T(x,T(y * z,y)) = T(x,z * y)
    ]]></literal>
    <justification jstring="[para(4(a,1),12253(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4 12253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12255">
    <literal><![CDATA[
      T(x,T(T(y * z,u),y)) = T(x,T(z * y,u))
    ]]></literal>
    <justification jstring="[para(4596(a,1),12253(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4596 12253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12256">
    <literal><![CDATA[
      T(x,T(y * z,y)) = x * K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(320,a,4755,a(flip),b,12254,a),flip(a)].">
      <j1 rule="hyper" parents="320 4755 12254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12257">
    <literal><![CDATA[
      T(T(x,K(y,z)),z * y) = T(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,8041,a,b,12254,a)].">
      <j1 rule="hyper" parents="58 8041 12254"/>
    </justification>
  </clause>

  <clause id="12258">
    <literal><![CDATA[
      K(x / y,y * z) = K(y \ x,z * y)
    ]]></literal>
    <justification jstring="[hyper(8339,a,12256,a)].">
      <j1 rule="hyper" parents="8339 12256"/>
    </justification>
  </clause>

  <clause id="12259">
    <literal><![CDATA[
      K(x,T((y \ 1) * z,y)) = K(x,z * (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(8224,a,12256,a)].">
      <j1 rule="hyper" parents="8224 12256"/>
    </justification>
  </clause>

  <clause id="12260">
    <literal><![CDATA[
      K(T(x,y),y * z) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(7312,a,12256,a)].">
      <j1 rule="hyper" parents="7312 12256"/>
    </justification>
  </clause>

  <clause id="12261">
    <literal><![CDATA[
      T(K(x,y * z),y) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(7309,a,12256,a)].">
      <j1 rule="hyper" parents="7309 12256"/>
    </justification>
  </clause>

  <clause id="12262">
    <literal><![CDATA[
      K(x,T(y * z,y)) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(4837,a,12256,a)].">
      <j1 rule="hyper" parents="4837 12256"/>
    </justification>
  </clause>

  <clause id="12263">
    <literal><![CDATA[
      T(x,T(y * z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z * y) = u
    ]]></literal>
    <justification jstring="[para(12256(a,2),4766(a,1))].">
      <j1 rule="para" parents="12256 4766"/>
    </justification>
  </clause>

  <clause id="12264">
    <literal><![CDATA[
      T(x * y,T(z,x)) \ 1 = (x * y) \ K(z,y * x)
    ]]></literal>
    <justification jstring="[hyper(116,a,12260,a(flip),b,4796,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="116 12260 4796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12265">
    <literal><![CDATA[
      L(x,K(y,z * u),u * z) = x
    ]]></literal>
    <justification jstring="[para(12260(a,1),5465(a,1,2))].">
      <j1 rule="para" parents="12260 5465"/>
    </justification>
  </clause>

  <clause id="12266">
    <literal><![CDATA[
      K(x,K(y,(z \ 1) \ u)) = K(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[para(12260(a,1),11840(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12260 11840"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12267">
    <literal><![CDATA[
      ((x * y) * K(z,y * x)) \ u = K(y * x,z) * ((x * y) \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,5154,a(flip),b,12265,a)].">
      <j1 rule="hyper" parents="58 5154 12265"/>
    </justification>
  </clause>

  <clause id="12268">
    <literal><![CDATA[
      K(x,T(y * z,z)) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(7898,a,12261,a)].">
      <j1 rule="hyper" parents="7898 12261"/>
    </justification>
  </clause>

  <clause id="12269">
    <literal><![CDATA[
      L(x,y,K(z,u * y)) = L(x,y,K(z,y * u))
    ]]></literal>
    <justification jstring="[para(12261(a,1),11193(a,1,3))].">
      <j1 rule="para" parents="12261 11193"/>
    </justification>
  </clause>

  <clause id="12270">
    <literal><![CDATA[
      K(x,T((1 / y) * z,y)) = K(x,z * (1 / y))
    ]]></literal>
    <justification jstring="[hyper(8274,a,12262,a)].">
      <j1 rule="hyper" parents="8274 12262"/>
    </justification>
  </clause>

  <clause id="12271">
    <literal><![CDATA[
      K(x,T(y * (z \ x),z)) = K(x,(z \ x) * y)
    ]]></literal>
    <justification jstring="[hyper(8273,a,12262,a)].">
      <j1 rule="hyper" parents="8273 12262"/>
    </justification>
  </clause>

  <clause id="12272">
    <literal><![CDATA[
      K(x,(y \ z) * y) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(5(a,1),12262(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 12262"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12273">
    <literal><![CDATA[
      K(x,T(y * z,z)) = K(x,T(y,z) * z)
    ]]></literal>
    <justification jstring="[para(105(a,1),12262(a,1,2,1))].">
      <j1 rule="para" parents="105 12262"/>
    </justification>
  </clause>

  <clause id="12274">
    <literal><![CDATA[
      K(x,K(y,z * y)) * K(x,z * y) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(8087,a,12268,a)].">
      <j1 rule="hyper" parents="8087 12268"/>
    </justification>
  </clause>

  <clause id="12275">
    <literal><![CDATA[
      T(x,T(y * z,z)) = T(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(118,a,12268,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 12268 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12276">
    <literal><![CDATA[
      K(x,T(y,z \ y)) = K(x,(z \ y) * z)
    ]]></literal>
    <justification jstring="[para(5(a,1),12268(a,1,2,1))].">
      <j1 rule="para" parents="5 12268"/>
    </justification>
  </clause>

  <clause id="12277">
    <literal><![CDATA[
      K(x,y * (z / y)) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(7(a,1),12268(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7 12268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12278">
    <literal><![CDATA[
      T(K(x,y * z),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z * y) = u
    ]]></literal>
    <justification jstring="[para(12268(a,1),7982(a,1,1))].">
      <j1 rule="para" parents="12268 7982"/>
    </justification>
  </clause>

  <clause id="12279">
    <literal><![CDATA[
      K(x,T(T(y * z,u),y)) = K(x,T(z * y,u))
    ]]></literal>
    <justification jstring="[para(4596(a,1),12272(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4596 12272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12280">
    <literal><![CDATA[
      T(x,T(y * z,z \ 1)) = T(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(8270,a,12275,a)].">
      <j1 rule="hyper" parents="8270 12275"/>
    </justification>
  </clause>

  <clause id="12281">
    <literal><![CDATA[
      T(x,y * (z / y)) = T(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(7(a,1),12275(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7 12275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12282">
    <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(12275(a,1),11950(a,1,2,1,1))].">
      <j1 rule="para" parents="12275 11950"/>
    </justification>
  </clause>

  <clause id="12283">
    <literal><![CDATA[
      K(x,T(y / (z \ 1),z)) = K(x,y / (T(z,y) \ 1))
    ]]></literal>
    <justification jstring="[para(10109(a,2),12277(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10109 12277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12284">
    <literal><![CDATA[
      (x * (y / x)) * T(z,T(y,x)) = z * (x * (y / x))
    ]]></literal>
    <justification jstring="[hyper(119,a,12281,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 12281 17"/>
    </justification>
  </clause>

  <clause id="12285">
    <literal><![CDATA[
      T(x,T(T(y * z,u),z)) = T(x,T(z * y,u))
    ]]></literal>
    <justification jstring="[para(4583(a,1),12281(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4583 12281"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12286">
    <literal><![CDATA[
      T(T(x,y * z),K(y,z)) = T(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(7848,a,12257,a)].">
      <j1 rule="hyper" parents="7848 12257"/>
    </justification>
  </clause>

  <clause id="12287">
    <literal><![CDATA[
      T(K(x,y) * z,x * y) = T(z * K(x,y),y * x)
    ]]></literal>
    <justification jstring="[para(6337(a,1),12257(a,1,1))].">
      <j1 rule="para" parents="6337 12257"/>
    </justification>
  </clause>

  <clause id="12288">
    <literal><![CDATA[
      K(1 / x,x * T(y,z)) = K(x \ 1,T(y * x,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,11267,a,b,12258,a),flip(a)].">
      <j1 rule="hyper" parents="320 11267 12258"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12289">
    <literal><![CDATA[
      K(1 / x,y * x) = K(1 / x,x * y)
    ]]></literal>
    <justification jstring="[hyper(320,a,3312,a,b,12258,a)].">
      <j1 rule="hyper" parents="320 3312 12258"/>
    </justification>
  </clause>

  <clause id="12290">
    <literal><![CDATA[
      K(x,T(y,z) * z) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,12268,a(flip),b,12273,a),flip(a)].">
      <j1 rule="hyper" parents="58 12268 12273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12291">
    <literal><![CDATA[
      T(x,T(y,z) * z) = T(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(118,a,12290,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 12290 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12292">
    <literal><![CDATA[
      K(x,y * (z * K(y,z))) = K(x,z * y)
    ]]></literal>
    <justification jstring="[para(4816(a,1),12290(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4816 12290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12293">
    <literal><![CDATA[
      T(x,T(y \ z,u) * y) = T(x,y * T(z / y,u))
    ]]></literal>
    <justification jstring="[para(246(a,1),12291(a,1,2,1))].">
      <j1 rule="para" parents="246 12291"/>
    </justification>
  </clause>

  <clause id="12294">
    <literal><![CDATA[
      K(x,(y \ z) * y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z,y)) = u
    ]]></literal>
    <justification jstring="[para(12276(a,1),8251(a,1))].">
      <j1 rule="para" parents="12276 8251"/>
    </justification>
  </clause>

  <clause id="12295">
    <literal><![CDATA[
      T(T(x,y * z),K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z * y) = u
    ]]></literal>
    <justification jstring="[para(12286(a,1),5632(a,1,1))].">
      <j1 rule="para" parents="12286 5632"/>
    </justification>
  </clause>

  <clause id="12296">
    <literal><![CDATA[
      x * K(1 / y,z * y) = x * K(1 / y,y * z)
    ]]></literal>
    <justification jstring="[hyper(119,a,12289,a,b,4,a)].">
      <j1 rule="hyper" parents="119 12289 4"/>
    </justification>
  </clause>

  <clause id="12297">
    <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(4750(a,2),12239(a,1,1))].">
      <j1 rule="para" parents="4750 12239"/>
    </justification>
  </clause>

  <clause id="12298">
    <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(6116(a,1),12244(a,1,1))].">
      <j1 rule="para" parents="6116 12244"/>
    </justification>
  </clause>

  <clause id="12299">
    <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(11173(a,1),12250(a,1,1,1))].">
      <j1 rule="para" parents="11173 12250"/>
    </justification>
  </clause>

  <clause id="12300">
    <literal><![CDATA[
      T(T(x,K(y,z)),z * y) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y * z) = u
    ]]></literal>
    <justification jstring="[para(8041(a,2),12263(a,1))].">
      <j1 rule="para" parents="8041 12263"/>
    </justification>
  </clause>

  <clause id="12301">
    <literal><![CDATA[
      K(x,T(y * z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z * y) = u
    ]]></literal>
    <justification jstring="[para(7158(a,2),12278(a,1))].">
      <j1 rule="para" parents="7158 12278"/>
    </justification>
  </clause>

  <clause id="12302">
    <literal><![CDATA[
      K(x,T(y * z,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z * y) = u
    ]]></literal>
    <justification jstring="[para(8232(a,2),12301(a,1))].">
      <j1 rule="para" parents="8232 12301"/>
    </justification>
  </clause>

  <clause id="12303">
    <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(636(a,1),12302(a,1,2,1))].">
      <j1 rule="para" parents="636 12302"/>
    </justification>
  </clause>

  <clause id="12304">
    <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(11182(a,1),12302(a,1,2,1))].">
      <j1 rule="para" parents="11182 12302"/>
    </justification>
  </clause>

  <clause id="12305">
    <literal><![CDATA[
      K(x,T(y,z) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z * y) = u
    ]]></literal>
    <justification jstring="[para(12273(a,1),12302(a,1))].">
      <j1 rule="para" parents="12273 12302"/>
    </justification>
  </clause>

  <clause id="12306">
    <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(12253(a,1),12305(a,1,2,1))].">
      <j1 rule="para" parents="12253 12305"/>
    </justification>
  </clause>

  <clause id="12307">
    <literal><![CDATA[
      K(((x \ y) \ 1) * z,x / y) = K(z * ((x \ y) \ 1),x / y)
    ]]></literal>
    <justification jstring="[hyper(5784,a,12232,a),flip(a)].">
      <j1 rule="hyper" parents="5784 12232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12308">
    <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),12232(a,1,1))].">
      <j1 rule="para" parents="453 12232"/>
    </justification>
  </clause>

  <clause id="12309">
    <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(2024(a,1),12233(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2024 12233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12310">
    <literal><![CDATA[
      T(x,y) * K(y * x,y \ 1) = (x * y) * (x / (y * x))
    ]]></literal>
    <justification jstring="[para(12241(a,1),6781(a,1,2))].">
      <j1 rule="para" parents="12241 6781"/>
    </justification>
  </clause>

  <clause id="12311">
    <literal><![CDATA[
      T(x,T(T(y * z,y),u)) = T(x,T(z * y,u))
    ]]></literal>
    <justification jstring="[para(18(a,1),12255(a,1,2))].">
      <j1 rule="para" parents="18 12255"/>
    </justification>
  </clause>

  <clause id="12312">
    <literal><![CDATA[
      K(x,T((y \ 1) * (z * y),y)) = R(K(x,z),y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,11914,a(flip),b,12259,a),flip(a)].">
      <j1 rule="hyper" parents="320 11914 12259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12313">
    <literal><![CDATA[
      K(x,K(y,z \ (u \ 1))) = K(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(8216,a,12266,a)].">
      <j1 rule="hyper" parents="8216 12266"/>
    </justification>
  </clause>

  <clause id="12314">
    <literal><![CDATA[
      x \ T(x * y,K(z,u)) = y * K(z,K(u,x * y))
    ]]></literal>
    <justification jstring="[para(12266(a,1),7806(a,2,2))].">
      <j1 rule="para" parents="12266 7806"/>
    </justification>
  </clause>

  <clause id="12315">
    <literal><![CDATA[
      K(x \ y,(1 / (y / x)) * z) = K(x \ y,z * (1 / (y / x)))
    ]]></literal>
    <justification jstring="[hyper(8053,a,12270,a)].">
      <j1 rule="hyper" parents="8053 12270"/>
    </justification>
  </clause>

  <clause id="12316">
    <literal><![CDATA[
      K(x,(y \ x) * R(y,z,u)) = K(x,x * (y \ R(y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,9891,a(flip),b,12271,a),flip(a)].">
      <j1 rule="hyper" parents="58 9891 12271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12317">
    <literal><![CDATA[
      K(x / y,T(z * y,u)) = K(y \ x,T(y * z,u))
    ]]></literal>
    <justification jstring="[hyper(7718,a,12279,a),flip(a)].">
      <j1 rule="hyper" parents="7718 12279"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12318">
    <literal><![CDATA[
      K(x,T(y * x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(x * y,z)) = u
    ]]></literal>
    <justification jstring="[para(12279(a,1),4967(a,1))].">
      <j1 rule="para" parents="12279 4967"/>
    </justification>
  </clause>

  <clause id="12319">
    <literal><![CDATA[
      T(x,T(T(y * z,z),u)) = T(x,T(z * y,u))
    ]]></literal>
    <justification jstring="[para(18(a,1),12285(a,1,2))].">
      <j1 rule="para" parents="18 12285"/>
    </justification>
  </clause>

  <clause id="12320">
    <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),12285(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="454 12285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12321">
    <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(8001(a,1),12311(a,1,2,1,1))].">
      <j1 rule="para" parents="8001 12311"/>
    </justification>
  </clause>

  <clause id="12322">
    <literal><![CDATA[
      K(x,K(y \ (z * u),z * u)) = K(x,K(z * u,(z \ y) \ u))
    ]]></literal>
    <justification jstring="[hyper(58,a,8215,a(flip),b,12313,a),flip(a)].">
      <j1 rule="hyper" parents="58 8215 12313"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12323">
    <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),12319(a,1,2,1,1))].">
      <j1 rule="para" parents="453 12319"/>
    </justification>
  </clause>

  <clause id="12324">
    <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(6397(a,2),12319(a,2,2,1))].">
      <j1 rule="para" parents="6397 12319"/>
    </justification>
  </clause>

  <clause id="12325">
    <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(7797(a,1),12300(a,1,1,2))].">
      <j1 rule="para" parents="7797 12300"/>
    </justification>
  </clause>

  <clause id="12326">
    <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(7883(a,1),12300(a,1,1,2))].">
      <j1 rule="para" parents="7883 12300"/>
    </justification>
  </clause>

  <clause id="12327">
    <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(7869(a,1),12300(a,1,1,2))].">
      <j1 rule="para" parents="7869 12300"/>
    </justification>
  </clause>

  <clause id="12328">
    <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,11745,a(flip),b,12264,a),flip(a)].">
      <j1 rule="hyper" parents="320 11745 12264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12329">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,z * y) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(7777(a,1),12274(a,1,1))].">
      <j1 rule="para" parents="7777 12274"/>
    </justification>
  </clause>

  <clause id="12330">
    <literal><![CDATA[
      K(x,y * z) * K(x,K(z,y)) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(5640,a,12329,a)].">
      <j1 rule="hyper" parents="5640 12329"/>
    </justification>
  </clause>

  <clause id="12331">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y,z * x) = K(y,x * z)
    ]]></literal>
    <justification jstring="[para(7779(a,1),12329(a,1,1))].">
      <j1 rule="para" parents="7779 12329"/>
    </justification>
  </clause>

  <clause id="12332">
    <literal><![CDATA[
      K(x,y * z) * K(z,K(y,x)) = K(x,z * y)
    ]]></literal>
    <justification jstring="[para(7784(a,2),12330(a,1,2))].">
      <j1 rule="para" parents="7784 12330"/>
    </justification>
  </clause>

  <clause id="12333">
    <literal><![CDATA[
      K(x,y / (T(z,y) \ 1)) = K(x,(z \ 1) \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,8236,a(flip),b,12283,a),flip(a)].">
      <j1 rule="hyper" parents="58 8236 12283"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12334">
    <literal><![CDATA[
      K(x,(y / z) / (z \ 1)) = K(x,(z \ 1) \ (z \ y))
    ]]></literal>
    <justification jstring="[para(10150(a,1),12333(a,1,2))].">
      <j1 rule="para" parents="10150 12333"/>
    </justification>
  </clause>

  <clause id="12335">
    <literal><![CDATA[
      (x * (y / x)) * z != u * (x * (y / x))
    ]]></literal>
    <literal><![CDATA[
      T(u,T(y,x)) = z
    ]]></literal>
    <justification jstring="[para(12284(a,1),38(a,1)),flip(a)].">
      <j1 rule="para" parents="12284 38"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12336">
    <literal><![CDATA[
      K(T(K(x,y) * z,x * y),u) = K(z * K(x,y),T(u,y * x))
    ]]></literal>
    <justification jstring="[para(12287(a,2),7160(a,1,1))].">
      <j1 rule="para" parents="12287 7160"/>
    </justification>
  </clause>

  <clause id="12337">
    <literal><![CDATA[
      K(1 / x,T(y * x,z)) = K(1 / x,x * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,3312,a,b,12288,a)].">
      <j1 rule="hyper" parents="320 3312 12288"/>
    </justification>
  </clause>

  <clause id="12338">
    <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(4573(a,1),12293(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="4573 12293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12339">
    <literal><![CDATA[
      x * K(1 / (y / z),(y / z) * u) = x * K(z / y,u * (y / z))
    ]]></literal>
    <justification jstring="[para(5429(a,1),12296(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5429 12296"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12340">
    <literal><![CDATA[
      x * (y * K(z,K(u,x * y))) = T(x * y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(134,a,12314,a)].">
      <j1 rule="hyper" parents="134 12314"/>
    </justification>
  </clause>

  <clause id="12341">
    <literal><![CDATA[
      K(x,(y \ 1) \ (y \ K(z,u))) = K(z,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(58,a,11892,a(flip),b,12334,a),flip(a)].">
      <j1 rule="hyper" parents="58 11892 12334"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12342">
    <literal><![CDATA[
      (x \ K(y,z)) \ (x \ K(y,T(z,u))) = K(y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,11629,a,b,12341,a)].">
      <j1 rule="hyper" parents="58 11629 12341"/>
    </justification>
  </clause>

  <clause id="12343">
    <literal><![CDATA[
      (x \ K(y,z)) * K(y,K(z,u)) = x \ K(y,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(119,a,12341,a(flip),b,11629,a)].">
      <j1 rule="hyper" parents="119 12341 11629"/>
    </justification>
  </clause>

  <clause id="12344">
    <literal><![CDATA[
      K(1 / x,T(y / (1 / x),z)) = K(1 / x,x * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(11118,a,12337,a)].">
      <j1 rule="hyper" parents="11118 12337"/>
    </justification>
  </clause>

  <clause id="12345">
    <literal><![CDATA[
      K(1 / (x / y),(x / y) * T(z,x)) = K(1 / (y \ x),z * (x / y))
    ]]></literal>
    <justification jstring="[hyper(8629,a,12337,a),flip(a)].">
      <j1 rule="hyper" parents="8629 12337"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12346">
    <literal><![CDATA[
      T(1 / x,T(y * x,z)) = T(1 / x,x * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(118,a,12337,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 12337 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12347">
    <literal><![CDATA[
      T(x * y,K(z,L(u,y,x))) = T(x * y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(10945,a,12340,a)].">
      <j1 rule="hyper" parents="10945 12340"/>
    </justification>
  </clause>

  <clause id="12348">
    <literal><![CDATA[
      (x * (y * K(z,u))) / T(x * y,K(z,u)) = L(K(z,u),y,x)
    ]]></literal>
    <justification jstring="[para(12347(a,1),10820(a,1,2))].">
      <j1 rule="para" parents="12347 10820"/>
    </justification>
  </clause>

  <clause id="12350">
    <literal><![CDATA[
      (x \ K(y,z)) * K(z,K(y,u)) = x \ K(y,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(119,a,7779,a,b,12342,a)].">
      <j1 rule="hyper" parents="119 7779 12342"/>
    </justification>
  </clause>

  <clause id="12351">
    <literal><![CDATA[
      (x \ K(y,z)) * K(u,K(y,z)) = x \ K(y,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(119,a,7784,a(flip),b,12342,a)].">
      <j1 rule="hyper" parents="119 7784 12342"/>
    </justification>
  </clause>

  <clause id="12352">
    <literal><![CDATA[
      R(K(x,y),z,z \ 1) = K(x,L(y,z,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(58,a,9230,a(flip),b,12312,a),flip(a)].">
      <j1 rule="hyper" parents="58 9230 12312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12353">
    <literal><![CDATA[
      K(x,R(y,z,z \ 1)) = K(x,L(y,z,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(58,a,11913,a(flip),b,12352,a)].">
      <j1 rule="hyper" parents="58 11913 12352"/>
    </justification>
  </clause>

  <clause id="12354">
    <literal><![CDATA[
      K(x,L(y / z,z,z \ 1)) = K(x,y * (z \ 1))
    ]]></literal>
    <justification jstring="[para(523(a,1),12353(a,1,2)),flip(a)].">
      <j1 rule="para" parents="523 12353"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12355">
    <literal><![CDATA[
      K(x,K(y,L(z,u,u \ 1))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(12353(a,1),11827(a,1,2))].">
      <j1 rule="para" parents="12353 11827"/>
    </justification>
  </clause>

  <clause id="12356">
    <literal><![CDATA[
      K(x,K(y,L(z,u \ 1,u))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(3689(a,1),12355(a,1,2,2))].">
      <j1 rule="para" parents="3689 12355"/>
    </justification>
  </clause>

  <clause id="12357">
    <literal><![CDATA[
      (x / y) \ T(x,K(z,u)) = y * K(x,K(z,u))
    ]]></literal>
    <justification jstring="[para(12356(a,1),11883(a,2,2))].">
      <j1 rule="para" parents="12356 11883"/>
    </justification>
  </clause>

  <clause id="12358">
    <literal><![CDATA[
      (x \ y) * K(y,K(z,u)) = x \ T(y,K(z,u))
    ]]></literal>
    <justification jstring="[para(72(a,1),12357(a,1,1)),flip(a)].">
      <j1 rule="para" parents="72 12357"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12359">
    <literal><![CDATA[
      (x / y) \ T(x,K(z,u)) = y * K(z,K(u,x))
    ]]></literal>
    <justification jstring="[para(7784(a,2),12357(a,2,2))].">
      <j1 rule="para" parents="7784 12357"/>
    </justification>
  </clause>

  <clause id="12361">
    <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(12348(a,1),107(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12348 107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12362">
    <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(12348(a,1),5017(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12348 5017"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12363">
    <literal><![CDATA[
      K(((x \ y) \ 1) * z,x / y) = K((x \ y) \ z,x / y)
    ]]></literal>
    <justification jstring="[hyper(320,a,9798,a(flip),b,12307,a),flip(a)].">
      <j1 rule="hyper" parents="320 9798 12307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12364">
    <literal><![CDATA[
      K(x \ y,(1 / (y / x)) * z) = K(x \ y,z / (y / x))
    ]]></literal>
    <justification jstring="[hyper(320,a,6816,a(flip),b,12315,a),flip(a)].">
      <j1 rule="hyper" parents="320 6816 12315"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12365">
    <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(4414(a,2),12364(a,1,1))].">
      <j1 rule="para" parents="4414 12364"/>
    </justification>
  </clause>

  <clause id="12366">
    <literal><![CDATA[
      K(x,K(y * z,(y \ u) \ z)) = K(x,K(u,y * z))
    ]]></literal>
    <justification jstring="[hyper(8168,a,12322,a),flip(a)].">
      <j1 rule="hyper" parents="8168 12322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12367">
    <literal><![CDATA[
      K(x,K(y * z,z \ (y \ u))) = K(x,K(u,y * z))
    ]]></literal>
    <justification jstring="[hyper(8216,a,12366,a)].">
      <j1 rule="hyper" parents="8216 12366"/>
    </justification>
  </clause>

  <clause id="12368">
    <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(5387(a,2),12367(a,2,2))].">
      <j1 rule="para" parents="5387 12367"/>
    </justification>
  </clause>

  <clause id="12369">
    <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,12255,a(flip),b,12320,a),flip(a)].">
      <j1 rule="hyper" parents="320 12255 12320"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12370">
    <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),12369(a,1,2,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="5 12369"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12371">
    <literal><![CDATA[
      x * K(y / z,(z / y) * u) = x * K(y / z,u * (z / y))
    ]]></literal>
    <justification jstring="[para(5429(a,1),12339(a,1,2))].">
      <j1 rule="para" parents="5429 12339"/>
    </justification>
  </clause>

  <clause id="12372">
    <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,8356,a(flip),b,12371,a),flip(a)].">
      <j1 rule="hyper" parents="320 8356 12371"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12373">
    <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(12371(a,1),39(a,2))].">
      <j1 rule="para" parents="12371 39"/>
    </justification>
  </clause>

  <clause id="12374">
    <literal><![CDATA[
      K(1 / (x \ y),z * (y / x)) = K(x / y,(y / x) * T(z,y))
    ]]></literal>
    <justification jstring="[hyper(5669,a,12345,a),flip(a)].">
      <j1 rule="hyper" parents="5669 12345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12375">
    <literal><![CDATA[
      K(x / y,(y / x) * T(z,y)) = K(y \ x,z * (y / x))
    ]]></literal>
    <justification jstring="[hyper(6493,a,12374,a),flip(a)].">
      <j1 rule="hyper" parents="6493 12374"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12376">
    <literal><![CDATA[
      ((x * y) * ((T(y,x) * x) \ z)) / (x * y) = z / (T(y,x) * x)
    ]]></literal>
    <justification jstring="[hyper(4821,a,12252,a)].">
      <j1 rule="hyper" parents="4821 12252"/>
    </justification>
  </clause>

  <clause id="12377">
    <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,12319,a(flip),b,12324,a),flip(a)].">
      <j1 rule="hyper" parents="58 12319 12324"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12378">
    <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(10029(a,1),12328(a,1,1))].">
      <j1 rule="para" parents="10029 12328"/>
    </justification>
  </clause>

  <clause id="12379">
    <literal><![CDATA[
      K(x,T(y,z)) * K(u,T(x,z)) = T(K(x,y) * K(u,x),z)
    ]]></literal>
    <justification jstring="[hyper(11554,a,12378,a),flip(a)].">
      <j1 rule="hyper" parents="11554 12378"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12380">
    <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(12379(a,1),10001(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12379 10001"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12381">
    <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,10749,a(flip),b,12380,a),flip(a)].">
      <j1 rule="hyper" parents="58 10749 12380"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12382">
    <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),12338(a,2,2))].">
      <j1 rule="para" parents="453 12338"/>
    </justification>
  </clause>

  <clause id="12383">
    <literal><![CDATA[
      K(x \ T(x * y,z),T(u,x)) = K((x \ 1) * T(y / (x \ 1),z),u)
    ]]></literal>
    <justification jstring="[para(939(a,1),12308(a,1,1))].">
      <j1 rule="para" parents="939 12308"/>
    </justification>
  </clause>

  <clause id="12384">
    <literal><![CDATA[
      K((x \ 1) * T(y / (x \ 1),z),u) = K(x \ T(y * x,z),u)
    ]]></literal>
    <justification jstring="[hyper(7726,a,12383,a),flip(a)].">
      <j1 rule="hyper" parents="7726 12383"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12385">
    <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,4251,a(flip),b,12361,a),flip(a)].">
      <j1 rule="hyper" parents="320 4251 12361"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12386">
    <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(7158(a,2),12385(a,2,1))].">
      <j1 rule="para" parents="7158 12385"/>
    </justification>
  </clause>

  <clause id="12387">
    <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(10601(a,1),12381(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10601 12381"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12389">
    <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(12387(a,1),11729(a,2,1))].">
      <j1 rule="para" parents="12387 11729"/>
    </justification>
  </clause>

  <clause id="12390">
    <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(11720(a,1),12389(a,2,1,1))].">
      <j1 rule="para" parents="11720 12389"/>
    </justification>
  </clause>

  <clause id="12392">
    <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(7123(a,1),12390(a,1,1,1))].">
      <j1 rule="para" parents="7123 12390"/>
    </justification>
  </clause>

  <clause id="12394">
    <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(9800(a,1),12392(a,1,1))].">
      <j1 rule="para" parents="9800 12392"/>
    </justification>
  </clause>

  <clause id="12395">
    <literal><![CDATA[
      (R(a(x,y,x),z,u) * z) * u = (z * a(x,y,x)) * u
    ]]></literal>
    <justification jstring="[para(9099(a,1),12394(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9099 12394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12396">
    <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,12395,a(flip),b,693,a)].">
      <j1 rule="hyper" parents="116 12395 693"/>
    </justification>
  </clause>

  <clause id="12397">
    <literal><![CDATA[
      a(R(a(x,y,x),z,u),z,u) = K(z,T(a(x,y,x),u))
    ]]></literal>
    <justification jstring="[hyper(11119,a,12396,a),flip(a)].">
      <j1 rule="hyper" parents="11119 12396"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12398">
    <literal><![CDATA[
      a(R(a(x,y,x),z,u),z,u) = K(z,a(x,y,x))
    ]]></literal>
    <justification jstring="[para(9535(a,1),12397(a,2,2))].">
      <j1 rule="para" parents="9535 12397"/>
    </justification>
  </clause>

  <clause id="12399">
    <literal><![CDATA[
      a(R(a(x,y,x),z,u),z,u) = 1
    ]]></literal>
    <justification jstring="[hyper(320,a,9543,a(flip),b,12398,a),flip(a)].">
      <j1 rule="hyper" parents="320 9543 12398"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12402">
    <literal><![CDATA[
      L(x,y,R(a(z,u,z),y,x)) = x
    ]]></literal>
    <justification jstring="[hyper(47,a,12399,a)].">
      <j1 rule="hyper" parents="47 12399"/>
    </justification>
  </clause>

  <clause id="12403">
    <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(12402(a,1),11212(a,1,2))].">
      <j1 rule="para" parents="12402 11212"/>
    </justification>
  </clause>

  <clause id="12404">
    <literal><![CDATA[
      (R(a(x,y,x),z,u) * (z * u)) / u = z * R(a(x,y,x),z,u)
    ]]></literal>
    <justification jstring="[para(9579(a,1),12403(a,1,1,2,1))].">
      <j1 rule="para" parents="9579 12403"/>
    </justification>
  </clause>

  <clause id="12405">
    <literal><![CDATA[
      x * R(a(y,z,y),x,u) = a(y,z,y) * x
    ]]></literal>
    <justification jstring="[hyper(519,a,12404,a),flip(a)].">
      <j1 rule="hyper" parents="519 12404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12406">
    <literal><![CDATA[
      R(a(x,y,x),z,u) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(29,a,9522,a(flip),b,12405,a),flip(a)].">
      <j1 rule="hyper" parents="29 9522 12405"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12408">
    <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,12406,a)].">
      <j1 rule="hyper" parents="58 511 12406"/>
    </justification>
  </clause>

  <clause id="12409">
    <literal><![CDATA[
      a(x,y,R(x,z,u)) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,11718,a(flip),b,12406,a)].">
      <j1 rule="hyper" parents="58 11718 12406"/>
    </justification>
  </clause>

  <clause id="12410">
    <literal><![CDATA[
      a(x,y * K(z,y),x) = L(a(x,y,x),y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,10030,a(flip),b,12406,a),flip(a)].">
      <j1 rule="hyper" parents="58 10030 12406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12411">
    <literal><![CDATA[
      (a(x,y,x) * z) * u = a(x,y,x) * (z * u)
    ]]></literal>
    <justification jstring="[para(12406(a,1),101(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12406 101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12413">
    <literal><![CDATA[
      a(a(x,y,x),z,u) = 1
    ]]></literal>
    <justification jstring="[para(12406(a,1),12399(a,1,1))].">
      <j1 rule="para" parents="12406 12399"/>
    </justification>
  </clause>

  <clause id="12414">
    <literal><![CDATA[
      L(x,y,a(z,u,z)) = x
    ]]></literal>
    <justification jstring="[para(12406(a,1),12402(a,1,3))].">
      <j1 rule="para" parents="12406 12402"/>
    </justification>
  </clause>

  <clause id="12415">
    <literal><![CDATA[
      a(x,y,x) * ((a(x,y,x) \ z) * u) = z * u
    ]]></literal>
    <justification jstring="[hyper(167,a,81,a,b,12413,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="167 81 12413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12417">
    <literal><![CDATA[
      (a(x,y,x) * z) \ x = z \ L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,9090,a(flip),b,12414,a)].">
      <j1 rule="hyper" parents="58 9090 12414"/>
    </justification>
  </clause>

  <clause id="12418">
    <literal><![CDATA[
      (a(x,y,x) * z) \ u = z \ (a(x,y,x) \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,298,a(flip),b,12414,a)].">
      <j1 rule="hyper" parents="58 298 12414"/>
    </justification>
  </clause>

  <clause id="12419">
    <literal><![CDATA[
      L(x,y,a(z,u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(12414(a,1),45(a,2))].">
      <j1 rule="para" parents="12414 45"/>
    </justification>
  </clause>

  <clause id="12420">
    <literal><![CDATA[
      (a(x,y,x) * z) / u = a(x,y,x) * (z / u)
    ]]></literal>
    <justification jstring="[para(12414(a,1),544(a,1,2))].">
      <j1 rule="para" parents="12414 544"/>
    </justification>
  </clause>

  <clause id="12421">
    <literal><![CDATA[
      x \ (a(y,z,y) * u) != w
    ]]></literal>
    <literal><![CDATA[
      (a(y,z,y) \ x) \ u = w
    ]]></literal>
    <justification jstring="[para(12414(a,1),760(a,1)),flip(a)].">
      <j1 rule="para" parents="12414 760"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12422">
    <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(12414(a,1),478(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12414 478"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12423">
    <literal><![CDATA[
      a(x,y,x) * ((a(x,y,x) \ z) / u) = z / u
    ]]></literal>
    <justification jstring="[para(12414(a,1),10422(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12414 10422"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12426">
    <literal><![CDATA[
      K(x,R(x,y,z) \ u) = K(x,u) * a(x,x \ u,x)
    ]]></literal>
    <justification jstring="[para(12409(a,1),11725(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12409 11725"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12428">
    <literal><![CDATA[
      (x * y) \ L(y,x,y) = T(y * x,y) \ y
    ]]></literal>
    <justification jstring="[para(8970(a,1),12417(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8970 12417"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12430">
    <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(5517(a,1),12410(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5517 12410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12431">
    <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(4648(a,1),12428(a,1,1))].">
      <j1 rule="para" parents="4648 12428"/>
    </justification>
  </clause>

  <clause id="12432">
    <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(12411(a,1),9(a,2,1)),flip(a)].">
      <j1 rule="para" parents="12411 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12433">
    <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(12411(a,1),13(a,2,1)),flip(a)].">
      <j1 rule="para" parents="12411 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12434">
    <literal><![CDATA[
      a(x,y,x) * ((a(x,y,x) \ z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      z * u = w
    ]]></literal>
    <justification jstring="[para(12411(a,1),568(a,1))].">
      <j1 rule="para" parents="12411 568"/>
    </justification>
  </clause>

  <clause id="12435">
    <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(12411(a,1),482(a,1,2,2))].">
      <j1 rule="para" parents="12411 482"/>
    </justification>
  </clause>

  <clause id="12436">
    <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(12411(a,1),616(a,1))].">
      <j1 rule="para" parents="12411 616"/>
    </justification>
  </clause>

  <clause id="12437">
    <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(12411(a,1),691(a,1,1,2))].">
      <j1 rule="para" parents="12411 691"/>
    </justification>
  </clause>

  <clause id="12438">
    <literal><![CDATA[
      (x * a(y,z,y)) * u = a(y,z,y) * (x * u)
    ]]></literal>
    <justification jstring="[para(9522(a,1),12411(a,1,1))].">
      <j1 rule="para" parents="9522 12411"/>
    </justification>
  </clause>

  <clause id="12439">
    <literal><![CDATA[
      (x * a(y,z,y)) \ u = x \ (a(y,z,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(9559,a,12418,a)].">
      <j1 rule="hyper" parents="9559 12418"/>
    </justification>
  </clause>

  <clause id="12440">
    <literal><![CDATA[
      (x * y) \ (a(y,z,y) \ u) = (x * R(y,z,y)) \ u
    ]]></literal>
    <justification jstring="[para(9529(a,1),12418(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9529 12418"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12441">
    <literal><![CDATA[
      (a(x,y,x) * z) / u = (z / u) * a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,9522,a(flip),b,12420,a),flip(a)].">
      <j1 rule="hyper" parents="320 9522 12420"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12442">
    <literal><![CDATA[
      a(x,y,x) * (x / z) = R(x,y,x) / z
    ]]></literal>
    <justification jstring="[para(8956(a,1),12420(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8956 12420"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12443">
    <literal><![CDATA[
      (x / y) * a(x,z,x) = R(x,z,x) / y
    ]]></literal>
    <justification jstring="[hyper(9550,a,12442,a)].">
      <j1 rule="hyper" parents="9550 12442"/>
    </justification>
  </clause>

  <clause id="12444">
    <literal><![CDATA[
      (a(x,y,x) \ z) / u = a(x,y,x) \ (z / u)
    ]]></literal>
    <justification jstring="[hyper(123,a,12423,a),flip(a)].">
      <j1 rule="hyper" parents="123 12423"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12445">
    <literal><![CDATA[
      (x * a(y,x,y)) * z = x * (a(y,x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(320,a,11040,a(flip),b,12438,a),flip(a)].">
      <j1 rule="hyper" parents="320 11040 12438"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12446">
    <literal><![CDATA[
      (x * a(y,z,y)) / u = (x / u) * a(y,z,y)
    ]]></literal>
    <justification jstring="[para(9522(a,1),12441(a,1,1))].">
      <j1 rule="para" parents="9522 12441"/>
    </justification>
  </clause>

  <clause id="12447">
    <literal><![CDATA[
      a(x,y,x) \ (x / z) = L(x,y,x) / z
    ]]></literal>
    <justification jstring="[para(9089(a,1),12444(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9089 12444"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12448">
    <literal><![CDATA[
      K(x,R(x,y,z) \ u) = K(x,x \ u)
    ]]></literal>
    <justification jstring="[hyper(320,a,8971,a(flip),b,12426,a),flip(a)].">
      <j1 rule="hyper" parents="320 8971 12426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12450">
    <literal><![CDATA[
      K(x,x \ ((x * R(T(x,y),z,u)) / w)) = K(x,w \ x)
    ]]></literal>
    <justification jstring="[hyper(10064,a,12448,a),flip(a)].">
      <j1 rule="hyper" parents="10064 12448"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12451">
    <literal><![CDATA[
      K(x,x \ ((x * y) * z)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(184(a,1),12448(a,1,2)),flip(a)].">
      <j1 rule="para" parents="184 12448"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12452">
    <literal><![CDATA[
      K(x,x \ (y * z)) = K(x,(x \ y) * z)
    ]]></literal>
    <justification jstring="[para(505(a,1),12448(a,1,2)),flip(a)].">
      <j1 rule="para" parents="505 12448"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12453">
    <literal><![CDATA[
      K(x,y * ((x * y) \ z)) = K(x,x \ z)
    ]]></literal>
    <justification jstring="[para(367(a,1),12448(a,1,2))].">
      <j1 rule="para" parents="367 12448"/>
    </justification>
  </clause>

  <clause id="12454">
    <literal><![CDATA[
      K(x,x \ ((y * x) * z)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(11177,a,12451,a)].">
      <j1 rule="hyper" parents="11177 12451"/>
    </justification>
  </clause>

  <clause id="12455">
    <literal><![CDATA[
      K(x,y * (x \ (y \ (z * u)))) = K(x,(x \ z) * u)
    ]]></literal>
    <justification jstring="[hyper(10409,a,12452,a)].">
      <j1 rule="hyper" parents="10409 12452"/>
    </justification>
  </clause>

  <clause id="12456">
    <literal><![CDATA[
      K(x,(x \ y) * z) = K(x,y * (x \ z))
    ]]></literal>
    <justification jstring="[hyper(10330,a,12452,a),flip(a)].">
      <j1 rule="hyper" parents="10330 12452"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12457">
    <literal><![CDATA[
      K(x,y * ((y * x) \ z)) = K(x,x \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,11171,a,b,12453,a)].">
      <j1 rule="hyper" parents="58 11171 12453"/>
    </justification>
  </clause>

  <clause id="12458">
    <literal><![CDATA[
      T(x,(x \ y) * z) = T(x,y * (x \ z))
    ]]></literal>
    <justification jstring="[hyper(118,a,12456,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 12456 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12459">
    <literal><![CDATA[
      K(x,(y * x) * (x \ z)) = K(x,T(y,x) * z)
    ]]></literal>
    <justification jstring="[para(17(a,2),12456(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="17 12456"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12460">
    <literal><![CDATA[
      K(x \ y,(x \ y) \ z) = K(x \ y,x * (y \ z))
    ]]></literal>
    <justification jstring="[para(5(a,1),12457(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5 12457"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12461">
    <literal><![CDATA[
      T(x,(y / x) * z) = T(x,y * (x \ z))
    ]]></literal>
    <justification jstring="[hyper(8413,a,12458,a)].">
      <j1 rule="hyper" parents="8413 12458"/>
    </justification>
  </clause>

  <clause id="12462">
    <literal><![CDATA[
      T(x,(x \ y) * z) \ u = T(x,y * (x \ z)) \ u
    ]]></literal>
    <justification jstring="[hyper(56,a,12458,a)].">
      <j1 rule="hyper" parents="56 12458"/>
    </justification>
  </clause>

  <clause id="12463">
    <literal><![CDATA[
      K(x,(y * x) * (x \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = u
    ]]></literal>
    <justification jstring="[para(12459(a,2),8401(a,1))].">
      <j1 rule="para" parents="12459 8401"/>
    </justification>
  </clause>

  <clause id="12464">
    <literal><![CDATA[
      K(x,y * (x \ T(z,y))) = K(x,(x \ z) * y)
    ]]></literal>
    <justification jstring="[para(17(a,2),12455(a,1,2,2,2))].">
      <j1 rule="para" parents="17 12455"/>
    </justification>
  </clause>

  <clause id="12465">
    <literal><![CDATA[
      K((x \ y) * z,x) = K(y * (x \ z),x)
    ]]></literal>
    <justification jstring="[hyper(5660,a,12462,a)].">
      <j1 rule="hyper" parents="5660 12462"/>
    </justification>
  </clause>

  <clause id="12466">
    <literal><![CDATA[
      K(x \ (y * z),x) = K((x \ y) * z,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,10428,a,b,12465,a)].">
      <j1 rule="hyper" parents="320 10428 12465"/>
    </justification>
  </clause>

  <clause id="12467">
    <literal><![CDATA[
      K(x \ ((x * y) * z),x) = K(y * z,x)
    ]]></literal>
    <justification jstring="[para(4(a,1),12466(a,2,1,1))].">
      <j1 rule="para" parents="4 12466"/>
    </justification>
  </clause>

  <clause id="12468">
    <literal><![CDATA[
      K(x \ ((y * x) * z),x) = K(y * z,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,11178,a,b,12467,a)].">
      <j1 rule="hyper" parents="58 11178 12467"/>
    </justification>
  </clause>

  <clause id="12469">
    <literal><![CDATA[
      K(x * ((x * y) \ z),y) = K(y \ z,y)
    ]]></literal>
    <justification jstring="[para(5(a,1),12468(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5 12468"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12470">
    <literal><![CDATA[
      K((x \ y) \ z,x \ y) = K(x * (y \ z),x \ y)
    ]]></literal>
    <justification jstring="[para(5(a,1),12469(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 12469"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12471">
    <literal><![CDATA[
      K((x / y) \ z,y \ x) = K(y * (x \ z),y \ x)
    ]]></literal>
    <justification jstring="[hyper(7429,a,12470,a)].">
      <j1 rule="hyper" parents="7429 12470"/>
    </justification>
  </clause>

  <clause id="12472">
    <literal><![CDATA[
      a(x,y,K(z * (u \ w),z \ u)) = a(x,y,K(w,z \ u))
    ]]></literal>
    <justification jstring="[para(12470(a,1),11016(a,1,3))].">
      <j1 rule="para" parents="12470 11016"/>
    </justification>
  </clause>

  <clause id="12473">
    <literal><![CDATA[
      K(x / (y / z),z \ y) = K(z * (y \ x),z \ y)
    ]]></literal>
    <justification jstring="[hyper(8267,a,12471,a)].">
      <j1 rule="hyper" parents="8267 12471"/>
    </justification>
  </clause>

  <clause id="12474">
    <literal><![CDATA[
      a(x,y,x) * (z * u) != w
    ]]></literal>
    <literal><![CDATA[
      (z * a(x,y,x)) * u = w
    ]]></literal>
    <justification jstring="[para(9537(a,1),12434(a,1,2,1))].">
      <j1 rule="para" parents="9537 12434"/>
    </justification>
  </clause>

  <clause id="12475">
    <literal><![CDATA[
      K(x,R(T(x,y),z,u) / w) = K(x,w \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,11124,a(flip),b,12450,a)].">
      <j1 rule="hyper" parents="58 11124 12450"/>
    </justification>
  </clause>

  <clause id="12476">
    <literal><![CDATA[
      K(x,y \ R(x,z,u)) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,11793,a(flip),b,12475,a)].">
      <j1 rule="hyper" parents="58 11793 12475"/>
    </justification>
  </clause>

  <clause id="12479">
    <literal><![CDATA[
      K(R(x,y,z),u \ x) = K(x,R(u,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,11947,a(flip),b,12476,a)].">
      <j1 rule="hyper" parents="58 11947 12476"/>
    </justification>
  </clause>

  <clause id="12480">
    <literal><![CDATA[
      K(x,y \ (z * R(x,u,w))) = K(x,(z \ y) \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,10733,a(flip),b,12476,a)].">
      <j1 rule="hyper" parents="58 10733 12476"/>
    </justification>
  </clause>

  <clause id="12482">
    <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,11620,a(flip),b,12479,a),flip(a)].">
      <j1 rule="hyper" parents="58 11620 12479"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12484">
    <literal><![CDATA[
      K(x,y \ (z * R(x,u,w))) = K(x,x * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(320,a,10478,a(flip),b,12480,a),flip(a)].">
      <j1 rule="hyper" parents="320 10478 12480"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12485">
    <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(9526(a,1),12408(a,1,1,1))].">
      <j1 rule="para" parents="9526 12408"/>
    </justification>
  </clause>

  <clause id="12486">
    <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,11456,a(flip),b,12430,a)].">
      <j1 rule="hyper" parents="58 11456 12430"/>
    </justification>
  </clause>

  <clause id="12487">
    <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,11676,a(flip),b,12482,a)].">
      <j1 rule="hyper" parents="58 11676 12482"/>
    </justification>
  </clause>

  <clause id="12488">
    <literal><![CDATA[
      R(K(x,y),z,u) = K(R(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(5472(a,1),12487(a,1,1))].">
      <j1 rule="para" parents="5472 12487"/>
    </justification>
  </clause>

  <clause id="12489">
    <literal><![CDATA[
      R(K(x,y),K(x,z),u) = K(x,y)
    ]]></literal>
    <justification jstring="[para(4419(a,1),12488(a,2,1))].">
      <j1 rule="para" parents="4419 12488"/>
    </justification>
  </clause>

  <clause id="12490">
    <literal><![CDATA[
      R(K(x,y),z,u) \ 1 = K(y,R(x,z,u))
    ]]></literal>
    <justification jstring="[para(12488(a,2),4969(a,1,1))].">
      <j1 rule="para" parents="12488 4969"/>
    </justification>
  </clause>

  <clause id="12492">
    <literal><![CDATA[
      (K(x,y) * K(x,z)) * u = K(x,y) * (K(x,z) * u)
    ]]></literal>
    <justification jstring="[para(12489(a,1),101(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12489 101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12493">
    <literal><![CDATA[
      R(K(x,y),z,u) = K(x,R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(6935,a,12490,a)].">
      <j1 rule="hyper" parents="6935 12490"/>
    </justification>
  </clause>

  <clause id="12494">
    <literal><![CDATA[
      K(x,R(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      R(K(x,y),z,u) = w
    ]]></literal>
    <justification jstring="[para(12490(a,1),6935(a,1))].">
      <j1 rule="para" parents="12490 6935"/>
    </justification>
  </clause>

  <clause id="12495">
    <literal><![CDATA[
      K(x,R(y,z,u)) * 1 = R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(320,a,3,a,b,12493,a)].">
      <j1 rule="hyper" parents="320 3 12493"/>
    </justification>
  </clause>

  <clause id="12496">
    <literal><![CDATA[
      K(R(x,y,z),u) = K(x,R(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,12488,a(flip),b,12493,a)].">
      <j1 rule="hyper" parents="58 12488 12493"/>
    </justification>
  </clause>

  <clause id="12497">
    <literal><![CDATA[
      K(x,R(y,z,u)) * (z * u) = (K(x,y) * z) * u
    ]]></literal>
    <justification jstring="[para(12493(a,1),101(a,1,1))].">
      <j1 rule="para" parents="12493 101"/>
    </justification>
  </clause>

  <clause id="12500">
    <literal><![CDATA[
      K(x,y) * K(y,R(x,z,u)) = a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(12493(a,1),11962(a,1,2))].">
      <j1 rule="para" parents="12493 11962"/>
    </justification>
  </clause>

  <clause id="12501">
    <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(12493(a,1),11997(a,2,1,2))].">
      <j1 rule="para" parents="12493 11997"/>
    </justification>
  </clause>

  <clause id="12502">
    <literal><![CDATA[
      K(R(x,y,z),R(x * y,y * z,u)) = K(x,R(x * y,z,u))
    ]]></literal>
    <justification jstring="[hyper(6992,a,12496,a),flip(a)].">
      <j1 rule="hyper" parents="6992 12496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12504">
    <literal><![CDATA[
      R(K(x,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,R(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(12495(a,1),127(a,1)),flip(b)].">
      <j1 rule="para" parents="12495 127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12505">
    <literal><![CDATA[
      K(R(x,y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      R(K(x,u),y,z) = w
    ]]></literal>
    <justification jstring="[para(12496(a,2),12494(a,1))].">
      <j1 rule="para" parents="12496 12494"/>
    </justification>
  </clause>

  <clause id="12506">
    <literal><![CDATA[
      K(R(x,y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,R(u,y,z)) = w
    ]]></literal>
    <justification jstring="[para(12488(a,1),12504(a,1))].">
      <j1 rule="para" parents="12488 12504"/>
    </justification>
  </clause>

  <clause id="12507">
    <literal><![CDATA[
      a(K(x,y),z * y,u) = a(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,11967,a(flip),b,12500,a)].">
      <j1 rule="hyper" parents="58 11967 12500"/>
    </justification>
  </clause>

  <clause id="12508">
    <literal><![CDATA[
      K(a(K(x,y),z * y,u),w) = a(K(y,K(x,w)),z,u)
    ]]></literal>
    <justification jstring="[para(12507(a,2),12012(a,2,1)),flip(a)].">
      <j1 rule="para" parents="12507 12012"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12509">
    <literal><![CDATA[
      ((x * y) * z) / ((K(u,x) * y) * z) = T(R(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(12497(a,1),5255(a,1,2))].">
      <j1 rule="para" parents="12497 5255"/>
    </justification>
  </clause>

  <clause id="12510">
    <literal><![CDATA[
      L(x,K(y,z),K(y,u)) = x
    ]]></literal>
    <justification jstring="[hyper(479,a,12492,a)].">
      <j1 rule="hyper" parents="479 12492"/>
    </justification>
  </clause>

  <clause id="12511">
    <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(12492(a,1),12017(a,1,2))].">
      <j1 rule="para" parents="12492 12017"/>
    </justification>
  </clause>

  <clause id="12512">
    <literal><![CDATA[
      (K(x,y) * K(x,z)) \ u = K(z,x) * (K(y,x) * u)
    ]]></literal>
    <justification jstring="[hyper(58,a,5766,a(flip),b,12510,a)].">
      <j1 rule="hyper" parents="58 5766 12510"/>
    </justification>
  </clause>

  <clause id="12513">
    <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,12014,a,b,12508,a)].">
      <j1 rule="hyper" parents="58 12014 12508"/>
    </justification>
  </clause>

  <clause id="12514">
    <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,6036,a(flip),b,12512,a),flip(a)].">
      <j1 rule="hyper" parents="58 6036 12512"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12515">
    <literal><![CDATA[
      ((x * y) * z) / (T(y,x) * z) = T(R(x,y,z),y)
    ]]></literal>
    <justification jstring="[para(4770(a,2),12509(a,1,2,1))].">
      <j1 rule="para" parents="4770 12509"/>
    </justification>
  </clause>

  <clause id="12516">
    <literal><![CDATA[
      R(T(x,y),T(y,x),z) = T(R(x,y,z),y)
    ]]></literal>
    <justification jstring="[hyper(4275,a,12515,a)].">
      <j1 rule="hyper" parents="4275 12515"/>
    </justification>
  </clause>

  <clause id="12517">
    <literal><![CDATA[
      R(x,T(y,x),z) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(140,a,12516,a(flip))].">
      <j1 rule="hyper" parents="140 12516"/>
    </justification>
  </clause>

  <clause id="12523">
    <literal><![CDATA[
      R(x,y,z) \ ((y * x) * z) = T(y,x) * z
    ]]></literal>
    <justification jstring="[para(12517(a,1),540(a,1,1))].">
      <j1 rule="para" parents="12517 540"/>
    </justification>
  </clause>

  <clause id="12524">
    <literal><![CDATA[
      R(x,y,T(z,y * x)) \ (z * (y * x)) = T(y,x) * T(z,y * x)
    ]]></literal>
    <justification jstring="[para(12517(a,1),938(a,1,1))].">
      <j1 rule="para" parents="12517 938"/>
    </justification>
  </clause>

  <clause id="12525">
    <literal><![CDATA[
      K(x,(((y * x) * z) / R(x,y,z)) \ u) = K(x,(T(y,x) * z) \ u)
    ]]></literal>
    <justification jstring="[para(12523(a,1),7427(a,2,2,1))].">
      <j1 rule="para" parents="12523 7427"/>
    </justification>
  </clause>

  <clause id="12526">
    <literal><![CDATA[
      K(x,R(R(x * y,y * z,u),y,z)) = K(x,R(x * y,z,u))
    ]]></literal>
    <justification jstring="[hyper(12506,a,12502,a)].">
      <j1 rule="hyper" parents="12506 12502"/>
    </justification>
  </clause>

  <clause id="12527">
    <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(4755(a,2),12501(a,2,1))].">
      <j1 rule="para" parents="4755 12501"/>
    </justification>
  </clause>

  <clause id="12528">
    <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(12525(a,2),8590(a,1))].">
      <j1 rule="para" parents="12525 8590"/>
    </justification>
  </clause>

  <clause id="12529">
    <literal><![CDATA[
      ((x \ K(x,y)) * T(x,z)) \ 1 = K(z,x) * (x * (K(y,x) / x))
    ]]></literal>
    <justification jstring="[para(3361(a,1),12514(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3361 12514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12530">
    <literal><![CDATA[
      ((x \ K(x,y)) * T(x,z)) \ 1 = x * (K(z,x) * (K(y,x) / x))
    ]]></literal>
    <justification jstring="[hyper(320,a,5256,a(flip),b,12529,a),flip(a)].">
      <j1 rule="hyper" parents="320 5256 12529"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12531">
    <literal><![CDATA[
      ((x \ K(x,y)) * T(x,z)) \ 1 = x * (K(y,x) / T(x,z))
    ]]></literal>
    <justification jstring="[para(8334(a,1),12530(a,2,2))].">
      <j1 rule="para" parents="8334 12530"/>
    </justification>
  </clause>

  <clause id="12532">
    <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(12531(a,1),12164(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12531 12164"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12533">
    <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),12485(a,1,1))].">
      <j1 rule="para" parents="101 12485"/>
    </justification>
  </clause>

  <clause id="12534">
    <literal><![CDATA[
      ((x * (a(y,x,y) * z)) * u) / ((x * z) * u) = a(y,R(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(12445(a,1),12533(a,1,1,1))].">
      <j1 rule="para" parents="12445 12533"/>
    </justification>
  </clause>

  <clause id="12535">
    <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),12534(a,1,2,1))].">
      <j1 rule="para" parents="5 12534"/>
    </justification>
  </clause>

  <clause id="12536">
    <literal><![CDATA[
      a(x,R(y,y \ z,u),x) = ((a(x,y,x) * z) * u) / (z * u)
    ]]></literal>
    <justification jstring="[para(11041(a,1),12535(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="11041 12535"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12537">
    <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,12536,a),flip(a)].">
      <j1 rule="hyper" parents="320 15 12536"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12538">
    <literal><![CDATA[
      R(a(x,y,x),y * z,u) = a(x,R(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(4(a,1),12537(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 12537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12539">
    <literal><![CDATA[
      a(x,R(y,z,u),x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,12406,a(flip),b,12538,a),flip(a)].">
      <j1 rule="hyper" parents="58 12406 12538"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12540">
    <literal><![CDATA[
      R(a(x,y,x),z,u) = a(x,R(y,w,v5),x)
    ]]></literal>
    <justification jstring="[hyper(320,a,12406,a,b,12539,a)].">
      <j1 rule="hyper" parents="320 12406 12539"/>
    </justification>
  </clause>

  <clause id="12541">
    <literal><![CDATA[
      a(x,y,x) * (R(y,z,u) * x) = T(x * R(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(12539(a,1),8970(a,1,1))].">
      <j1 rule="para" parents="12539 8970"/>
    </justification>
  </clause>

  <clause id="12542">
    <literal><![CDATA[
      R(T(x,y),R(z,u,w),x) = a(x,z,x) * T(x,y)
    ]]></literal>
    <justification jstring="[para(12539(a,1),8983(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12539 8983"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12544">
    <literal><![CDATA[
      a(x,R(y,z,u),x) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,x) = w
    ]]></literal>
    <justification jstring="[para(12540(a,1),380(a,1)),flip(b)].">
      <j1 rule="para" parents="12540 380"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12545">
    <literal><![CDATA[
      a(x,(y \ z) \ z,x) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,T(y,z),x) = u
    ]]></literal>
    <justification jstring="[para(4375(a,1),12544(a,1,2))].">
      <j1 rule="para" parents="4375 12544"/>
    </justification>
  </clause>

  <clause id="12546">
    <literal><![CDATA[
      R(T(x,y),R(z,u,w),x) = R(T(x,y),z,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,8983,a(flip),b,12542,a),flip(a)].">
      <j1 rule="hyper" parents="320 8983 12542"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12547">
    <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(12546(a,1),12157(a,1,2))].">
      <j1 rule="para" parents="12546 12157"/>
    </justification>
  </clause>

  <clause id="12548">
    <literal><![CDATA[
      R(x,y,z) * R(u,x,u) = T(u * R(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(9549,a,12541,a)].">
      <j1 rule="hyper" parents="9549 12541"/>
    </justification>
  </clause>

  <clause id="12549">
    <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(12548(a,2),4240(a,1,1))].">
      <j1 rule="para" parents="12548 4240"/>
    </justification>
  </clause>

  <clause id="12550">
    <literal><![CDATA[
      T(x * R(y,z,u),x * y) = R(y,z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[para(807(a,1),12547(a,1,2)),flip(a)].">
      <j1 rule="para" parents="807 12547"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12552">
    <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(12550(a,1),4794(a,2,2)),flip(a)].">
      <j1 rule="para" parents="12550 4794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12553">
    <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,12122,a(flip),b,12552,a)].">
      <j1 rule="hyper" parents="58 12122 12552"/>
    </justification>
  </clause>

  <clause id="12554">
    <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(11967(a,1),12553(a,1,1))].">
      <j1 rule="para" parents="11967 12553"/>
    </justification>
  </clause>

  <clause id="12555">
    <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,12200,a,b,12554,a),flip(a)].">
      <j1 rule="hyper" parents="58 12200 12554"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12556">
    <literal><![CDATA[
      K(x * y,x * R(y,z,u)) = a(K(x,y),z * y,u)
    ]]></literal>
    <justification jstring="[para(172(a,1),12555(a,2,1,2))].">
      <j1 rule="para" parents="172 12555"/>
    </justification>
  </clause>

  <clause id="12557">
    <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(6952,a,12556,a)].">
      <j1 rule="hyper" parents="6952 12556"/>
    </justification>
  </clause>

  <clause id="12558">
    <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),12556(a,1,1))].">
      <j1 rule="para" parents="7 12556"/>
    </justification>
  </clause>

  <clause id="12559">
    <literal><![CDATA[
      K(x,(y \ x) * R(y,z,u)) = a(K(x / y,y),z * y,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,8771,a(flip),b,12558,a)].">
      <j1 rule="hyper" parents="58 8771 12558"/>
    </justification>
  </clause>

  <clause id="12560">
    <literal><![CDATA[
      K(x,x * (y \ R(y,z,u))) = a(K(x / y,y),z * y,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,12316,a(flip),b,12559,a)].">
      <j1 rule="hyper" parents="58 12316 12559"/>
    </justification>
  </clause>

  <clause id="12561">
    <literal><![CDATA[
      K(x,x * (y \ R(y,z,u))) = a(K(y \ x,y),z * y,u)
    ]]></literal>
    <justification jstring="[para(4964(a,1),12560(a,2,1))].">
      <j1 rule="para" parents="4964 12560"/>
    </justification>
  </clause>

  <clause id="12562">
    <literal><![CDATA[
      L(T(x,R(y,z,u)),y,T(x,w)) = T(x,x * R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(9788,a,12549,a)].">
      <j1 rule="hyper" parents="9788 12549"/>
    </justification>
  </clause>

  <clause id="12563">
    <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(12556(a,1),12557(a,1,1))].">
      <j1 rule="para" parents="12556 12557"/>
    </justification>
  </clause>

  <clause id="12564">
    <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(12411(a,1),12433(a,1,2))].">
      <j1 rule="para" parents="12411 12433"/>
    </justification>
  </clause>

  <clause id="12565">
    <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(833,a,12564,a)].">
      <j1 rule="hyper" parents="833 12564"/>
    </justification>
  </clause>

  <clause id="12566">
    <literal><![CDATA[
      L(x,y,a(z,u,z) * w) = L(x,y,w)
    ]]></literal>
    <justification jstring="[hyper(12419,a,12565,a),flip(a)].">
      <j1 rule="hyper" parents="12419 12565"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12568">
    <literal><![CDATA[
      L(x,y,a(z,u,z) \ w) = L(x,y,w)
    ]]></literal>
    <justification jstring="[para(5(a,1),12566(a,1,3)),flip(a)].">
      <j1 rule="para" parents="5 12566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12569">
    <literal><![CDATA[
      L(x,y,R(z,u,z)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(8956(a,1),12566(a,1,3))].">
      <j1 rule="para" parents="8956 12566"/>
    </justification>
  </clause>

  <clause id="12570">
    <literal><![CDATA[
      L(x,y,K(z * u,z)) = L(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[para(8966(a,1),12566(a,1,3))].">
      <j1 rule="para" parents="8966 12566"/>
    </justification>
  </clause>

  <clause id="12571">
    <literal><![CDATA[
      L(x,y,K(z,z * u)) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[para(8967(a,1),12566(a,1,3)),flip(a)].">
      <j1 rule="para" parents="8967 12566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12572">
    <literal><![CDATA[
      L(x,y,T(z * u,z)) = L(x,y,u * z)
    ]]></literal>
    <justification jstring="[para(8970(a,1),12566(a,1,3))].">
      <j1 rule="para" parents="8970 12566"/>
    </justification>
  </clause>

  <clause id="12573">
    <literal><![CDATA[
      L(x,y,K(z,z \ u)) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[para(8939(a,1),12566(a,1,3))].">
      <j1 rule="para" parents="8939 12566"/>
    </justification>
  </clause>

  <clause id="12574">
    <literal><![CDATA[
      L(x,y,z * a(u,w,u)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(9522(a,1),12566(a,1,3))].">
      <j1 rule="para" parents="9522 12566"/>
    </justification>
  </clause>

  <clause id="12575">
    <literal><![CDATA[
      L(x,y,R(z,u,z) \ w) = L(x,y,z \ w)
    ]]></literal>
    <justification jstring="[para(9527(a,1),12566(a,1,3)),flip(a)].">
      <j1 rule="para" parents="9527 12566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12576">
    <literal><![CDATA[
      L(x,y,z * R(u,w,u)) = L(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(9529(a,1),12566(a,1,3))].">
      <j1 rule="para" parents="9529 12566"/>
    </justification>
  </clause>

  <clause id="12577">
    <literal><![CDATA[
      L(x,y,L(z,u,z) \ w) = L(x,y,z \ w)
    ]]></literal>
    <justification jstring="[para(9531(a,1),12566(a,1,3))].">
      <j1 rule="para" parents="9531 12566"/>
    </justification>
  </clause>

  <clause id="12579">
    <literal><![CDATA[
      L(x,y,T(z,z * u)) = L(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[para(4385(a,1),12569(a,1,3)),flip(a)].">
      <j1 rule="para" parents="4385 12569"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12580">
    <literal><![CDATA[
      L(x,y,T(z,z \ u)) = L(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[para(4440(a,1),12569(a,1,3))].">
      <j1 rule="para" parents="4440 12569"/>
    </justification>
  </clause>

  <clause id="12581">
    <literal><![CDATA[
      L(x,y,(z \ u) \ u) = L(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[para(7529(a,1),12569(a,1,3))].">
      <j1 rule="para" parents="7529 12569"/>
    </justification>
  </clause>

  <clause id="12582">
    <literal><![CDATA[
      L(x,y,K(z \ u,z)) = L(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[para(8938(a,1),12568(a,1,3))].">
      <j1 rule="para" parents="8938 12568"/>
    </justification>
  </clause>

  <clause id="12583">
    <literal><![CDATA[
      L(x,y,L(z,u,z)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(9089(a,1),12568(a,1,3))].">
      <j1 rule="para" parents="9089 12568"/>
    </justification>
  </clause>

  <clause id="12584">
    <literal><![CDATA[
      L(x,y,z / R(u,w,u)) = L(x,y,z / u)
    ]]></literal>
    <justification jstring="[para(9539(a,1),12568(a,1,3))].">
      <j1 rule="para" parents="9539 12568"/>
    </justification>
  </clause>

  <clause id="12585">
    <literal><![CDATA[
      L(x,y,T(z / u,z)) = L(x,y,u \ z)
    ]]></literal>
    <justification jstring="[para(4404(a,1),12583(a,1,3))].">
      <j1 rule="para" parents="4404 12583"/>
    </justification>
  </clause>

  <clause id="12586">
    <literal><![CDATA[
      L(x,y,T(z,u) / u) = L(x,y,u \ z)
    ]]></literal>
    <justification jstring="[para(8974(a,1),12574(a,1,3))].">
      <j1 rule="para" parents="8974 12574"/>
    </justification>
  </clause>

  <clause id="12587">
    <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,11689,a(flip),b,12570,a),flip(a)].">
      <j1 rule="hyper" parents="58 11689 12570"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12588">
    <literal><![CDATA[
      L(x,y,K(z,u * z)) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[para(5385(a,2),12571(a,1,3))].">
      <j1 rule="para" parents="5385 12571"/>
    </justification>
  </clause>

  <clause id="12589">
    <literal><![CDATA[
      L(x,y,K(z * u,(z * u) * (u \ 1))) = L(x,y,K(u * z,u \ 1))
    ]]></literal>
    <justification jstring="[para(5871(a,1),12571(a,2,3))].">
      <j1 rule="para" parents="5871 12571"/>
    </justification>
  </clause>

  <clause id="12590">
    <literal><![CDATA[
      L(x,y \ z,K(y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(5475,a,12573,a),flip(a)].">
      <j1 rule="hyper" parents="5475 12573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12591">
    <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,12414,a,b,12573,a)].">
      <j1 rule="hyper" parents="320 12414 12573"/>
    </justification>
  </clause>

  <clause id="12592">
    <literal><![CDATA[
      L(x \ y,z,K(x,y)) = x \ y
    ]]></literal>
    <justification jstring="[hyper(58,a,7518,a(flip),b,12573,a),flip(a)].">
      <j1 rule="hyper" parents="58 7518 12573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12593">
    <literal><![CDATA[
      (K(x,y) * (x \ y)) * z = K(x,y) * ((x \ y) * z)
    ]]></literal>
    <justification jstring="[hyper(1338,a,12590,a),flip(a)].">
      <j1 rule="hyper" parents="1338 12590"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12594">
    <literal><![CDATA[
      (K(x,y) * z) / (x \ y) = K(x,y) * (z / (x \ y))
    ]]></literal>
    <justification jstring="[para(12592(a,1),544(a,1,2))].">
      <j1 rule="para" parents="12592 544"/>
    </justification>
  </clause>

  <clause id="12595">
    <literal><![CDATA[
      L(x,y * z,T(y,z)) = L(x,y * z,y)
    ]]></literal>
    <justification jstring="[hyper(11194,a,12579,a),flip(a)].">
      <j1 rule="hyper" parents="11194 12579"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12596">
    <literal><![CDATA[
      L(x,y,T(z * u,u \ 1)) = L(x,y,T(z * u,z))
    ]]></literal>
    <justification jstring="[para(6174(a,1),12580(a,1,3))].">
      <j1 rule="para" parents="6174 12580"/>
    </justification>
  </clause>

  <clause id="12597">
    <literal><![CDATA[
      L(x,y / z,K(y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(7293,a,12582,a)].">
      <j1 rule="hyper" parents="7293 12582"/>
    </justification>
  </clause>

  <clause id="12598">
    <literal><![CDATA[
      L(x,y \ z,K(z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(4214,a,12582,a),flip(a)].">
      <j1 rule="hyper" parents="4214 12582"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12599">
    <literal><![CDATA[
      L(x,y,K(z * u,z \ 1)) = L(x,y,K(u,z \ 1))
    ]]></literal>
    <justification jstring="[para(4488(a,1),12582(a,1,3))].">
      <j1 rule="para" parents="4488 12582"/>
    </justification>
  </clause>

  <clause id="12600">
    <literal><![CDATA[
      L(x,y,K(z,u \ z)) = L(x,y,K(u,u \ z))
    ]]></literal>
    <justification jstring="[para(4965(a,1),12582(a,1,3)),flip(a)].">
      <j1 rule="para" parents="4965 12582"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12601">
    <literal><![CDATA[
      K(x,y) * ((x / y) * z) = (x / T(y,x)) * z
    ]]></literal>
    <justification jstring="[para(12597(a,1),5274(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12597 5274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12602">
    <literal><![CDATA[
      (K(x,y) * (y \ x)) \ z = (y \ x) \ (K(x,y) \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,298,a(flip),b,12598,a)].">
      <j1 rule="hyper" parents="58 298 12598"/>
    </justification>
  </clause>

  <clause id="12603">
    <literal><![CDATA[
      L(x,y,y / z) = L(x,y,z \ y)
    ]]></literal>
    <justification jstring="[hyper(11194,a,12585,a)].">
      <j1 rule="hyper" parents="11194 12585"/>
    </justification>
  </clause>

  <clause id="12604">
    <literal><![CDATA[
      L(x,y * z,(y * z) / y) = L(x,y * z,z)
    ]]></literal>
    <justification jstring="[para(4(a,1),12603(a,2,3))].">
      <j1 rule="para" parents="4 12603"/>
    </justification>
  </clause>

  <clause id="12605">
    <literal><![CDATA[
      L(x,y,z / T(u,z)) = L(x,y,u \ z)
    ]]></literal>
    <justification jstring="[para(4246(a,1),12586(a,1,3))].">
      <j1 rule="para" parents="4246 12586"/>
    </justification>
  </clause>

  <clause id="12606">
    <literal><![CDATA[
      L(x,T(y,z),T(y,z) \ z) = L(x,T(y,z),y \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,11196,a(flip),b,12605,a)].">
      <j1 rule="hyper" parents="58 11196 12605"/>
    </justification>
  </clause>

  <clause id="12607">
    <literal><![CDATA[
      L(x,y,(z \ T(u,z \ u)) \ w) = L(x,y,(u / z) \ w)
    ]]></literal>
    <justification jstring="[para(4423(a,1),12575(a,1,3,1))].">
      <j1 rule="para" parents="4423 12575"/>
    </justification>
  </clause>

  <clause id="12608">
    <literal><![CDATA[
      L(x,y,z * T(u,u \ w)) = L(x,y,z * T(u,w))
    ]]></literal>
    <justification jstring="[para(4440(a,1),12576(a,1,3,2))].">
      <j1 rule="para" parents="4440 12576"/>
    </justification>
  </clause>

  <clause id="12609">
    <literal><![CDATA[
      L(x,y,T(z / u,z) \ w) = L(x,y,(u \ z) \ w)
    ]]></literal>
    <justification jstring="[para(4404(a,1),12577(a,1,3,1))].">
      <j1 rule="para" parents="4404 12577"/>
    </justification>
  </clause>

  <clause id="12610">
    <literal><![CDATA[
      L(x,y,K(z,u) * (z \ u)) = L(x,y,u / z)
    ]]></literal>
    <justification jstring="[para(6080(a,1),12584(a,1,3))].">
      <j1 rule="para" parents="6080 12584"/>
    </justification>
  </clause>

  <clause id="12611">
    <literal><![CDATA[
      L(x,y,K(z,u \ z)) = L(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,12573,a(flip),b,12600,a),flip(a)].">
      <j1 rule="hyper" parents="320 12573 12600"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12612">
    <literal><![CDATA[
      L(x,y,K(z,y \ 1)) = x
    ]]></literal>
    <justification jstring="[hyper(10205,a,12611,a),flip(a)].">
      <j1 rule="hyper" parents="10205 12611"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12614">
    <literal><![CDATA[
      (K(x,y \ 1) * y) * z = K(x,y \ 1) * (y * z)
    ]]></literal>
    <justification jstring="[hyper(1338,a,12612,a),flip(a)].">
      <j1 rule="hyper" parents="1338 12612"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12622">
    <literal><![CDATA[
      K(x,y) * ((y / T(x,y)) * z) = (y / x) * z
    ]]></literal>
    <justification jstring="[hyper(5147,a,12601,a)].">
      <j1 rule="hyper" parents="5147 12601"/>
    </justification>
  </clause>

  <clause id="12623">
    <literal><![CDATA[
      L(x,y * z,z * K(y,z)) = L(x,y * z,z)
    ]]></literal>
    <justification jstring="[para(4752(a,1),12604(a,1,3))].">
      <j1 rule="para" parents="4752 12604"/>
    </justification>
  </clause>

  <clause id="12624">
    <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,12610,a)].">
      <j1 rule="hyper" parents="58 13 12610"/>
    </justification>
  </clause>

  <clause id="12625">
    <literal><![CDATA[
      R(K(x,y),x \ y,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(9265,a,12622,a)].">
      <j1 rule="hyper" parents="9265 12622"/>
    </justification>
  </clause>

  <clause id="12626">
    <literal><![CDATA[
      R(K(x,x * y),y,z) = K(x,x * y)
    ]]></literal>
    <justification jstring="[para(4(a,1),12625(a,1,2))].">
      <j1 rule="para" parents="4 12625"/>
    </justification>
  </clause>

  <clause id="12628">
    <literal><![CDATA[
      K(x,R(y \ 1,y,z) \ x) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,11673,a,b,12626,a)].">
      <j1 rule="hyper" parents="58 11673 12626"/>
    </justification>
  </clause>

  <clause id="12629">
    <literal><![CDATA[
      T(x,R(y \ 1,y,z) \ x) = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(118,a,12628,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 12628 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12630">
    <literal><![CDATA[
      R(K(x,x * y),y * z,u) = K(x,((z * u) / ((y * z) * u)) \ x)
    ]]></literal>
    <justification jstring="[para(12628(a,1),11677(a,1,1))].">
      <j1 rule="para" parents="12628 11677"/>
    </justification>
  </clause>

  <clause id="12631">
    <literal><![CDATA[
      T(x,(y / (z * y)) \ x) = T(x,x * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,3781,a(flip),b,12629,a)].">
      <j1 rule="hyper" parents="58 3781 12629"/>
    </justification>
  </clause>

  <clause id="12632">
    <literal><![CDATA[
      T(x,(y / z) \ x) = T(x,x * (z / y))
    ]]></literal>
    <justification jstring="[para(7(a,1),12631(a,1,2,1,2))].">
      <j1 rule="para" parents="7 12631"/>
    </justification>
  </clause>

  <clause id="12633">
    <literal><![CDATA[
      T(x,(y * x) / z) = T(x,x * (y / z))
    ]]></literal>
    <justification jstring="[hyper(58,a,8492,a,b,12632,a)].">
      <j1 rule="hyper" parents="58 8492 12632"/>
    </justification>
  </clause>

  <clause id="12634">
    <literal><![CDATA[
      x * K(x,x * (y / z)) = T(x,(y * x) / z)
    ]]></literal>
    <justification jstring="[hyper(320,a,4755,a(flip),b,12633,a)].">
      <j1 rule="hyper" parents="320 4755 12633"/>
    </justification>
  </clause>

  <clause id="12635">
    <literal><![CDATA[
      K(x,(y * x) / z) = K(x,x * (y / z))
    ]]></literal>
    <justification jstring="[hyper(29,a,4755,a(flip),b,12634,a)].">
      <j1 rule="hyper" parents="29 4755 12634"/>
    </justification>
  </clause>

  <clause id="12636">
    <literal><![CDATA[
      K(x,(y / z) \ x) = K(x,x * (z / y))
    ]]></literal>
    <justification jstring="[hyper(8497,a,12635,a)].">
      <j1 rule="hyper" parents="8497 12635"/>
    </justification>
  </clause>

  <clause id="12637">
    <literal><![CDATA[
      K(x,x * (y / ((z * x) * u))) = K(x,y / (z * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,11100,a(flip),b,12635,a),flip(a)].">
      <j1 rule="hyper" parents="58 11100 12635"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12638">
    <literal><![CDATA[
      (x * K(y,y * (z / u))) \ x = K((u / z) \ y,y)
    ]]></literal>
    <justification jstring="[para(12636(a,1),6338(a,1,1,2))].">
      <j1 rule="para" parents="12636 6338"/>
    </justification>
  </clause>

  <clause id="12639">
    <literal><![CDATA[
      R(K(x,x * (y / z)),x * u,w) = K(R(x,u,w),(z / y) \ x)
    ]]></literal>
    <justification jstring="[para(12636(a,1),6743(a,1,1))].">
      <j1 rule="para" parents="12636 6743"/>
    </justification>
  </clause>

  <clause id="12640">
    <literal><![CDATA[
      L(x,y,T(z * u,u \ 1)) = L(x,y,u * z)
    ]]></literal>
    <justification jstring="[hyper(320,a,12572,a(flip),b,12596,a),flip(a)].">
      <j1 rule="hyper" parents="320 12572 12596"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12641">
    <literal><![CDATA[
      (x \ y) \ (K(y,x) \ z) = (T(x,y) \ y) \ z
    ]]></literal>
    <justification jstring="[para(5131(a,1),12602(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5131 12602"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12642">
    <literal><![CDATA[
      (x \ y) \ (K(x,y) * z) = (T(x,y) \ y) \ z
    ]]></literal>
    <justification jstring="[para(5130(a,1),12641(a,1,2))].">
      <j1 rule="para" parents="5130 12641"/>
    </justification>
  </clause>

  <clause id="12643">
    <literal><![CDATA[
      L(T(x,y) \ z,T(x,y),x \ y) = y \ ((T(y,x) / x) * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,11214,a(flip),b,12606,a),flip(a)].">
      <j1 rule="hyper" parents="58 11214 12606"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12644">
    <literal><![CDATA[
      L(x,y,(z / u) * T(u,w)) = L(x,y,z * K(u,u \ w))
    ]]></literal>
    <justification jstring="[para(6151(a,1),12608(a,1,3)),flip(a)].">
      <j1 rule="para" parents="6151 12608"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12645">
    <literal><![CDATA[
      (x * K(y,x \ 1)) * z = K(y,x \ 1) * (x * z)
    ]]></literal>
    <justification jstring="[para(2285(a,1),12614(a,1,1))].">
      <j1 rule="para" parents="2285 12614"/>
    </justification>
  </clause>

  <clause id="12646">
    <literal><![CDATA[
      K((x / y) \ z,z) = K(z * (y / x),z)
    ]]></literal>
    <justification jstring="[hyper(6345,a,12638,a),flip(a)].">
      <j1 rule="hyper" parents="6345 12638"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12647">
    <literal><![CDATA[
      K(x / y,z) * a(z,y \ x,z) = K(z * (x / y),z)
    ]]></literal>
    <justification jstring="[hyper(58,a,12142,a,b,12646,a)].">
      <j1 rule="hyper" parents="58 12142 12646"/>
    </justification>
  </clause>

  <clause id="12648">
    <literal><![CDATA[
      (x * K(y,x \ 1)) * z = x * (K(y,x \ 1) * z)
    ]]></literal>
    <justification jstring="[hyper(320,a,5929,a(flip),b,12645,a),flip(a)].">
      <j1 rule="hyper" parents="320 5929 12645"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12649">
    <literal><![CDATA[
      L(x,K(y,z \ 1),z) = x
    ]]></literal>
    <justification jstring="[hyper(479,a,12648,a)].">
      <j1 rule="hyper" parents="479 12648"/>
    </justification>
  </clause>

  <clause id="12655">
    <literal><![CDATA[
      L(x,K(y,z \ u),u \ z) = x
    ]]></literal>
    <justification jstring="[para(6108(a,1),12649(a,1,2))].">
      <j1 rule="para" parents="6108 12649"/>
    </justification>
  </clause>

  <clause id="12656">
    <literal><![CDATA[
      L(x,K(y,z),u \ (u / z)) = x
    ]]></literal>
    <justification jstring="[para(6131(a,1),12649(a,1,2))].">
      <j1 rule="para" parents="6131 12649"/>
    </justification>
  </clause>

  <clause id="12657">
    <literal><![CDATA[
      L(x,K(y,z \ u),u \ z) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(12655(a,1),45(a,2))].">
      <j1 rule="para" parents="12655 45"/>
    </justification>
  </clause>

  <clause id="12658">
    <literal><![CDATA[
      L(x,K(y,z),u \ (u / z)) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(12656(a,1),45(a,2))].">
      <j1 rule="para" parents="12656 45"/>
    </justification>
  </clause>

  <clause id="12659">
    <literal><![CDATA[
      a(x,y / z,x) = a(x,z \ y,x)
    ]]></literal>
    <justification jstring="[hyper(29,a,8968,a,b,12647,a)].">
      <j1 rule="hyper" parents="29 8968 12647"/>
    </justification>
  </clause>

  <clause id="12661">
    <literal><![CDATA[
      a(x,y / (z * y),x) = a(x,z \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,12148,a(flip),b,12659,a),flip(a)].">
      <j1 rule="hyper" parents="320 12148 12659"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12662">
    <literal><![CDATA[
      a(x,(y \ z) \ z,x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[para(72(a,1),12659(a,1,2)),flip(a)].">
      <j1 rule="para" parents="72 12659"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12663">
    <literal><![CDATA[
      a(x,T(y,z),x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(12545,a,12662,a)].">
      <j1 rule="hyper" parents="12545 12662"/>
    </justification>
  </clause>

  <clause id="12664">
    <literal><![CDATA[
      a(x,y * K(z,y),x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[para(5663(a,1),12662(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5663 12662"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12665">
    <literal><![CDATA[
      a(x,T(y / z,u),x) = a(x,z \ y,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,12659,a(flip),b,12663,a),flip(a)].">
      <j1 rule="hyper" parents="320 12659 12663"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12667">
    <literal><![CDATA[
      L(x,T(y,z),x) = a(x,y,x) \ x
    ]]></literal>
    <justification jstring="[para(12663(a,1),9089(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12663 9089"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12668">
    <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(12663(a,1),8980(a,1,1))].">
      <j1 rule="para" parents="12663 8980"/>
    </justification>
  </clause>

  <clause id="12669">
    <literal><![CDATA[
      L(a(x,y,x),y,z) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,12410,a(flip),b,12664,a)].">
      <j1 rule="hyper" parents="58 12410 12664"/>
    </justification>
  </clause>

  <clause id="12672">
    <literal><![CDATA[
      L(x,T(y,z),x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,9089,a(flip),b,12667,a),flip(a)].">
      <j1 rule="hyper" parents="320 9089 12667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12673">
    <literal><![CDATA[
      L(x,T(y,z),x) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,x) = u
    ]]></literal>
    <justification jstring="[para(12667(a,2),9571(a,1))].">
      <j1 rule="para" parents="12667 9571"/>
    </justification>
  </clause>

  <clause id="12674">
    <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,9659,a,b,12672,a),flip(a)].">
      <j1 rule="hyper" parents="320 9659 12672"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12677">
    <literal><![CDATA[
      L(x,y / z,x) = L(x,z \ y,x)
    ]]></literal>
    <justification jstring="[para(107(a,1),12672(a,1,2)),flip(a)].">
      <j1 rule="para" parents="107 12672"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12681">
    <literal><![CDATA[
      L(x,y * K(z,y),x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[para(4816(a,1),12672(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4816 12672"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12683">
    <literal><![CDATA[
      L(x,R(y * K(z,y),z,u),x) = L(x,(z * u) \ ((z * y) * u),x)
    ]]></literal>
    <justification jstring="[para(4927(a,2),12677(a,1,2))].">
      <j1 rule="para" parents="4927 12677"/>
    </justification>
  </clause>

  <clause id="12684">
    <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(5923(a,2),12677(a,1,2))].">
      <j1 rule="para" parents="5923 12677"/>
    </justification>
  </clause>

  <clause id="12685">
    <literal><![CDATA[
      L(x,R(y * K(z,y),u,w),x) = L(x,R(y,u,w),x)
    ]]></literal>
    <justification jstring="[para(5518(a,1),12681(a,1,2))].">
      <j1 rule="para" parents="5518 12681"/>
    </justification>
  </clause>

  <clause id="12686">
    <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(4052(a,1),12661(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4052 12661"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12687">
    <literal><![CDATA[
      a(x,R(y \ z,y,u),x) = a(x,(y * u) \ (z * u),x)
    ]]></literal>
    <justification jstring="[para(648(a,1),12665(a,1,2))].">
      <j1 rule="para" parents="648 12665"/>
    </justification>
  </clause>

  <clause id="12688">
    <literal><![CDATA[
      T(x,T(x * y,z)) = T(x,x * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(8727,a,12674,a),flip(a)].">
      <j1 rule="hyper" parents="8727 12674"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12689">
    <literal><![CDATA[
      T(x,T(x * (x \ y),z)) = T(x,y * K(x \ y,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,11297,a,b,12688,a),flip(a)].">
      <j1 rule="hyper" parents="320 11297 12688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12690">
    <literal><![CDATA[
      T(x / T(y,x),z) * T(y,T(y * (y \ x),z)) = y * T(y \ x,z)
    ]]></literal>
    <justification jstring="[para(12688(a,2),11481(a,1,2))].">
      <j1 rule="para" parents="12688 11481"/>
    </justification>
  </clause>

  <clause id="12692">
    <literal><![CDATA[
      T(x,y * K(x \ y,z)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(5(a,1),12689(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 12689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12693">
    <literal><![CDATA[
      T(x \ y,y * K(x,T(z,y))) = T(x \ y,T(y,z))
    ]]></literal>
    <justification jstring="[para(7165(a,1),12692(a,1,2,2))].">
      <j1 rule="para" parents="7165 12692"/>
    </justification>
  </clause>

  <clause id="12694">
    <literal><![CDATA[
      T(x \ y,K(x,z) * y) = T(x \ y,T(y,z))
    ]]></literal>
    <justification jstring="[para(7179(a,1),12693(a,1,2))].">
      <j1 rule="para" parents="7179 12693"/>
    </justification>
  </clause>

  <clause id="12695">
    <literal><![CDATA[
      a(x,(y * z) \ (u * z),x) = a(x,y \ u,x)
    ]]></literal>
    <justification jstring="[hyper(12544,a,12687,a),flip(a)].">
      <j1 rule="hyper" parents="12544 12687"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12697">
    <literal><![CDATA[
      L(x,(y * z) \ (u * z),x) = (w / x) \ (a(x,y \ u,x) \ w)
    ]]></literal>
    <justification jstring="[para(12695(a,1),9557(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12695 9557"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12698">
    <literal><![CDATA[
      L(x,y,K(z,z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,K(z,u)) = w
    ]]></literal>
    <justification jstring="[para(12591(a,1),373(a,1)),flip(b)].">
      <j1 rule="para" parents="12591 373"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12699">
    <literal><![CDATA[
      L(x,y,K(z,u \ z)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(12600(a,2),12698(a,1))].">
      <j1 rule="para" parents="12600 12698"/>
    </justification>
  </clause>

  <clause id="12700">
    <literal><![CDATA[
      L(x,y,z * K(u,u \ w)) = L(x,y,z * K(u,w))
    ]]></literal>
    <justification jstring="[para(6151(a,1),12644(a,1,3)),flip(a)].">
      <j1 rule="para" parents="6151 12644"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12701">
    <literal><![CDATA[
      K(R(x,y,z),(u / w) \ x) = K(R(x,y,z),x * (w / u))
    ]]></literal>
    <justification jstring="[hyper(58,a,6743,a(flip),b,12639,a),flip(a)].">
      <j1 rule="hyper" parents="58 6743 12639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12702">
    <literal><![CDATA[
      L(x,(y * z) \ (u * z),x) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y \ u,x) = w
    ]]></literal>
    <justification jstring="[para(12697(a,2),9573(a,1))].">
      <j1 rule="para" parents="12697 9573"/>
    </justification>
  </clause>

  <clause id="12703">
    <literal><![CDATA[
      R(K(x,x * y),y * z,u) = K(x,x * (((y * z) * u) / (z * u)))
    ]]></literal>
    <justification jstring="[hyper(320,a,12636,a(flip),b,12630,a),flip(a)].">
      <j1 rule="hyper" parents="320 12636 12630"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12705">
    <literal><![CDATA[
      L(x,(y * z) \ ((y * u) * z),x) = L(x,R(u,y,z),x)
    ]]></literal>
    <justification jstring="[hyper(58,a,12685,a(flip),b,12683,a),flip(a)].">
      <j1 rule="hyper" parents="58 12685 12683"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12706">
    <literal><![CDATA[
      L(x,R(y,z,u),x) = L(x,z \ (z * y),x)
    ]]></literal>
    <justification jstring="[hyper(12702,a,12705,a),flip(a)].">
      <j1 rule="hyper" parents="12702 12705"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12708">
    <literal><![CDATA[
      L(x,R(y,z,u),x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[para(4(a,1),12706(a,2,2))].">
      <j1 rule="para" parents="4 12706"/>
    </justification>
  </clause>

  <clause id="12709">
    <literal><![CDATA[
      R(K(x,x * y),y * z,u) = K(x,x * R(y,z,u))
    ]]></literal>
    <justification jstring="[para(15(a,2),12703(a,2,2,2))].">
      <j1 rule="para" parents="15 12703"/>
    </justification>
  </clause>

  <clause id="12710">
    <literal><![CDATA[
      K(x,R(x * y,y * z,u)) = K(x,x * R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(12504,a,12709,a)].">
      <j1 rule="hyper" parents="12504 12709"/>
    </justification>
  </clause>

  <clause id="12711">
    <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),12589(a,1,3,2))].">
      <j1 rule="para" parents="261 12589"/>
    </justification>
  </clause>

  <clause id="12712">
    <literal><![CDATA[
      L(x,y,K(z * u,z \ 1)) = L(x,y,K(u * z,u))
    ]]></literal>
    <justification jstring="[para(6958(a,1),12711(a,1,3)),flip(a)].">
      <j1 rule="para" parents="6958 12711"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12713">
    <literal><![CDATA[
      L(x,y,K(z * u,z \ 1)) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,12570,a(flip),b,12712,a),flip(a)].">
      <j1 rule="hyper" parents="320 12570 12712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12715">
    <literal><![CDATA[
      L(x,y,K(z,u \ 1)) = L(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,12599,a(flip),b,12713,a)].">
      <j1 rule="hyper" parents="58 12599 12713"/>
    </justification>
  </clause>

  <clause id="12716">
    <literal><![CDATA[
      L(x,y,K(z \ u,w)) = L(x,y,K(w,u \ z))
    ]]></literal>
    <justification jstring="[para(6108(a,1),12715(a,1,3)),flip(a)].">
      <j1 rule="para" parents="6108 12715"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12717">
    <literal><![CDATA[
      L(x,y,K(z \ u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(12716(a,2),12699(a,1))].">
      <j1 rule="para" parents="12716 12699"/>
    </justification>
  </clause>

  <clause id="12718">
    <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),12717(a,1,3,1))].">
      <j1 rule="para" parents="4 12717"/>
    </justification>
  </clause>

  <clause id="12719">
    <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),12690(a,1,2,2,1))].">
      <j1 rule="para" parents="5 12690"/>
    </justification>
  </clause>

  <clause id="12720">
    <literal><![CDATA[
      x * K(T(x,y) / y,z) = y * T(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,9689,a(flip),b,12719,a)].">
      <j1 rule="hyper" parents="58 9689 12719"/>
    </justification>
  </clause>

  <clause id="12721">
    <literal><![CDATA[
      K(T(x,y) / y,z) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(29,a,6114,a(flip),b,12720,a),flip(a)].">
      <j1 rule="hyper" parents="29 6114 12720"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12722">
    <literal><![CDATA[
      K(x / T(y,x),z) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,9640,a(flip),b,12721,a)].">
      <j1 rule="hyper" parents="58 9640 12721"/>
    </justification>
  </clause>

  <clause id="12723">
    <literal><![CDATA[
      T(x * K(x / y,z),x) = x * K(y \ x,z)
    ]]></literal>
    <justification jstring="[para(12721(a,1),9815(a,2,2))].">
      <j1 rule="para" parents="12721 9815"/>
    </justification>
  </clause>

  <clause id="12724">
    <literal><![CDATA[
      (x \ (x * K(y \ x,z))) \ (x * K(x / y,z)) = L(x,K(y \ x,z),x)
    ]]></literal>
    <justification jstring="[para(12723(a,1),9890(a,1,1,2))].">
      <j1 rule="para" parents="12723 9890"/>
    </justification>
  </clause>

  <clause id="12725">
    <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),12724(a,1,1))].">
      <j1 rule="para" parents="4 12724"/>
    </justification>
  </clause>

  <clause id="12726">
    <literal><![CDATA[
      L(x,K(y \ x,z),x) = x
    ]]></literal>
    <justification jstring="[hyper(8115,a,12725,a)].">
      <j1 rule="hyper" parents="8115 12725"/>
    </justification>
  </clause>

  <clause id="12728">
    <literal><![CDATA[
      L(x,K(y,z),x) = x
    ]]></literal>
    <justification jstring="[para(75(a,1),12726(a,1,2,1))].">
      <j1 rule="para" parents="75 12726"/>
    </justification>
  </clause>

  <clause id="12729">
    <literal><![CDATA[
      T(K(x,y) * z,z) = z * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(10052,a,12728,a)].">
      <j1 rule="hyper" parents="10052 12728"/>
    </justification>
  </clause>

  <clause id="12732">
    <literal><![CDATA[
      T(x * T(x \ y,z),y) = y * K(y / x,z)
    ]]></literal>
    <justification jstring="[para(4817(a,1),12729(a,1,1))].">
      <j1 rule="para" parents="4817 12729"/>
    </justification>
  </clause>

  <clause id="12733">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ y,z) = y * K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,1960,a,b,12732,a)].">
      <j1 rule="hyper" parents="58 1960 12732"/>
    </justification>
  </clause>

  <clause id="12734">
    <literal><![CDATA[
      K(T(x,y) \ y,z) = K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(6155,a,12733,a)].">
      <j1 rule="hyper" parents="6155 12733"/>
    </justification>
  </clause>

  <clause id="12735">
    <literal><![CDATA[
      K(x / y,z) * a(z,T(y,x) \ x,z) = K(z * (T(y,x) \ x),z)
    ]]></literal>
    <justification jstring="[para(12734(a,1),8968(a,1,1))].">
      <j1 rule="para" parents="12734 8968"/>
    </justification>
  </clause>

  <clause id="12736">
    <literal><![CDATA[
      T(x,y / z) \ R(x,T(z,y) \ y,x) = K(x * (T(z,y) \ y),x)
    ]]></literal>
    <justification jstring="[hyper(8953,a,12735,a)].">
      <j1 rule="hyper" parents="8953 12735"/>
    </justification>
  </clause>

  <clause id="12737">
    <literal><![CDATA[
      T(x,T(y,z) \ z) = T(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(5295,a,12736,a)].">
      <j1 rule="hyper" parents="5295 12736"/>
    </justification>
  </clause>

  <clause id="12738">
    <literal><![CDATA[
      T(x,y \ T(z,y)) = T(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(58,a,6601,a(flip),b,12737,a)].">
      <j1 rule="hyper" parents="58 6601 12737"/>
    </justification>
  </clause>

  <clause id="12739">
    <literal><![CDATA[
      T(T(x,K(y,z)),y / z) = T(x,y / T(z,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,9115,a(flip),b,12738,a),flip(a)].">
      <j1 rule="hyper" parents="58 9115 12738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12740">
    <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,12738,a(flip),b,8378,a),flip(a)].">
      <j1 rule="hyper" parents="119 12738 8378"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12741">
    <literal><![CDATA[
      T(x,y / T(z,y)) = T(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(8368,a,12739,a),flip(a)].">
      <j1 rule="hyper" parents="8368 12739"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12742">
    <literal><![CDATA[
      T(x,y / T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(12739(a,1),8368(a,1))].">
      <j1 rule="para" parents="12739 8368"/>
    </justification>
  </clause>

  <clause id="12743">
    <literal><![CDATA[
      T(x,T(y,z) / z) = T(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(9500,a,12741,a)].">
      <j1 rule="hyper" parents="9500 12741"/>
    </justification>
  </clause>

  <clause id="12744">
    <literal><![CDATA[
      T(x,y / T(T(z,y),u)) = T(x,T(z,u) \ y)
    ]]></literal>
    <justification jstring="[para(18(a,1),12741(a,1,2,2))].">
      <j1 rule="para" parents="18 12741"/>
    </justification>
  </clause>

  <clause id="12745">
    <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(12741(a,1),12742(a,1,2,2))].">
      <j1 rule="para" parents="12741 12742"/>
    </justification>
  </clause>

  <clause id="12746">
    <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(12694(a,1),12744(a,1,2,2,1))].">
      <j1 rule="para" parents="12694 12744"/>
    </justification>
  </clause>

  <clause id="12747">
    <literal><![CDATA[
      T(x,T(y \ T(z,y),u)) = T(x,T(z / y,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,8379,a(flip),b,12740,a),flip(a)].">
      <j1 rule="hyper" parents="320 8379 12740"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12748">
    <literal><![CDATA[
      (K(x,y) * ((x \ y) * z)) \ ((K(x,y) * (x \ y)) * (z * u)) = L(u,z,y / x)
    ]]></literal>
    <justification jstring="[para(12593(a,1),12624(a,1,1))].">
      <j1 rule="para" parents="12593 12624"/>
    </justification>
  </clause>

  <clause id="12749">
    <literal><![CDATA[
      (K(x,y) * ((x \ y) * z)) \ (K(x,y) * ((x \ y) * (z * u))) = L(u,z,y / x)
    ]]></literal>
    <justification jstring="[para(12593(a,1),12748(a,1,2))].">
      <j1 rule="para" parents="12593 12748"/>
    </justification>
  </clause>

  <clause id="12750">
    <literal><![CDATA[
      L(L(x,y,z \ u),(z \ u) * y,K(z,u)) = L(x,y,u / z)
    ]]></literal>
    <justification jstring="[hyper(833,a,12749,a)].">
      <j1 rule="hyper" parents="833 12749"/>
    </justification>
  </clause>

  <clause id="12751">
    <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),12684(a,2,2))].">
      <j1 rule="para" parents="9 12684"/>
    </justification>
  </clause>

  <clause id="12752">
    <literal><![CDATA[
      L(x,y \ R(y,z,u),x) = L(x,a(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(58,a,12708,a(flip),b,12751,a)].">
      <j1 rule="hyper" parents="58 12708 12751"/>
    </justification>
  </clause>

  <clause id="12754">
    <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(12411(a,1),12422(a,2,1))].">
      <j1 rule="para" parents="12411 12422"/>
    </justification>
  </clause>

  <clause id="12755">
    <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,12420,a(flip),b,12754,a),flip(a)].">
      <j1 rule="hyper" parents="320 12420 12754"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12756">
    <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),12755(a,2,2))].">
      <j1 rule="para" parents="15 12755"/>
    </justification>
  </clause>

  <clause id="12757">
    <literal><![CDATA[
      R(a(x,y,x) * z,u,w) = a(x,y,x) * R(z,u,w)
    ]]></literal>
    <justification jstring="[para(12414(a,1),12756(a,1,2))].">
      <j1 rule="para" parents="12414 12756"/>
    </justification>
  </clause>

  <clause id="12758">
    <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(12757(a,2),12186(a,1,1,2))].">
      <j1 rule="para" parents="12757 12186"/>
    </justification>
  </clause>

  <clause id="12759">
    <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(12411(a,1),12432(a,1,2,1))].">
      <j1 rule="para" parents="12411 12432"/>
    </justification>
  </clause>

  <clause id="12760">
    <literal><![CDATA[
      (x * (y * z)) \ (x * (y * (T(u * z,u) / u))) = a(u,(x * (y * z)) / (x * y),u)
    ]]></literal>
    <justification jstring="[para(4937(a,1),12486(a,2,2))].">
      <j1 rule="para" parents="4937 12486"/>
    </justification>
  </clause>

  <clause id="12761">
    <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(8978,a,12760,a)].">
      <j1 rule="hyper" parents="8978 12760"/>
    </justification>
  </clause>

  <clause id="12762">
    <literal><![CDATA[
      L(a(x,y,x),z * y,u) = a(x,(u * (z * y)) / (u * z),x)
    ]]></literal>
    <justification jstring="[para(12669(a,1),12761(a,1,1))].">
      <j1 rule="para" parents="12669 12761"/>
    </justification>
  </clause>

  <clause id="12763">
    <literal><![CDATA[
      L(a(x,y,x),z * y,u) = a(x,(u * z) \ (u * (z * y)),x)
    ]]></literal>
    <justification jstring="[hyper(320,a,12659,a(flip),b,12762,a),flip(a)].">
      <j1 rule="hyper" parents="320 12659 12762"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12765">
    <literal><![CDATA[
      L(a(x,y,x),z * y,u) = a(x,L(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(13(a,2),12763(a,2,2))].">
      <j1 rule="para" parents="13 12763"/>
    </justification>
  </clause>

  <clause id="12766">
    <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(12411(a,1),12759(a,1,2))].">
      <j1 rule="para" parents="12411 12759"/>
    </justification>
  </clause>

  <clause id="12767">
    <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(835,a,12766,a)].">
      <j1 rule="hyper" parents="835 12766"/>
    </justification>
  </clause>

  <clause id="12768">
    <literal><![CDATA[
      a(a(x,y,x) * z,u,w) = a(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(12419,a,12767,a),flip(a)].">
      <j1 rule="hyper" parents="12419 12767"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12770">
    <literal><![CDATA[
      a(a(x,y,x) \ z,u,w) = a(z,u,w)
    ]]></literal>
    <justification jstring="[para(5(a,1),12768(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5 12768"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12771">
    <literal><![CDATA[
      a(R(x,y,x),z,u) = a(x,z,u)
    ]]></literal>
    <justification jstring="[para(8956(a,1),12768(a,1,1))].">
      <j1 rule="para" parents="8956 12768"/>
    </justification>
  </clause>

  <clause id="12772">
    <literal><![CDATA[
      a(K(x * y,y),z,u) = a(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(8965(a,1),12768(a,1,1))].">
      <j1 rule="para" parents="8965 12768"/>
    </justification>
  </clause>

  <clause id="12773">
    <literal><![CDATA[
      a(T(x * y,x),z,u) = a(y * x,z,u)
    ]]></literal>
    <justification jstring="[para(8970(a,1),12768(a,1,1))].">
      <j1 rule="para" parents="8970 12768"/>
    </justification>
  </clause>

  <clause id="12774">
    <literal><![CDATA[
      a(K(x,x \ y),z,u) = a(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(8939(a,1),12768(a,1,1))].">
      <j1 rule="para" parents="8939 12768"/>
    </justification>
  </clause>

  <clause id="12775">
    <literal><![CDATA[
      a(x * a(y,z,y),u,w) = a(x,u,w)
    ]]></literal>
    <justification jstring="[para(9522(a,1),12768(a,1,1))].">
      <j1 rule="para" parents="9522 12768"/>
    </justification>
  </clause>

  <clause id="12776">
    <literal><![CDATA[
      a(R(x,y,x) * z,u,w) = a(x * z,u,w)
    ]]></literal>
    <justification jstring="[para(9528(a,1),12768(a,1,1))].">
      <j1 rule="para" parents="9528 12768"/>
    </justification>
  </clause>

  <clause id="12777">
    <literal><![CDATA[
      a(T(x * (y / x),x),z,u) = a(y,z,u)
    ]]></literal>
    <justification jstring="[para(9530(a,1),12768(a,1,1))].">
      <j1 rule="para" parents="9530 12768"/>
    </justification>
  </clause>

  <clause id="12778">
    <literal><![CDATA[
      a(T(x,x \ y),z,u) = a(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(4440(a,1),12771(a,1,1))].">
      <j1 rule="para" parents="4440 12771"/>
    </justification>
  </clause>

  <clause id="12779">
    <literal><![CDATA[
      a((x \ y) \ y,z,u) = a(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(7529(a,1),12771(a,1,1))].">
      <j1 rule="para" parents="7529 12771"/>
    </justification>
  </clause>

  <clause id="12780">
    <literal><![CDATA[
      a(K(x \ y,x),z,u) = a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(8938(a,1),12770(a,1,1))].">
      <j1 rule="para" parents="8938 12770"/>
    </justification>
  </clause>

  <clause id="12781">
    <literal><![CDATA[
      a(K(x \ 1,y),z,u) = a(K(x \ y,y),z,u)
    ]]></literal>
    <justification jstring="[para(8972(a,1),12770(a,1,1))].">
      <j1 rule="para" parents="8972 12770"/>
    </justification>
  </clause>

  <clause id="12782">
    <literal><![CDATA[
      a(L(x,y,x),z,u) = a(x,z,u)
    ]]></literal>
    <justification jstring="[para(9089(a,1),12770(a,1,1))].">
      <j1 rule="para" parents="9089 12770"/>
    </justification>
  </clause>

  <clause id="12783">
    <literal><![CDATA[
      a(T(x / y,x),z,u) = a(y \ x,z,u)
    ]]></literal>
    <justification jstring="[para(4404(a,1),12782(a,1,1))].">
      <j1 rule="para" parents="4404 12782"/>
    </justification>
  </clause>

  <clause id="12784">
    <literal><![CDATA[
      a(T(x,x \ y),z,u) = a((x \ y) \ y,z,u)
    ]]></literal>
    <justification jstring="[para(6309(a,1),12782(a,1,1))].">
      <j1 rule="para" parents="6309 12782"/>
    </justification>
  </clause>

  <clause id="12785">
    <literal><![CDATA[
      a(T(x,y) / y,z,u) = a(y \ x,z,u)
    ]]></literal>
    <justification jstring="[para(8974(a,1),12775(a,1,1))].">
      <j1 rule="para" parents="8974 12775"/>
    </justification>
  </clause>

  <clause id="12786">
    <literal><![CDATA[
      a(K(x,y \ x),z,u) = a(K(y,y \ x),z,u)
    ]]></literal>
    <justification jstring="[para(5(a,1),12772(a,1,1,1))].">
      <j1 rule="para" parents="5 12772"/>
    </justification>
  </clause>

  <clause id="12787">
    <literal><![CDATA[
      a(T(x * y,y \ 1),z,u) = a(T(x * y,x),z,u)
    ]]></literal>
    <justification jstring="[para(6174(a,1),12778(a,1,1))].">
      <j1 rule="para" parents="6174 12778"/>
    </justification>
  </clause>

  <clause id="12788">
    <literal><![CDATA[
      K(x,x * (y \ R(y,z,u))) = a(K(x,y),z * y,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,12561,a,b,12780,a)].">
      <j1 rule="hyper" parents="58 12561 12780"/>
    </justification>
  </clause>

  <clause id="12789">
    <literal><![CDATA[
      a(T(x,x \ y) * z,u,w) = a(T(x,y) * z,u,w)
    ]]></literal>
    <justification jstring="[para(4440(a,1),12776(a,1,1,1))].">
      <j1 rule="para" parents="4440 12776"/>
    </justification>
  </clause>

  <clause id="12790">
    <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(3911(a,1),12784(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="3911 12784"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12791">
    <literal><![CDATA[
      a(K(x,y \ x),z,u) = a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(320,a,12774,a(flip),b,12786,a),flip(a)].">
      <j1 rule="hyper" parents="320 12774 12786"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12792">
    <literal><![CDATA[
      a(K(x \ y,y),z,u) = a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(5196(a,1),12791(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5196 12791"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12793">
    <literal><![CDATA[
      a(K(x \ 1,y),z,u) = a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,12781,a,b,12792,a)].">
      <j1 rule="hyper" parents="58 12781 12792"/>
    </justification>
  </clause>

  <clause id="12794">
    <literal><![CDATA[
      a(K(x,y \ 1),z,u) = a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(3317(a,1),12793(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3317 12793"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12795">
    <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(11148(a,2),12793(a,2,1)),flip(a)].">
      <j1 rule="para" parents="11148 12793"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12796">
    <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,11966,a,b,12794,a)].">
      <j1 rule="hyper" parents="58 11966 12794"/>
    </justification>
  </clause>

  <clause id="12797">
    <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(12496(a,1),12794(a,2,1))].">
      <j1 rule="para" parents="12496 12794"/>
    </justification>
  </clause>

  <clause id="12798">
    <literal><![CDATA[
      a(T(x * y,y \ 1),z,u) = a(y * x,z,u)
    ]]></literal>
    <justification jstring="[hyper(320,a,12773,a(flip),b,12787,a),flip(a)].">
      <j1 rule="hyper" parents="320 12773 12787"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12799">
    <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,5610,a,b,12788,a)].">
      <j1 rule="hyper" parents="58 5610 12788"/>
    </justification>
  </clause>

  <clause id="12800">
    <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,12052,a,b,12797,a)].">
      <j1 rule="hyper" parents="58 12052 12797"/>
    </justification>
  </clause>

  <clause id="12801">
    <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(6959(a,1),12795(a,2,1))].">
      <j1 rule="para" parents="6959 12795"/>
    </justification>
  </clause>

  <clause id="12802">
    <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,12793,a(flip),b,12801,a),flip(a)].">
      <j1 rule="hyper" parents="320 12793 12801"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12803">
    <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(11148(a,1),12802(a,1,1))].">
      <j1 rule="para" parents="11148 12802"/>
    </justification>
  </clause>

  <clause id="12804">
    <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(12496(a,1),12803(a,2,1))].">
      <j1 rule="para" parents="12496 12803"/>
    </justification>
  </clause>

  <clause id="12805">
    <literal><![CDATA[
      a(K(x,R(y,z,u)),w,v5) = R(a(K(x,y),w,v5),z,u)
    ]]></literal>
    <justification jstring="[para(12796(a,1),12800(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12796 12800"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12806">
    <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,12563,a(flip),b,12805,a),flip(a)].">
      <j1 rule="hyper" parents="320 12563 12805"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12807">
    <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,12804,a(flip),b,12806,a)].">
      <j1 rule="hyper" parents="58 12804 12806"/>
    </justification>
  </clause>

  <clause id="12808">
    <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(12752(a,1),12799(a,1,2))].">
      <j1 rule="para" parents="12752 12799"/>
    </justification>
  </clause>

  <clause id="12809">
    <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(5462,a,12808,a)].">
      <j1 rule="hyper" parents="5462 12808"/>
    </justification>
  </clause>

  <clause id="12810">
    <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),12309(a,2,1,2,2,1,2))].">
      <j1 rule="para" parents="60 12309"/>
    </justification>
  </clause>

  <clause id="12811">
    <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),12810(a,2,1,2))].">
      <j1 rule="para" parents="2 12810"/>
    </justification>
  </clause>

  <clause id="12812">
    <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(12811(a,2),8061(a,1))].">
      <j1 rule="para" parents="12811 8061"/>
    </justification>
  </clause>

  <clause id="12813">
    <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,11439,a(flip),b,12511,a)].">
      <j1 rule="hyper" parents="58 11439 12511"/>
    </justification>
  </clause>

  <clause id="12814">
    <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,5763,a(flip),b,12587,a),flip(a)].">
      <j1 rule="hyper" parents="58 5763 12587"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12815">
    <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(7275(a,1),12814(a,1,1,1))].">
      <j1 rule="para" parents="7275 12814"/>
    </justification>
  </clause>

  <clause id="12816">
    <literal><![CDATA[
      (K(x,x * y) \ z) \ T(x * y,x) = (K(x,y) \ z) \ (y * x)
    ]]></literal>
    <justification jstring="[para(4147(a,1),12815(a,1,2,1))].">
      <j1 rule="para" parents="4147 12815"/>
    </justification>
  </clause>

  <clause id="12818">
    <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(5133(a,1),12813(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5133 12813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12819">
    <literal><![CDATA[
      L(x,K(y,z) * K(y,u),K(z,y) * K(u,y)) = x
    ]]></literal>
    <justification jstring="[hyper(320,a,5133,a(flip),b,12818,a),flip(a)].">
      <j1 rule="hyper" parents="320 5133 12818"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12822">
    <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),12758(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 12758"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12823">
    <literal><![CDATA[
      R(x,y \ R(y,z,u),x) = x
    ]]></literal>
    <justification jstring="[hyper(1327,a,12822,a)].">
      <j1 rule="hyper" parents="1327 12822"/>
    </justification>
  </clause>

  <clause id="12824">
    <literal><![CDATA[
      L(x,y \ R(y,z,u),x) = x
    ]]></literal>
    <justification jstring="[para(12823(a,1),4332(a,1,1))].">
      <j1 rule="para" parents="12823 4332"/>
    </justification>
  </clause>

  <clause id="12825">
    <literal><![CDATA[
      L(x,a(y,z,u),x) = x
    ]]></literal>
    <justification jstring="[hyper(58,a,12752,a(flip),b,12824,a)].">
      <j1 rule="hyper" parents="58 12752 12824"/>
    </justification>
  </clause>

  <clause id="12826">
    <literal><![CDATA[
      R(x,a(y,z,u),x) = x
    ]]></literal>
    <justification jstring="[hyper(6845,a,12825,a),flip(a)].">
      <j1 rule="hyper" parents="6845 12825"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12828">
    <literal><![CDATA[
      L(T(x,y),a(z,u,w),x) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,7503,a(flip),b,12825,a)].">
      <j1 rule="hyper" parents="58 7503 12825"/>
    </justification>
  </clause>

  <clause id="12829">
    <literal><![CDATA[
      a(x,a(y,z,u),x) = 1
    ]]></literal>
    <justification jstring="[hyper(48,a,12825,a)].">
      <j1 rule="hyper" parents="48 12825"/>
    </justification>
  </clause>

  <clause id="12830">
    <literal><![CDATA[
      T(x,x * a(y,z,u)) = T(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(12825(a,1),712(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12825 712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12831">
    <literal><![CDATA[
      T(x,a(y,z,u) \ x) = a(y,z,u) * (x / a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(119,a,12826,a(flip),b,4423,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 12826 4423"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12832">
    <literal><![CDATA[
      a(x,a(y,z,u),x) \ w = w
    ]]></literal>
    <justification jstring="[hyper(280,a,12829,a(flip))].">
      <j1 rule="hyper" parents="280 12829"/>
    </justification>
  </clause>

  <clause id="12833">
    <literal><![CDATA[
      (a(x,y,z) \ 1) \ 1 = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(116,a,12829,a(flip),b,2223,a(flip))].">
      <j1 rule="hyper" parents="116 12829 2223"/>
    </justification>
  </clause>

  <clause id="12834">
    <literal><![CDATA[
      a(x,a(y,z,u),x) \ w != v5
    ]]></literal>
    <literal><![CDATA[
      w = v5
    ]]></literal>
    <justification jstring="[para(12829(a,2),165(a,1,1))].">
      <j1 rule="para" parents="12829 165"/>
    </justification>
  </clause>

  <clause id="12835">
    <literal><![CDATA[
      x * (y \ L(y,a(z,u,w),y)) = x
    ]]></literal>
    <justification jstring="[hyper(58,a,9555,a,b,12832,a)].">
      <j1 rule="hyper" parents="58 9555 12832"/>
    </justification>
  </clause>

  <clause id="12836">
    <literal><![CDATA[
      a(x,y,z) = (((x * (y * z)) \ ((x * y) * z)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(9(a,1),12833(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9 12833"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12837">
    <literal><![CDATA[
      a(K(x,y),z * y,u) = K(x,y \ R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,12809,a(flip),b,12835,a)].">
      <j1 rule="hyper" parents="58 12809 12835"/>
    </justification>
  </clause>

  <clause id="12838">
    <literal><![CDATA[
      K(x,x * a(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,a(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(8957(a,1),12834(a,1))].">
      <j1 rule="para" parents="8957 12834"/>
    </justification>
  </clause>

  <clause id="12840">
    <literal><![CDATA[
      a(K(x,K(y,z)),u * y,w) = K(x,K(z,y \ R(y,u,w)))
    ]]></literal>
    <justification jstring="[para(12837(a,1),12013(a,2,2))].">
      <j1 rule="para" parents="12837 12013"/>
    </justification>
  </clause>

  <clause id="12841">
    <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,12831,a,b,5013,a),flip(a)].">
      <j1 rule="hyper" parents="116 12831 5013"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12842">
    <literal><![CDATA[
      T(a(x,y,z),x) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,11640,a(flip),b,12836,a)].">
      <j1 rule="hyper" parents="320 11640 12836"/>
    </justification>
  </clause>

  <clause id="12843">
    <literal><![CDATA[
      a(x,y,z) * x = x * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(119,a,12842,a(flip),b,17,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 12842 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12844">
    <literal><![CDATA[
      T(a(1 / x,y,z),x \ 1) = a(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(4063(a,2),12842(a,1,1))].">
      <j1 rule="para" parents="4063 12842"/>
    </justification>
  </clause>

  <clause id="12845">
    <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,9914,a(flip),b,12843,a),flip(a)].">
      <j1 rule="hyper" parents="58 9914 12843"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12846">
    <literal><![CDATA[
      a((x / y) \ 1,z,(x / y) \ 1) = a(x \ y,z,x \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,12040,a(flip),b,12844,a),flip(a)].">
      <j1 rule="hyper" parents="58 12040 12844"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12847">
    <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,12513,a(flip),b,12840,a),flip(a)].">
      <j1 rule="hyper" parents="58 12513 12840"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12848">
    <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,9304,a,b,12847,a)].">
      <j1 rule="hyper" parents="58 9304 12847"/>
    </justification>
  </clause>

  <clause id="12849">
    <literal><![CDATA[
      K((x \ y) \ z,x / y) * K(x / y,z) = a(y \ x,z,y \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,11459,a,b,12846,a)].">
      <j1 rule="hyper" parents="58 11459 12846"/>
    </justification>
  </clause>

  <clause id="12850">
    <literal><![CDATA[
      K(x,K(y,R(z,u,w) * (z \ y))) = a(K(x,K(y,z)),u,w)
    ]]></literal>
    <justification jstring="[para(7784(a,2),12848(a,2,1))].">
      <j1 rule="para" parents="7784 12848"/>
    </justification>
  </clause>

  <clause id="12851">
    <literal><![CDATA[
      K(x,K(y,R(z,u,w) \ z)) = a(K(x,K(y,z)),u,w)
    ]]></literal>
    <justification jstring="[hyper(9460,a,12850,a)].">
      <j1 rule="hyper" parents="9460 12850"/>
    </justification>
  </clause>

  <clause id="12852">
    <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,9872,a(flip),b,12851,a)].">
      <j1 rule="hyper" parents="58 9872 12851"/>
    </justification>
  </clause>

  <clause id="12853">
    <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(12841(a,2),4838(a,1))].">
      <j1 rule="para" parents="12841 4838"/>
    </justification>
  </clause>

  <clause id="12854">
    <literal><![CDATA[
      K(x,y * (1 / (z * K(x,u)))) = K(x,y * (K(u,x) / z))
    ]]></literal>
    <justification jstring="[para(12845(a,1),9644(a,1,2,2))].">
      <j1 rule="para" parents="12845 9644"/>
    </justification>
  </clause>

  <clause id="12855">
    <literal><![CDATA[
      K(x,y * ((z * K(x,u)) \ 1)) = K(x,y * (K(u,x) / z))
    ]]></literal>
    <justification jstring="[hyper(58,a,5315,a(flip),b,12854,a)].">
      <j1 rule="hyper" parents="58 5315 12854"/>
    </justification>
  </clause>

  <clause id="12856">
    <literal><![CDATA[
      K(x,y * ((K(x,z) * u) \ 1)) = K(x,y * (K(z,x) / u))
    ]]></literal>
    <justification jstring="[hyper(58,a,9629,a,b,12855,a)].">
      <j1 rule="hyper" parents="58 9629 12855"/>
    </justification>
  </clause>

  <clause id="12857">
    <literal><![CDATA[
      K(x,y * ((K(x,z) * u) \ 1)) = K(x,y * (u \ 1))
    ]]></literal>
    <justification jstring="[hyper(320,a,11396,a(flip),b,12856,a),flip(a)].">
      <j1 rule="hyper" parents="320 11396 12856"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12859">
    <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,10291,a,b,12857,a)].">
      <j1 rule="hyper" parents="58 10291 12857"/>
    </justification>
  </clause>

  <clause id="12860">
    <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(7797(a,1),12852(a,2,1))].">
      <j1 rule="para" parents="7797 12852"/>
    </justification>
  </clause>

  <clause id="12861">
    <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(11105(a,1),12860(a,2,1,2))].">
      <j1 rule="para" parents="11105 12860"/>
    </justification>
  </clause>

  <clause id="12862">
    <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(9889,a,12861,a)].">
      <j1 rule="hyper" parents="9889 12861"/>
    </justification>
  </clause>

  <clause id="12865">
    <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,10666,a(flip),b,12862,a)].">
      <j1 rule="hyper" parents="58 10666 12862"/>
    </justification>
  </clause>

  <clause id="12868">
    <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),12859(a,2,2))].">
      <j1 rule="para" parents="261 12859"/>
    </justification>
  </clause>

  <clause id="12869">
    <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,9452,a(flip),b,12868,a),flip(a)].">
      <j1 rule="hyper" parents="320 9452 12868"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12871">
    <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,8888,a(flip),b,12869,a)].">
      <j1 rule="hyper" parents="58 8888 12869"/>
    </justification>
  </clause>

  <clause id="12872">
    <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,12353,a(flip),b,12871,a),flip(a)].">
      <j1 rule="hyper" parents="320 12353 12871"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12874">
    <literal><![CDATA[
      R(K(x,y),z,(K(x,u) * z) \ 1) = K(x,L(y,z,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(12494,a,12872,a)].">
      <j1 rule="hyper" parents="12494 12872"/>
    </justification>
  </clause>

  <clause id="12875">
    <literal><![CDATA[
      x / (K(y,L(z,u,u \ 1)) * x) = u * ((K(y,z) * u) \ 1)
    ]]></literal>
    <justification jstring="[para(12874(a,1),6982(a,1,2,1))].">
      <j1 rule="para" parents="12874 6982"/>
    </justification>
  </clause>

  <clause id="12876">
    <literal><![CDATA[
      x * ((K(y,z) * x) \ 1) = K(L(z,x,x \ 1),y)
    ]]></literal>
    <justification jstring="[hyper(5150,a,12875,a),flip(a)].">
      <j1 rule="hyper" parents="5150 12875"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12878">
    <literal><![CDATA[
      x * ((K(y,z) * x) \ 1) = K(z,L(y,x,x \ 1))
    ]]></literal>
    <justification jstring="[hyper(320,a,10840,a(flip),b,12876,a),flip(a)].">
      <j1 rule="hyper" parents="320 10840 12876"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12879">
    <literal><![CDATA[
      x \ K(y,L(z,x,x \ 1)) = (K(z,y) * x) \ 1
    ]]></literal>
    <justification jstring="[hyper(116,a,10840,a(flip),b,12876,a)].">
      <j1 rule="hyper" parents="116 10840 12876"/>
    </justification>
  </clause>

  <clause id="12880">
    <literal><![CDATA[
      K(x,((K(y,x) * (z \ 1)) \ 1) \ u) = K(x,z \ u)
    ]]></literal>
    <justification jstring="[para(12879(a,1),9277(a,1,2,1))].">
      <j1 rule="para" parents="12879 9277"/>
    </justification>
  </clause>

  <clause id="12881">
    <literal><![CDATA[
      K(x,(((y \ 1) * K(z,x)) \ 1) \ u) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[para(7288(a,1),12880(a,1,2,1,1))].">
      <j1 rule="para" parents="7288 12880"/>
    </justification>
  </clause>

  <clause id="12882">
    <literal><![CDATA[
      K(x,((y * K(z,x)) \ 1) \ u) = K(x,(y \ 1) \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,5575,a(flip),b,12881,a)].">
      <j1 rule="hyper" parents="58 5575 12881"/>
    </justification>
  </clause>

  <clause id="12883">
    <literal><![CDATA[
      K(x,((T(y,x) / z) \ 1) \ u) = K(x,((y / z) \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(1439(a,1),12882(a,1,2,1,1))].">
      <j1 rule="para" parents="1439 12882"/>
    </justification>
  </clause>

  <clause id="12884">
    <literal><![CDATA[
      (T(x,y) / z) \ x = z * K(y,((x / z) \ 1) \ z)
    ]]></literal>
    <justification jstring="[hyper(119,a,12883,a(flip),b,8589,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 12883 8589"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12885">
    <literal><![CDATA[
      (T(x,y) / z) \ x = (1 / z) \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,11598,a(flip),b,12884,a),flip(a)].">
      <j1 rule="hyper" parents="320 11598 12884"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12886">
    <literal><![CDATA[
      (1 / (x \ T(y,z))) \ K(z,y) = x \ y
    ]]></literal>
    <justification jstring="[para(72(a,1),12885(a,1,1)),flip(a)].">
      <j1 rule="para" parents="72 12885"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12888">
    <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(12886(a,2),7264(a,2,2)),flip(a)].">
      <j1 rule="para" parents="12886 7264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12889">
    <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(4586(a,1),12790(a,2,1))].">
      <j1 rule="para" parents="4586 12790"/>
    </justification>
  </clause>

  <clause id="12890">
    <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,12779,a(flip),b,12889,a)].">
      <j1 rule="hyper" parents="58 12779 12889"/>
    </justification>
  </clause>

  <clause id="12891">
    <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(10508,a,12686,a)].">
      <j1 rule="hyper" parents="10508 12686"/>
    </justification>
  </clause>

  <clause id="12892">
    <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,7264,a(flip),b,12888,a),flip(a)].">
      <j1 rule="hyper" parents="320 7264 12888"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12893">
    <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),12892(a,1,2,1,2,2))].">
      <j1 rule="para" parents="20 12892"/>
    </justification>
  </clause>

  <clause id="12894">
    <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),12893(a,1,2,1,2,2,1))].">
      <j1 rule="para" parents="20 12893"/>
    </justification>
  </clause>

  <clause id="12895">
    <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,10619,a(flip),b,12894,a)].">
      <j1 rule="hyper" parents="58 10619 12894"/>
    </justification>
  </clause>

  <clause id="12897">
    <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),12895(a,1,2))].">
      <j1 rule="para" parents="75 12895"/>
    </justification>
  </clause>

  <clause id="12898">
    <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,11795,a,b,12897,a)].">
      <j1 rule="hyper" parents="58 11795 12897"/>
    </justification>
  </clause>

  <clause id="12900">
    <literal><![CDATA[
      K(x,y \ L(L(x,z,x),u,w)) = K(x,y \ L(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(11659,a,12898,a),flip(a)].">
      <j1 rule="hyper" parents="11659 12898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12902">
    <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(12900(a,1),11424(a,1,1))].">
      <j1 rule="para" parents="12900 11424"/>
    </justification>
  </clause>

  <clause id="12903">
    <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(10775(a,1),12902(a,1,1))].">
      <j1 rule="para" parents="10775 12902"/>
    </justification>
  </clause>

  <clause id="12905">
    <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),12903(a,1,1,2))].">
      <j1 rule="para" parents="60 12903"/>
    </justification>
  </clause>

  <clause id="12906">
    <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(4777(a,1),12905(a,1,2))].">
      <j1 rule="para" parents="4777 12905"/>
    </justification>
  </clause>

  <clause id="12907">
    <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(12105,a,12906,a)].">
      <j1 rule="hyper" parents="12105 12906"/>
    </justification>
  </clause>

  <clause id="12908">
    <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(2003(a,1),12907(a,1,2))].">
      <j1 rule="para" parents="2003 12907"/>
    </justification>
  </clause>

  <clause id="12909">
    <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(9966(a,1),12908(a,1,2))].">
      <j1 rule="para" parents="9966 12908"/>
    </justification>
  </clause>

  <clause id="12910">
    <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,12909,a)].">
      <j1 rule="hyper" parents="123 12909"/>
    </justification>
  </clause>

  <clause id="12911">
    <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(12910(a,1),12177(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12910 12177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12912">
    <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,12911,a,b,12833,a(flip))].">
      <j1 rule="hyper" parents="114 12911 12833"/>
    </justification>
  </clause>

  <clause id="12913">
    <literal><![CDATA[
      a(L(x,y,z),u,L(x,y,z)) = a(x,u,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,10541,a(flip),b,12912,a),flip(a)].">
      <j1 rule="hyper" parents="320 10541 12912"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12915">
    <literal><![CDATA[
      L(a(x,y,x),z,u) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,10549,a(flip),b,12913,a)].">
      <j1 rule="hyper" parents="58 10549 12913"/>
    </justification>
  </clause>

  <clause id="12918">
    <literal><![CDATA[
      a(x,L(y,z,u),x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,12765,a(flip),b,12915,a)].">
      <j1 rule="hyper" parents="58 12765 12915"/>
    </justification>
  </clause>

  <clause id="12919">
    <literal><![CDATA[
      x * ((x \ y) * a(z,u,z)) = y * a(z,u,z)
    ]]></literal>
    <justification jstring="[hyper(119,a,12915,a(flip),b,4563,a),flip(a)].">
      <j1 rule="hyper" parents="119 12915 4563"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12920">
    <literal><![CDATA[
      (x * y) * a(z,u,z) = x * (y * a(z,u,z))
    ]]></literal>
    <justification jstring="[hyper(119,a,12915,a(flip),b,4560,a)].">
      <j1 rule="hyper" parents="119 12915 4560"/>
    </justification>
  </clause>

  <clause id="12922">
    <literal><![CDATA[
      x \ (y * a(z,u,z)) = (x \ y) * a(z,u,z)
    ]]></literal>
    <justification jstring="[para(12915(a,1),474(a,1,2,2))].">
      <j1 rule="para" parents="12915 474"/>
    </justification>
  </clause>

  <clause id="12925">
    <literal><![CDATA[
      R(x,L(y,z,u),x) = x * a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,12918,a(flip),b,8942,a),flip(a)].">
      <j1 rule="hyper" parents="119 12918 8942"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12926">
    <literal><![CDATA[
      a(x,(y * z) \ u,x) = a(x,z \ (y \ u),x)
    ]]></literal>
    <justification jstring="[para(298(a,1),12918(a,1,2))].">
      <j1 rule="para" parents="298 12918"/>
    </justification>
  </clause>

  <clause id="12927">
    <literal><![CDATA[
      L(x,L(y,z,u),x) = a(x,y,x) \ x
    ]]></literal>
    <justification jstring="[para(12918(a,1),9089(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12918 9089"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12928">
    <literal><![CDATA[
      R(x,L(y,z,u),x) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,8949,a(flip),b,12925,a),flip(a)].">
      <j1 rule="hyper" parents="320 8949 12925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12929">
    <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(12928(a,1),12162(a,1,2,1))].">
      <j1 rule="para" parents="12928 12162"/>
    </justification>
  </clause>

  <clause id="12930">
    <literal><![CDATA[
      L(x,L(y,z,u),x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,9089,a(flip),b,12927,a),flip(a)].">
      <j1 rule="hyper" parents="320 9089 12927"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12931">
    <literal><![CDATA[
      L(x,L(y,z,u) \ y,x) = L(x,a(u,z,y),x)
    ]]></literal>
    <justification jstring="[para(1929(a,2),12930(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1929 12930"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12932">
    <literal><![CDATA[
      x * ((x \ y) * a(z,u,z)) = a(z,u,z) * y
    ]]></literal>
    <justification jstring="[hyper(320,a,9522,a,b,12919,a),flip(a)].">
      <j1 rule="hyper" parents="320 9522 12919"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12933">
    <literal><![CDATA[
      x \ (a(y,z,y) * u) = (x \ u) * a(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(116,a,9522,a,b,12919,a)].">
      <j1 rule="hyper" parents="116 9522 12919"/>
    </justification>
  </clause>

  <clause id="12934">
    <literal><![CDATA[
      (x \ K(y,z)) * a(y,y \ z,y) = x \ K(y,y \ z)
    ]]></literal>
    <justification jstring="[hyper(116,a,8971,a(flip),b,12919,a),flip(a)].">
      <j1 rule="hyper" parents="116 8971 12919"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12935">
    <literal><![CDATA[
      (x \ y) * a(y,z,y) = x \ R(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(116,a,8949,a(flip),b,12919,a),flip(a)].">
      <j1 rule="hyper" parents="116 8949 12919"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12936">
    <literal><![CDATA[
      a(x,y,x) * (z * u) = z * (u * a(x,y,x))
    ]]></literal>
    <justification jstring="[hyper(9553,a,12920,a)].">
      <j1 rule="hyper" parents="9553 12920"/>
    </justification>
  </clause>

  <clause id="12937">
    <literal><![CDATA[
      R(x,y,a(z,u,z)) = x
    ]]></literal>
    <justification jstring="[hyper(4038,a,12920,a)].">
      <j1 rule="hyper" parents="4038 12920"/>
    </justification>
  </clause>

  <clause id="12938">
    <literal><![CDATA[
      x \ (y * (z * a(u,w,u))) = (x \ (y * z)) * a(u,w,u)
    ]]></literal>
    <justification jstring="[hyper(116,a,12920,a(flip),b,12919,a)].">
      <j1 rule="hyper" parents="116 12920 12919"/>
    </justification>
  </clause>

  <clause id="12939">
    <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(12920(a,1),510(a,1,1))].">
      <j1 rule="para" parents="12920 510"/>
    </justification>
  </clause>

  <clause id="12940">
    <literal><![CDATA[
      (x * (y * a(z,u,z))) \ w = (x * y) \ (a(z,u,z) \ w)
    ]]></literal>
    <justification jstring="[para(12920(a,1),12439(a,1,1))].">
      <j1 rule="para" parents="12920 12439"/>
    </justification>
  </clause>

  <clause id="12941">
    <literal><![CDATA[
      a(x * (y * a(z,u,z)),w,v5) = a(x * y,w,v5)
    ]]></literal>
    <justification jstring="[para(12920(a,1),12775(a,1,1))].">
      <j1 rule="para" parents="12920 12775"/>
    </justification>
  </clause>

  <clause id="12942">
    <literal><![CDATA[
      L(T(x,y),y,a(z,u,z)) = T(x,y * a(z,u,z))
    ]]></literal>
    <justification jstring="[hyper(10063,a,12937,a)].">
      <j1 rule="hyper" parents="10063 12937"/>
    </justification>
  </clause>

  <clause id="12944">
    <literal><![CDATA[
      x \ (y * a(z,u,z)) = a(z,u,z) * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(320,a,9522,a,b,12922,a),flip(a)].">
      <j1 rule="hyper" parents="320 9522 12922"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12945">
    <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,12891,a(flip),b,12926,a),flip(a)].">
      <j1 rule="hyper" parents="58 12891 12926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12946">
    <literal><![CDATA[
      (x \ (y * x)) * a(z,u,z) = T(y * a(z,u,z),x)
    ]]></literal>
    <justification jstring="[hyper(239,a,12438,a,b,12932,a),flip(a)].">
      <j1 rule="hyper" parents="239 12438 12932"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12948">
    <literal><![CDATA[
      (a(x,y,x) \ z) \ u = (z \ u) * a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(12421,a,12933,a)].">
      <j1 rule="hyper" parents="12421 12933"/>
    </justification>
  </clause>

  <clause id="12949">
    <literal><![CDATA[
      a(x,y,x) \ (z \ (a(x,y,x) * u)) = z \ u
    ]]></literal>
    <justification jstring="[hyper(116,a,12933,a,b,9522,a)].">
      <j1 rule="hyper" parents="116 12933 9522"/>
    </justification>
  </clause>

  <clause id="12950">
    <literal><![CDATA[
      (x * y) / (y * a(z,u,z)) = a(z,u,z) \ x
    ]]></literal>
    <justification jstring="[hyper(12436,a,12936,a)].">
      <j1 rule="hyper" parents="12436 12936"/>
    </justification>
  </clause>

  <clause id="12951">
    <literal><![CDATA[
      a(x,y,x) * (z * u) = z * (a(x,y,x) * u)
    ]]></literal>
    <justification jstring="[para(9522(a,2),12936(a,2,2))].">
      <j1 rule="para" parents="9522 12936"/>
    </justification>
  </clause>

  <clause id="12952">
    <literal><![CDATA[
      a(x,y,x) * (z * (a(x,y,x) \ u)) = z * u
    ]]></literal>
    <justification jstring="[para(9533(a,1),12936(a,2,2))].">
      <j1 rule="para" parents="9533 12936"/>
    </justification>
  </clause>

  <clause id="12953">
    <literal><![CDATA[
      a(x,y,x) * (z \ (a(x,y,x) \ u)) = z \ u
    ]]></literal>
    <justification jstring="[para(9533(a,1),12944(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9533 12944"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12954">
    <literal><![CDATA[
      ((a(x,y,x) * z) \ u) * a(x,y,x) = z \ u
    ]]></literal>
    <justification jstring="[para(4(a,1),12948(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4 12948"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12955">
    <literal><![CDATA[
      a(x,y,x) \ (z \ u) = z \ (a(x,y,x) \ u)
    ]]></literal>
    <justification jstring="[para(5(a,1),12949(a,1,2,2))].">
      <j1 rule="para" parents="5 12949"/>
    </justification>
  </clause>

  <clause id="12956">
    <literal><![CDATA[
      a(x,y,x) \ (z \ (x * u)) = z \ (L(x,y,x) * u)
    ]]></literal>
    <justification jstring="[para(9569(a,1),12949(a,1,2,2))].">
      <j1 rule="para" parents="9569 12949"/>
    </justification>
  </clause>

  <clause id="12957">
    <literal><![CDATA[
      x / (y * a(z,u,z)) = a(z,u,z) \ (x / y)
    ]]></literal>
    <justification jstring="[hyper(576,a,12950,a)].">
      <j1 rule="hyper" parents="576 12950"/>
    </justification>
  </clause>

  <clause id="12958">
    <literal><![CDATA[
      (x * a(y,z,y)) * u = x * (a(y,z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(12474,a,12951,a)].">
      <j1 rule="hyper" parents="12474 12951"/>
    </justification>
  </clause>

  <clause id="12959">
    <literal><![CDATA[
      a(x,y,x) \ (z * u) = z * (a(x,y,x) \ u)
    ]]></literal>
    <justification jstring="[hyper(116,a,151,a(flip),b,12951,a)].">
      <j1 rule="hyper" parents="116 151 12951"/>
    </justification>
  </clause>

  <clause id="12960">
    <literal><![CDATA[
      x \ (y * (a(z,u,z) * w)) = (x \ (y * w)) * a(z,u,z)
    ]]></literal>
    <justification jstring="[hyper(116,a,12951,a(flip),b,12932,a)].">
      <j1 rule="hyper" parents="116 12951 12932"/>
    </justification>
  </clause>

  <clause id="12962">
    <literal><![CDATA[
      (x * (a(y,z,y) * u)) \ w = (x * u) \ (a(y,z,y) \ w)
    ]]></literal>
    <justification jstring="[para(12951(a,1),12418(a,1,1))].">
      <j1 rule="para" parents="12951 12418"/>
    </justification>
  </clause>

  <clause id="12963">
    <literal><![CDATA[
      (a(x,y,x) \ z) * u = z * (a(x,y,x) \ u)
    ]]></literal>
    <justification jstring="[hyper(12434,a,12952,a),flip(a)].">
      <j1 rule="hyper" parents="12434 12952"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12964">
    <literal><![CDATA[
      a(x,y,x) * (z \ L(x,y,x)) = z \ x
    ]]></literal>
    <justification jstring="[para(9089(a,1),12953(a,1,2,2))].">
      <j1 rule="para" parents="9089 12953"/>
    </justification>
  </clause>

  <clause id="12965">
    <literal><![CDATA[
      a(x,y,x) \ (z \ x) = z \ L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(123,a,12964,a)].">
      <j1 rule="hyper" parents="123 12964"/>
    </justification>
  </clause>

  <clause id="12966">
    <literal><![CDATA[
      a(x \ L(y,z,y),u,w) = a(x \ y,u,w)
    ]]></literal>
    <justification jstring="[para(12964(a,1),12768(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12964 12768"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12967">
    <literal><![CDATA[
      (x \ (a(y,z,y) \ u)) * a(y,z,y) != w
    ]]></literal>
    <literal><![CDATA[
      x \ u = w
    ]]></literal>
    <justification jstring="[para(12955(a,1),9546(a,1,1))].">
      <j1 rule="para" parents="12955 9546"/>
    </justification>
  </clause>

  <clause id="12968">
    <literal><![CDATA[
      L(x,y,z / (u * a(w,v5,w))) = L(x,y,z / u)
    ]]></literal>
    <justification jstring="[para(12957(a,2),12568(a,1,3))].">
      <j1 rule="para" parents="12957 12568"/>
    </justification>
  </clause>

  <clause id="12971">
    <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(12958(a,1),9(a,2,1)),flip(a)].">
      <j1 rule="para" parents="12958 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12972">
    <literal><![CDATA[
      a(x * K(y * z,y),u,w) = a(x * K(z,y),u,w)
    ]]></literal>
    <justification jstring="[para(8968(a,1),12941(a,1,1,2))].">
      <j1 rule="para" parents="8968 12941"/>
    </justification>
  </clause>

  <clause id="12973">
    <literal><![CDATA[
      a(x * K(y,y \ z),u,w) = a(x * K(y,z),u,w)
    ]]></literal>
    <justification jstring="[para(8971(a,1),12941(a,1,1,2))].">
      <j1 rule="para" parents="8971 12941"/>
    </justification>
  </clause>

  <clause id="12974">
    <literal><![CDATA[
      T(x,y * a(z,u,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(12419,a,12942,a),flip(a)].">
      <j1 rule="hyper" parents="12419 12942"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12975">
    <literal><![CDATA[
      T(x,y * a(z,u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = w
    ]]></literal>
    <justification jstring="[para(12942(a,1),12419(a,1))].">
      <j1 rule="para" parents="12942 12419"/>
    </justification>
  </clause>

  <clause id="12977">
    <literal><![CDATA[
      K(x,y * a(z,u,z)) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(116,a,12974,a(flip),b,4755,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="116 12974 4755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12978">
    <literal><![CDATA[
      K(x * a(y,z,y),u) = u / T(u,x)
    ]]></literal>
    <justification jstring="[para(12974(a,1),4794(a,2,2))].">
      <j1 rule="para" parents="12974 4794"/>
    </justification>
  </clause>

  <clause id="12979">
    <literal><![CDATA[
      T(x,y * L(z,u,z)) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(9095(a,1),12974(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9095 12974"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12980">
    <literal><![CDATA[
      T(x,y * R(z,u,z)) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(9123(a,1),12974(a,1,2))].">
      <j1 rule="para" parents="9123 12974"/>
    </justification>
  </clause>

  <clause id="12981">
    <literal><![CDATA[
      T(x,R(y,z,y) * u) = T(x,y * u)
    ]]></literal>
    <justification jstring="[para(9133(a,1),12974(a,1,2))].">
      <j1 rule="para" parents="9133 12974"/>
    </justification>
  </clause>

  <clause id="12982">
    <literal><![CDATA[
      T(x,y / R(z,u,z)) = T(x,y / z)
    ]]></literal>
    <justification jstring="[para(9136(a,1),12974(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9136 12974"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12983">
    <literal><![CDATA[
      T(x,a(y,z,y) * u) = T(x,u)
    ]]></literal>
    <justification jstring="[para(9522(a,2),12974(a,1,2))].">
      <j1 rule="para" parents="9522 12974"/>
    </justification>
  </clause>

  <clause id="12984">
    <literal><![CDATA[
      T(x,a(y,z,y) \ u) = T(x,u)
    ]]></literal>
    <justification jstring="[para(9533(a,1),12974(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9533 12974"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12985">
    <literal><![CDATA[
      T(x,R(y,z,y) / u) = T(x,y / u)
    ]]></literal>
    <justification jstring="[para(12443(a,1),12974(a,1,2))].">
      <j1 rule="para" parents="12443 12974"/>
    </justification>
  </clause>

  <clause id="12986">
    <literal><![CDATA[
      T(x,y \ R(z,u,z)) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[para(12935(a,1),12974(a,1,2))].">
      <j1 rule="para" parents="12935 12974"/>
    </justification>
  </clause>

  <clause id="12988">
    <literal><![CDATA[
      T(x,T(y * z,y) \ u) = T(x,(z * y) \ u)
    ]]></literal>
    <justification jstring="[para(11230(a,1),12983(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11230 12983"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12989">
    <literal><![CDATA[
      T(x,(a(y,z,y) \ u) * w) = T(x,u * w)
    ]]></literal>
    <justification jstring="[para(12415(a,1),12983(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12415 12983"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12990">
    <literal><![CDATA[
      T(x,y * (a(z,u,z) * w)) = T(x,y * w)
    ]]></literal>
    <justification jstring="[para(12951(a,1),12983(a,1,2))].">
      <j1 rule="para" parents="12951 12983"/>
    </justification>
  </clause>

  <clause id="12991">
    <literal><![CDATA[
      T(x,(R(y,z,y) \ y) * u) = T(x,u)
    ]]></literal>
    <justification jstring="[para(10020(a,2),12984(a,1,2))].">
      <j1 rule="para" parents="10020 12984"/>
    </justification>
  </clause>

  <clause id="12992">
    <literal><![CDATA[
      K(x,y * a(z,u,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,4729,a,b,12977,a),flip(a)].">
      <j1 rule="hyper" parents="320 4729 12977"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12993">
    <literal><![CDATA[
      K(x,y * a(z,u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = w
    ]]></literal>
    <justification jstring="[para(12977(a,2),4838(a,1))].">
      <j1 rule="para" parents="12977 4838"/>
    </justification>
  </clause>

  <clause id="12994">
    <literal><![CDATA[
      K(x,T(y,z) / z) = K(x,z \ y)
    ]]></literal>
    <justification jstring="[para(8974(a,1),12992(a,1,2))].">
      <j1 rule="para" parents="8974 12992"/>
    </justification>
  </clause>

  <clause id="12995">
    <literal><![CDATA[
      K(x,y / L(z,u,z)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(9085(a,1),12992(a,1,2))].">
      <j1 rule="para" parents="9085 12992"/>
    </justification>
  </clause>

  <clause id="12996">
    <literal><![CDATA[
      K(x,y * L(z,u,z)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(9095(a,1),12992(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9095 12992"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12997">
    <literal><![CDATA[
      K(x,L(y,z,y) \ u) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[para(9105(a,1),12992(a,1,2))].">
      <j1 rule="para" parents="9105 12992"/>
    </justification>
  </clause>

  <clause id="12998">
    <literal><![CDATA[
      K(x,R(y,z,y) * u) = K(x,y * u)
    ]]></literal>
    <justification jstring="[para(9133(a,1),12992(a,1,2))].">
      <j1 rule="para" parents="9133 12992"/>
    </justification>
  </clause>

  <clause id="12999">
    <literal><![CDATA[
      K(x,a(y,z,y) * u) = K(x,u)
    ]]></literal>
    <justification jstring="[para(9522(a,2),12992(a,1,2))].">
      <j1 rule="para" parents="9522 12992"/>
    </justification>
  </clause>

  <clause id="13000">
    <literal><![CDATA[
      K(x,a(y,z,y) \ u) = K(x,u)
    ]]></literal>
    <justification jstring="[para(9533(a,1),12992(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9533 12992"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13001">
    <literal><![CDATA[
      K(x,R(y,z,y) / u) = K(x,y / u)
    ]]></literal>
    <justification jstring="[para(12443(a,1),12992(a,1,2))].">
      <j1 rule="para" parents="12443 12992"/>
    </justification>
  </clause>

  <clause id="13002">
    <literal><![CDATA[
      K(x,(a(y,z,y) * u) / w) = K(x,u / w)
    ]]></literal>
    <justification jstring="[para(12441(a,2),12992(a,1,2))].">
      <j1 rule="para" parents="12441 12992"/>
    </justification>
  </clause>

  <clause id="13003">
    <literal><![CDATA[
      K(x,y \ R(z,u,z)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(12935(a,1),12992(a,1,2))].">
      <j1 rule="para" parents="12935 12992"/>
    </justification>
  </clause>

  <clause id="13004">
    <literal><![CDATA[
      K(x,y * (z * a(u,w,u))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(12920(a,1),12992(a,1,2))].">
      <j1 rule="para" parents="12920 12992"/>
    </justification>
  </clause>

  <clause id="13005">
    <literal><![CDATA[
      K(x,y \ (a(z,u,z) * w)) = K(x,y \ w)
    ]]></literal>
    <justification jstring="[para(12933(a,2),12992(a,1,2))].">
      <j1 rule="para" parents="12933 12992"/>
    </justification>
  </clause>

  <clause id="13006">
    <literal><![CDATA[
      K(x,(a(y,z,y) * u) \ w) = K(x,u \ w)
    ]]></literal>
    <justification jstring="[para(12954(a,1),12992(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12954 12992"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13007">
    <literal><![CDATA[
      K(x,L(y,z,y) * u) = K(x,y * u)
    ]]></literal>
    <justification jstring="[para(9569(a,1),12999(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9569 12999"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13008">
    <literal><![CDATA[
      K(x,K(y,y \ z) * u) = K(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[para(9833(a,1),12999(a,1,2))].">
      <j1 rule="para" parents="9833 12999"/>
    </justification>
  </clause>

  <clause id="13009">
    <literal><![CDATA[
      K(x,T(y * z,y) \ u) = K(x,(z * y) \ u)
    ]]></literal>
    <justification jstring="[para(11230(a,1),12999(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11230 12999"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13010">
    <literal><![CDATA[
      K(x,(a(y,z,y) \ u) * w) = K(x,u * w)
    ]]></literal>
    <justification jstring="[para(12415(a,1),12999(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12415 12999"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13011">
    <literal><![CDATA[
      K(x,y * (a(z,u,z) * w)) = K(x,y * w)
    ]]></literal>
    <justification jstring="[para(12951(a,1),12999(a,1,2))].">
      <j1 rule="para" parents="12951 12999"/>
    </justification>
  </clause>

  <clause id="13012">
    <literal><![CDATA[
      K(x,y * (a(z,u,z) \ w)) = K(x,y * w)
    ]]></literal>
    <justification jstring="[para(12952(a,1),12999(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12952 12999"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13013">
    <literal><![CDATA[
      K(x,y \ (a(z,u,z) \ w)) = K(x,y \ w)
    ]]></literal>
    <justification jstring="[para(12953(a,1),12999(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12953 12999"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13014">
    <literal><![CDATA[
      K(x,(y \ R(y,z,y)) \ u) = K(x,u)
    ]]></literal>
    <justification jstring="[para(8940(a,1),13000(a,1,2,1))].">
      <j1 rule="para" parents="8940 13000"/>
    </justification>
  </clause>

  <clause id="13015">
    <literal><![CDATA[
      K(x,L(y,z,y) / u) = K(x,y / u)
    ]]></literal>
    <justification jstring="[para(12447(a,1),13000(a,1,2))].">
      <j1 rule="para" parents="12447 13000"/>
    </justification>
  </clause>

  <clause id="13016">
    <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),12994(a,1,2,1))].">
      <j1 rule="para" parents="20 12994"/>
    </justification>
  </clause>

  <clause id="13017">
    <literal><![CDATA[
      K(x,y / T(z,y)) = K(x,z \ y)
    ]]></literal>
    <justification jstring="[para(4246(a,1),12994(a,1,2))].">
      <j1 rule="para" parents="4246 12994"/>
    </justification>
  </clause>

  <clause id="13018">
    <literal><![CDATA[
      K(x,y / T(z,y)) = K(x,T(y / z,y))
    ]]></literal>
    <justification jstring="[hyper(320,a,7077,a,b,13017,a),flip(a)].">
      <j1 rule="hyper" parents="320 7077 13017"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13019">
    <literal><![CDATA[
      K(x * a(y,z,y),u) = K(x,u)
    ]]></literal>
    <justification jstring="[hyper(320,a,4794,a,b,12978,a),flip(a)].">
      <j1 rule="hyper" parents="320 4794 12978"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13020">
    <literal><![CDATA[
      K(x * a(y,z,y),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u) = w
    ]]></literal>
    <justification jstring="[para(12978(a,2),4862(a,1))].">
      <j1 rule="para" parents="12978 4862"/>
    </justification>
  </clause>

  <clause id="13025">
    <literal><![CDATA[
      K(a(x,y,x) * z,u) = K(z,u)
    ]]></literal>
    <justification jstring="[para(9522(a,2),13019(a,1,1))].">
      <j1 rule="para" parents="9522 13019"/>
    </justification>
  </clause>

  <clause id="13026">
    <literal><![CDATA[
      K((x * a(y,z,y)) / u,w) = K(x / u,w)
    ]]></literal>
    <justification jstring="[para(12446(a,2),13019(a,1,1))].">
      <j1 rule="para" parents="12446 13019"/>
    </justification>
  </clause>

  <clause id="13027">
    <literal><![CDATA[
      K(x * (y * a(z,u,z)),w) = K(x * y,w)
    ]]></literal>
    <justification jstring="[para(12920(a,1),13019(a,1,1))].">
      <j1 rule="para" parents="12920 13019"/>
    </justification>
  </clause>

  <clause id="13028">
    <literal><![CDATA[
      K(x \ (a(y,z,y) * u),w) = K(x \ u,w)
    ]]></literal>
    <justification jstring="[para(12933(a,2),13019(a,1,1))].">
      <j1 rule="para" parents="12933 13019"/>
    </justification>
  </clause>

  <clause id="13029">
    <literal><![CDATA[
      K((a(x,y,x) \ z) \ u,w) = K(z \ u,w)
    ]]></literal>
    <justification jstring="[para(12948(a,2),13019(a,1,1))].">
      <j1 rule="para" parents="12948 13019"/>
    </justification>
  </clause>

  <clause id="13030">
    <literal><![CDATA[
      K(L(x,y,x) * z,u) = K(x * z,u)
    ]]></literal>
    <justification jstring="[para(9569(a,1),13025(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9569 13025"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13031">
    <literal><![CDATA[
      K(T(x * y,x) \ z,u) = K((y * x) \ z,u)
    ]]></literal>
    <justification jstring="[para(11230(a,1),13025(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11230 13025"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13032">
    <literal><![CDATA[
      K((a(x,y,x) \ z) * u,w) = K(z * u,w)
    ]]></literal>
    <justification jstring="[para(12415(a,1),13025(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12415 13025"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13033">
    <literal><![CDATA[
      K(x \ (a(y,z,y) \ u),w) = K(x \ u,w)
    ]]></literal>
    <justification jstring="[para(12953(a,1),13025(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12953 13025"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13034">
    <literal><![CDATA[
      K(x \ L(y,z,y),u) = K(x \ y,u)
    ]]></literal>
    <justification jstring="[para(12964(a,1),13025(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12964 13025"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13035">
    <literal><![CDATA[
      T(x,y * ((z \ u) \ u)) = T(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[para(11772(a,1),12979(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11772 12979"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13036">
    <literal><![CDATA[
      T(x,y * T(z,z * u)) = T(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[para(4385(a,1),12980(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4385 12980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13037">
    <literal><![CDATA[
      T(x,((y \ z) \ z) * u) = T(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[para(7529(a,1),12981(a,1,2,1))].">
      <j1 rule="para" parents="7529 12981"/>
    </justification>
  </clause>

  <clause id="13038">
    <literal><![CDATA[
      T(x,y / T(z,z \ u)) = T(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[para(4440(a,1),12982(a,1,2,2))].">
      <j1 rule="para" parents="4440 12982"/>
    </justification>
  </clause>

  <clause id="13039">
    <literal><![CDATA[
      T(x,y / ((z \ u) \ u)) = T(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[para(7529(a,1),12982(a,1,2,2))].">
      <j1 rule="para" parents="7529 12982"/>
    </justification>
  </clause>

  <clause id="13040">
    <literal><![CDATA[
      T(x,((y \ z) \ z) / u) = T(x,T(y,z) / u)
    ]]></literal>
    <justification jstring="[para(7529(a,1),12985(a,1,2,1))].">
      <j1 rule="para" parents="7529 12985"/>
    </justification>
  </clause>

  <clause id="13041">
    <literal><![CDATA[
      T(x,y \ T(z,z * u)) = T(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[para(4385(a,1),12986(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4385 12986"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13042">
    <literal><![CDATA[
      T(x,y \ T(z,z \ u)) = T(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[para(4440(a,1),12986(a,1,2,2))].">
      <j1 rule="para" parents="4440 12986"/>
    </justification>
  </clause>

  <clause id="13043">
    <literal><![CDATA[
      T(x,y \ ((z \ u) \ u)) = T(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[para(7529(a,1),12986(a,1,2,2))].">
      <j1 rule="para" parents="7529 12986"/>
    </justification>
  </clause>

  <clause id="13044">
    <literal><![CDATA[
      T(x,K(y * z,y) * u) = T(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(10022(a,1),12991(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10022 12991"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13045">
    <literal><![CDATA[
      K(x,y / T(z / u,z)) = K(x,y / (u \ z))
    ]]></literal>
    <justification jstring="[para(4404(a,1),12995(a,1,2,2))].">
      <j1 rule="para" parents="4404 12995"/>
    </justification>
  </clause>

  <clause id="13046">
    <literal><![CDATA[
      K(x,y * ((z \ u) \ u)) = K(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[para(11772(a,1),12996(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11772 12996"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13047">
    <literal><![CDATA[
      K(x,T(y / z,y) \ u) = K(x,(z \ y) \ u)
    ]]></literal>
    <justification jstring="[para(4404(a,1),12997(a,1,2,1))].">
      <j1 rule="para" parents="4404 12997"/>
    </justification>
  </clause>

  <clause id="13048">
    <literal><![CDATA[
      K(x,T(y,y \ z) \ u) = K(x,((y \ z) \ z) \ u)
    ]]></literal>
    <justification jstring="[para(6309(a,1),12997(a,1,2,1))].">
      <j1 rule="para" parents="6309 12997"/>
    </justification>
  </clause>

  <clause id="13049">
    <literal><![CDATA[
      K(x,((y \ z) \ z) \ u) = K(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(11772(a,1),12997(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11772 12997"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13051">
    <literal><![CDATA[
      K(x,T(y,y * z) * u) = K(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[para(4385(a,1),12998(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4385 12998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13052">
    <literal><![CDATA[
      K(x,((y \ z) \ z) / u) = K(x,T(y,z) / u)
    ]]></literal>
    <justification jstring="[para(7529(a,1),13001(a,1,2,1))].">
      <j1 rule="para" parents="7529 13001"/>
    </justification>
  </clause>

  <clause id="13053">
    <literal><![CDATA[
      K(x,y \ T(z,z \ u)) = K(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[para(4440(a,1),13003(a,1,2,2))].">
      <j1 rule="para" parents="4440 13003"/>
    </justification>
  </clause>

  <clause id="13054">
    <literal><![CDATA[
      K(x,y \ ((z \ u) \ u)) = K(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[para(7529(a,1),13003(a,1,2,2))].">
      <j1 rule="para" parents="7529 13003"/>
    </justification>
  </clause>

  <clause id="13055">
    <literal><![CDATA[
      K(x,T(y / z,y) * u) = K(x,(z \ y) * u)
    ]]></literal>
    <justification jstring="[para(4404(a,1),13007(a,1,2,1))].">
      <j1 rule="para" parents="4404 13007"/>
    </justification>
  </clause>

  <clause id="13056">
    <literal><![CDATA[
      K(x,K(y * z,y) * u) = K(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(9581(a,1),13014(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9581 13014"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13057">
    <literal><![CDATA[
      K(x,T(y / z,y) / u) = K(x,(z \ y) / u)
    ]]></literal>
    <justification jstring="[para(4404(a,1),13015(a,1,2,1))].">
      <j1 rule="para" parents="4404 13015"/>
    </justification>
  </clause>

  <clause id="13058">
    <literal><![CDATA[
      K(x \ T(y / z,y),u) = K(x \ (z \ y),u)
    ]]></literal>
    <justification jstring="[para(4404(a,1),13034(a,1,1,2))].">
      <j1 rule="para" parents="4404 13034"/>
    </justification>
  </clause>

  <clause id="13059">
    <literal><![CDATA[
      T(x,K(y,y \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8971(a,1),12975(a,1,2))].">
      <j1 rule="para" parents="8971 12975"/>
    </justification>
  </clause>

  <clause id="13060">
    <literal><![CDATA[
      K(x,K(y,y \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8971(a,1),12993(a,1,2))].">
      <j1 rule="para" parents="8971 12993"/>
    </justification>
  </clause>

  <clause id="13061">
    <literal><![CDATA[
      K(x,T(y,z) / z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(8974(a,1),12993(a,1,2))].">
      <j1 rule="para" parents="8974 12993"/>
    </justification>
  </clause>

  <clause id="13062">
    <literal><![CDATA[
      K(x,R(y,z,y) / u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / u) = w
    ]]></literal>
    <justification jstring="[para(12443(a,1),12993(a,1,2))].">
      <j1 rule="para" parents="12443 12993"/>
    </justification>
  </clause>

  <clause id="13063">
    <literal><![CDATA[
      K(x,y / T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(13018(a,2),7194(a,1))].">
      <j1 rule="para" parents="13018 7194"/>
    </justification>
  </clause>

  <clause id="13064">
    <literal><![CDATA[
      T(x,K(y \ z,y) * u) = T(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(8938(a,1),12989(a,1,2,1))].">
      <j1 rule="para" parents="8938 12989"/>
    </justification>
  </clause>

  <clause id="13065">
    <literal><![CDATA[
      T(x,y * T(z * u,z)) = T(x,y * (u * z))
    ]]></literal>
    <justification jstring="[para(8970(a,1),12990(a,1,2,2))].">
      <j1 rule="para" parents="8970 12990"/>
    </justification>
  </clause>

  <clause id="13066">
    <literal><![CDATA[
      K(x,T(y * z,y) / u) = K(x,(z * y) / u)
    ]]></literal>
    <justification jstring="[para(8970(a,1),13002(a,1,2,1))].">
      <j1 rule="para" parents="8970 13002"/>
    </justification>
  </clause>

  <clause id="13067">
    <literal><![CDATA[
      K(x,(y * R(z,u,z)) / w) = K(x,(y * z) / w)
    ]]></literal>
    <justification jstring="[para(9529(a,1),13002(a,1,2,1))].">
      <j1 rule="para" parents="9529 13002"/>
    </justification>
  </clause>

  <clause id="13068">
    <literal><![CDATA[
      K(x,y * K(z,z * u)) = K(x,y * K(z,u))
    ]]></literal>
    <justification jstring="[para(8954(a,1),13004(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="8954 13004"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13069">
    <literal><![CDATA[
      K(x,y * T(z * u,z)) = K(x,y * (u * z))
    ]]></literal>
    <justification jstring="[para(8969(a,1),13004(a,1,2,2))].">
      <j1 rule="para" parents="8969 13004"/>
    </justification>
  </clause>

  <clause id="13070">
    <literal><![CDATA[
      K(x,y * K(z,z \ u)) = K(x,y * K(z,u))
    ]]></literal>
    <justification jstring="[para(8971(a,1),13004(a,1,2,2))].">
      <j1 rule="para" parents="8971 13004"/>
    </justification>
  </clause>

  <clause id="13071">
    <literal><![CDATA[
      K(x,y * (T(z,u) / u)) = K(x,y * (u \ z))
    ]]></literal>
    <justification jstring="[para(8974(a,1),13004(a,1,2,2))].">
      <j1 rule="para" parents="8974 13004"/>
    </justification>
  </clause>

  <clause id="13072">
    <literal><![CDATA[
      K(x,y * (z * L(u,w,u))) = K(x,y * (z * u))
    ]]></literal>
    <justification jstring="[para(9095(a,1),13004(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9095 13004"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13073">
    <literal><![CDATA[
      K(x,y * (L(z,u,z) \ w)) = K(x,y * (z \ w))
    ]]></literal>
    <justification jstring="[para(9105(a,1),13004(a,1,2,2))].">
      <j1 rule="para" parents="9105 13004"/>
    </justification>
  </clause>

  <clause id="13074">
    <literal><![CDATA[
      K(x,y * (z \ R(u,w,u))) = K(x,y * (z \ u))
    ]]></literal>
    <justification jstring="[para(12935(a,1),13004(a,1,2,2))].">
      <j1 rule="para" parents="12935 13004"/>
    </justification>
  </clause>

  <clause id="13075">
    <literal><![CDATA[
      K(x,y * (z * (u * a(w,v5,w)))) = K(x,y * (z * u))
    ]]></literal>
    <justification jstring="[para(12920(a,1),13004(a,1,2,2))].">
      <j1 rule="para" parents="12920 13004"/>
    </justification>
  </clause>

  <clause id="13076">
    <literal><![CDATA[
      K(x,y \ T(z * u,z)) = K(x,y \ (u * z))
    ]]></literal>
    <justification jstring="[para(8970(a,1),13005(a,1,2,2))].">
      <j1 rule="para" parents="8970 13005"/>
    </justification>
  </clause>

  <clause id="13077">
    <literal><![CDATA[
      K(x,y \ (z * R(u,w,u))) = K(x,y \ (z * u))
    ]]></literal>
    <justification jstring="[para(9529(a,1),13005(a,1,2,2))].">
      <j1 rule="para" parents="9529 13005"/>
    </justification>
  </clause>

  <clause id="13078">
    <literal><![CDATA[
      K(x,y \ (L(z,u,z) * w)) = K(x,y \ (z * w))
    ]]></literal>
    <justification jstring="[para(9569(a,1),13005(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9569 13005"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13079">
    <literal><![CDATA[
      K(x,K(y * z,z) \ u) = K(x,K(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(8965(a,1),13006(a,1,2,1))].">
      <j1 rule="para" parents="8965 13006"/>
    </justification>
  </clause>

  <clause id="13080">
    <literal><![CDATA[
      K(x,K(y * z,y) \ u) = K(x,K(z,y) \ u)
    ]]></literal>
    <justification jstring="[para(8966(a,1),13006(a,1,2,1))].">
      <j1 rule="para" parents="8966 13006"/>
    </justification>
  </clause>

  <clause id="13081">
    <literal><![CDATA[
      K(x,(L(y,z,y) * u) \ w) = K(x,(y * u) \ w)
    ]]></literal>
    <justification jstring="[para(9569(a,1),13006(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9569 13006"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13082">
    <literal><![CDATA[
      K(x,(T(y * z,y) \ u) \ w) = K(x,((z * y) \ u) \ w)
    ]]></literal>
    <justification jstring="[para(11230(a,1),13006(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11230 13006"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13083">
    <literal><![CDATA[
      K(x,(y * (z * a(u,w,u))) \ v5) = K(x,(y * z) \ v5)
    ]]></literal>
    <justification jstring="[para(12936(a,1),13006(a,1,2,1))].">
      <j1 rule="para" parents="12936 13006"/>
    </justification>
  </clause>

  <clause id="13084">
    <literal><![CDATA[
      K(x,K(y \ z,y) * u) = K(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(8938(a,1),13010(a,1,2,1))].">
      <j1 rule="para" parents="8938 13010"/>
    </justification>
  </clause>

  <clause id="13085">
    <literal><![CDATA[
      K(x,(R(y,z,y) \ u) * w) = K(x,(y \ u) * w)
    ]]></literal>
    <justification jstring="[para(9540(a,1),13010(a,1,2,1))].">
      <j1 rule="para" parents="9540 13010"/>
    </justification>
  </clause>

  <clause id="13086">
    <literal><![CDATA[
      K(x,y * (K(z,z \ u) * w)) = K(x,y * (K(z,u) * w))
    ]]></literal>
    <justification jstring="[para(9833(a,1),13011(a,1,2,2))].">
      <j1 rule="para" parents="9833 13011"/>
    </justification>
  </clause>

  <clause id="13087">
    <literal><![CDATA[
      K(x,y * (z \ (a(u,w,u) \ v5))) = K(x,y * (z \ v5))
    ]]></literal>
    <justification jstring="[para(12953(a,1),13011(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12953 13011"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13088">
    <literal><![CDATA[
      K(x,y * (z \ L(u,w,u))) = K(x,y * (z \ u))
    ]]></literal>
    <justification jstring="[para(12964(a,1),13011(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12964 13011"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13089">
    <literal><![CDATA[
      K(x,y * K(z \ u,z)) = K(x,y * K(u,z))
    ]]></literal>
    <justification jstring="[para(8938(a,1),13012(a,1,2,2))].">
      <j1 rule="para" parents="8938 13012"/>
    </justification>
  </clause>

  <clause id="13090">
    <literal><![CDATA[
      K(x,y \ K(z \ 1,u)) = K(x,y \ K(z \ u,u))
    ]]></literal>
    <justification jstring="[para(8972(a,1),13013(a,1,2,2))].">
      <j1 rule="para" parents="8972 13013"/>
    </justification>
  </clause>

  <clause id="13091">
    <literal><![CDATA[
      K(T(x * y,x) / z,u) = K((y * x) / z,u)
    ]]></literal>
    <justification jstring="[para(8969(a,1),13026(a,1,1,1))].">
      <j1 rule="para" parents="8969 13026"/>
    </justification>
  </clause>

  <clause id="13092">
    <literal><![CDATA[
      K(x * K(y,y \ z),u) = K(x * K(y,z),u)
    ]]></literal>
    <justification jstring="[para(8971(a,1),13027(a,1,1,2))].">
      <j1 rule="para" parents="8971 13027"/>
    </justification>
  </clause>

  <clause id="13093">
    <literal><![CDATA[
      K(x * (y \ R(z,u,z)),w) = K(x * (y \ z),w)
    ]]></literal>
    <justification jstring="[para(12935(a,1),13027(a,1,1,2))].">
      <j1 rule="para" parents="12935 13027"/>
    </justification>
  </clause>

  <clause id="13094">
    <literal><![CDATA[
      K(x \ T(y * z,y),u) = K(x \ (z * y),u)
    ]]></literal>
    <justification jstring="[para(8970(a,1),13028(a,1,1,2))].">
      <j1 rule="para" parents="8970 13028"/>
    </justification>
  </clause>

  <clause id="13095">
    <literal><![CDATA[
      K(x \ K(y,y \ z),u) = K(x \ K(y,z),u)
    ]]></literal>
    <justification jstring="[para(8939(a,1),13028(a,1,1,2))].">
      <j1 rule="para" parents="8939 13028"/>
    </justification>
  </clause>

  <clause id="13096">
    <literal><![CDATA[
      K((L(x,y,x) * z) \ u,w) = K((x * z) \ u,w)
    ]]></literal>
    <justification jstring="[para(9568(a,1),13029(a,1,1,1))].">
      <j1 rule="para" parents="9568 13029"/>
    </justification>
  </clause>

  <clause id="13097">
    <literal><![CDATA[
      K(K(x * y,x) * z,u) = K(K(y,x) * z,u)
    ]]></literal>
    <justification jstring="[para(8958(a,1),13032(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="8958 13032"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13098">
    <literal><![CDATA[
      K((x * R(y,z,y)) \ u,w) = K((x * y) \ u,w)
    ]]></literal>
    <justification jstring="[para(12440(a,1),13033(a,1,1))].">
      <j1 rule="para" parents="12440 13033"/>
    </justification>
  </clause>

  <clause id="13099">
    <literal><![CDATA[
      T(x,K(y \ z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7832(a,1),13059(a,1))].">
      <j1 rule="para" parents="7832 13059"/>
    </justification>
  </clause>

  <clause id="13100">
    <literal><![CDATA[
      K(x,K(y,z / y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(4912(a,2),13060(a,1,2))].">
      <j1 rule="para" parents="4912 13060"/>
    </justification>
  </clause>

  <clause id="13101">
    <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),13100(a,1,2,2))].">
      <j1 rule="para" parents="185 13100"/>
    </justification>
  </clause>

  <clause id="13102">
    <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,12988,a(flip),b,8378,a),flip(a)].">
      <j1 rule="hyper" parents="119 12988 8378"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13103">
    <literal><![CDATA[
      T(x,((y \ z) * y) \ u) = T(x,T(z,y) \ u)
    ]]></literal>
    <justification jstring="[para(5(a,1),12988(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="5 12988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13104">
    <literal><![CDATA[
      K(x,K(y \ z,y * (z \ u)) * w) = K(x,K(y \ z,u) * w)
    ]]></literal>
    <justification jstring="[para(12460(a,1),13008(a,1,2,1))].">
      <j1 rule="para" parents="12460 13008"/>
    </justification>
  </clause>

  <clause id="13105">
    <literal><![CDATA[
      K(x,((y \ z) * y) \ u) = K(x,T(z,y) \ u)
    ]]></literal>
    <justification jstring="[para(5(a,1),13009(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="5 13009"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13106">
    <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(13009(a,1),8385(a,1,1,2))].">
      <j1 rule="para" parents="13009 8385"/>
    </justification>
  </clause>

  <clause id="13107">
    <literal><![CDATA[
      K(((x \ y) * x) \ z,u) = K(T(y,x) \ z,u)
    ]]></literal>
    <justification jstring="[para(5(a,1),13031(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5 13031"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13108">
    <literal><![CDATA[
      K((x * y) \ 1,T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K((y * x) \ 1,z) = u
    ]]></literal>
    <justification jstring="[para(13031(a,1),8054(a,1))].">
      <j1 rule="para" parents="13031 8054"/>
    </justification>
  </clause>

  <clause id="13110">
    <literal><![CDATA[
      T(x,y * T(T(z / u,w),z)) = T(x,y * T(u \ z,w))
    ]]></literal>
    <justification jstring="[para(7630(a,1),13035(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7630 13035"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13111">
    <literal><![CDATA[
      K(x,y * T(z,z * u)) = x \ T(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[hyper(116,a,13036,a(flip),b,4755,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="116 13036 4755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13112">
    <literal><![CDATA[
      K(x,((y \ z) \ z) * u) = x \ T(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(116,a,13037,a(flip),b,4755,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="116 13037 4755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13114">
    <literal><![CDATA[
      T(x,y / T((z \ u) \ u,w)) = T(x,y / T(T(z,w),u))
    ]]></literal>
    <justification jstring="[para(7658(a,2),13039(a,1,2,2))].">
      <j1 rule="para" parents="7658 13039"/>
    </justification>
  </clause>

  <clause id="13115">
    <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(8548(a,1),13039(a,2,2,2))].">
      <j1 rule="para" parents="8548 13039"/>
    </justification>
  </clause>

  <clause id="13116">
    <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(13040(a,1),12305(a,1,2,1))].">
      <j1 rule="para" parents="13040 12305"/>
    </justification>
  </clause>

  <clause id="13117">
    <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,13041,a(flip),b,8378,a),flip(a)].">
      <j1 rule="hyper" parents="119 13041 8378"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13118">
    <literal><![CDATA[
      T(x,y \ T(T(z,u),z \ w)) = T(x,y \ T(T(z,u),w))
    ]]></literal>
    <justification jstring="[para(7625(a,1),13042(a,1,2,2))].">
      <j1 rule="para" parents="7625 13042"/>
    </justification>
  </clause>

  <clause id="13119">
    <literal><![CDATA[
      T(x \ T(y,y \ z),x \ T(y,z)) = x \ ((y \ z) \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,658,a(flip),b,13043,a),flip(a)].">
      <j1 rule="hyper" parents="58 658 13043"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13120">
    <literal><![CDATA[
      T(x,K(y,z) * ((z * y) * u)) = T(x,T(z * y,z) * u)
    ]]></literal>
    <justification jstring="[para(4781(a,1),13044(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4781 13044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13121">
    <literal><![CDATA[
      K(x,y * ((z \ u) \ u)) = w / (K(y * T(z,u),x) * w)
    ]]></literal>
    <justification jstring="[hyper(320,a,5142,a,b,13046,a),flip(a)].">
      <j1 rule="hyper" parents="320 5142 13046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13122">
    <literal><![CDATA[
      K(x,y * T(z,u * z)) = K(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[para(4268(a,2),13046(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4268 13046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13123">
    <literal><![CDATA[
      K(x,y * T(T(z / u,w),z)) = K(x,y * T(u \ z,w))
    ]]></literal>
    <justification jstring="[para(7630(a,1),13046(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7630 13046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13124">
    <literal><![CDATA[
      K(T(x / y,x) \ z,u) = (w * K(u,(y \ x) \ z)) \ w
    ]]></literal>
    <justification jstring="[para(13047(a,1),6338(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="13047 6338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13125">
    <literal><![CDATA[
      K(x,L(((y \ z) \ z) \ u,w,v5)) = K(L(x,w,v5),T(y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(10870,a,13049,a)].">
      <j1 rule="hyper" parents="10870 13049"/>
    </justification>
  </clause>

  <clause id="13126">
    <literal><![CDATA[
      K(x,((y \ z) \ z) \ u) = (w * K(T(y,z) \ u,x)) \ w
    ]]></literal>
    <justification jstring="[hyper(320,a,6338,a,b,13049,a),flip(a)].">
      <j1 rule="hyper" parents="320 6338 13049"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13127">
    <literal><![CDATA[
      K(x,((y \ x) \ x) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(13049(a,2),7421(a,1))].">
      <j1 rule="para" parents="13049 7421"/>
    </justification>
  </clause>

  <clause id="13128">
    <literal><![CDATA[
      K(x,T(((y / z) \ 1) * y,y) \ u) = K(x,(((z \ y) \ 1) * y) \ u)
    ]]></literal>
    <justification jstring="[para(10147(a,1),13049(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10147 13049"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13129">
    <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(10870,a,13051,a)].">
      <j1 rule="hyper" parents="10870 13051"/>
    </justification>
  </clause>

  <clause id="13130">
    <literal><![CDATA[
      K(x,T(y * (1 / z),z) / u) = K(x,T(y * (1 / z),y) / u)
    ]]></literal>
    <justification jstring="[para(6430(a,2),13052(a,1,2,1))].">
      <j1 rule="para" parents="6430 13052"/>
    </justification>
  </clause>

  <clause id="13131">
    <literal><![CDATA[
      K(x,y \ T(z,y)) = K(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(8352,a,13053,a),flip(a)].">
      <j1 rule="hyper" parents="8352 13053"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13132">
    <literal><![CDATA[
      K(x,y \ T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(13053(a,1),8352(a,1))].">
      <j1 rule="para" parents="13053 8352"/>
    </justification>
  </clause>

  <clause id="13133">
    <literal><![CDATA[
      K(x,T(y,z) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(4248(a,2),13132(a,1,2))].">
      <j1 rule="para" parents="4248 13132"/>
    </justification>
  </clause>

  <clause id="13134">
    <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(6125(a,1),13132(a,1,2,2))].">
      <j1 rule="para" parents="6125 13132"/>
    </justification>
  </clause>

  <clause id="13135">
    <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(7980(a,1),13132(a,1,2,2))].">
      <j1 rule="para" parents="7980 13132"/>
    </justification>
  </clause>

  <clause id="13136">
    <literal><![CDATA[
      K(x,K(y \ z,y) * u) = x \ T(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(116,a,13064,a(flip),b,4755,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="116 13064 4755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13137">
    <literal><![CDATA[
      K(K(x \ y,x) * z,u) = u / T(u,K(y,x) * z)
    ]]></literal>
    <justification jstring="[para(13064(a,1),4794(a,2,2))].">
      <j1 rule="para" parents="13064 4794"/>
    </justification>
  </clause>

  <clause id="13138">
    <literal><![CDATA[
      T(x,y * ((z \ u) * z)) = T(x,y * T(u,z))
    ]]></literal>
    <justification jstring="[para(5(a,1),13065(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5 13065"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13139">
    <literal><![CDATA[
      K(x,((y \ z) * y) / u) = K(x,T(z,y) / u)
    ]]></literal>
    <justification jstring="[para(5(a,1),13066(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="5 13066"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13140">
    <literal><![CDATA[
      K(x,y * ((z \ u) * z)) = K(x,y * T(u,z))
    ]]></literal>
    <justification jstring="[para(5(a,1),13069(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5 13069"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13141">
    <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(10503(a,2),13070(a,2,2,2))].">
      <j1 rule="para" parents="10503 13070"/>
    </justification>
  </clause>

  <clause id="13142">
    <literal><![CDATA[
      K(x,y * (z / T(u,z))) = K(x,y * (u \ z))
    ]]></literal>
    <justification jstring="[para(4246(a,1),13071(a,1,2,2))].">
      <j1 rule="para" parents="4246 13071"/>
    </justification>
  </clause>

  <clause id="13143">
    <literal><![CDATA[
      K(x,K(y,z \ y) \ u) = K(x,K(z,z \ y) \ u)
    ]]></literal>
    <justification jstring="[para(5(a,1),13079(a,1,2,1,1))].">
      <j1 rule="para" parents="5 13079"/>
    </justification>
  </clause>

  <clause id="13144">
    <literal><![CDATA[
      K(x,K(y \ z,y) \ u) = K(x,K(z,y) \ u)
    ]]></literal>
    <justification jstring="[para(5(a,1),13080(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="5 13080"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13145">
    <literal><![CDATA[
      K(x,K(y,z) * ((z \ y) \ u)) = K(x,(y / z) \ u)
    ]]></literal>
    <justification jstring="[para(5399(a,1),13084(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5399 13084"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13146">
    <literal><![CDATA[
      K(x,(y / (z \ u)) * K(u,z)) = K(x,y / (u / z))
    ]]></literal>
    <justification jstring="[para(6470(a,1),13089(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6470 13089"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13147">
    <literal><![CDATA[
      K(((x \ y) * x) / z,u) = K(T(y,x) / z,u)
    ]]></literal>
    <justification jstring="[para(5(a,1),13091(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5 13091"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13148">
    <literal><![CDATA[
      K(x \ (y * z),T(x,y)) = K(x \ (z * y),x)
    ]]></literal>
    <justification jstring="[hyper(58,a,11255,a(flip),b,13094,a)].">
      <j1 rule="hyper" parents="58 11255 13094"/>
    </justification>
  </clause>

  <clause id="13149">
    <literal><![CDATA[
      K(x \ ((y \ z) * y),u) = K(x \ T(z,y),u)
    ]]></literal>
    <justification jstring="[para(5(a,1),13094(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 13094"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13150">
    <literal><![CDATA[
      K(x \ K(y,z \ 1),u) = K(x \ K(y,z \ y),u)
    ]]></literal>
    <justification jstring="[para(5012(a,1),13095(a,1,1,2))].">
      <j1 rule="para" parents="5012 13095"/>
    </justification>
  </clause>

  <clause id="13151">
    <literal><![CDATA[
      K(x \ K(y,(z * y) * u),w) = K(x \ K(y,z * u),w)
    ]]></literal>
    <justification jstring="[para(12454(a,1),13095(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="12454 13095"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13152">
    <literal><![CDATA[
      K(K(x * y,y) * z,u) = K(K(x,y) * z,u)
    ]]></literal>
    <justification jstring="[para(5266(a,2),13097(a,1,1,1))].">
      <j1 rule="para" parents="5266 13097"/>
    </justification>
  </clause>

  <clause id="13153">
    <literal><![CDATA[
      T(x,T(y,z) \ (z \ y)) = T(x,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(6507,a,13103,a),flip(a)].">
      <j1 rule="hyper" parents="6507 13103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13154">
    <literal><![CDATA[
      K(x,T(T(y * z,u),y) \ w) = K(x,T(z * y,u) \ w)
    ]]></literal>
    <justification jstring="[para(4596(a,1),13105(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4596 13105"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13155">
    <literal><![CDATA[
      K(((x * (a(y,z,u) * a(w,x,a(y,z,u)))) * w) \ v5,v6) = K(T((w * x) * a(y,z,u),w) \ v5,v6)
    ]]></literal>
    <justification jstring="[para(1708(a,1),13107(a,1,1,1,1))].">
      <j1 rule="para" parents="1708 13107"/>
    </justification>
  </clause>

  <clause id="13156">
    <literal><![CDATA[
      K(x,T(y,T(z,u)) * T(z,u)) = K(x,((u \ z) * u) * y)
    ]]></literal>
    <justification jstring="[hyper(12306,a,13140,a),flip(a)].">
      <j1 rule="hyper" parents="12306 13140"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13157">
    <literal><![CDATA[
      K(x,y * T((z \ 1) \ u,z)) = K(x,y * ((z \ K(z,u)) \ u))
    ]]></literal>
    <justification jstring="[para(10136(a,2),13140(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10136 13140"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13158">
    <literal><![CDATA[
      K(x \ T(T(y * z,u),y),w) = K(x \ T(z * y,u),w)
    ]]></literal>
    <justification jstring="[para(4596(a,1),13149(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4596 13149"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13159">
    <literal><![CDATA[
      K(x \ ((y \ z) * y),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ z,y) = u
    ]]></literal>
    <justification jstring="[para(13149(a,2),7411(a,1))].">
      <j1 rule="para" parents="13149 7411"/>
    </justification>
  </clause>

  <clause id="13160">
    <literal><![CDATA[
      L(x,y,z / T(u * (w / u),u)) = L(x,y,z / w)
    ]]></literal>
    <justification jstring="[para(9107(a,1),12968(a,1,3,2))].">
      <j1 rule="para" parents="9107 12968"/>
    </justification>
  </clause>

  <clause id="13161">
    <literal><![CDATA[
      K(x,(y * ((z \ u) \ u)) / w) = K(x,(y * T(z,u)) / w)
    ]]></literal>
    <justification jstring="[para(7529(a,1),13067(a,1,2,1,2))].">
      <j1 rule="para" parents="7529 13067"/>
    </justification>
  </clause>

  <clause id="13162">
    <literal><![CDATA[
      K(x,y * (z * L(T(u,w),v5,u))) = K(x,y * (z * T(u,w)))
    ]]></literal>
    <justification jstring="[para(7503(a,1),13072(a,1,2,2,2))].">
      <j1 rule="para" parents="7503 13072"/>
    </justification>
  </clause>

  <clause id="13163">
    <literal><![CDATA[
      K(x,y * (((z \ u) \ u) \ w)) = K(x,y * (T(z,u) \ w))
    ]]></literal>
    <justification jstring="[para(11772(a,1),13073(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="11772 13073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13164">
    <literal><![CDATA[
      K(x,y * (z \ T(u,u * w))) = K(x,y * (z \ T(u,w)))
    ]]></literal>
    <justification jstring="[para(4385(a,1),13074(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="4385 13074"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13165">
    <literal><![CDATA[
      K(x,y \ (z * ((u \ w) \ w))) = K(x,y \ (z * T(u,w)))
    ]]></literal>
    <justification jstring="[para(7529(a,1),13077(a,1,2,2,2))].">
      <j1 rule="para" parents="7529 13077"/>
    </justification>
  </clause>

  <clause id="13166">
    <literal><![CDATA[
      K(x,y \ (T(z / u,z) * w)) = K(x,y \ ((u \ z) * w))
    ]]></literal>
    <justification jstring="[para(4404(a,1),13078(a,1,2,2,1))].">
      <j1 rule="para" parents="4404 13078"/>
    </justification>
  </clause>

  <clause id="13167">
    <literal><![CDATA[
      K(x,y \ (((z \ u) \ u) * w)) = K(x,y \ (T(z,u) * w))
    ]]></literal>
    <justification jstring="[para(11772(a,1),13078(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="11772 13078"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13168">
    <literal><![CDATA[
      K(x,(((y \ z) \ z) \ u) * w) = K(x,(T(y,z) \ u) * w)
    ]]></literal>
    <justification jstring="[para(7529(a,1),13085(a,1,2,1,1))].">
      <j1 rule="para" parents="7529 13085"/>
    </justification>
  </clause>

  <clause id="13169">
    <literal><![CDATA[
      K(x,y * (z \ T(u / w,u))) = K(x,y * (z \ (w \ u)))
    ]]></literal>
    <justification jstring="[para(4404(a,1),13088(a,1,2,2,2))].">
      <j1 rule="para" parents="4404 13088"/>
    </justification>
  </clause>

  <clause id="13170">
    <literal><![CDATA[
      K(x * (y \ T(z,z * u)),w) = K(x * (y \ T(z,u)),w)
    ]]></literal>
    <justification jstring="[para(4385(a,1),13093(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4385 13093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13171">
    <literal><![CDATA[
      K((x * y) \ z,y * x) * (z * u) = (((y * x) \ z) * (y * x)) * u
    ]]></literal>
    <justification jstring="[para(13096(a,1),11302(a,1,1))].">
      <j1 rule="para" parents="13096 11302"/>
    </justification>
  </clause>

  <clause id="13172">
    <literal><![CDATA[
      K((x * T(y,y \ z)) \ u,w) = K((x * T(y,z)) \ u,w)
    ]]></literal>
    <justification jstring="[para(4440(a,1),13098(a,1,1,1,2))].">
      <j1 rule="para" parents="4440 13098"/>
    </justification>
  </clause>

  <clause id="13173">
    <literal><![CDATA[
      K((x \ 1) \ (y \ z),y) != u
    ]]></literal>
    <literal><![CDATA[
      K((x \ y) \ z,y) = u
    ]]></literal>
    <justification jstring="[para(8365(a,1),13159(a,1))].">
      <j1 rule="para" parents="8365 13159"/>
    </justification>
  </clause>

  <clause id="13174">
    <literal><![CDATA[
      T(x * a(y,z,y),u) = T(x,u) * a(y,z,y)
    ]]></literal>
    <justification jstring="[para(17(a,2),12946(a,1,1)),flip(a)].">
      <j1 rule="para" parents="17 12946"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13175">
    <literal><![CDATA[
      T(a(x,y,x) * z,u) = T(z,u) * a(x,y,x)
    ]]></literal>
    <justification jstring="[para(9522(a,2),13174(a,1,1))].">
      <j1 rule="para" parents="9522 13174"/>
    </justification>
  </clause>

  <clause id="13176">
    <literal><![CDATA[
      K(x,T(a(y,z,y) * u,w)) = K(x,T(u,w))
    ]]></literal>
    <justification jstring="[para(13175(a,2),12992(a,1,2))].">
      <j1 rule="para" parents="13175 12992"/>
    </justification>
  </clause>

  <clause id="13177">
    <literal><![CDATA[
      K(x,y * T(a(z,u,z) * w,v5)) = K(x,y * T(w,v5))
    ]]></literal>
    <justification jstring="[para(13175(a,2),13004(a,1,2,2))].">
      <j1 rule="para" parents="13175 13004"/>
    </justification>
  </clause>

  <clause id="13178">
    <literal><![CDATA[
      K(x,T(K(y,y \ z) * u,w)) = K(x,T(K(y,z) * u,w))
    ]]></literal>
    <justification jstring="[para(9833(a,1),13176(a,1,2,1))].">
      <j1 rule="para" parents="9833 13176"/>
    </justification>
  </clause>

  <clause id="13179">
    <literal><![CDATA[
      K(x,y * (z \ (L(u,w,u) * v5))) = K(x,y * (z \ (u * v5)))
    ]]></literal>
    <justification jstring="[para(12956(a,1),13012(a,1,2,2))].">
      <j1 rule="para" parents="12956 13012"/>
    </justification>
  </clause>

  <clause id="13180">
    <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(4457(a,1),13016(a,1,2,1,1))].">
      <j1 rule="para" parents="4457 13016"/>
    </justification>
  </clause>

  <clause id="13181">
    <literal><![CDATA[
      K(x,y * T(z,z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(13111(a,2),4838(a,1))].">
      <j1 rule="para" parents="13111 4838"/>
    </justification>
  </clause>

  <clause id="13182">
    <literal><![CDATA[
      K(x,((y \ z) \ z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z) * u) = w
    ]]></literal>
    <justification jstring="[para(13112(a,2),4838(a,1))].">
      <j1 rule="para" parents="13112 4838"/>
    </justification>
  </clause>

  <clause id="13183">
    <literal><![CDATA[
      K(x,K(y \ z,y) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y) * u) = w
    ]]></literal>
    <justification jstring="[para(13136(a,2),4838(a,1))].">
      <j1 rule="para" parents="13136 4838"/>
    </justification>
  </clause>

  <clause id="13184">
    <literal><![CDATA[
      K(K(x \ y,x) * z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(K(y,x) * z,u) = w
    ]]></literal>
    <justification jstring="[para(13137(a,2),4862(a,1))].">
      <j1 rule="para" parents="13137 4862"/>
    </justification>
  </clause>

  <clause id="13185">
    <literal><![CDATA[
      L(x,y,(z * (u / z)) \ z) = L(x,y,z / u)
    ]]></literal>
    <justification jstring="[hyper(58,a,12605,a(flip),b,13160,a)].">
      <j1 rule="hyper" parents="58 12605 13160"/>
    </justification>
  </clause>

  <clause id="13186">
    <literal><![CDATA[
      L(x,y,z / (u * z)) = L(x,y,(z * u) \ z)
    ]]></literal>
    <justification jstring="[para(6(a,1),13185(a,1,3,1,2)),flip(a)].">
      <j1 rule="para" parents="6 13185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13187">
    <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(4918(a,2),13185(a,2,3))].">
      <j1 rule="para" parents="4918 13185"/>
    </justification>
  </clause>

  <clause id="13188">
    <literal><![CDATA[
      L(x,y,z \ (z / (z / u))) = L(x,y,u / z)
    ]]></literal>
    <justification jstring="[para(5071(a,1),13185(a,1,3))].">
      <j1 rule="para" parents="5071 13185"/>
    </justification>
  </clause>

  <clause id="13189">
    <literal><![CDATA[
      L(x,y,(z \ u) / u) = L(x,y,u \ (u / z))
    ]]></literal>
    <justification jstring="[para(72(a,1),13188(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="72 13188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13190">
    <literal><![CDATA[
      L(x,y,z \ K(u,u \ w)) = L(x,y,z \ K(u,w))
    ]]></literal>
    <justification jstring="[para(12934(a,1),12574(a,1,3))].">
      <j1 rule="para" parents="12934 12574"/>
    </justification>
  </clause>

  <clause id="13191">
    <literal><![CDATA[
      K(x \ K(y,y \ z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x \ K(y,z),u) = w
    ]]></literal>
    <justification jstring="[para(12934(a,1),13020(a,1,1))].">
      <j1 rule="para" parents="12934 13020"/>
    </justification>
  </clause>

  <clause id="13192">
    <literal><![CDATA[
      K(x,y * (z * (T(u,w) / w))) = K(x,y * (z * (w \ u)))
    ]]></literal>
    <justification jstring="[para(8974(a,1),13075(a,1,2,2,2))].">
      <j1 rule="para" parents="8974 13075"/>
    </justification>
  </clause>

  <clause id="13193">
    <literal><![CDATA[
      K(x,y * (z * (u \ K(w,w \ v5)))) = K(x,y * (z * (u \ K(w,v5))))
    ]]></literal>
    <justification jstring="[para(12934(a,1),13075(a,1,2,2,2))].">
      <j1 rule="para" parents="12934 13075"/>
    </justification>
  </clause>

  <clause id="13194">
    <literal><![CDATA[
      K(x,(y * K(z * u,u)) \ w) = K(x,(y * K(z,u)) \ w)
    ]]></literal>
    <justification jstring="[para(8964(a,1),13083(a,1,2,1,2))].">
      <j1 rule="para" parents="8964 13083"/>
    </justification>
  </clause>

  <clause id="13195">
    <literal><![CDATA[
      K(x,y * (z \ K(u \ w,u))) = K(x,y * (z \ K(w,u)))
    ]]></literal>
    <justification jstring="[para(8938(a,1),13087(a,1,2,2,2))].">
      <j1 rule="para" parents="8938 13087"/>
    </justification>
  </clause>

  <clause id="13196">
    <literal><![CDATA[
      K(x,y * T(T(z * u,z),w)) = K(x,y * T(u * z,w))
    ]]></literal>
    <justification jstring="[para(8970(a,1),13177(a,1,2,2,1))].">
      <j1 rule="para" parents="8970 13177"/>
    </justification>
  </clause>

  <clause id="13197">
    <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(10336(a,2),13182(a,1,2,1))].">
      <j1 rule="para" parents="10336 13182"/>
    </justification>
  </clause>

  <clause id="13198">
    <literal><![CDATA[
      K((x * (y / x)) \ z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(K(y,x) * (y \ z),u) = w
    ]]></literal>
    <justification jstring="[para(11220(a,1),13184(a,1,1))].">
      <j1 rule="para" parents="11220 13184"/>
    </justification>
  </clause>

  <clause id="13199">
    <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,12938,a),flip(a)].">
      <j1 rule="hyper" parents="691 12938"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13200">
    <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),12938(a,2,1))].">
      <j1 rule="para" parents="13 12938"/>
    </justification>
  </clause>

  <clause id="13201">
    <literal><![CDATA[
      (x * (y * (z * a(u,w,u)))) \ v5 = (x * (y * z)) \ (a(u,w,u) \ v5)
    ]]></literal>
    <justification jstring="[para(12920(a,1),12940(a,1,1,2))].">
      <j1 rule="para" parents="12920 12940"/>
    </justification>
  </clause>

  <clause id="13202">
    <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(12435,a,12960,a),flip(a)].">
      <j1 rule="hyper" parents="12435 12960"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13203">
    <literal><![CDATA[
      K(x,y * ((z / (z / u)) \ w)) = K(x,y * (K(u,z) * (u \ w)))
    ]]></literal>
    <justification jstring="[para(5401(a,2),13086(a,1,2,2))].">
      <j1 rule="para" parents="5401 13086"/>
    </justification>
  </clause>

  <clause id="13204">
    <literal><![CDATA[
      T(x,T(y * z,y) * u) = T(x,(z * y) * u)
    ]]></literal>
    <justification jstring="[para(11157(a,1),13120(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11157 13120"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13205">
    <literal><![CDATA[
      T(x,((y \ z) * y) * u) = T(x,T(z,y) * u)
    ]]></literal>
    <justification jstring="[para(5(a,1),13204(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="5 13204"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13206">
    <literal><![CDATA[
      T(x,T(T(y * z,u),y) * w) = T(x,T(z * y,u) * w)
    ]]></literal>
    <justification jstring="[para(4596(a,1),13205(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4596 13205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13207">
    <literal><![CDATA[
      K(x,y * ((z \ u) \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(13121(a,2),5150(a,1))].">
      <j1 rule="para" parents="13121 5150"/>
    </justification>
  </clause>

  <clause id="13208">
    <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),13207(a,1,2,2))].">
      <j1 rule="para" parents="106 13207"/>
    </justification>
  </clause>

  <clause id="13209">
    <literal><![CDATA[
      K(T(x / y,x) \ z,u) = K((y \ x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(320,a,6338,a(flip),b,13124,a),flip(a)].">
      <j1 rule="hyper" parents="320 6338 13124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13210">
    <literal><![CDATA[
      K(((x \ y) \ y) \ z,u) = K(T(x,y) \ z,u)
    ]]></literal>
    <justification jstring="[para(72(a,1),13209(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="72 13209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13211">
    <literal><![CDATA[
      K(T(x,x \ y) \ z,u) = K(T(x,y) \ z,u)
    ]]></literal>
    <justification jstring="[para(106(a,2),13210(a,1,1,1))].">
      <j1 rule="para" parents="106 13210"/>
    </justification>
  </clause>

  <clause id="13212">
    <literal><![CDATA[
      K(x,((y \ z) \ z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z) \ u) = w
    ]]></literal>
    <justification jstring="[para(13126(a,2),6345(a,1))].">
      <j1 rule="para" parents="13126 6345"/>
    </justification>
  </clause>

  <clause id="13213">
    <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),13212(a,1,2,1))].">
      <j1 rule="para" parents="106 13212"/>
    </justification>
  </clause>

  <clause id="13214">
    <literal><![CDATA[
      K(x,((y \ z) * y) * u) = K(x,T(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(12305,a,13156,a),flip(a)].">
      <j1 rule="hyper" parents="12305 13156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13215">
    <literal><![CDATA[
      K(x,y * (z * (u / T(w,u)))) = K(x,y * (z * (w \ u)))
    ]]></literal>
    <justification jstring="[para(4246(a,1),13192(a,1,2,2,2))].">
      <j1 rule="para" parents="4246 13192"/>
    </justification>
  </clause>

  <clause id="13216">
    <literal><![CDATA[
      K(x,y * T((z / u) \ 1,z)) = K(x,y * ((z / u) \ K(u,z)))
    ]]></literal>
    <justification jstring="[para(5436(a,1),13195(a,1,2,2))].">
      <j1 rule="para" parents="5436 13195"/>
    </justification>
  </clause>

  <clause id="13217">
    <literal><![CDATA[
      K(x,y * (z * T(T(u / w,u),v5))) = K(x,y * (z * T(w \ u,v5)))
    ]]></literal>
    <justification jstring="[para(9066(a,1),13162(a,1,2,2,2))].">
      <j1 rule="para" parents="9066 13162"/>
    </justification>
  </clause>

  <clause id="13218">
    <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(13125(a,2),10870(a,1))].">
      <j1 rule="para" parents="13125 10870"/>
    </justification>
  </clause>

  <clause id="13219">
    <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(13129(a,2),10870(a,1))].">
      <j1 rule="para" parents="13129 10870"/>
    </justification>
  </clause>

  <clause id="13220">
    <literal><![CDATA[
      K(x,T(y * (1 / z),z) / u) = K(x,((1 / z) * y) / u)
    ]]></literal>
    <justification jstring="[hyper(320,a,13066,a(flip),b,13130,a),flip(a)].">
      <j1 rule="hyper" parents="320 13066 13130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13221">
    <literal><![CDATA[
      K(x,T(y * (1 / z),z) / u) = K(x,((z \ 1) * y) / u)
    ]]></literal>
    <justification jstring="[hyper(320,a,5581,a(flip),b,13220,a),flip(a)].">
      <j1 rule="hyper" parents="320 5581 13220"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13222">
    <literal><![CDATA[
      (x * y) \ (x * (y * (z * a(u,w,u)))) = L(z,y,x) * a(u,w,u)
    ]]></literal>
    <justification jstring="[para(12920(a,1),13200(a,1,2,2))].">
      <j1 rule="para" parents="12920 13200"/>
    </justification>
  </clause>

  <clause id="13223">
    <literal><![CDATA[
      L(x * a(y,z,y),u,w) = L(x,u,w) * a(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(482,a,13222,a)].">
      <j1 rule="hyper" parents="482 13222"/>
    </justification>
  </clause>

  <clause id="13224">
    <literal><![CDATA[
      L(a(x,y,x) \ z,u,w) = a(x,y,x) \ L(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(3535,a,13223,a),flip(a)].">
      <j1 rule="hyper" parents="3535 13223"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13225">
    <literal><![CDATA[
      x * L(y * a(x,z,x),u,w) = R(x,z,x) * L(y,u,w)
    ]]></literal>
    <justification jstring="[para(13223(a,2),9135(a,1,2))].">
      <j1 rule="para" parents="13223 9135"/>
    </justification>
  </clause>

  <clause id="13226">
    <literal><![CDATA[
      K(x,L(y * a(z,u,z),w,v5)) = K(x,L(y,w,v5))
    ]]></literal>
    <justification jstring="[para(13223(a,2),12992(a,1,2))].">
      <j1 rule="para" parents="13223 12992"/>
    </justification>
  </clause>

  <clause id="13227">
    <literal><![CDATA[
      K(x,L(a(y,z,y) * u,w,v5)) = K(x,L(u,w,v5))
    ]]></literal>
    <justification jstring="[para(9522(a,2),13226(a,1,2,1))].">
      <j1 rule="para" parents="9522 13226"/>
    </justification>
  </clause>

  <clause id="13228">
    <literal><![CDATA[
      K(x,L(T(y * z,y) \ u,w,v5)) = K(x,L((z * y) \ u,w,v5))
    ]]></literal>
    <justification jstring="[para(11230(a,1),13227(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11230 13227"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13229">
    <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(13224(a,2),9546(a,1,1))].">
      <j1 rule="para" parents="13224 9546"/>
    </justification>
  </clause>

  <clause id="13230">
    <literal><![CDATA[
      L(a(x,y,x) \ z,u,w) * v5 = L(z,u,w) * (a(x,y,x) \ v5)
    ]]></literal>
    <justification jstring="[para(13224(a,2),12963(a,1,1))].">
      <j1 rule="para" parents="13224 12963"/>
    </justification>
  </clause>

  <clause id="13231">
    <literal><![CDATA[
      R(x,y,x) * L(R(x,y,x) \ z,u,w) = x * L(x \ z,u,w)
    ]]></literal>
    <justification jstring="[para(9134(a,1),13225(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9134 13225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13232">
    <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,10807,a,b,13228,a)].">
      <j1 rule="hyper" parents="320 10807 13228"/>
    </justification>
  </clause>

  <clause id="13233">
    <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(12965(a,1),13230(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="12965 13230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13234">
    <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,13231,a(flip),b,11416,a),flip(a)].">
      <j1 rule="hyper" parents="119 13231 11416"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13236">
    <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(13102(a,2),8380(a,1))].">
      <j1 rule="para" parents="13102 8380"/>
    </justification>
  </clause>

  <clause id="13237">
    <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,8379,a(flip),b,13117,a),flip(a)].">
      <j1 rule="hyper" parents="320 8379 13117"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13238">
    <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(12962(a,1),13202(a,1,1))].">
      <j1 rule="para" parents="12962 13202"/>
    </justification>
  </clause>

  <clause id="13239">
    <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,2138,a(flip),b,13234,a)].">
      <j1 rule="hyper" parents="58 2138 13234"/>
    </justification>
  </clause>

  <clause id="13240">
    <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),13234(a,1,1,1))].">
      <j1 rule="para" parents="5 13234"/>
    </justification>
  </clause>

  <clause id="13242">
    <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,1850,a(flip),b,13239,a),flip(a)].">
      <j1 rule="hyper" parents="320 1850 13239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13243">
    <literal><![CDATA[
      T(x * (y * L(y \ 1,z,u)),x) = (y * L(y \ 1,z,u)) * x
    ]]></literal>
    <justification jstring="[para(918(a,1),13242(a,1,1))].">
      <j1 rule="para" parents="918 13242"/>
    </justification>
  </clause>

  <clause id="13244">
    <literal><![CDATA[
      R(x,y * L(y \ 1,z,u),x) = x
    ]]></literal>
    <justification jstring="[hyper(4339,a,13243,a)].">
      <j1 rule="hyper" parents="4339 13243"/>
    </justification>
  </clause>

  <clause id="13245">
    <literal><![CDATA[
      R(x,y \ L(y,z,u),x) = x
    ]]></literal>
    <justification jstring="[para(1193(a,1),13244(a,1,2))].">
      <j1 rule="para" parents="1193 13244"/>
    </justification>
  </clause>

  <clause id="13246">
    <literal><![CDATA[
      R(T(x,y),z \ L(z,u,w),x) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,7123,a(flip),b,13245,a)].">
      <j1 rule="hyper" parents="58 7123 13245"/>
    </justification>
  </clause>

  <clause id="13247">
    <literal><![CDATA[
      a(x,y \ L(y,z,u),x) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,13245,a(flip),b,8949,a),flip(a)].">
      <j1 rule="hyper" parents="115 13245 8949"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13248">
    <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(12959(a,1),13238(a,1,1,2))].">
      <j1 rule="para" parents="12959 13238"/>
    </justification>
  </clause>

  <clause id="13249">
    <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(12959(a,1),13248(a,1,1,2,2))].">
      <j1 rule="para" parents="12959 13248"/>
    </justification>
  </clause>

  <clause id="13250">
    <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),13249(a,1,1))].">
      <j1 rule="para" parents="13 13249"/>
    </justification>
  </clause>

  <clause id="13251">
    <literal><![CDATA[
      L(x,a(y,z,y) * u,w) = L(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(13229,a,13250,a),flip(a)].">
      <j1 rule="hyper" parents="13229 13250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13252">
    <literal><![CDATA[
      L(x,a(y,z,y) \ u,w) = L(x,u,w)
    ]]></literal>
    <justification jstring="[para(5(a,1),13251(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5 13251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13253">
    <literal><![CDATA[
      L(x,R(y,z,y),u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[para(8956(a,1),13251(a,1,2))].">
      <j1 rule="para" parents="8956 13251"/>
    </justification>
  </clause>

  <clause id="13254">
    <literal><![CDATA[
      L(x,K(y * z,y),u) = L(x,K(z,y),u)
    ]]></literal>
    <justification jstring="[para(8966(a,1),13251(a,1,2))].">
      <j1 rule="para" parents="8966 13251"/>
    </justification>
  </clause>

  <clause id="13255">
    <literal><![CDATA[
      L(x,K(y,y * z),u) = L(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[para(8967(a,1),13251(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8967 13251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13256">
    <literal><![CDATA[
      L(x,T(y * z,y),u) = L(x,z * y,u)
    ]]></literal>
    <justification jstring="[para(8970(a,1),13251(a,1,2))].">
      <j1 rule="para" parents="8970 13251"/>
    </justification>
  </clause>

  <clause id="13257">
    <literal><![CDATA[
      L(x,K(y,y \ z),u) = L(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[para(8939(a,1),13251(a,1,2))].">
      <j1 rule="para" parents="8939 13251"/>
    </justification>
  </clause>

  <clause id="13258">
    <literal><![CDATA[
      L(x,L(y,z,y) \ u,w) = L(x,y \ u,w)
    ]]></literal>
    <justification jstring="[para(9531(a,1),13251(a,1,2))].">
      <j1 rule="para" parents="9531 13251"/>
    </justification>
  </clause>

  <clause id="13259">
    <literal><![CDATA[
      L(x,y / L(z,u,z),w) = L(x,y / z,w)
    ]]></literal>
    <justification jstring="[para(9532(a,1),13251(a,1,2))].">
      <j1 rule="para" parents="9532 13251"/>
    </justification>
  </clause>

  <clause id="13260">
    <literal><![CDATA[
      L(x,T(y * (z / y),y),u) = L(x,z,u)
    ]]></literal>
    <justification jstring="[para(9530(a,1),13251(a,1,2))].">
      <j1 rule="para" parents="9530 13251"/>
    </justification>
  </clause>

  <clause id="13261">
    <literal><![CDATA[
      L(x,K(y,y \ z) * u,w) = L(x,K(y,z) * u,w)
    ]]></literal>
    <justification jstring="[para(9833(a,1),13251(a,1,2))].">
      <j1 rule="para" parents="9833 13251"/>
    </justification>
  </clause>

  <clause id="13262">
    <literal><![CDATA[
      L(x,T(y,y \ z),u) = L(x,T(y,z),u)
    ]]></literal>
    <justification jstring="[para(4440(a,1),13253(a,1,2))].">
      <j1 rule="para" parents="4440 13253"/>
    </justification>
  </clause>

  <clause id="13263">
    <literal><![CDATA[
      L(x,(y \ z) \ z,u) = L(x,T(y,z),u)
    ]]></literal>
    <justification jstring="[para(7529(a,1),13253(a,1,2))].">
      <j1 rule="para" parents="7529 13253"/>
    </justification>
  </clause>

  <clause id="13264">
    <literal><![CDATA[
      L(x,a(y,z,y) \ 1,u) = x
    ]]></literal>
    <justification jstring="[hyper(320,a,372,a(flip),b,13252,a),flip(a)].">
      <j1 rule="hyper" parents="320 372 13252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13265">
    <literal><![CDATA[
      L(x,K(y \ z,y),u) = L(x,K(z,y),u)
    ]]></literal>
    <justification jstring="[para(8938(a,1),13252(a,1,2))].">
      <j1 rule="para" parents="8938 13252"/>
    </justification>
  </clause>

  <clause id="13266">
    <literal><![CDATA[
      L(x,R(y,z,y) \ y,u) = x
    ]]></literal>
    <justification jstring="[para(8960(a,2),13264(a,1,2))].">
      <j1 rule="para" parents="8960 13264"/>
    </justification>
  </clause>

  <clause id="13267">
    <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,13266,a),flip(a)].">
      <j1 rule="hyper" parents="320 92 13266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13268">
    <literal><![CDATA[
      L(x,K(y * z,(y * z) * (z \ 1)),u) = L(x,K(z * y,z \ 1),u)
    ]]></literal>
    <justification jstring="[para(5871(a,1),13255(a,2,2))].">
      <j1 rule="para" parents="5871 13255"/>
    </justification>
  </clause>

  <clause id="13269">
    <literal><![CDATA[
      L(x,y * z,z) = L(x,z * y,z)
    ]]></literal>
    <justification jstring="[hyper(11199,a,13256,a),flip(a)].">
      <j1 rule="hyper" parents="11199 13256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13270">
    <literal><![CDATA[
      L(x,(y \ z) * y,u) = L(x,T(z,y),u)
    ]]></literal>
    <justification jstring="[para(5(a,1),13256(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 13256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13271">
    <literal><![CDATA[
      L(x,K(y,z),z \ y) = x
    ]]></literal>
    <justification jstring="[hyper(12657,a,13257,a),flip(a)].">
      <j1 rule="hyper" parents="12657 13257"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13272">
    <literal><![CDATA[
      (x \ y) * (K(y,x) * z) = (x \ T(y,x)) * z
    ]]></literal>
    <justification jstring="[hyper(119,a,13271,a(flip),b,6385,a),flip(a)].">
      <j1 rule="hyper" parents="119 13271 6385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13273">
    <literal><![CDATA[
      L(x,y * (z / T(y,z)),u) = L(x,z,u)
    ]]></literal>
    <justification jstring="[para(4278(a,1),13260(a,1,2))].">
      <j1 rule="para" parents="4278 13260"/>
    </justification>
  </clause>

  <clause id="13274">
    <literal><![CDATA[
      L(x,T(y,z),y \ z) = L(x,y,y \ z)
    ]]></literal>
    <justification jstring="[hyper(11199,a,13262,a),flip(a)].">
      <j1 rule="hyper" parents="11199 13262"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13275">
    <literal><![CDATA[
      L(x,T(y * z,z \ 1),u) = L(x,T(y * z,y),u)
    ]]></literal>
    <justification jstring="[para(6174(a,1),13262(a,1,2))].">
      <j1 rule="para" parents="6174 13262"/>
    </justification>
  </clause>

  <clause id="13276">
    <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(13262(a,1),4570(a,1))].">
      <j1 rule="para" parents="13262 4570"/>
    </justification>
  </clause>

  <clause id="13277">
    <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(13262(a,1),11206(a,1))].">
      <j1 rule="para" parents="13262 11206"/>
    </justification>
  </clause>

  <clause id="13278">
    <literal><![CDATA[
      L(x,T(T(y,z),z \ 1),u) = L(x,T(T(y,z),z \ y),u)
    ]]></literal>
    <justification jstring="[para(13153(a,1),13262(a,1,2))].">
      <j1 rule="para" parents="13153 13262"/>
    </justification>
  </clause>

  <clause id="13280">
    <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(13263(a,1),6631(a,1,2))].">
      <j1 rule="para" parents="13263 6631"/>
    </justification>
  </clause>

  <clause id="13281">
    <literal><![CDATA[
      L(x,K(y * z,y \ 1),u) = L(x,K(z,y \ 1),u)
    ]]></literal>
    <justification jstring="[para(4488(a,1),13265(a,1,2))].">
      <j1 rule="para" parents="4488 13265"/>
    </justification>
  </clause>

  <clause id="13282">
    <literal><![CDATA[
      L(x,T(y,z \ y),u) = L(x,z * (y / z),u)
    ]]></literal>
    <justification jstring="[para(4148(a,1),13270(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4148 13270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13283">
    <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,13256,a,b,13273,a)].">
      <j1 rule="hyper" parents="58 13256 13273"/>
    </justification>
  </clause>

  <clause id="13284">
    <literal><![CDATA[
      L(T(x,y) \ z,x,x \ y) = y \ ((T(y,x) / x) * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,12643,a(flip),b,13274,a),flip(a)].">
      <j1 rule="hyper" parents="58 12643 13274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13285">
    <literal><![CDATA[
      L(x,T(y / z,y) \ u,w) = L(x,(z \ y) \ u,w)
    ]]></literal>
    <justification jstring="[para(4404(a,1),13258(a,1,2,1))].">
      <j1 rule="para" parents="4404 13258"/>
    </justification>
  </clause>

  <clause id="13286">
    <literal><![CDATA[
      L(x,(y * z) / y,u) = L(x,y * (z / y),u)
    ]]></literal>
    <justification jstring="[para(544(a,1),13259(a,1,2)),flip(a)].">
      <j1 rule="para" parents="544 13259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13287">
    <literal><![CDATA[
      K(x,y) * ((y \ T(x,y)) \ z) = (y \ x) \ z
    ]]></literal>
    <justification jstring="[hyper(116,a,5,a(flip),b,13272,a),flip(a)].">
      <j1 rule="hyper" parents="116 5 13272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13288">
    <literal><![CDATA[
      K(x,y) * ((T(y,x) \ x) \ z) = (y \ x) \ z
    ]]></literal>
    <justification jstring="[para(4248(a,2),13287(a,1,2,1))].">
      <j1 rule="para" parents="4248 13287"/>
    </justification>
  </clause>

  <clause id="13289">
    <literal><![CDATA[
      L(x,T(y * z,z \ 1),u) = L(x,z * y,u)
    ]]></literal>
    <justification jstring="[hyper(320,a,13256,a(flip),b,13275,a),flip(a)].">
      <j1 rule="hyper" parents="320 13256 13275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13290">
    <literal><![CDATA[
      L(x,y * z,z \ 1) = L(x,z * y,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(11199,a,13289,a)].">
      <j1 rule="hyper" parents="11199 13289"/>
    </justification>
  </clause>

  <clause id="13291">
    <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(13289(a,1),10900(a,1,2))].">
      <j1 rule="para" parents="13289 10900"/>
    </justification>
  </clause>

  <clause id="13292">
    <literal><![CDATA[
      L(x,(x / y) \ z,u) = L(x,(y \ x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,10956,a(flip),b,13285,a)].">
      <j1 rule="hyper" parents="58 10956 13285"/>
    </justification>
  </clause>

  <clause id="13293">
    <literal><![CDATA[
      L(x,T(T(y,z),y / T(z,y)),u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[para(4242(a,1),13283(a,1,2,1))].">
      <j1 rule="para" parents="4242 13283"/>
    </justification>
  </clause>

  <clause id="13294">
    <literal><![CDATA[
      L(x,y,x) != z
    ]]></literal>
    <literal><![CDATA[
      L(x,T(y,u),x) = z
    ]]></literal>
    <justification jstring="[para(13293(a,1),12673(a,1))].">
      <j1 rule="para" parents="13293 12673"/>
    </justification>
  </clause>

  <clause id="13295">
    <literal><![CDATA[
      L(x,T(T(y,z),z \ y),u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[para(12741(a,1),13293(a,1,2))].">
      <j1 rule="para" parents="12741 13293"/>
    </justification>
  </clause>

  <clause id="13296">
    <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(9659(a,2),13294(a,1))].">
      <j1 rule="para" parents="9659 13294"/>
    </justification>
  </clause>

  <clause id="13297">
    <literal><![CDATA[
      L(x,T(T(y,z),z \ 1),u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,13278,a,b,13295,a)].">
      <j1 rule="hyper" parents="58 13278 13295"/>
    </justification>
  </clause>

  <clause id="13298">
    <literal><![CDATA[
      L(x,T(y,z),z \ 1) = L(x,y,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(11199,a,13297,a)].">
      <j1 rule="hyper" parents="11199 13297"/>
    </justification>
  </clause>

  <clause id="13300">
    <literal><![CDATA[
      L(x,y * (z / y),(y \ z) \ 1) = L(x,z,(y \ z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,13282,a(flip),b,13298,a)].">
      <j1 rule="hyper" parents="58 13282 13298"/>
    </justification>
  </clause>

  <clause id="13301">
    <literal><![CDATA[
      L(x \ y,x,z) != u
    ]]></literal>
    <literal><![CDATA[
      (z * x) \ (z * y) = u
    ]]></literal>
    <justification jstring="[para(13267(a,1),3666(a,1))].">
      <j1 rule="para" parents="13267 3666"/>
    </justification>
  </clause>

  <clause id="13302">
    <literal><![CDATA[
      a(x \ L(y \ z,y,u),w,v5) = a(x \ ((u * y) \ (u * z)),w,v5)
    ]]></literal>
    <justification jstring="[para(13267(a,1),12966(a,1,1,2))].">
      <j1 rule="para" parents="13267 12966"/>
    </justification>
  </clause>

  <clause id="13303">
    <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),13301(a,1,1))].">
      <j1 rule="para" parents="92 13301"/>
    </justification>
  </clause>

  <clause id="13304">
    <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),13268(a,1,2,2))].">
      <j1 rule="para" parents="261 13268"/>
    </justification>
  </clause>

  <clause id="13305">
    <literal><![CDATA[
      L(x,K(y * z,y \ 1),u) = L(x,K(z * y,z),u)
    ]]></literal>
    <justification jstring="[para(6958(a,1),13304(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6958 13304"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13306">
    <literal><![CDATA[
      L(x,K(y * z,y \ 1),u) = L(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(320,a,13254,a(flip),b,13305,a),flip(a)].">
      <j1 rule="hyper" parents="320 13254 13305"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13308">
    <literal><![CDATA[
      L(x,K(y,z),y \ 1) = x
    ]]></literal>
    <justification jstring="[hyper(5468,a,13306,a),flip(a)].">
      <j1 rule="hyper" parents="5468 13306"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13309">
    <literal><![CDATA[
      L(x,K(y,z \ 1),u) = L(x,K(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(58,a,13281,a(flip),b,13306,a)].">
      <j1 rule="hyper" parents="58 13281 13306"/>
    </justification>
  </clause>

  <clause id="13310">
    <literal><![CDATA[
      (1 / x) * (K(x,y) * z) = (K(x,y) / x) * z
    ]]></literal>
    <justification jstring="[para(13308(a,1),6246(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13308 6246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13312">
    <literal><![CDATA[
      L(x,K(y \ 1,z),u) = L(x,K(z,y),u)
    ]]></literal>
    <justification jstring="[para(3554(a,1),13309(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3554 13309"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13313">
    <literal><![CDATA[
      L(x,K(y,z),u \ (z \ u)) = x
    ]]></literal>
    <justification jstring="[hyper(8051,a,13312,a),flip(a)].">
      <j1 rule="hyper" parents="8051 13312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13314">
    <literal><![CDATA[
      (K(x,y) / x) * ((1 / x) \ z) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(6008,a,13310,a),flip(a)].">
      <j1 rule="hyper" parents="6008 13310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13315">
    <literal><![CDATA[
      (K(x,y) / x) * (x * z) = (1 / x) * (T(x,y) * z)
    ]]></literal>
    <justification jstring="[para(4781(a,1),13310(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4781 13310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13316">
    <literal><![CDATA[
      K(x,y) * ((1 / x) * z) != u
    ]]></literal>
    <literal><![CDATA[
      (K(x,y) / x) * z = u
    ]]></literal>
    <justification jstring="[para(13314(a,1),585(a,1))].">
      <j1 rule="para" parents="13314 585"/>
    </justification>
  </clause>

  <clause id="13317">
    <literal><![CDATA[
      (K(x,y) / x) * (x * (T(y,x) * z)) = (1 / x) * (x * (y * z))
    ]]></literal>
    <justification jstring="[para(4553(a,1),13315(a,2,2))].">
      <j1 rule="para" parents="4553 13315"/>
    </justification>
  </clause>

  <clause id="13318">
    <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(13317(a,2),2830(a,1))].">
      <j1 rule="para" parents="13317 2830"/>
    </justification>
  </clause>

  <clause id="13319">
    <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(12958(a,1),12971(a,1,2,1))].">
      <j1 rule="para" parents="12958 12971"/>
    </justification>
  </clause>

  <clause id="13320">
    <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(6127(a,1),13141(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6127 13141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13321">
    <literal><![CDATA[
      K(x,y * K((z * (1 / u)) \ w,u)) = K(x,y * K(u * (z \ w),w \ z))
    ]]></literal>
    <justification jstring="[para(6108(a,1),13320(a,2,2,2))].">
      <j1 rule="para" parents="6108 13320"/>
    </justification>
  </clause>

  <clause id="13323">
    <literal><![CDATA[
      K(x,y * K(z * (u \ w),w \ u)) = K(x,y * K(z * (u \ w),z))
    ]]></literal>
    <justification jstring="[para(10503(a,1),13321(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10503 13321"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13324">
    <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(13201(a,1),13199(a,1,1))].">
      <j1 rule="para" parents="13201 13199"/>
    </justification>
  </clause>

  <clause id="13325">
    <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(13232(a,1),10866(a,1))].">
      <j1 rule="para" parents="13232 10866"/>
    </justification>
  </clause>

  <clause id="13326">
    <literal><![CDATA[
      a(x * a(y,z,y),u,w) = a(x,a(y,z,y) * u,w)
    ]]></literal>
    <justification jstring="[hyper(12437,a,13319,a),flip(a)].">
      <j1 rule="hyper" parents="12437 13319"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13327">
    <literal><![CDATA[
      a(x,a(y,z,y) * u,w) = a(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(58,a,12775,a(flip),b,13326,a),flip(a)].">
      <j1 rule="hyper" parents="58 12775 13326"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13329">
    <literal><![CDATA[
      a(x,R(y,z,y),u) = a(x,y,u)
    ]]></literal>
    <justification jstring="[para(8956(a,1),13327(a,1,2))].">
      <j1 rule="para" parents="8956 13327"/>
    </justification>
  </clause>

  <clause id="13330">
    <literal><![CDATA[
      a(x,T(y * z,y),u) = a(x,z * y,u)
    ]]></literal>
    <justification jstring="[para(8970(a,1),13327(a,1,2))].">
      <j1 rule="para" parents="8970 13327"/>
    </justification>
  </clause>

  <clause id="13331">
    <literal><![CDATA[
      a(x,T(y,y \ z),u) = a(x,T(y,z),u)
    ]]></literal>
    <justification jstring="[para(4440(a,1),13329(a,1,2))].">
      <j1 rule="para" parents="4440 13329"/>
    </justification>
  </clause>

  <clause id="13332">
    <literal><![CDATA[
      a(x,(y \ z) * y,u) = a(x,T(z,y),u)
    ]]></literal>
    <justification jstring="[para(5(a,1),13330(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 13330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13333">
    <literal><![CDATA[
      a(x \ y,T(x,y),z) = a(y / x,x,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,4657,a(flip),b,13331,a),flip(a)].">
      <j1 rule="hyper" parents="58 4657 13331"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13334">
    <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(13332(a,1),4406(a,1,2))].">
      <j1 rule="para" parents="13332 4406"/>
    </justification>
  </clause>

  <clause id="13335">
    <literal><![CDATA[
      a(x,y,z * a(u,w,u)) = (x * (y * z)) \ ((x * y) * z)
    ]]></literal>
    <justification jstring="[hyper(12967,a,13324,a),flip(a)].">
      <j1 rule="hyper" parents="12967 13324"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13336">
    <literal><![CDATA[
      a(x,y,z * a(u,w,u)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,9,a,b,13335,a),flip(a)].">
      <j1 rule="hyper" parents="320 9 13335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13337">
    <literal><![CDATA[
      a(x,y,a(z,u,z) * w) = a(x,y,w)
    ]]></literal>
    <justification jstring="[para(9522(a,2),13336(a,1,3))].">
      <j1 rule="para" parents="9522 13336"/>
    </justification>
  </clause>

  <clause id="13338">
    <literal><![CDATA[
      a(x,y,z * (a(u,w,u) \ v5)) = a(x,y,z * v5)
    ]]></literal>
    <justification jstring="[para(12952(a,1),13337(a,1,3)),flip(a)].">
      <j1 rule="para" parents="12952 13337"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13339">
    <literal><![CDATA[
      a(x,y,z * K(u,u * w)) = a(x,y,z * K(u,w))
    ]]></literal>
    <justification jstring="[para(8957(a,1),13338(a,1,3,2))].">
      <j1 rule="para" parents="8957 13338"/>
    </justification>
  </clause>

  <clause id="13340">
    <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(12928(a,1),12929(a,1,2,2,1))].">
      <j1 rule="para" parents="12928 12929"/>
    </justification>
  </clause>

  <clause id="13342">
    <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(4307(a,2),13340(a,1,2))].">
      <j1 rule="para" parents="4307 13340"/>
    </justification>
  </clause>

  <clause id="13344">
    <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(12980(a,1),13342(a,1,2))].">
      <j1 rule="para" parents="12980 13342"/>
    </justification>
  </clause>

  <clause id="13345">
    <literal><![CDATA[
      T(T(x,x * y) * L(y,z,u),x) = L(y,z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[para(806(a,1),13344(a,1,2)),flip(a)].">
      <j1 rule="para" parents="806 13344"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13347">
    <literal><![CDATA[
      T(x * L(y,z,u),x * y) = L(y,z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,9809,a(flip),b,13345,a)].">
      <j1 rule="hyper" parents="58 9809 13345"/>
    </justification>
  </clause>

  <clause id="13348">
    <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,13347,a(flip),b,4755,a(flip))].">
      <j1 rule="hyper" parents="116 13347 4755"/>
    </justification>
  </clause>

  <clause id="13349">
    <literal><![CDATA[
      K(x * L(y,z,u),x * y) = K(x,y) * K(L(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(8935,a,13348,a),flip(a)].">
      <j1 rule="hyper" parents="8935 13348"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13350">
    <literal><![CDATA[
      K(x * L(y,z,u),x * y) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(320,a,10844,a(flip),b,13349,a),flip(a)].">
      <j1 rule="hyper" parents="320 10844 13349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13351">
    <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),13350(a,1,1))].">
      <j1 rule="para" parents="7 13350"/>
    </justification>
  </clause>

  <clause id="13352">
    <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,6981,a(flip),b,13351,a)].">
      <j1 rule="hyper" parents="58 6981 13351"/>
    </justification>
  </clause>

  <clause id="13353">
    <literal><![CDATA[
      K(x,y * (L(y,z,u) \ x)) = a(u,z,K(y \ x,y))
    ]]></literal>
    <justification jstring="[para(10537(a,1),13352(a,2,3))].">
      <j1 rule="para" parents="10537 13352"/>
    </justification>
  </clause>

  <clause id="13354">
    <literal><![CDATA[
      K(x,y * (L(y,z,u) \ x)) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(320,a,11016,a(flip),b,13353,a),flip(a)].">
      <j1 rule="hyper" parents="320 11016 13353"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13356">
    <literal><![CDATA[
      K(x,x * (L(y,z,u) \ y)) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(10505,a,13354,a)].">
      <j1 rule="hyper" parents="10505 13354"/>
    </justification>
  </clause>

  <clause id="13357">
    <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,5610,a,b,13356,a)].">
      <j1 rule="hyper" parents="58 5610 13356"/>
    </justification>
  </clause>

  <clause id="13358">
    <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),13356(a,1,2))].">
      <j1 rule="para" parents="7 13356"/>
    </justification>
  </clause>

  <clause id="13359">
    <literal><![CDATA[
      K(x * (L(y,z,u) \ y),x) = w / (a(u,z,K(x,y)) * w)
    ]]></literal>
    <justification jstring="[para(13356(a,1),5142(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="13356 5142"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13360">
    <literal><![CDATA[
      K(x * (L(y,z,u) \ y),x) = a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(320,a,9912,a(flip),b,13359,a),flip(a)].">
      <j1 rule="hyper" parents="320 9912 13359"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13361">
    <literal><![CDATA[
      L(x,y,a(z,u,K(w,y))) = x
    ]]></literal>
    <justification jstring="[para(13360(a,1),5473(a,1,3))].">
      <j1 rule="para" parents="13360 5473"/>
    </justification>
  </clause>

  <clause id="13362">
    <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(13360(a,1),11019(a,1,3)),flip(a)].">
      <j1 rule="para" parents="13360 11019"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13363">
    <literal><![CDATA[
      (a(x,y,K(z,u)) * u) * w = a(x,y,K(z,u)) * (u * w)
    ]]></literal>
    <justification jstring="[hyper(1338,a,13361,a),flip(a)].">
      <j1 rule="hyper" parents="1338 13361"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13364">
    <literal><![CDATA[
      a(x,y,K(L(z,u,w) \ z,v5)) = 1
    ]]></literal>
    <justification jstring="[hyper(320,a,27,a(flip),b,13362,a),flip(a)].">
      <j1 rule="hyper" parents="320 27 13362"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13365">
    <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,11036,a(flip),b,13362,a)].">
      <j1 rule="hyper" parents="58 11036 13362"/>
    </justification>
  </clause>

  <clause id="13367">
    <literal><![CDATA[
      a(x,y,K(z,u \ L(u,w,v5))) = 1
    ]]></literal>
    <justification jstring="[hyper(58,a,11036,a(flip),b,13364,a)].">
      <j1 rule="hyper" parents="58 11036 13364"/>
    </justification>
  </clause>

  <clause id="13368">
    <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,10887,a,b,13364,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="167 10887 13364"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13369">
    <literal><![CDATA[
      K(L(x,y,z) \ x,u) = K(a(z,y,x),u) * 1
    ]]></literal>
    <justification jstring="[para(13364(a,1),6659(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13364 6659"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13371">
    <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,10887,a,b,13367,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="167 10887 13367"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13372">
    <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,13369,a),flip(a)].">
      <j1 rule="hyper" parents="320 3 13369"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13374">
    <literal><![CDATA[
      K(x,L(y,z,u) \ y) = w / (K(a(u,z,y),x) * w)
    ]]></literal>
    <justification jstring="[para(13372(a,1),5142(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="13372 5142"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13375">
    <literal><![CDATA[
      K(x,L(y,z,u) \ y) = K(x,a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(320,a,5142,a(flip),b,13374,a),flip(a)].">
      <j1 rule="hyper" parents="320 5142 13374"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13376">
    <literal><![CDATA[
      T(x,L(y,z,u) \ y) = T(x,a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(118,a,13375,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 13375 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13378">
    <literal><![CDATA[
      T(x,a(y,z,u) \ 1) = T(x,u \ L(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,6700,a(flip),b,13371,a)].">
      <j1 rule="hyper" parents="58 6700 13371"/>
    </justification>
  </clause>

  <clause id="13380">
    <literal><![CDATA[
      T(x * K(y \ L(y,z,u),x),a(u,z,y) \ 1) = x
    ]]></literal>
    <justification jstring="[hyper(320,a,4816,a(flip),b,13378,a),flip(a)].">
      <j1 rule="hyper" parents="320 4816 13378"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13381">
    <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(13378(a,2),711(a,1,1))].">
      <j1 rule="para" parents="13378 711"/>
    </justification>
  </clause>

  <clause id="13382">
    <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(13380(a,1),4931(a,1,1))].">
      <j1 rule="para" parents="13380 4931"/>
    </justification>
  </clause>

  <clause id="13383">
    <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(6509,a,13358,a)].">
      <j1 rule="hyper" parents="6509 13358"/>
    </justification>
  </clause>

  <clause id="13384">
    <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,10495,a(flip),b,13383,a)].">
      <j1 rule="hyper" parents="58 10495 13383"/>
    </justification>
  </clause>

  <clause id="13385">
    <literal><![CDATA[
      K(x * (y \ L(y,z,u)),x) = a(u,z,K((y / x) \ y,y))
    ]]></literal>
    <justification jstring="[para(11411(a,1),13384(a,2,3))].">
      <j1 rule="para" parents="11411 13384"/>
    </justification>
  </clause>

  <clause id="13386">
    <literal><![CDATA[
      K(x * (y \ L(y,z,u)),x) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[para(75(a,1),13385(a,2,3,1))].">
      <j1 rule="para" parents="75 13385"/>
    </justification>
  </clause>

  <clause id="13389">
    <literal><![CDATA[
      K(x,x * (y \ L(y,z,u))) = w / (a(u,z,K(x,y)) * w)
    ]]></literal>
    <justification jstring="[para(13386(a,1),5142(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="13386 5142"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13390">
    <literal><![CDATA[
      K(x,x * (y \ L(y,z,u))) = a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(320,a,9912,a(flip),b,13389,a),flip(a)].">
      <j1 rule="hyper" parents="320 9912 13389"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13391">
    <literal><![CDATA[
      T(x,x * (y \ L(y,z,u))) = x * a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(119,a,13390,a(flip),b,4729,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 13390 4729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13392">
    <literal><![CDATA[
      L(x,a(y,z,K(u,w)),L(w,v5,v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      x = v7
    ]]></literal>
    <justification jstring="[para(13390(a,1),4514(a,1,2))].">
      <j1 rule="para" parents="13390 4514"/>
    </justification>
  </clause>

  <clause id="13393">
    <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(13390(a,1),4766(a,1,2))].">
      <j1 rule="para" parents="13390 4766"/>
    </justification>
  </clause>

  <clause id="13394">
    <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(12931(a,1),13357(a,1,2))].">
      <j1 rule="para" parents="12931 13357"/>
    </justification>
  </clause>

  <clause id="13395">
    <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(5462,a,13394,a)].">
      <j1 rule="hyper" parents="5462 13394"/>
    </justification>
  </clause>

  <clause id="13396">
    <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(7749,a,13395,a)].">
      <j1 rule="hyper" parents="7749 13395"/>
    </justification>
  </clause>

  <clause id="13397">
    <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(13376(a,1),13396(a,1,2,1))].">
      <j1 rule="para" parents="13376 13396"/>
    </justification>
  </clause>

  <clause id="13398">
    <literal><![CDATA[
      K(x,x * a(y,z,u)) = a(y,z,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(5033,a,13397,a)].">
      <j1 rule="hyper" parents="5033 13397"/>
    </justification>
  </clause>

  <clause id="13399">
    <literal><![CDATA[
      x \ T(x,a(y,z,u)) = a(y,z,K(x,u))
    ]]></literal>
    <justification jstring="[para(12828(a,1),13397(a,1,2))].">
      <j1 rule="para" parents="12828 13397"/>
    </justification>
  </clause>

  <clause id="13400">
    <literal><![CDATA[
      a(x,y,K(z,u)) = K(z,a(x,y,u))
    ]]></literal>
    <justification jstring="[hyper(12838,a,13398,a),flip(a)].">
      <j1 rule="hyper" parents="12838 13398"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13401">
    <literal><![CDATA[
      a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(z,a(x,y,u)) = w
    ]]></literal>
    <justification jstring="[para(13398(a,1),12838(a,1))].">
      <j1 rule="para" parents="13398 12838"/>
    </justification>
  </clause>

  <clause id="13402">
    <literal><![CDATA[
      (x * y) * a(z,u,K(y,w)) = x * T(y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(119,a,13400,a,b,6154,a)].">
      <j1 rule="hyper" parents="119 13400 6154"/>
    </justification>
  </clause>

  <clause id="13403">
    <literal><![CDATA[
      x * a(y,z,K(x,u)) = T(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(119,a,13400,a,b,4729,a(flip))].">
      <j1 rule="hyper" parents="119 13400 4729"/>
    </justification>
  </clause>

  <clause id="13405">
    <literal><![CDATA[
      a(x,y,K(z,a(u,w,v5))) = 1
    ]]></literal>
    <justification jstring="[para(13400(a,1),27(a,1,3))].">
      <j1 rule="para" parents="13400 27"/>
    </justification>
  </clause>

  <clause id="13406">
    <literal><![CDATA[
      a(x,y,K(z,u)) != 1
    ]]></literal>
    <literal><![CDATA[
      T(z,a(x,y,u)) = z
    ]]></literal>
    <justification jstring="[para(13400(a,2),51(a,1))].">
      <j1 rule="para" parents="13400 51"/>
    </justification>
  </clause>

  <clause id="13407">
    <literal><![CDATA[
      a(x,y,K(z,u)) * z = T(z,a(x,y,u))
    ]]></literal>
    <justification jstring="[para(13400(a,2),4770(a,2,1)),flip(a)].">
      <j1 rule="para" parents="13400 4770"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13408">
    <literal><![CDATA[
      x * a(y,z,K(x,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,a(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(13400(a,2),4766(a,1,2))].">
      <j1 rule="para" parents="13400 4766"/>
    </justification>
  </clause>

  <clause id="13409">
    <literal><![CDATA[
      a(x,y,K(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      1 = u
    ]]></literal>
    <justification jstring="[para(13400(a,2),9560(a,1))].">
      <j1 rule="para" parents="13400 9560"/>
    </justification>
  </clause>

  <clause id="13410">
    <literal><![CDATA[
      K(x,a(y,z,a(u,w,v5))) = 1
    ]]></literal>
    <justification jstring="[hyper(58,a,13400,a(flip),b,13405,a)].">
      <j1 rule="hyper" parents="58 13400 13405"/>
    </justification>
  </clause>

  <clause id="13411">
    <literal><![CDATA[
      a(x,y,K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      1 = u
    ]]></literal>
    <justification jstring="[para(6103(a,1),13409(a,1))].">
      <j1 rule="para" parents="6103 13409"/>
    </justification>
  </clause>

  <clause id="13412">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * v5 = v5 * a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(5572,a,13410,a),flip(a)].">
      <j1 rule="hyper" parents="5572 13410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13413">
    <literal><![CDATA[
      (a(x,y,a(z,u,w)) \ v5) * a(x,y,a(z,u,w)) = v5
    ]]></literal>
    <justification jstring="[hyper(5296,a,13410,a)].">
      <j1 rule="hyper" parents="5296 13410"/>
    </justification>
  </clause>

  <clause id="13414">
    <literal><![CDATA[
      T(a(x,y,a(z,u,w)),v5) = a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(4953,a,13410,a)].">
      <j1 rule="hyper" parents="4953 13410"/>
    </justification>
  </clause>

  <clause id="13415">
    <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,13405,a,b,13410,a),flip(a)].">
      <j1 rule="hyper" parents="320 13405 13410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13416">
    <literal><![CDATA[
      T(x,a(y,z,a(u,w,v5))) = x
    ]]></literal>
    <justification jstring="[hyper(51,a,13410,a)].">
      <j1 rule="hyper" parents="51 13410"/>
    </justification>
  </clause>

  <clause id="13417">
    <literal><![CDATA[
      x / a(y,z,a(u,w,v5)) = a(y,z,a(u,w,v5)) \ x
    ]]></literal>
    <justification jstring="[hyper(168,a,5016,a,b,13410,a(flip))].">
      <j1 rule="hyper" parents="168 5016 13410"/>
    </justification>
  </clause>

  <clause id="13418">
    <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,6619,a,b,13410,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="167 6619 13410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13419">
    <literal><![CDATA[
      a(x,y,K(z,L(y,u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      1 = v5
    ]]></literal>
    <justification jstring="[para(10612(a,1),13411(a,1,3))].">
      <j1 rule="para" parents="10612 13411"/>
    </justification>
  </clause>

  <clause id="13420">
    <literal><![CDATA[
      a(x,L(y,z,u),K(w,y)) != v5
    ]]></literal>
    <literal><![CDATA[
      1 = v5
    ]]></literal>
    <justification jstring="[para(11803(a,1),13411(a,1))].">
      <j1 rule="para" parents="11803 13411"/>
    </justification>
  </clause>

  <clause id="13421">
    <literal><![CDATA[
      T(x,a(y,z,z \ 1)) = x
    ]]></literal>
    <justification jstring="[hyper(167,a,13399,a,b,10096,a(flip))].">
      <j1 rule="hyper" parents="167 13399 10096"/>
    </justification>
  </clause>

  <clause id="13423">
    <literal><![CDATA[
      T(x,a(y,z,L(u,w,v5))) = x * a(y,z,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(119,a,11803,a(flip),b,13399,a),flip(a)].">
      <j1 rule="hyper" parents="119 11803 13399"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13425">
    <literal><![CDATA[
      (a(x,y,y \ 1) \ z) * a(x,y,y \ 1) = z
    ]]></literal>
    <justification jstring="[hyper(2341,a,13421,a)].">
      <j1 rule="hyper" parents="2341 13421"/>
    </justification>
  </clause>

  <clause id="13426">
    <literal><![CDATA[
      a(x,y,K(z,u)) \ u = T(u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,9911,a,b,13407,a)].">
      <j1 rule="hyper" parents="58 9911 13407"/>
    </justification>
  </clause>

  <clause id="13427">
    <literal><![CDATA[
      a(x,y,K(z,u)) = K(a(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(34,a,4790,a(flip),b,13426,a),flip(a)].">
      <j1 rule="hyper" parents="34 4790 13426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13428">
    <literal><![CDATA[
      (x / y) * a(z,u,K(w,y)) = x / T(y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(119,a,13427,a,b,6364,a)].">
      <j1 rule="hyper" parents="119 13427 6364"/>
    </justification>
  </clause>

  <clause id="13429">
    <literal><![CDATA[
      K(x,a(y,z,u) \ x) = a(y,z,K(u,a(y,z,u) \ x))
    ]]></literal>
    <justification jstring="[hyper(12853,a,13427,a(flip))].">
      <j1 rule="hyper" parents="12853 13427"/>
    </justification>
  </clause>

  <clause id="13430">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (u * a(x,y,z)) = a(x,y,z) * u
    ]]></literal>
    <justification jstring="[para(13427(a,2),4813(a,1,1))].">
      <j1 rule="para" parents="13427 4813"/>
    </justification>
  </clause>

  <clause id="13431">
    <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(13427(a,2),4771(a,1,1))].">
      <j1 rule="para" parents="13427 4771"/>
    </justification>
  </clause>

  <clause id="13432">
    <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(13427(a,2),4783(a,1,1))].">
      <j1 rule="para" parents="13427 4783"/>
    </justification>
  </clause>

  <clause id="13433">
    <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(13427(a,2),5180(a,1,1))].">
      <j1 rule="para" parents="13427 5180"/>
    </justification>
  </clause>

  <clause id="13434">
    <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(11035(a,1),13408(a,1,2))].">
      <j1 rule="para" parents="11035 13408"/>
    </justification>
  </clause>

  <clause id="13435">
    <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(13423(a,2),13408(a,1))].">
      <j1 rule="para" parents="13423 13408"/>
    </justification>
  </clause>

  <clause id="13436">
    <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,13412,a),flip(a)].">
      <j1 rule="hyper" parents="320 346 13412"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13437">
    <literal><![CDATA[
      x * a(y,z,a(u,w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(y,z,a(u,w,v5)) \ v6 = x
    ]]></literal>
    <justification jstring="[para(13412(a,1),123(a,1))].">
      <j1 rule="para" parents="13412 123"/>
    </justification>
  </clause>

  <clause id="13438">
    <literal><![CDATA[
      (a(x,y,a(z,u,w)) \ v5) * a(x,y,a(z,u,w)) != v6
    ]]></literal>
    <literal><![CDATA[
      v5 = v6
    ]]></literal>
    <justification jstring="[para(13412(a,1),256(a,1))].">
      <j1 rule="para" parents="13412 256"/>
    </justification>
  </clause>

  <clause id="13439">
    <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(13412(a,1),691(a,1,2,1))].">
      <j1 rule="para" parents="13412 691"/>
    </justification>
  </clause>

  <clause id="13440">
    <literal><![CDATA[
      x \ (y * (a(z,u,a(w,v5,v6)) * v7)) = (x \ (y * v7)) * a(z,u,a(w,v5,v6))
    ]]></literal>
    <justification jstring="[para(13412(a,2),1372(a,1,2,2))].">
      <j1 rule="para" parents="13412 1372"/>
    </justification>
  </clause>

  <clause id="13441">
    <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,13413,a(flip),b,894,a),flip(a)].">
      <j1 rule="hyper" parents="116 13413 894"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13442">
    <literal><![CDATA[
      a(x,y,K(z,a(u,w,v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      1 = v6
    ]]></literal>
    <justification jstring="[para(13415(a,1),9560(a,1))].">
      <j1 rule="para" parents="13415 9560"/>
    </justification>
  </clause>

  <clause id="13443">
    <literal><![CDATA[
      a(x,y,a(z,u,K(w,v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      1 = v6
    ]]></literal>
    <justification jstring="[para(13400(a,2),13442(a,1,3))].">
      <j1 rule="para" parents="13400 13442"/>
    </justification>
  </clause>

  <clause id="13444">
    <literal><![CDATA[
      a(x,y,K(z,u \ L(u,w,v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      1 = v6
    ]]></literal>
    <justification jstring="[para(13365(a,2),13443(a,1))].">
      <j1 rule="para" parents="13365 13443"/>
    </justification>
  </clause>

  <clause id="13445">
    <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(13417(a,1),1366(a,1,1,2))].">
      <j1 rule="para" parents="13417 1366"/>
    </justification>
  </clause>

  <clause id="13446">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (u * a(x,y,z)) != u * w
    ]]></literal>
    <literal><![CDATA[
      T(a(x,y,z),u) = w
    ]]></literal>
    <justification jstring="[para(13430(a,2),240(a,2)),flip(a)].">
      <j1 rule="para" parents="13430 240"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13447">
    <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,13418,a,b,13436,a),flip(a)].">
      <j1 rule="hyper" parents="320 13418 13436"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13448">
    <literal><![CDATA[
      (a(x,y,a(z,u,w)) * (v5 * v6)) \ ((v6 * a(x,y,a(z,u,w))) * v5) = K(v6 * a(x,y,a(z,u,w)),v5)
    ]]></literal>
    <justification jstring="[para(13436(a,2),11(a,2,1)),flip(a)].">
      <j1 rule="para" parents="13436 11"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13449">
    <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(1936(a,1),13436(a,2,2))].">
      <j1 rule="para" parents="1936 13436"/>
    </justification>
  </clause>

  <clause id="13450">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) \ (v5 \ v6) = v5 \ (a(x,y,a(z,u,w)) \ v6)
    ]]></literal>
    <justification jstring="[hyper(13437,a,13441,a)].">
      <j1 rule="hyper" parents="13437 13441"/>
    </justification>
  </clause>

  <clause id="13451">
    <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,13447,a)].">
      <j1 rule="hyper" parents="116 151 13447"/>
    </justification>
  </clause>

  <clause id="13452">
    <literal><![CDATA[
      x * (a(y,z,a(u,w,v5)) \ 1) = a(y,z,a(u,w,v5)) \ x
    ]]></literal>
    <justification jstring="[hyper(116,a,65,a(flip),b,13447,a),flip(a)].">
      <j1 rule="hyper" parents="116 65 13447"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13453">
    <literal><![CDATA[
      (a(x,y,a(z,u,w)) * (v5 * v6)) \ v7 = (v5 * (a(x,y,a(z,u,w)) * v6)) \ v7
    ]]></literal>
    <justification jstring="[hyper(56,a,13447,a)].">
      <j1 rule="hyper" parents="56 13447"/>
    </justification>
  </clause>

  <clause id="13454">
    <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(13447(a,2),9(a,2,1)),flip(a)].">
      <j1 rule="para" parents="13447 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13455">
    <literal><![CDATA[
      (a(x,y,a(z,u,w)) * v5) \ v5 = a(x,y,a(z,u,w)) \ 1
    ]]></literal>
    <justification jstring="[hyper(116,a,4,a(flip),b,13452,a)].">
      <j1 rule="hyper" parents="116 4 13452"/>
    </justification>
  </clause>

  <clause id="13456">
    <literal><![CDATA[
      (x * y) \ (a(z,u,a(w,v5,v6)) \ (x * (y * v7))) = a(z,u,a(w,v5,v6)) \ L(v7,y,x)
    ]]></literal>
    <justification jstring="[para(13(a,2),13450(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13 13450"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13457">
    <literal><![CDATA[
      L(a(x,y,a(z,u,w)) \ (v5 \ v6),v5,a(x,y,a(z,u,w))) = (a(x,y,a(z,u,w)) * v5) \ v6
    ]]></literal>
    <justification jstring="[para(13450(a,2),298(a,1,1))].">
      <j1 rule="para" parents="13450 298"/>
    </justification>
  </clause>

  <clause id="13458">
    <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,12069,a(flip),b,13449,a)].">
      <j1 rule="hyper" parents="117 12069 13449"/>
    </justification>
  </clause>

  <clause id="13459">
    <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,13391,a(flip),b,13381,a),flip(a)].">
      <j1 rule="hyper" parents="320 13391 13381"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13460">
    <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(13451(a,1),13456(a,1,2))].">
      <j1 rule="para" parents="13451 13456"/>
    </justification>
  </clause>

  <clause id="13461">
    <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(13451(a,1),13460(a,1,2,2))].">
      <j1 rule="para" parents="13451 13460"/>
    </justification>
  </clause>

  <clause id="13462">
    <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(626,a,13461,a)].">
      <j1 rule="hyper" parents="626 13461"/>
    </justification>
  </clause>

  <clause id="13463">
    <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,13462,a(flip),b,3532,a),flip(a)].">
      <j1 rule="hyper" parents="119 13462 3532"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13464">
    <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(12920(a,1),12939(a,1,2))].">
      <j1 rule="para" parents="12920 12939"/>
    </justification>
  </clause>

  <clause id="13465">
    <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(13464(a,1),518(a,1))].">
      <j1 rule="para" parents="13464 518"/>
    </justification>
  </clause>

  <clause id="13466">
    <literal><![CDATA[
      R(x,y,z * a(u,w,u)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(13465,a,12937,a)].">
      <j1 rule="hyper" parents="13465 12937"/>
    </justification>
  </clause>

  <clause id="13467">
    <literal><![CDATA[
      R(x,y,z \ R(u,w,u)) = R(x,y,z \ u)
    ]]></literal>
    <justification jstring="[para(12935(a,1),13466(a,1,3))].">
      <j1 rule="para" parents="12935 13466"/>
    </justification>
  </clause>

  <clause id="13468">
    <literal><![CDATA[
      R(x,y,z \ ((u \ w) \ w)) = R(x,y,z \ T(u,w))
    ]]></literal>
    <justification jstring="[para(7529(a,1),13467(a,1,3,2))].">
      <j1 rule="para" parents="7529 13467"/>
    </justification>
  </clause>

  <clause id="13469">
    <literal><![CDATA[
      L(x,y,((z \ u) * z) \ (u * (1 / z))) = L(x,y,K(u,z \ 1) / z)
    ]]></literal>
    <justification jstring="[para(6000(a,1),13187(a,1,3,1))].">
      <j1 rule="para" parents="6000 13187"/>
    </justification>
  </clause>

  <clause id="13470">
    <literal><![CDATA[
      L(x,y,K(z,z \ u) * (1 / z)) = L(x,y,K(u,z \ 1) / z)
    ]]></literal>
    <justification jstring="[para(11155(a,1),13469(a,1,3))].">
      <j1 rule="para" parents="11155 13469"/>
    </justification>
  </clause>

  <clause id="13471">
    <literal><![CDATA[
      L(x,y,K(z,u \ 1) / u) = L(x,y,K(u,u \ z) / u)
    ]]></literal>
    <justification jstring="[para(6245(a,1),13470(a,1,3)),flip(a)].">
      <j1 rule="para" parents="6245 13470"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13472">
    <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),13240(a,1,2,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5 13240"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13473">
    <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(13463(a,2),13458(a,1,2))].">
      <j1 rule="para" parents="13463 13458"/>
    </justification>
  </clause>

  <clause id="13474">
    <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(12069(a,1),13473(a,1,2,1))].">
      <j1 rule="para" parents="12069 13473"/>
    </justification>
  </clause>

  <clause id="13475">
    <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(13474(a,1),5950(a,1,1))].">
      <j1 rule="para" parents="13474 5950"/>
    </justification>
  </clause>

  <clause id="13476">
    <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),12945(a,1,2,2))].">
      <j1 rule="para" parents="13 12945"/>
    </justification>
  </clause>

  <clause id="13477">
    <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(3541(a,1),13476(a,1,2))].">
      <j1 rule="para" parents="3541 13476"/>
    </justification>
  </clause>

  <clause id="13478">
    <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(4056,a,13477,a)].">
      <j1 rule="hyper" parents="4056 13477"/>
    </justification>
  </clause>

  <clause id="13479">
    <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,12659,a(flip),b,13478,a)].">
      <j1 rule="hyper" parents="320 12659 13478"/>
    </justification>
  </clause>

  <clause id="13481">
    <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),13479(a,1,2,2))].">
      <j1 rule="para" parents="201 13479"/>
    </justification>
  </clause>

  <clause id="13482">
    <literal><![CDATA[
      a(x,a(y,z,u) \ 1,x) = 1
    ]]></literal>
    <justification jstring="[hyper(320,a,13247,a(flip),b,13481,a),flip(a)].">
      <j1 rule="hyper" parents="320 13247 13481"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13483">
    <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(13481(a,1),10054(a,1,1,2))].">
      <j1 rule="para" parents="13481 10054"/>
    </justification>
  </clause>

  <clause id="13485">
    <literal><![CDATA[
      L(x,a(y,z,u) \ 1,x) = x
    ]]></literal>
    <justification jstring="[hyper(47,a,13482,a)].">
      <j1 rule="hyper" parents="47 13482"/>
    </justification>
  </clause>

  <clause id="13486">
    <literal><![CDATA[
      T(x * (a(y,z,u) \ 1),x) = (a(y,z,u) \ 1) * x
    ]]></literal>
    <justification jstring="[para(13485(a,1),4376(a,1,1,1))].">
      <j1 rule="para" parents="13485 4376"/>
    </justification>
  </clause>

  <clause id="13487">
    <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(13256(a,1),13280(a,1,2))].">
      <j1 rule="para" parents="13256 13280"/>
    </justification>
  </clause>

  <clause id="13488">
    <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(13439,a,13454,a)].">
      <j1 rule="hyper" parents="13439 13454"/>
    </justification>
  </clause>

  <clause id="13489">
    <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),12368(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="13 12368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13490">
    <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(12581(a,1),12282(a,1,2))].">
      <j1 rule="para" parents="12581 12282"/>
    </justification>
  </clause>

  <clause id="13493">
    <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),12365(a,1,2,1))].">
      <j1 rule="para" parents="190 12365"/>
    </justification>
  </clause>

  <clause id="13494">
    <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(7704,a,13493,a),flip(a)].">
      <j1 rule="hyper" parents="7704 13493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13497">
    <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,12317,a,b,13494,a),flip(a)].">
      <j1 rule="hyper" parents="320 12317 13494"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13499">
    <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,12337,a(flip),b,13497,a),flip(a)].">
      <j1 rule="hyper" parents="320 12337 13497"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13501">
    <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,5429,a(flip),b,13499,a),flip(a)].">
      <j1 rule="hyper" parents="320 5429 13499"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13503">
    <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,12375,a(flip),b,13501,a),flip(a)].">
      <j1 rule="hyper" parents="320 12375 13501"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13505">
    <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),13503(a,1,2,2))].">
      <j1 rule="para" parents="72 13503"/>
    </justification>
  </clause>

  <clause id="13507">
    <literal><![CDATA[
      K((((x / y) \ 1) \ y) \ y,z / (1 / (x / y))) = K(x \ y,z * (x / y))
    ]]></literal>
    <justification jstring="[hyper(58,a,5316,a,b,13505,a)].">
      <j1 rule="hyper" parents="58 5316 13505"/>
    </justification>
  </clause>

  <clause id="13508">
    <literal><![CDATA[
      K((x / y) \ 1,T(z / (1 / (x / y)),y)) = K(x \ y,z * (x / y))
    ]]></literal>
    <justification jstring="[hyper(7709,a,13507,a)].">
      <j1 rule="hyper" parents="7709 13507"/>
    </justification>
  </clause>

  <clause id="13509">
    <literal><![CDATA[
      K(1 / (x / y),T(z / (1 / (x / y)),y)) = K(x \ y,z * (x / y))
    ]]></literal>
    <justification jstring="[hyper(5282,a,13508,a)].">
      <j1 rule="hyper" parents="5282 13508"/>
    </justification>
  </clause>

  <clause id="13510">
    <literal><![CDATA[
      K(1 / (x / y),(x / y) * T(z,y)) = K(x \ y,z * (x / y))
    ]]></literal>
    <justification jstring="[hyper(58,a,12344,a(flip),b,13509,a)].">
      <j1 rule="hyper" parents="58 12344 13509"/>
    </justification>
  </clause>

  <clause id="13511">
    <literal><![CDATA[
      K(x / y,(y / x) * T(z,x)) = K(y \ x,z * (y / x))
    ]]></literal>
    <justification jstring="[hyper(5669,a,13510,a)].">
      <j1 rule="hyper" parents="5669 13510"/>
    </justification>
  </clause>

  <clause id="13512">
    <literal><![CDATA[
      K((x / y) \ x,z * ((x / y) / x)) = K(y,T(((x / y) / x) * T(z,x),x))
    ]]></literal>
    <justification jstring="[hyper(7938,a,13511,a),flip(a)].">
      <j1 rule="hyper" parents="7938 13511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13513">
    <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(4111(a,1),13511(a,2,1))].">
      <j1 rule="para" parents="4111 13511"/>
    </justification>
  </clause>

  <clause id="13514">
    <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(13512(a,1),6303(a,1))].">
      <j1 rule="para" parents="13512 6303"/>
    </justification>
  </clause>

  <clause id="13515">
    <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(13445(a,1),1367(a,1))].">
      <j1 rule="para" parents="13445 1367"/>
    </justification>
  </clause>

  <clause id="13516">
    <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,6892,a(flip),b,12532,a),flip(a)].">
      <j1 rule="hyper" parents="320 6892 12532"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13517">
    <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,13475,a),flip(a)].">
      <j1 rule="hyper" parents="58 145 13475"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13518">
    <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,13517,a)].">
      <j1 rule="hyper" parents="691 13517"/>
    </justification>
  </clause>

  <clause id="13520">
    <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,4050,a(flip),b,13518,a)].">
      <j1 rule="hyper" parents="58 4050 13518"/>
    </justification>
  </clause>

  <clause id="13521">
    <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,13518,a,b,13520,a)].">
      <j1 rule="hyper" parents="320 13518 13520"/>
    </justification>
  </clause>

  <clause id="13522">
    <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(8894(a,1),13516(a,2,1,2))].">
      <j1 rule="para" parents="8894 13516"/>
    </justification>
  </clause>

  <clause id="13523">
    <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(7044(a,1),13522(a,2,1))].">
      <j1 rule="para" parents="7044 13522"/>
    </justification>
  </clause>

  <clause id="13524">
    <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(3327(a,1),13523(a,2,1,1))].">
      <j1 rule="para" parents="3327 13523"/>
    </justification>
  </clause>

  <clause id="13525">
    <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(6325(a,1),13524(a,2,2))].">
      <j1 rule="para" parents="6325 13524"/>
    </justification>
  </clause>

  <clause id="13526">
    <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,11990,a(flip),b,13525,a),flip(a)].">
      <j1 rule="hyper" parents="320 11990 13525"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13528">
    <literal><![CDATA[
      K((x \ K(x,y)) * T(x,z),T(x,z) \ ((x \ 1) \ K(y,x))) = 1
    ]]></literal>
    <justification jstring="[para(11492(a,1),13526(a,1,1))].">
      <j1 rule="para" parents="11492 13526"/>
    </justification>
  </clause>

  <clause id="13529">
    <literal><![CDATA[
      1 / (((x \ K(x,y)) \ 1) \ T(x,z)) = ((x \ K(x,y)) * T(x,z)) \ 1
    ]]></literal>
    <justification jstring="[para(13528(a,1),12180(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13528 12180"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13530">
    <literal><![CDATA[
      1 / (((x \ K(x,y)) \ 1) \ T(x,z)) = x * (K(y,x) / T(x,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,12531,a(flip),b,13529,a),flip(a)].">
      <j1 rule="hyper" parents="320 12531 13529"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13532">
    <literal><![CDATA[
      1 / (((x \ 1) \ K(y,x)) \ T(x,z)) = x * (K(y,x) / T(x,z))
    ]]></literal>
    <justification jstring="[para(5613(a,1),13530(a,1,2,1))].">
      <j1 rule="para" parents="5613 13530"/>
    </justification>
  </clause>

  <clause id="13533">
    <literal><![CDATA[
      1 / ((x \ K(x,y)) * T(x,z)) = x * (K(y,x) / T(x,z))
    ]]></literal>
    <justification jstring="[para(11492(a,1),13532(a,1,2))].">
      <j1 rule="para" parents="11492 13532"/>
    </justification>
  </clause>

  <clause id="13534">
    <literal><![CDATA[
      (x * (K(y,x) / T(x,z))) \ 1 = (x \ K(x,y)) * T(x,z)
    ]]></literal>
    <justification jstring="[hyper(188,a,13533,a)].">
      <j1 rule="hyper" parents="188 13533"/>
    </justification>
  </clause>

  <clause id="13535">
    <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(13534(a,1),3692(a,1,1,1))].">
      <j1 rule="para" parents="13534 3692"/>
    </justification>
  </clause>

  <clause id="13536">
    <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),12362(a,2,2))].">
      <j1 rule="para" parents="186 12362"/>
    </justification>
  </clause>

  <clause id="13537">
    <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,4744,a,b,13536,a),flip(a)].">
      <j1 rule="hyper" parents="320 4744 13536"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13539">
    <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,7784,a,b,13537,a),flip(a)].">
      <j1 rule="hyper" parents="320 7784 13537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13540">
    <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(12386(a,1),13539(a,1,2))].">
      <j1 rule="para" parents="12386 13539"/>
    </justification>
  </clause>

  <clause id="13541">
    <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(10937,a,13540,a)].">
      <j1 rule="hyper" parents="10937 13540"/>
    </justification>
  </clause>

  <clause id="13542">
    <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(7781,a,13541,a)].">
      <j1 rule="hyper" parents="7781 13541"/>
    </justification>
  </clause>

  <clause id="13543">
    <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,7235,a(flip),b,13542,a)].">
      <j1 rule="hyper" parents="58 7235 13542"/>
    </justification>
  </clause>

  <clause id="13545">
    <literal><![CDATA[
      K(x,K(y * z,L(u,z,y))) = K(x,K(u,y * z))
    ]]></literal>
    <justification jstring="[para(4911(a,1),13543(a,1,2))].">
      <j1 rule="para" parents="4911 13543"/>
    </justification>
  </clause>

  <clause id="13546">
    <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(10321(a,1),12668(a,1,1))].">
      <j1 rule="para" parents="10321 12668"/>
    </justification>
  </clause>

  <clause id="13548">
    <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,12359,a(flip),b,12201,a)].">
      <j1 rule="hyper" parents="58 12359 12201"/>
    </justification>
  </clause>

  <clause id="13549">
    <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(9865(a,1),13548(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9865 13548"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13550">
    <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(7797(a,1),13549(a,2,2))].">
      <j1 rule="para" parents="7797 13549"/>
    </justification>
  </clause>

  <clause id="13552">
    <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(13545(a,1),13550(a,2,2))].">
      <j1 rule="para" parents="13545 13550"/>
    </justification>
  </clause>

  <clause id="13553">
    <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(7779(a,1),13552(a,2,2))].">
      <j1 rule="para" parents="7779 13552"/>
    </justification>
  </clause>

  <clause id="13554">
    <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(10794(a,1),13553(a,1,1,2))].">
      <j1 rule="para" parents="10794 13553"/>
    </justification>
  </clause>

  <clause id="13555">
    <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,10667,a,b,13554,a)].">
      <j1 rule="hyper" parents="58 10667 13554"/>
    </justification>
  </clause>

  <clause id="13556">
    <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(11753(a,1),13555(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11753 13555"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13557">
    <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(13556(a,1),536(a,1))].">
      <j1 rule="para" parents="13556 536"/>
    </justification>
  </clause>

  <clause id="13558">
    <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(12531(a,1),13535(a,1,1))].">
      <j1 rule="para" parents="12531 13535"/>
    </justification>
  </clause>

  <clause id="13559">
    <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(13534(a,1),13558(a,1,2,2))].">
      <j1 rule="para" parents="13534 13558"/>
    </justification>
  </clause>

  <clause id="13560">
    <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(8595(a,1),13559(a,1,2))].">
      <j1 rule="para" parents="8595 13559"/>
    </justification>
  </clause>

  <clause id="13561">
    <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(6037(a,1),13560(a,1,2))].">
      <j1 rule="para" parents="6037 13560"/>
    </justification>
  </clause>

  <clause id="13562">
    <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(12819(a,1),13561(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12819 13561"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13563">
    <literal><![CDATA[
      ((((x \ K(x,y)) * T(x,z)) \ 1) \ 1) * u = (x * (K(y,x) / T(x,z))) \ u
    ]]></literal>
    <justification jstring="[para(13534(a,1),13562(a,1,1,1,1))].">
      <j1 rule="para" parents="13534 13562"/>
    </justification>
  </clause>

  <clause id="13564">
    <literal><![CDATA[
      ((x * (K(y,x) / T(x,z))) \ 1) * u = (x * (K(y,x) / T(x,z))) \ u
    ]]></literal>
    <justification jstring="[para(12531(a,1),13563(a,1,1,1))].">
      <j1 rule="para" parents="12531 13563"/>
    </justification>
  </clause>

  <clause id="13565">
    <literal><![CDATA[
      (x * (K(y,x) / T(x,z))) \ u = ((x \ K(x,y)) * T(x,z)) * u
    ]]></literal>
    <justification jstring="[para(13534(a,1),13564(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13534 13564"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13566">
    <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(13565(a,1),9052(a,1,1))].">
      <j1 rule="para" parents="13565 9052"/>
    </justification>
  </clause>

  <clause id="13567">
    <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(8643(a,1),13566(a,1,2))].">
      <j1 rule="para" parents="8643 13566"/>
    </justification>
  </clause>

  <clause id="13568">
    <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,9777,a(flip),b,13567,a)].">
      <j1 rule="hyper" parents="58 9777 13567"/>
    </justification>
  </clause>

  <clause id="13569">
    <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(4818(a,1),13568(a,1,2))].">
      <j1 rule="para" parents="4818 13568"/>
    </justification>
  </clause>

  <clause id="13570">
    <literal><![CDATA[
      ((x \ 1) \ K(y,x)) \ (T(x,z) * u) = ((x \ K(x,y)) * T(x,z)) * u
    ]]></literal>
    <justification jstring="[hyper(11448,a,13569,a),flip(a)].">
      <j1 rule="hyper" parents="11448 13569"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13572">
    <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(5613(a,1),9330(a,1,1,1))].">
      <j1 rule="para" parents="5613 9330"/>
    </justification>
  </clause>

  <clause id="13573">
    <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(13570(a,1),13572(a,1,1))].">
      <j1 rule="para" parents="13570 13572"/>
    </justification>
  </clause>

  <clause id="13574">
    <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(5561(a,1),13573(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5561 13573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13575">
    <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(5319(a,1),13574(a,2,2))].">
      <j1 rule="para" parents="5319 13574"/>
    </justification>
  </clause>

  <clause id="13576">
    <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(5881(a,1),13575(a,2,2))].">
      <j1 rule="para" parents="5881 13575"/>
    </justification>
  </clause>

  <clause id="13577">
    <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(8717(a,1),13576(a,2,2))].">
      <j1 rule="para" parents="8717 13576"/>
    </justification>
  </clause>

  <clause id="13578">
    <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),13577(a,2,2,1))].">
      <j1 rule="para" parents="4 13577"/>
    </justification>
  </clause>

  <clause id="13579">
    <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,6116,a(flip),b,13578,a),flip(a)].">
      <j1 rule="hyper" parents="320 6116 13578"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13581">
    <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,9037,a(flip),b,13579,a),flip(a)].">
      <j1 rule="hyper" parents="320 9037 13579"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13582">
    <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(5613(a,1),13581(a,1,1,1))].">
      <j1 rule="para" parents="5613 13581"/>
    </justification>
  </clause>

  <clause id="13583">
    <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(13570(a,1),13582(a,1,1))].">
      <j1 rule="para" parents="13570 13582"/>
    </justification>
  </clause>

  <clause id="13584">
    <literal><![CDATA[
      T(K(x,y) * z,T(x,x \ 1) * z) = T(z,x * z) * K(x,y)
    ]]></literal>
    <justification jstring="[para(5561(a,1),13583(a,1,1,1))].">
      <j1 rule="para" parents="5561 13583"/>
    </justification>
  </clause>

  <clause id="13585">
    <literal><![CDATA[
      T(K(x,y) * z,x * z) = T(z,x * z) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,3767,a(flip),b,13584,a)].">
      <j1 rule="hyper" parents="58 3767 13584"/>
    </justification>
  </clause>

  <clause id="13586">
    <literal><![CDATA[
      T(K(x,y) * z,x * z) = T(z,z * x) * K(x,y)
    ]]></literal>
    <justification jstring="[para(4307(a,1),13585(a,2,1))].">
      <j1 rule="para" parents="4307 13585"/>
    </justification>
  </clause>

  <clause id="13587">
    <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(13390(a,1),13586(a,2,2))].">
      <j1 rule="para" parents="13390 13586"/>
    </justification>
  </clause>

  <clause id="13588">
    <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(13390(a,1),13587(a,1,1,1))].">
      <j1 rule="para" parents="13390 13587"/>
    </justification>
  </clause>

  <clause id="13589">
    <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(1687(a,1),13483(a,2,1))].">
      <j1 rule="para" parents="1687 13483"/>
    </justification>
  </clause>

  <clause id="13590">
    <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,12937,a(flip),b,13589,a),flip(a)].">
      <j1 rule="hyper" parents="320 12937 13589"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13592">
    <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(9123(a,1),13590(a,1,1))].">
      <j1 rule="para" parents="9123 13590"/>
    </justification>
  </clause>

  <clause id="13593">
    <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,9786,a(flip),b,13592,a)].">
      <j1 rule="hyper" parents="58 9786 13592"/>
    </justification>
  </clause>

  <clause id="13594">
    <literal><![CDATA[
      T(x,a(y,z,u) \ x) = x * a(y,z,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(58,a,13459,a(flip),b,13593,a),flip(a)].">
      <j1 rule="hyper" parents="58 13459 13593"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13595">
    <literal><![CDATA[
      T(T(x,a(y,z,u) \ x),x * u) = T(x,L(u * x,z,y))
    ]]></literal>
    <justification jstring="[para(13594(a,2),11614(a,1,1))].">
      <j1 rule="para" parents="13594 11614"/>
    </justification>
  </clause>

  <clause id="13596">
    <literal><![CDATA[
      T(T(x,x * y),a(z,u,y) \ x) = T(x,L(y * x,u,z))
    ]]></literal>
    <justification jstring="[hyper(434,a,13595,a)].">
      <j1 rule="hyper" parents="434 13595"/>
    </justification>
  </clause>

  <clause id="13597">
    <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(5342(a,1),8119(a,1,1))].">
      <j1 rule="para" parents="5342 8119"/>
    </justification>
  </clause>

  <clause id="13598">
    <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),13597(a,1,1,2,2))].">
      <j1 rule="para" parents="261 13597"/>
    </justification>
  </clause>

  <clause id="13599">
    <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(3414(a,1),9917(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3414 9917"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13600">
    <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(2248(a,1),13599(a,2,2,2))].">
      <j1 rule="para" parents="2248 13599"/>
    </justification>
  </clause>

  <clause id="13602">
    <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(12044(a,1),13600(a,2,2))].">
      <j1 rule="para" parents="12044 13600"/>
    </justification>
  </clause>

  <clause id="13603">
    <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,5130,a(flip),b,13602,a),flip(a)].">
      <j1 rule="hyper" parents="320 5130 13602"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13604">
    <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,5749,a(flip),b,13603,a),flip(a)].">
      <j1 rule="hyper" parents="320 5749 13603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13605">
    <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(3414(a,1),13604(a,1,2,2,2))].">
      <j1 rule="para" parents="3414 13604"/>
    </justification>
  </clause>

  <clause id="13607">
    <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(5130(a,1),13605(a,1,2,2))].">
      <j1 rule="para" parents="5130 13605"/>
    </justification>
  </clause>

  <clause id="13608">
    <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(10675(a,1),13607(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10675 13607"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13609">
    <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,11143,a(flip),b,13608,a),flip(a)].">
      <j1 rule="hyper" parents="320 11143 13608"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13610">
    <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),13609(a,2,2))].">
      <j1 rule="para" parents="198 13609"/>
    </justification>
  </clause>

  <clause id="13611">
    <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(3513(a,1),9938(a,1,2,1,2,2,2))].">
      <j1 rule="para" parents="3513 9938"/>
    </justification>
  </clause>

  <clause id="13612">
    <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(3763(a,1),13611(a,1,2,1,2,2))].">
      <j1 rule="para" parents="3763 13611"/>
    </justification>
  </clause>

  <clause id="13613">
    <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(7779(a,1),13612(a,1,2,1))].">
      <j1 rule="para" parents="7779 13612"/>
    </justification>
  </clause>

  <clause id="13614">
    <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(8623(a,1),13613(a,1,2,1,2))].">
      <j1 rule="para" parents="8623 13613"/>
    </justification>
  </clause>

  <clause id="13615">
    <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(7535(a,1),13614(a,1,2,1,2))].">
      <j1 rule="para" parents="7535 13614"/>
    </justification>
  </clause>

  <clause id="13617">
    <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(8192(a,1),13615(a,1,2,1))].">
      <j1 rule="para" parents="8192 13615"/>
    </justification>
  </clause>

  <clause id="13618">
    <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(3513(a,1),13617(a,1,2,2,1,2,1,2,2))].">
      <j1 rule="para" parents="3513 13617"/>
    </justification>
  </clause>

  <clause id="13619">
    <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(3763(a,1),13618(a,1,2,2,1,2,1,2))].">
      <j1 rule="para" parents="3763 13618"/>
    </justification>
  </clause>

  <clause id="13620">
    <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(7755(a,1),13619(a,1,2,2,1,2))].">
      <j1 rule="para" parents="7755 13619"/>
    </justification>
  </clause>

  <clause id="13621">
    <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(9944(a,1),13620(a,1,2,2,1,2,2))].">
      <j1 rule="para" parents="9944 13620"/>
    </justification>
  </clause>

  <clause id="13622">
    <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(7286(a,1),13621(a,1,2,2,1,2,2))].">
      <j1 rule="para" parents="7286 13621"/>
    </justification>
  </clause>

  <clause id="13624">
    <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(8176(a,1),13622(a,1,2,2,1,2))].">
      <j1 rule="para" parents="8176 13622"/>
    </justification>
  </clause>

  <clause id="13625">
    <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(4733(a,2),13624(a,1,2,2,1))].">
      <j1 rule="para" parents="4733 13624"/>
    </justification>
  </clause>

  <clause id="13626">
    <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(9442(a,2),13625(a,1,2))].">
      <j1 rule="para" parents="9442 13625"/>
    </justification>
  </clause>

  <clause id="13627">
    <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,9438,a(flip),b,13626,a)].">
      <j1 rule="hyper" parents="58 9438 13626"/>
    </justification>
  </clause>

  <clause id="13628">
    <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(1446(a,1),13627(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1446 13627"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13629">
    <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,7826,a(flip),b,13628,a),flip(a)].">
      <j1 rule="hyper" parents="320 7826 13628"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13630">
    <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(1193(a,1),13629(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1193 13629"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13631">
    <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,11932,a,b,13630,a)].">
      <j1 rule="hyper" parents="58 11932 13630"/>
    </justification>
  </clause>

  <clause id="13632">
    <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(1193(a,1),13631(a,1,1))].">
      <j1 rule="para" parents="1193 13631"/>
    </justification>
  </clause>

  <clause id="13633">
    <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(13632(a,1),12070(a,1,2))].">
      <j1 rule="para" parents="13632 12070"/>
    </justification>
  </clause>

  <clause id="13634">
    <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(12071,a,13633,a),flip(a)].">
      <j1 rule="hyper" parents="12071 13633"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13635">
    <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,7784,a,b,13634,a),flip(a)].">
      <j1 rule="hyper" parents="320 7784 13634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13636">
    <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,11918,a(flip),b,13635,a)].">
      <j1 rule="hyper" parents="58 11918 13635"/>
    </justification>
  </clause>

  <clause id="13637">
    <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,7779,a,b,13636,a),flip(a)].">
      <j1 rule="hyper" parents="320 7779 13636"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13638">
    <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(11919,a,13637,a)].">
      <j1 rule="hyper" parents="11919 13637"/>
    </justification>
  </clause>

  <clause id="13639">
    <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,13489,a,b,13638,a)].">
      <j1 rule="hyper" parents="58 13489 13638"/>
    </justification>
  </clause>

  <clause id="13640">
    <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,11698,a(flip),b,13639,a),flip(a)].">
      <j1 rule="hyper" parents="320 11698 13639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13641">
    <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(8049,a,13640,a)].">
      <j1 rule="hyper" parents="8049 13640"/>
    </justification>
  </clause>

  <clause id="13642">
    <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(13640(a,1),8049(a,1))].">
      <j1 rule="para" parents="13640 8049"/>
    </justification>
  </clause>

  <clause id="13643">
    <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(13101,a,13641,a)].">
      <j1 rule="hyper" parents="13101 13641"/>
    </justification>
  </clause>

  <clause id="13644">
    <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,12188,a,b,13643,a)].">
      <j1 rule="hyper" parents="58 12188 13643"/>
    </justification>
  </clause>

  <clause id="13645">
    <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(9269,a,13644,a)].">
      <j1 rule="hyper" parents="9269 13644"/>
    </justification>
  </clause>

  <clause id="13646">
    <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,12865,a(flip),b,13645,a)].">
      <j1 rule="hyper" parents="58 12865 13645"/>
    </justification>
  </clause>

  <clause id="13647">
    <literal><![CDATA[
      K(x,K(y * z,a(y,z,u))) = a(K(y,K(x,z * u)),z,u)
    ]]></literal>
    <justification jstring="[para(9218(a,1),13646(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9218 13646"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13648">
    <literal><![CDATA[
      K(x,K(y * z,a(y,z,u))) = 1
    ]]></literal>
    <justification jstring="[hyper(320,a,11868,a(flip),b,13647,a),flip(a)].">
      <j1 rule="hyper" parents="320 11868 13647"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13649">
    <literal><![CDATA[
      K(x,K(a(y,z,u),y * (z * u))) = 1
    ]]></literal>
    <justification jstring="[hyper(13642,a,13648,a)].">
      <j1 rule="hyper" parents="13642 13648"/>
    </justification>
  </clause>

  <clause id="13652">
    <literal><![CDATA[
      K(x,((y * z) * u) / (y * (z * u))) = K(x,a(y,z,u)) * 1
    ]]></literal>
    <justification jstring="[para(13649(a,1),9727(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13649 9727"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13653">
    <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,13652,a),flip(a)].">
      <j1 rule="hyper" parents="320 3 13652"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13655">
    <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,9245,a,b,13653,a)].">
      <j1 rule="hyper" parents="58 9245 13653"/>
    </justification>
  </clause>

  <clause id="13656">
    <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(12837(a,2),13655(a,1,1))].">
      <j1 rule="para" parents="12837 13655"/>
    </justification>
  </clause>

  <clause id="13657">
    <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,12805,a,b,13656,a)].">
      <j1 rule="hyper" parents="58 12805 13656"/>
    </justification>
  </clause>

  <clause id="13658">
    <literal><![CDATA[
      a(K(x,y),z * y,u) = K(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,12807,a(flip),b,13657,a)].">
      <j1 rule="hyper" parents="58 12807 13657"/>
    </justification>
  </clause>

  <clause id="13660">
    <literal><![CDATA[
      a(K(x,y),z,u) = K(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,12507,a(flip),b,13658,a)].">
      <j1 rule="hyper" parents="58 12507 13658"/>
    </justification>
  </clause>

  <clause id="13661">
    <literal><![CDATA[
      a(K(x,y),z,u) = a(y,z,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,13400,a,b,13660,a),flip(a)].">
      <j1 rule="hyper" parents="320 13400 13660"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13662">
    <literal><![CDATA[
      a(K(x,y),z,z \ x) = 1
    ]]></literal>
    <justification jstring="[hyper(320,a,10488,a(flip),b,13661,a),flip(a)].">
      <j1 rule="hyper" parents="320 10488 13661"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13663">
    <literal><![CDATA[
      a(K(x * y,z),x,y) = 1
    ]]></literal>
    <justification jstring="[hyper(320,a,10486,a(flip),b,13661,a),flip(a)].">
      <j1 rule="hyper" parents="320 10486 13661"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13664">
    <literal><![CDATA[
      x * a(K(y,z),u,w) = x * a(z,u,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(119,a,13661,a,b,4,a)].">
      <j1 rule="hyper" parents="119 13661 4"/>
    </justification>
  </clause>

  <clause id="13665">
    <literal><![CDATA[
      a(x,x,K(y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(58,a,5474,a(flip),b,13661,a),flip(a)].">
      <j1 rule="hyper" parents="58 5474 13661"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13666">
    <literal><![CDATA[
      a(x,y,K(z,u)) != 1
    ]]></literal>
    <literal><![CDATA[
      L(u,y,K(z,x)) = u
    ]]></literal>
    <justification jstring="[para(13661(a,1),47(a,1))].">
      <j1 rule="para" parents="13661 47"/>
    </justification>
  </clause>

  <clause id="13667">
    <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(13661(a,1),11985(a,1,1,2))].">
      <j1 rule="para" parents="13661 11985"/>
    </justification>
  </clause>

  <clause id="13668">
    <literal><![CDATA[
      a(K(x,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,a(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(13661(a,2),13401(a,1))].">
      <j1 rule="para" parents="13661 13401"/>
    </justification>
  </clause>

  <clause id="13669">
    <literal><![CDATA[
      a(x * y,x,K(y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(10934,a,13665,a)].">
      <j1 rule="hyper" parents="10934 13665"/>
    </justification>
  </clause>

  <clause id="13670">
    <literal><![CDATA[
      L(K(x,y),z,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(5893,a,13665,a)].">
      <j1 rule="hyper" parents="5893 13665"/>
    </justification>
  </clause>

  <clause id="13673">
    <literal><![CDATA[
      a(x,y,K(z,x * y)) = 1
    ]]></literal>
    <justification jstring="[hyper(58,a,11270,a(flip),b,13662,a)].">
      <j1 rule="hyper" parents="58 11270 13662"/>
    </justification>
  </clause>

  <clause id="13674">
    <literal><![CDATA[
      L(x \ y,x,K(y,z)) = x \ y
    ]]></literal>
    <justification jstring="[hyper(47,a,13662,a)].">
      <j1 rule="hyper" parents="47 13662"/>
    </justification>
  </clause>

  <clause id="13675">
    <literal><![CDATA[
      (x / y) * (y * K(x,z)) = T(x,z)
    ]]></literal>
    <justification jstring="[hyper(168,a,11265,a,b,13662,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="168 11265 13662"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13676">
    <literal><![CDATA[
      (K(x,y) * z) * (z \ x) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(168,a,10229,a,b,13662,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="168 10229 13662"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13677">
    <literal><![CDATA[
      L(x,y,K(y * x,z)) = x
    ]]></literal>
    <justification jstring="[hyper(47,a,13663,a)].">
      <j1 rule="hyper" parents="47 13663"/>
    </justification>
  </clause>

  <clause id="13678">
    <literal><![CDATA[
      K(x,(y \ z) \ y) = K(x,z \ (y * y))
    ]]></literal>
    <justification jstring="[hyper(58,a,6584,a(flip),b,13670,a),flip(a)].">
      <j1 rule="hyper" parents="58 6584 13670"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13679">
    <literal><![CDATA[
      (x * y) * K(z,x * y) = x * (y * K(z,x * y))
    ]]></literal>
    <justification jstring="[hyper(977,a,13673,a)].">
      <j1 rule="hyper" parents="977 13673"/>
    </justification>
  </clause>

  <clause id="13681">
    <literal><![CDATA[
      a(x,y,K(x * y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(58,a,11035,a(flip),b,13673,a)].">
      <j1 rule="hyper" parents="58 11035 13673"/>
    </justification>
  </clause>

  <clause id="13682">
    <literal><![CDATA[
      a(x,x \ y,K(z,y)) = 1
    ]]></literal>
    <justification jstring="[para(5(a,1),13673(a,1,3,2))].">
      <j1 rule="para" parents="5 13673"/>
    </justification>
  </clause>

  <clause id="13683">
    <literal><![CDATA[
      a(x,y,K(z,y * x)) = 1
    ]]></literal>
    <justification jstring="[para(12260(a,1),13673(a,1,3))].">
      <j1 rule="para" parents="12260 13673"/>
    </justification>
  </clause>

  <clause id="13684">
    <literal><![CDATA[
      L(x,y,K(z,y * x)) = x
    ]]></literal>
    <justification jstring="[hyper(12699,a,13677,a)].">
      <j1 rule="hyper" parents="12699 13677"/>
    </justification>
  </clause>

  <clause id="13685">
    <literal><![CDATA[
      T(x * y,L(z,y,x)) = T(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(167,a,10887,a,b,13681,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="167 10887 13681"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13686">
    <literal><![CDATA[
      a(x,x \ y,K(y,z)) = 1
    ]]></literal>
    <justification jstring="[para(5(a,1),13681(a,1,3,1))].">
      <j1 rule="para" parents="5 13681"/>
    </justification>
  </clause>

  <clause id="13687">
    <literal><![CDATA[
      a(x,y,K(y * x,z)) = 1
    ]]></literal>
    <justification jstring="[para(12230(a,1),13681(a,1,3))].">
      <j1 rule="para" parents="12230 13681"/>
    </justification>
  </clause>

  <clause id="13688">
    <literal><![CDATA[
      x * ((x \ y) * K(z,y)) = y * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(167,a,81,a,b,13682,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="167 81 13682"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13689">
    <literal><![CDATA[
      (x * y) * K(z,y * x) = x * (y * K(z,y * x))
    ]]></literal>
    <justification jstring="[hyper(977,a,13683,a)].">
      <j1 rule="hyper" parents="977 13683"/>
    </justification>
  </clause>

  <clause id="13690">
    <literal><![CDATA[
      a(x,y,K(z,z * (y * x))) = 1
    ]]></literal>
    <justification jstring="[hyper(58,a,11030,a,b,13683,a)].">
      <j1 rule="hyper" parents="58 11030 13683"/>
    </justification>
  </clause>

  <clause id="13691">
    <literal><![CDATA[
      L(x,y,K(z,x * y)) = x
    ]]></literal>
    <justification jstring="[hyper(58,a,12269,a,b,13684,a)].">
      <j1 rule="hyper" parents="58 12269 13684"/>
    </justification>
  </clause>

  <clause id="13692">
    <literal><![CDATA[
      L(x \ y,x,K(z,y)) = x \ y
    ]]></literal>
    <justification jstring="[para(5(a,1),13684(a,1,3,2))].">
      <j1 rule="para" parents="5 13684"/>
    </justification>
  </clause>

  <clause id="13693">
    <literal><![CDATA[
      T(x,L(y,z \ x,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(167,a,10887,a,b,13686,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="167 10887 13686"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13694">
    <literal><![CDATA[
      T(x * y,L(z,x,y)) = T(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(167,a,10887,a,b,13687,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="167 10887 13687"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13695">
    <literal><![CDATA[
      L(x,x \ y,K(z,y)) = x
    ]]></literal>
    <justification jstring="[para(5(a,1),13691(a,1,3,2))].">
      <j1 rule="para" parents="5 13691"/>
    </justification>
  </clause>

  <clause id="13696">
    <literal><![CDATA[
      (K(x,y) * z) \ T(x,y) = z \ x
    ]]></literal>
    <justification jstring="[hyper(58,a,4850,a(flip),b,13674,a)].">
      <j1 rule="hyper" parents="58 4850 13674"/>
    </justification>
  </clause>

  <clause id="13697">
    <literal><![CDATA[
      L(x \ (y \ z),x,K(y,z)) = x \ (y \ z)
    ]]></literal>
    <justification jstring="[hyper(12699,a,13692,a)].">
      <j1 rule="hyper" parents="12699 13692"/>
    </justification>
  </clause>

  <clause id="13698">
    <literal><![CDATA[
      (K(x,y) * z) * (z \ y) = y * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,13692,a(flip),b,2901,a(flip))].">
      <j1 rule="hyper" parents="119 13692 2901"/>
    </justification>
  </clause>

  <clause id="13699">
    <literal><![CDATA[
      (x \ y) * K(y,z) = x \ T(y,z)
    ]]></literal>
    <justification jstring="[hyper(116,a,13693,a(flip),b,10922,a),flip(a)].">
      <j1 rule="hyper" parents="116 13693 10922"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13700">
    <literal><![CDATA[
      T(x,(y \ x) \ z) = T(x,x \ (y * z))
    ]]></literal>
    <justification jstring="[para(490(a,1),13693(a,1,2)),flip(a)].">
      <j1 rule="para" parents="490 13693"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13701">
    <literal><![CDATA[
      K(x,T(y,z) * L(z,u \ y,u)) = K(x,L(z,u \ y,u) * y)
    ]]></literal>
    <justification jstring="[para(13693(a,1),12290(a,1,2,1))].">
      <j1 rule="para" parents="13693 12290"/>
    </justification>
  </clause>

  <clause id="13702">
    <literal><![CDATA[
      T(x,y) / (z * K(x,y)) = x / z
    ]]></literal>
    <justification jstring="[hyper(131,a,13675,a)].">
      <j1 rule="hyper" parents="131 13675"/>
    </justification>
  </clause>

  <clause id="13704">
    <literal><![CDATA[
      T(x,y) / (z \ x) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(117,a,13675,a(flip),b,11264,a)].">
      <j1 rule="hyper" parents="117 13675 11264"/>
    </justification>
  </clause>

  <clause id="13705">
    <literal><![CDATA[
      T(x,y) * K(x * y,z) = y \ T(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(116,a,13675,a(flip),b,4558,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="116 13675 4558"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13706">
    <literal><![CDATA[
      x * (y * K(x * y,z)) = T(x * y,z)
    ]]></literal>
    <justification jstring="[para(6(a,1),13675(a,1,1))].">
      <j1 rule="para" parents="6 13675"/>
    </justification>
  </clause>

  <clause id="13707">
    <literal><![CDATA[
      (x / (y / z)) * (y / T(z,x)) = T(x,z)
    ]]></literal>
    <justification jstring="[para(6322(a,1),13675(a,1,2))].">
      <j1 rule="para" parents="6322 13675"/>
    </justification>
  </clause>

  <clause id="13708">
    <literal><![CDATA[
      K(x,y) * (x / z) = T(x,y) / z
    ]]></literal>
    <justification jstring="[hyper(353,a,13676,a),flip(a)].">
      <j1 rule="hyper" parents="353 13676"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13710">
    <literal><![CDATA[
      (T(x,y) \ z) * ((x \ z) \ y) = T(y,x)
    ]]></literal>
    <justification jstring="[para(5131(a,1),13676(a,1,1))].">
      <j1 rule="para" parents="5131 13676"/>
    </justification>
  </clause>

  <clause id="13712">
    <literal><![CDATA[
      K(x,y) * (1 / z) = K(x,y) / z
    ]]></literal>
    <justification jstring="[hyper(34,a,11590,a,b,13696,a),flip(a)].">
      <j1 rule="hyper" parents="34 11590 13696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13713">
    <literal><![CDATA[
      (K(x,y) \ z) \ T(y,x) = z \ y
    ]]></literal>
    <justification jstring="[para(5130(a,2),13696(a,1,1))].">
      <j1 rule="para" parents="5130 13696"/>
    </justification>
  </clause>

  <clause id="13714">
    <literal><![CDATA[
      (K(x,y) * z) \ y = z \ T(y,x)
    ]]></literal>
    <justification jstring="[para(5133(a,1),13696(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5133 13696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13715">
    <literal><![CDATA[
      (T(x,y) * z) \ y = (x * z) \ T(y,x)
    ]]></literal>
    <justification jstring="[para(4819(a,1),13696(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4819 13696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13716">
    <literal><![CDATA[
      ((x / T(y,x)) * z) \ T(x,y) = ((x / y) * z) \ x
    ]]></literal>
    <justification jstring="[para(12601(a,1),13696(a,1,1))].">
      <j1 rule="para" parents="12601 13696"/>
    </justification>
  </clause>

  <clause id="13717">
    <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(13696(a,1),13468(a,1,3,2,1)),flip(a)].">
      <j1 rule="para" parents="13696 13468"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13718">
    <literal><![CDATA[
      K(x,T(y,z)) * (z \ x) = z \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(8742,a,13699,a)].">
      <j1 rule="hyper" parents="8742 13699"/>
    </justification>
  </clause>

  <clause id="13719">
    <literal><![CDATA[
      x \ T(y,T(z,x)) = K(y,z) * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(8242,a,13699,a),flip(a)].">
      <j1 rule="hyper" parents="8242 13699"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13720">
    <literal><![CDATA[
      (x \ T(y,z)) * K(z,y) = x \ y
    ]]></literal>
    <justification jstring="[hyper(6344,a,13699,a)].">
      <j1 rule="hyper" parents="6344 13699"/>
    </justification>
  </clause>

  <clause id="13722">
    <literal><![CDATA[
      (x \ y) \ (x \ T(y,z)) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(123,a,13699,a)].">
      <j1 rule="hyper" parents="123 13699"/>
    </justification>
  </clause>

  <clause id="13724">
    <literal><![CDATA[
      (x \ T(y,z)) / (x \ y) = K(y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(117,a,13699,a(flip),b,8243,a)].">
      <j1 rule="hyper" parents="117 13699 8243"/>
    </justification>
  </clause>

  <clause id="13725">
    <literal><![CDATA[
      (x \ T(y,z)) / T(y,z) = (x \ y) / y
    ]]></literal>
    <justification jstring="[hyper(117,a,13699,a(flip),b,6151,a)].">
      <j1 rule="hyper" parents="117 13699 6151"/>
    </justification>
  </clause>

  <clause id="13726">
    <literal><![CDATA[
      x \ T(x * y,z) = y * K(x * y,z)
    ]]></literal>
    <justification jstring="[para(4(a,1),13699(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4 13699"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13728">
    <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),13699(a,2,2))].">
      <j1 rule="para" parents="20 13699"/>
    </justification>
  </clause>

  <clause id="13730">
    <literal><![CDATA[
      (K(x,y) * (z \ x)) \ K(K(x,y),z \ x) = (z \ T(x,y)) \ 1
    ]]></literal>
    <justification jstring="[para(13699(a,1),5569(a,2,1))].">
      <j1 rule="para" parents="13699 5569"/>
    </justification>
  </clause>

  <clause id="13733">
    <literal><![CDATA[
      T(x \ T(y,z),K(z,y)) = K(y,z) * (x \ y)
    ]]></literal>
    <justification jstring="[para(13699(a,1),6337(a,1,1))].">
      <j1 rule="para" parents="13699 6337"/>
    </justification>
  </clause>

  <clause id="13734">
    <literal><![CDATA[
      K(x * (y \ T(z,u)),z) = K(x * (y \ z),z)
    ]]></literal>
    <justification jstring="[para(13699(a,1),7415(a,1,1,2))].">
      <j1 rule="para" parents="13699 7415"/>
    </justification>
  </clause>

  <clause id="13735">
    <literal><![CDATA[
      (x \ y) / (x \ T(y,z)) = K(z,T(y,x \ y))
    ]]></literal>
    <justification jstring="[para(13699(a,1),7997(a,1,2))].">
      <j1 rule="para" parents="13699 7997"/>
    </justification>
  </clause>

  <clause id="13736">
    <literal><![CDATA[
      x / (y * K(z,x)) = T(x,z) / y
    ]]></literal>
    <justification jstring="[para(6329(a,1),13702(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6329 13702"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13739">
    <literal><![CDATA[
      K(x,y) * (1 / z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) / z = u
    ]]></literal>
    <justification jstring="[para(13704(a,1),11594(a,1))].">
      <j1 rule="para" parents="13704 11594"/>
    </justification>
  </clause>

  <clause id="13740">
    <literal><![CDATA[
      K(x,y) \ (y / z) = T(y,x) / z
    ]]></literal>
    <justification jstring="[hyper(5167,a,13708,a)].">
      <j1 rule="hyper" parents="5167 13708"/>
    </justification>
  </clause>

  <clause id="13741">
    <literal><![CDATA[
      K(x,y) * (T(y,x) / z) = y / z
    ]]></literal>
    <justification jstring="[hyper(5147,a,13708,a)].">
      <j1 rule="hyper" parents="5147 13708"/>
    </justification>
  </clause>

  <clause id="13743">
    <literal><![CDATA[
      (x / y) \ (T(x,z) / y) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(116,a,13708,a(flip),b,8594,a)].">
      <j1 rule="hyper" parents="116 13708 8594"/>
    </justification>
  </clause>

  <clause id="13744">
    <literal><![CDATA[
      (T(x,y) / z) \ K(K(x,y),x / z) = ((x / z) * K(x,y)) \ 1
    ]]></literal>
    <justification jstring="[para(13708(a,1),5569(a,1,1))].">
      <j1 rule="para" parents="13708 5569"/>
    </justification>
  </clause>

  <clause id="13745">
    <literal><![CDATA[
      T(T(x,y) / z,K(x,y)) = (x / z) * K(x,y)
    ]]></literal>
    <justification jstring="[para(13708(a,1),6351(a,1,1))].">
      <j1 rule="para" parents="13708 6351"/>
    </justification>
  </clause>

  <clause id="13746">
    <literal><![CDATA[
      K(x,y) * (K(y,x) / z) = 1 / z
    ]]></literal>
    <justification jstring="[hyper(5147,a,13712,a)].">
      <j1 rule="hyper" parents="5147 13712"/>
    </justification>
  </clause>

  <clause id="13747">
    <literal><![CDATA[
      K(x,T(y,z)) / z = (1 / z) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,8246,a(flip),b,13712,a),flip(a)].">
      <j1 rule="hyper" parents="58 8246 13712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13748">
    <literal><![CDATA[
      R(K(x,y),z,z \ 1) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(2745,a,13712,a(flip))].">
      <j1 rule="hyper" parents="2745 13712"/>
    </justification>
  </clause>

  <clause id="13749">
    <literal><![CDATA[
      (x * y) * (K(y,x) / z) = (y * x) * (1 / z)
    ]]></literal>
    <justification jstring="[hyper(119,a,13712,a(flip),b,11153,a)].">
      <j1 rule="hyper" parents="119 13712 11153"/>
    </justification>
  </clause>

  <clause id="13750">
    <literal><![CDATA[
      K(x,y) / (z \ 1) = K(x,y) * z
    ]]></literal>
    <justification jstring="[para(72(a,1),13712(a,1,2)),flip(a)].">
      <j1 rule="para" parents="72 13712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13751">
    <literal><![CDATA[
      T(K(x,y) / z,K(x,y)) = (1 / z) * K(x,y)
    ]]></literal>
    <justification jstring="[para(13712(a,1),6351(a,1,1))].">
      <j1 rule="para" parents="13712 6351"/>
    </justification>
  </clause>

  <clause id="13752">
    <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(13712(a,1),5885(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="13712 5885"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13753">
    <literal><![CDATA[
      K(x,R(y,z,z \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(12504,a,13748,a)].">
      <j1 rule="hyper" parents="12504 13748"/>
    </justification>
  </clause>

  <clause id="13754">
    <literal><![CDATA[
      K(R(x,y,y \ 1),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,12488,a(flip),b,13748,a)].">
      <j1 rule="hyper" parents="58 12488 13748"/>
    </justification>
  </clause>

  <clause id="13755">
    <literal><![CDATA[
      K(x,L(y,z,z \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,12352,a(flip),b,13748,a)].">
      <j1 rule="hyper" parents="58 12352 13748"/>
    </justification>
  </clause>

  <clause id="13756">
    <literal><![CDATA[
      (K(x,y) * z) \ K(x,y) = z \ 1
    ]]></literal>
    <justification jstring="[hyper(116,a,13748,a(flip),b,261,a)].">
      <j1 rule="hyper" parents="116 13748 261"/>
    </justification>
  </clause>

  <clause id="13758">
    <literal><![CDATA[
      T(x,R(y,z,z \ 1)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(118,a,13753,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 13753 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13759">
    <literal><![CDATA[
      K(x,y * (z \ 1)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(523(a,1),13753(a,1,2))].">
      <j1 rule="para" parents="523 13753"/>
    </justification>
  </clause>

  <clause id="13763">
    <literal><![CDATA[
      K(x * (y \ 1),z) = K(x / y,z)
    ]]></literal>
    <justification jstring="[para(523(a,1),13754(a,1,1))].">
      <j1 rule="para" parents="523 13754"/>
    </justification>
  </clause>

  <clause id="13764">
    <literal><![CDATA[
      K(x,L(y,z,z \ x)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(11579,a,13755,a)].">
      <j1 rule="hyper" parents="11579 13755"/>
    </justification>
  </clause>

  <clause id="13765">
    <literal><![CDATA[
      K(L(x,y,y \ 1),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(10913,a,13755,a)].">
      <j1 rule="hyper" parents="10913 13755"/>
    </justification>
  </clause>

  <clause id="13766">
    <literal><![CDATA[
      L(K(x,y),z,z \ 1) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(10863,a,13755,a)].">
      <j1 rule="hyper" parents="10863 13755"/>
    </justification>
  </clause>

  <clause id="13768">
    <literal><![CDATA[
      R(K(x,y),z,z \ 1) = K(x,L(y,u,u \ 1))
    ]]></literal>
    <justification jstring="[hyper(320,a,13748,a,b,13755,a)].">
      <j1 rule="hyper" parents="320 13748 13755"/>
    </justification>
  </clause>

  <clause id="13770">
    <literal><![CDATA[
      T(x,L(y,z,z \ 1)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(118,a,13755,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 13755 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13771">
    <literal><![CDATA[
      a(x \ 1,x,K(y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,13755,a,b,10822,a),flip(a)].">
      <j1 rule="hyper" parents="115 13755 10822"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13772">
    <literal><![CDATA[
      K(x,L(y,z \ x,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,11580,a(flip),b,13755,a)].">
      <j1 rule="hyper" parents="58 11580 13755"/>
    </justification>
  </clause>

  <clause id="13773">
    <literal><![CDATA[
      (K(x,y) * z) \ 1 = z \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,13755,a(flip),b,12878,a),flip(a)].">
      <j1 rule="hyper" parents="116 13755 12878"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13774">
    <literal><![CDATA[
      K(x,(1 / y) * z) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(2815(a,1),13755(a,1,2))].">
      <j1 rule="para" parents="2815 13755"/>
    </justification>
  </clause>

  <clause id="13775">
    <literal><![CDATA[
      K(x,(y \ 1) \ z) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(2818(a,1),13755(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2818 13755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13776">
    <literal><![CDATA[
      K(x,L((1 / y) * z,u,w)) = K(x,L(y \ z,u,w))
    ]]></literal>
    <justification jstring="[para(2823(a,1),13755(a,1,2))].">
      <j1 rule="para" parents="2823 13755"/>
    </justification>
  </clause>

  <clause id="13777">
    <literal><![CDATA[
      K(x,L(y,z \ 1,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(3689(a,1),13755(a,1,2))].">
      <j1 rule="para" parents="3689 13755"/>
    </justification>
  </clause>

  <clause id="13779">
    <literal><![CDATA[
      T(x,a(y \ 1,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(13406,a,13771,a)].">
      <j1 rule="hyper" parents="13406 13771"/>
    </justification>
  </clause>

  <clause id="13780">
    <literal><![CDATA[
      a(1 / x,x,K(y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(58,a,4063,a,b,13771,a)].">
      <j1 rule="hyper" parents="58 4063 13771"/>
    </justification>
  </clause>

  <clause id="13781">
    <literal><![CDATA[
      a(x,x \ 1,K(y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(58,a,4064,a(flip),b,13771,a)].">
      <j1 rule="hyper" parents="58 4064 13771"/>
    </justification>
  </clause>

  <clause id="13782">
    <literal><![CDATA[
      x / a(y \ 1,y,z) = a(y \ 1,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(2446,a,13779,a),flip(a)].">
      <j1 rule="hyper" parents="2446 13779"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13785">
    <literal><![CDATA[
      L(K(x,y),z \ 1,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(5893,a,13781,a)].">
      <j1 rule="hyper" parents="5893 13781"/>
    </justification>
  </clause>

  <clause id="13787">
    <literal><![CDATA[
      R(x,y,y \ 1) * T(z,x) = z * R(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(119,a,13758,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 13758 17"/>
    </justification>
  </clause>

  <clause id="13788">
    <literal><![CDATA[
      T(x,y * (z \ 1)) = T(x,y / z)
    ]]></literal>
    <justification jstring="[para(523(a,1),13758(a,1,2))].">
      <j1 rule="para" parents="523 13758"/>
    </justification>
  </clause>

  <clause id="13789">
    <literal><![CDATA[
      T(x,R(y,z \ 1,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(2670(a,1),13758(a,1,2))].">
      <j1 rule="para" parents="2670 13758"/>
    </justification>
  </clause>

  <clause id="13791">
    <literal><![CDATA[
      ((x / y) * (y * z)) \ K(x,z) = (L(z,y,y \ x) * x) \ 1
    ]]></literal>
    <justification jstring="[para(13764(a,1),11217(a,1,2))].">
      <j1 rule="para" parents="13764 11217"/>
    </justification>
  </clause>

  <clause id="13792">
    <literal><![CDATA[
      K((1 / x) * y,z) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[para(2815(a,1),13765(a,1,1))].">
      <j1 rule="para" parents="2815 13765"/>
    </justification>
  </clause>

  <clause id="13794">
    <literal><![CDATA[
      K((x \ 1) \ y,z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(2818(a,1),13765(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2818 13765"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13796">
    <literal><![CDATA[
      K(x,y) / (z * K(x,y)) = 1 / z
    ]]></literal>
    <justification jstring="[hyper(117,a,13766,a(flip),b,2820,a)].">
      <j1 rule="hyper" parents="117 13766 2820"/>
    </justification>
  </clause>

  <clause id="13800">
    <literal><![CDATA[
      L(x,y,y \ 1) * T(z,x) = z * L(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(119,a,13770,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 13770 17"/>
    </justification>
  </clause>

  <clause id="13801">
    <literal><![CDATA[
      T(x,(1 / y) * z) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[para(2815(a,1),13770(a,1,2))].">
      <j1 rule="para" parents="2815 13770"/>
    </justification>
  </clause>

  <clause id="13802">
    <literal><![CDATA[
      T(x,(y \ 1) \ z) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(2818(a,1),13770(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2818 13770"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13803">
    <literal><![CDATA[
      T(x,T((1 / y) * z,u)) = T(x,T(y \ z,u))
    ]]></literal>
    <justification jstring="[para(2822(a,1),13770(a,1,2))].">
      <j1 rule="para" parents="2822 13770"/>
    </justification>
  </clause>

  <clause id="13804">
    <literal><![CDATA[
      K(x,(y * z) \ x) = K(x,z \ (y \ x))
    ]]></literal>
    <justification jstring="[hyper(10829,a,13772,a)].">
      <j1 rule="hyper" parents="10829 13772"/>
    </justification>
  </clause>

  <clause id="13806">
    <literal><![CDATA[
      K(x * y,L(z,y,x)) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(4(a,1),13772(a,1,2,2))].">
      <j1 rule="para" parents="4 13772"/>
    </justification>
  </clause>

  <clause id="13807">
    <literal><![CDATA[
      K(x,(y \ x) \ z) = K(x,x \ (y * z))
    ]]></literal>
    <justification jstring="[para(490(a,1),13772(a,1,2)),flip(a)].">
      <j1 rule="para" parents="490 13772"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13808">
    <literal><![CDATA[
      K(x,(y * z) \ 1) = K(x,z \ (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(10829,a,13777,a)].">
      <j1 rule="hyper" parents="10829 13777"/>
    </justification>
  </clause>

  <clause id="13810">
    <literal><![CDATA[
      x \ K(y,T(z,x)) = K(y,z) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(116,a,13777,a(flip),b,10911,a(flip))].">
      <j1 rule="hyper" parents="116 13777 10911"/>
    </justification>
  </clause>

  <clause id="13811">
    <literal><![CDATA[
      K(x,T((y \ 1) \ z,u)) = K(x,T(y * z,u))
    ]]></literal>
    <justification jstring="[para(608(a,1),13777(a,1,2)),flip(a)].">
      <j1 rule="para" parents="608 13777"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13812">
    <literal><![CDATA[
      (x \ 1) * K(y,z) = x \ K(y,z)
    ]]></literal>
    <justification jstring="[para(13777(a,1),10816(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13777 10816"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13813">
    <literal><![CDATA[
      L(K(x,y),z \ 1,z) = u \ (u * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(320,a,4,a,b,13785,a),flip(a)].">
      <j1 rule="hyper" parents="320 4 13785"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13814">
    <literal><![CDATA[
      K((x \ y) \ z,y) = K(y \ (x * z),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,10946,a(flip),b,13785,a),flip(a)].">
      <j1 rule="hyper" parents="58 10946 13785"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13815">
    <literal><![CDATA[
      T(x,y / (1 / z)) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(2609(a,1),13789(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2609 13789"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13816">
    <literal><![CDATA[
      (K(x,y) \ z) \ (y * x) = z \ (x * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,12816,a(flip),b,13713,a)].">
      <j1 rule="hyper" parents="58 12816 13713"/>
    </justification>
  </clause>

  <clause id="13817">
    <literal><![CDATA[
      T(x \ T(y,z),(K(z,y) * x) \ y) = (K(z,y) * x) \ y
    ]]></literal>
    <justification jstring="[hyper(443,a,xx,b,13714,a)].">
      <j1 rule="hyper" parents="443 13714"/>
    </justification>
  </clause>

  <clause id="13818">
    <literal><![CDATA[
      1 / (x \ K(y,z)) = K(z,y) * x
    ]]></literal>
    <justification jstring="[hyper(34,a,11591,a,b,13714,a)].">
      <j1 rule="hyper" parents="34 11591 13714"/>
    </justification>
  </clause>

  <clause id="13819">
    <literal><![CDATA[
      ((K(x,y) * z) / K(x,y)) \ T(y,x) = (T(K(x,y),z) * z) \ y
    ]]></literal>
    <justification jstring="[para(4092(a,2),13714(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4092 13714"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13821">
    <literal><![CDATA[
      (((x * y) \ y) * z) \ T(y,x) = (((y * x) \ y) * z) \ y
    ]]></literal>
    <justification jstring="[para(11236(a,1),13714(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11236 13714"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13822">
    <literal><![CDATA[
      (x * K(y * x,z)) \ z = x \ T(z,x * y)
    ]]></literal>
    <justification jstring="[para(12229(a,1),13714(a,1,1))].">
      <j1 rule="para" parents="12229 13714"/>
    </justification>
  </clause>

  <clause id="13823">
    <literal><![CDATA[
      (x \ T(x * y,z)) \ y = K(z,x * y)
    ]]></literal>
    <justification jstring="[hyper(116,a,4,a(flip),b,13720,a)].">
      <j1 rule="hyper" parents="116 4 13720"/>
    </justification>
  </clause>

  <clause id="13827">
    <literal><![CDATA[
      T(x,y) \ (y \ T(x * y,z)) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(17(a,2),13722(a,1,1))].">
      <j1 rule="para" parents="17 13722"/>
    </justification>
  </clause>

  <clause id="13828">
    <literal><![CDATA[
      T(x,y) / (1 / y) = x / (K(y,x) / y)
    ]]></literal>
    <justification jstring="[para(6222(a,1),13736(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6222 13736"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13830">
    <literal><![CDATA[
      x / (y * K(x,z)) = K(z,x) * (x / y)
    ]]></literal>
    <justification jstring="[hyper(119,a,13702,a(flip),b,13740,a),flip(a)].">
      <j1 rule="hyper" parents="119 13702 13740"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13831">
    <literal><![CDATA[
      T(x,(T(y,z) / u) \ 1) = T(x,(y / u) \ K(z,y))
    ]]></literal>
    <justification jstring="[para(13740(a,1),6125(a,1,2,1))].">
      <j1 rule="para" parents="13740 6125"/>
    </justification>
  </clause>

  <clause id="13832">
    <literal><![CDATA[
      K(x \ y,x) * (((x \ y) \ y) / z) = x / z
    ]]></literal>
    <justification jstring="[para(106(a,1),13741(a,1,2,1))].">
      <j1 rule="para" parents="106 13741"/>
    </justification>
  </clause>

  <clause id="13833">
    <literal><![CDATA[
      K(x,y) * (x / z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) / z = u
    ]]></literal>
    <justification jstring="[para(13741(a,1),5148(a,1,2)),flip(b)].">
      <j1 rule="para" parents="13741 5148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13834">
    <literal><![CDATA[
      (T(x,y) \ z) \ 1 = (x \ z) \ K(x,y)
    ]]></literal>
    <justification jstring="[para(5081(a,1),13756(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5081 13756"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13836">
    <literal><![CDATA[
      ((x * y) \ z) \ K(y,x) = ((y * x) \ z) \ 1
    ]]></literal>
    <justification jstring="[para(11156(a,1),13756(a,1,1))].">
      <j1 rule="para" parents="11156 13756"/>
    </justification>
  </clause>

  <clause id="13838">
    <literal><![CDATA[
      K(x,y * (z \ K(u,x))) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(58,a,11375,a,b,13759,a)].">
      <j1 rule="hyper" parents="58 11375 13759"/>
    </justification>
  </clause>

  <clause id="13839">
    <literal><![CDATA[
      K(x,y * (1 / z)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(58,a,5315,a,b,13759,a)].">
      <j1 rule="hyper" parents="58 5315 13759"/>
    </justification>
  </clause>

  <clause id="13840">
    <literal><![CDATA[
      K(x,y / (z \ 1)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,5312,a(flip),b,13759,a),flip(a)].">
      <j1 rule="hyper" parents="58 5312 13759"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13841">
    <literal><![CDATA[
      K(x,y / (1 / z)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(75(a,1),13759(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="75 13759"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13842">
    <literal><![CDATA[
      K(x * (1 / y),z) = K(x / y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,3975,a,b,13763,a)].">
      <j1 rule="hyper" parents="58 3975 13763"/>
    </justification>
  </clause>

  <clause id="13843">
    <literal><![CDATA[
      K(x / (y \ 1),z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,3977,a(flip),b,13763,a),flip(a)].">
      <j1 rule="hyper" parents="58 3977 13763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13844">
    <literal><![CDATA[
      K(x / (1 / y),z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(75(a,1),13763(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="75 13763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13846">
    <literal><![CDATA[
      x \ K(y,z) != u \ 1
    ]]></literal>
    <literal><![CDATA[
      K(z,y) * x = u
    ]]></literal>
    <justification jstring="[para(13773(a,1),43(a,1))].">
      <j1 rule="para" parents="13773 43"/>
    </justification>
  </clause>

  <clause id="13849">
    <literal><![CDATA[
      K(x,y / (K(z,u) * w)) = K(x,y * (w \ K(u,z)))
    ]]></literal>
    <justification jstring="[para(13773(a,1),13759(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="13773 13759"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13850">
    <literal><![CDATA[
      K(x,(y \ 1) * z) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,5322,a(flip),b,13774,a)].">
      <j1 rule="hyper" parents="58 5322 13774"/>
    </justification>
  </clause>

  <clause id="13851">
    <literal><![CDATA[
      K(x,(y \ z) * T(u,z \ y)) = K(x,u / ((y \ z) \ 1))
    ]]></literal>
    <justification jstring="[hyper(13134,a,13775,a),flip(a)].">
      <j1 rule="hyper" parents="13134 13775"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13852">
    <literal><![CDATA[
      K(x,T(y * z,y)) = K(x,(z \ 1) \ y)
    ]]></literal>
    <justification jstring="[hyper(320,a,12262,a,b,13775,a)].">
      <j1 rule="hyper" parents="320 12262 13775"/>
    </justification>
  </clause>

  <clause id="13853">
    <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,13180,a,b,13775,a)].">
      <j1 rule="hyper" parents="58 13180 13775"/>
    </justification>
  </clause>

  <clause id="13854">
    <literal><![CDATA[
      K(x,(1 / y) \ z) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,5323,a,b,13775,a)].">
      <j1 rule="hyper" parents="58 5323 13775"/>
    </justification>
  </clause>

  <clause id="13855">
    <literal><![CDATA[
      K(x,(y \ x) \ z) = K(x,y * (x \ z))
    ]]></literal>
    <justification jstring="[hyper(58,a,9040,a(flip),b,13775,a)].">
      <j1 rule="hyper" parents="58 9040 13775"/>
    </justification>
  </clause>

  <clause id="13856">
    <literal><![CDATA[
      K(x,L((y \ 1) \ z,u,w)) = L(K(x,y * z),u,w)
    ]]></literal>
    <justification jstring="[para(13775(a,1),10794(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13775 10794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13857">
    <literal><![CDATA[
      T(x,y * (1 / z)) = T(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(58,a,3765,a,b,13788,a)].">
      <j1 rule="hyper" parents="58 3765 13788"/>
    </justification>
  </clause>

  <clause id="13858">
    <literal><![CDATA[
      L(x,y \ 1,z) * (z * (y \ 1)) = z * ((y \ 1) * T(x,z / y))
    ]]></literal>
    <justification jstring="[para(13788(a,1),632(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="13788 632"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13859">
    <literal><![CDATA[
      T(x,y / (K(z,u) * w)) = T(x,y * (w \ K(u,z)))
    ]]></literal>
    <justification jstring="[para(13773(a,1),13788(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="13773 13788"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13860">
    <literal><![CDATA[
      K((x \ 1) * y,z) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,3981,a(flip),b,13792,a)].">
      <j1 rule="hyper" parents="58 3981 13792"/>
    </justification>
  </clause>

  <clause id="13862">
    <literal><![CDATA[
      K((x \ y) \ z,y) = K(x * (y \ z),y)
    ]]></literal>
    <justification jstring="[hyper(13173,a,13794,a)].">
      <j1 rule="hyper" parents="13173 13794"/>
    </justification>
  </clause>

  <clause id="13863">
    <literal><![CDATA[
      K((1 / x) \ y,z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(5967,a,13794,a)].">
      <j1 rule="hyper" parents="5967 13794"/>
    </justification>
  </clause>

  <clause id="13868">
    <literal><![CDATA[
      K((x \ 1) * y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,z) = u
    ]]></literal>
    <justification jstring="[para(13794(a,1),5966(a,1))].">
      <j1 rule="para" parents="13794 5966"/>
    </justification>
  </clause>

  <clause id="13869">
    <literal><![CDATA[
      (x * K(y * x,z)) * y = T(x * y,z)
    ]]></literal>
    <justification jstring="[para(13794(a,1),6530(a,1,1,2))].">
      <j1 rule="para" parents="13794 6530"/>
    </justification>
  </clause>

  <clause id="13870">
    <literal><![CDATA[
      T(x * K(y * x,z),y) = y \ T(x * y,z)
    ]]></literal>
    <justification jstring="[para(13794(a,1),6531(a,1,1,2))].">
      <j1 rule="para" parents="13794 6531"/>
    </justification>
  </clause>

  <clause id="13874">
    <literal><![CDATA[
      (x * K(y * (z \ x),z)) * y = (z \ (x * y)) * z
    ]]></literal>
    <justification jstring="[para(13794(a,1),9692(a,1,1,2))].">
      <j1 rule="para" parents="13794 9692"/>
    </justification>
  </clause>

  <clause id="13875">
    <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,12067,a(flip),b,13796,a),flip(a)].">
      <j1 rule="hyper" parents="320 12067 13796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13876">
    <literal><![CDATA[
      1 / (x * K(y,z)) = K(z,y) / x
    ]]></literal>
    <justification jstring="[para(6329(a,1),13796(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6329 13796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13878">
    <literal><![CDATA[
      T(x,(y \ 1) * z) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,3769,a(flip),b,13801,a)].">
      <j1 rule="hyper" parents="58 3769 13801"/>
    </justification>
  </clause>

  <clause id="13879">
    <literal><![CDATA[
      T(x,(1 / y) \ z) = T(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,3770,a,b,13802,a)].">
      <j1 rule="hyper" parents="58 3770 13802"/>
    </justification>
  </clause>

  <clause id="13880">
    <literal><![CDATA[
      T(x,(y \ K(z,u)) \ w) = T(x,(K(u,z) * y) * w)
    ]]></literal>
    <justification jstring="[para(13773(a,1),13802(a,1,2,1))].">
      <j1 rule="para" parents="13773 13802"/>
    </justification>
  </clause>

  <clause id="13881">
    <literal><![CDATA[
      K(x,T(y,z)) * (z \ 1) = z \ K(x,y)
    ]]></literal>
    <justification jstring="[hyper(8741,a,13812,a)].">
      <j1 rule="hyper" parents="8741 13812"/>
    </justification>
  </clause>

  <clause id="13886">
    <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(13812(a,1),687(a,2,2))].">
      <j1 rule="para" parents="13812 687"/>
    </justification>
  </clause>

  <clause id="13889">
    <literal><![CDATA[
      T(x,y * ((1 / z) * K(u,w))) = T(x,y * (z \ K(u,w)))
    ]]></literal>
    <justification jstring="[para(13812(a,1),3777(a,2,2,2))].">
      <j1 rule="para" parents="13812 3777"/>
    </justification>
  </clause>

  <clause id="13891">
    <literal><![CDATA[
      K(x,y * ((1 / z) * K(u,w))) = K(x,y * (z \ K(u,w)))
    ]]></literal>
    <justification jstring="[para(13812(a,1),5336(a,2,2,2))].">
      <j1 rule="para" parents="13812 5336"/>
    </justification>
  </clause>

  <clause id="13892">
    <literal><![CDATA[
      (x \ K(y,z)) * y = (x \ 1) * T(y,z)
    ]]></literal>
    <justification jstring="[para(13812(a,1),6196(a,1,1))].">
      <j1 rule="para" parents="13812 6196"/>
    </justification>
  </clause>

  <clause id="13893">
    <literal><![CDATA[
      (x \ K(y,z)) \ (x \ 1) = K(z,y)
    ]]></literal>
    <justification jstring="[para(13812(a,1),6338(a,1,1))].">
      <j1 rule="para" parents="13812 6338"/>
    </justification>
  </clause>

  <clause id="13895">
    <literal><![CDATA[
      T(x \ K(y,z),K(z,y)) = K(y,z) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(13812(a,1),6337(a,1,1))].">
      <j1 rule="para" parents="13812 6337"/>
    </justification>
  </clause>

  <clause id="13898">
    <literal><![CDATA[
      (K(x,y) * z) \ K(u,w) = (z \ K(y,x)) * K(u,w)
    ]]></literal>
    <justification jstring="[para(13773(a,1),13812(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13773 13812"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13899">
    <literal><![CDATA[
      T(x,y / (z \ 1)) = T(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(3956,a,13815,a)].">
      <j1 rule="hyper" parents="3956 13815"/>
    </justification>
  </clause>

  <clause id="13903">
    <literal><![CDATA[
      K(((x \ K(y,z)) \ 1) * u,w) = K((K(z,y) * x) * u,w)
    ]]></literal>
    <justification jstring="[para(13818(a,1),3981(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="13818 3981"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13904">
    <literal><![CDATA[
      K(x / (x / y),z / u) = K(y,T(z * (1 / u),x))
    ]]></literal>
    <justification jstring="[hyper(7938,a,13839,a),flip(a)].">
      <j1 rule="hyper" parents="7938 13839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13906">
    <literal><![CDATA[
      K(x,(y * (1 / z)) * K(u,y / z)) = K(x,T(y * (1 / z),u))
    ]]></literal>
    <justification jstring="[para(13839(a,1),7916(a,1,2,2))].">
      <j1 rule="para" parents="13839 7916"/>
    </justification>
  </clause>

  <clause id="13907">
    <literal><![CDATA[
      K(x,y * z) * (z \ T(z * y,x)) = y
    ]]></literal>
    <justification jstring="[para(13840(a,1),5113(a,1,1))].">
      <j1 rule="para" parents="13840 5113"/>
    </justification>
  </clause>

  <clause id="13908">
    <literal><![CDATA[
      K(x,L(y / (z \ 1),u,w)) = L(K(x,y * z),u,w)
    ]]></literal>
    <justification jstring="[para(13840(a,1),10794(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13840 10794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13910">
    <literal><![CDATA[
      K((x * (y \ 1)) * y,z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(6(a,1),13843(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6 13843"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13911">
    <literal><![CDATA[
      K(x / (1 / y),z) = K((x \ 1) \ y,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,13794,a,b,13844,a),flip(a)].">
      <j1 rule="hyper" parents="320 13794 13844"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13914">
    <literal><![CDATA[
      K(x,y * ((1 / y) * z)) = K(x,z)
    ]]></literal>
    <justification jstring="[para(4(a,1),13854(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4 13854"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13915">
    <literal><![CDATA[
      K(x,y * (T(1 / y,z) * u)) = K(x,K(1 / y,z) * u)
    ]]></literal>
    <justification jstring="[para(4777(a,1),13854(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4777 13854"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13916">
    <literal><![CDATA[
      K(x,L((1 / y) \ z,u,w)) = L(K(x,y * z),u,w)
    ]]></literal>
    <justification jstring="[para(13854(a,1),10794(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13854 10794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13920">
    <literal><![CDATA[
      T(x,y / (z \ K(u,w))) = T(x,y * (K(w,u) * z))
    ]]></literal>
    <justification jstring="[para(13818(a,1),13857(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="13818 13857"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13924">
    <literal><![CDATA[
      K(x \ (y / (x \ 1)),z) = K(y,T(z,x \ 1))
    ]]></literal>
    <justification jstring="[hyper(58,a,12237,a(flip),b,13860,a),flip(a)].">
      <j1 rule="hyper" parents="58 12237 13860"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13925">
    <literal><![CDATA[
      K(x \ ((x \ 1) \ y),z) = K(y,z)
    ]]></literal>
    <justification jstring="[para(5(a,1),13860(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5 13860"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13926">
    <literal><![CDATA[
      K((1 / x) \ y,z) = K(y * x,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(320,a,12230,a,b,13863,a),flip(a)].">
      <j1 rule="hyper" parents="320 12230 13863"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13927">
    <literal><![CDATA[
      K((x \ K(y,z)) * y,u) = K(x \ T(y,z),u)
    ]]></literal>
    <justification jstring="[para(11591(a,1),13863(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11591 13863"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13928">
    <literal><![CDATA[
      (K(x,y) / z) \ 1 = z * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(188,a,13876,a)].">
      <j1 rule="hyper" parents="188 13876"/>
    </justification>
  </clause>

  <clause id="13929">
    <literal><![CDATA[
      T(K(x,y) / z,z * K(y,x)) = (z * K(y,x)) \ 1
    ]]></literal>
    <justification jstring="[para(13876(a,1),107(a,1,1))].">
      <j1 rule="para" parents="13876 107"/>
    </justification>
  </clause>

  <clause id="13934">
    <literal><![CDATA[
      K(x,y * (z / ((u * K(w,v5)) \ 1))) = K(x,y * (z / (K(v5,w) / u)))
    ]]></literal>
    <justification jstring="[para(13876(a,1),5335(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="13876 5335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13935">
    <literal><![CDATA[
      K(x,(y / (1 / (K(z,u) / w))) * v5) = K(x,(y / (w * K(u,z))) * v5)
    ]]></literal>
    <justification jstring="[para(13876(a,1),5914(a,1,2,1,2,2))].">
      <j1 rule="para" parents="13876 5914"/>
    </justification>
  </clause>

  <clause id="13936">
    <literal><![CDATA[
      1 / T(x * K(y,z),y) = K(z,y) / T(x,y)
    ]]></literal>
    <justification jstring="[para(7437(a,2),13876(a,1,2))].">
      <j1 rule="para" parents="7437 13876"/>
    </justification>
  </clause>

  <clause id="13937">
    <literal><![CDATA[
      K(x,y / (z * K(u,w))) = K(x,y * (K(w,u) / z))
    ]]></literal>
    <justification jstring="[para(13876(a,1),13839(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="13876 13839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13938">
    <literal><![CDATA[
      K(x,y / (K(z,u) / w)) = K(x,y * (w * K(u,z)))
    ]]></literal>
    <justification jstring="[para(13876(a,1),13841(a,1,2,2))].">
      <j1 rule="para" parents="13876 13841"/>
    </justification>
  </clause>

  <clause id="13940">
    <literal><![CDATA[
      T(x,(y \ 1) / z) = T(x,y \ (z \ 1))
    ]]></literal>
    <justification jstring="[hyper(58,a,13788,a(flip),b,13878,a)].">
      <j1 rule="hyper" parents="58 13788 13878"/>
    </justification>
  </clause>

  <clause id="13941">
    <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(13878(a,1),8060(a,1,2))].">
      <j1 rule="para" parents="13878 8060"/>
    </justification>
  </clause>

  <clause id="13942">
    <literal><![CDATA[
      T(x,(y * (z \ 1)) * z) = T(x,y)
    ]]></literal>
    <justification jstring="[para(6(a,1),13899(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6 13899"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13943">
    <literal><![CDATA[
      K(x,T(y,(z \ 1) / u)) = K(x,T(y,u * z))
    ]]></literal>
    <justification jstring="[para(13899(a,1),8237(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13899 8237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13944">
    <literal><![CDATA[
      K(x * (y * (x \ 1)),z) = K(y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(12244,a,13910,a)].">
      <j1 rule="hyper" parents="12244 13910"/>
    </justification>
  </clause>

  <clause id="13945">
    <literal><![CDATA[
      K(x,L(y,z \ 1,z)) = K(x,u * ((1 / u) * y))
    ]]></literal>
    <justification jstring="[hyper(320,a,13777,a,b,13914,a)].">
      <j1 rule="hyper" parents="320 13777 13914"/>
    </justification>
  </clause>

  <clause id="13946">
    <literal><![CDATA[
      K(x,(y \ z) * K(z,u)) = K(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[para(11585(a,1),13914(a,1,2,2))].">
      <j1 rule="para" parents="11585 13914"/>
    </justification>
  </clause>

  <clause id="13949">
    <literal><![CDATA[
      K(x \ ((x \ 1) \ y),z) = K(K(u,u \ 1) * y,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,3978,a,b,13925,a),flip(a)].">
      <j1 rule="hyper" parents="320 3978 13925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13950">
    <literal><![CDATA[
      ((x * ((x \ y) * K(x / y,y))) / x) \ 1 = x / (x * ((((x / (1 / (x \ y))) / x) \ 1) \ 1))
    ]]></literal>
    <justification jstring="[para(13928(a,1),10660(a,1,1,1,2))].">
      <j1 rule="para" parents="13928 10660"/>
    </justification>
  </clause>

  <clause id="13951">
    <literal><![CDATA[
      T(x * (a(y,z,u) \ 1),a(y,z,u)) = T(x * (a(y,z,u) \ 1),x)
    ]]></literal>
    <justification jstring="[hyper(58,a,12830,a(flip),b,13942,a)].">
      <j1 rule="hyper" parents="58 12830 13942"/>
    </justification>
  </clause>

  <clause id="13952">
    <literal><![CDATA[
      L(x,y / x,z) \ (z * y) = T(z * (y / x),x)
    ]]></literal>
    <justification jstring="[hyper(771,a,13685,a)].">
      <j1 rule="hyper" parents="771 13685"/>
    </justification>
  </clause>

  <clause id="13953">
    <literal><![CDATA[
      L(x \ y,x,z) \ (z * y) = T(z * x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(606,a,13685,a)].">
      <j1 rule="hyper" parents="606 13685"/>
    </justification>
  </clause>

  <clause id="13954">
    <literal><![CDATA[
      L(x,y,z) \ (z * (y * x)) = T(z * y,x)
    ]]></literal>
    <justification jstring="[hyper(546,a,13685,a)].">
      <j1 rule="hyper" parents="546 13685"/>
    </justification>
  </clause>

  <clause id="13955">
    <literal><![CDATA[
      L(x,y,z) * T(z * y,x) = z * (y * x)
    ]]></literal>
    <justification jstring="[hyper(119,a,13685,a(flip),b,470,a)].">
      <j1 rule="hyper" parents="119 13685 470"/>
    </justification>
  </clause>

  <clause id="13956">
    <literal><![CDATA[
      L(x,y,z) = (z * (y * x)) / T(z * y,x)
    ]]></literal>
    <justification jstring="[para(13685(a,1),469(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13685 469"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13957">
    <literal><![CDATA[
      T(x,(y \ z) \ y) = T(x,z \ (y * y))
    ]]></literal>
    <justification jstring="[hyper(118,a,13678,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 13678 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13958">
    <literal><![CDATA[
      K(x,L(y,z \ y,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(10905,a,13688,a)].">
      <j1 rule="hyper" parents="10905 13688"/>
    </justification>
  </clause>

  <clause id="13959">
    <literal><![CDATA[
      (x / y) * (y * K(z,x)) = x * K(z,x)
    ]]></literal>
    <justification jstring="[hyper(5802,a,13688,a)].">
      <j1 rule="hyper" parents="5802 13688"/>
    </justification>
  </clause>

  <clause id="13960">
    <literal><![CDATA[
      x \ (y * K(z,y)) = (x \ y) * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(123,a,13688,a)].">
      <j1 rule="hyper" parents="123 13688"/>
    </justification>
  </clause>

  <clause id="13961">
    <literal><![CDATA[
      x \ ((y * z) / y) = (x \ z) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(116,a,4752,a,b,13688,a)].">
      <j1 rule="hyper" parents="116 4752 13688"/>
    </justification>
  </clause>

  <clause id="13963">
    <literal><![CDATA[
      (x \ (y \ z)) * K(y,y \ z) = x \ (z / y)
    ]]></literal>
    <justification jstring="[hyper(116,a,4776,a(flip),b,13688,a),flip(a)].">
      <j1 rule="hyper" parents="116 4776 13688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13964">
    <literal><![CDATA[
      K(x,L(y * z,z,y)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(4(a,1),13958(a,1,2,2))].">
      <j1 rule="para" parents="4 13958"/>
    </justification>
  </clause>

  <clause id="13965">
    <literal><![CDATA[
      K((x * y) \ z,x * y) = K(y \ (x \ z),x * y)
    ]]></literal>
    <justification jstring="[hyper(10947,a,13964,a)].">
      <j1 rule="hyper" parents="10947 13964"/>
    </justification>
  </clause>

  <clause id="13966">
    <literal><![CDATA[
      (K(x,y) * (y / z)) * z = y * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(586,a,13698,a)].">
      <j1 rule="hyper" parents="586 13698"/>
    </justification>
  </clause>

  <clause id="13967">
    <literal><![CDATA[
      (x * K(y,x)) / z = K(y,x) * (x / z)
    ]]></literal>
    <justification jstring="[hyper(353,a,13698,a)].">
      <j1 rule="hyper" parents="353 13698"/>
    </justification>
  </clause>

  <clause id="13968">
    <literal><![CDATA[
      (1 / x) * ((K(y,z) / x) \ y) = y * K(z,y)
    ]]></literal>
    <justification jstring="[para(13746(a,1),13698(a,1,1))].">
      <j1 rule="para" parents="13746 13698"/>
    </justification>
  </clause>

  <clause id="13969">
    <literal><![CDATA[
      T(T(x,x \ (y * z)),u) \ T(x,u) = K((y \ x) \ z,T(x,u))
    ]]></literal>
    <justification jstring="[para(13700(a,1),4797(a,1,1,1))].">
      <j1 rule="para" parents="13700 4797"/>
    </justification>
  </clause>

  <clause id="13971">
    <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(439,a,6337,a(flip),b,13707,a)].">
      <j1 rule="hyper" parents="439 6337 13707"/>
    </justification>
  </clause>

  <clause id="13973">
    <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(5948(a,1),13710(a,1,2,1))].">
      <j1 rule="para" parents="5948 13710"/>
    </justification>
  </clause>

  <clause id="13975">
    <literal><![CDATA[
      (x * ((x * y) / x)) \ y = (x * y) \ T(y,x)
    ]]></literal>
    <justification jstring="[para(4092(a,1),13715(a,1,1))].">
      <j1 rule="para" parents="4092 13715"/>
    </justification>
  </clause>

  <clause id="13976">
    <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(7841(a,1),13715(a,2,2))].">
      <j1 rule="para" parents="7841 13715"/>
    </justification>
  </clause>

  <clause id="13977">
    <literal><![CDATA[
      K(x / y,z) * (y \ (y \ x)) = y \ T(y \ x,z)
    ]]></literal>
    <justification jstring="[para(7907(a,1),13718(a,1,1))].">
      <j1 rule="para" parents="7907 13718"/>
    </justification>
  </clause>

  <clause id="13979">
    <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(13719(a,1),12293(a,1,2,1,1))].">
      <j1 rule="para" parents="13719 12293"/>
    </justification>
  </clause>

  <clause id="13980">
    <literal><![CDATA[
      (x \ T(y * x,z)) / (x \ (y * x)) = K(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,12230,a(flip),b,13724,a),flip(a)].">
      <j1 rule="hyper" parents="320 12230 13724"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13981">
    <literal><![CDATA[
      L(x * K(y * x,z),y,z) = (z * y) \ ((y * x) * z)
    ]]></literal>
    <justification jstring="[para(13726(a,1),450(a,1,1))].">
      <j1 rule="para" parents="13726 450"/>
    </justification>
  </clause>

  <clause id="13983">
    <literal><![CDATA[
      (x \ T(x * y,z)) \ y != u
    ]]></literal>
    <literal><![CDATA[
      K(z,x * y) = u
    ]]></literal>
    <justification jstring="[para(13726(a,2),6345(a,1,1))].">
      <j1 rule="para" parents="13726 6345"/>
    </justification>
  </clause>

  <clause id="13986">
    <literal><![CDATA[
      K(x * K(y * x,z),T(u,y)) = K(y \ T(x * y,z),u)
    ]]></literal>
    <justification jstring="[para(13726(a,1),7219(a,1,1))].">
      <j1 rule="para" parents="13726 7219"/>
    </justification>
  </clause>

  <clause id="13988">
    <literal><![CDATA[
      x \ T(x * y,T(z,y)) = y * K(y * x,z)
    ]]></literal>
    <justification jstring="[para(12230(a,1),13726(a,2,2))].">
      <j1 rule="para" parents="12230 13726"/>
    </justification>
  </clause>

  <clause id="13989">
    <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(13743(a,1),5570(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="13743 5570"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13990">
    <literal><![CDATA[
      (1 / x) * K(y,z / x) = K(y,x \ z) / x
    ]]></literal>
    <justification jstring="[para(107(a,1),13747(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="107 13747"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13991">
    <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(13747(a,2),687(a,2,2))].">
      <j1 rule="para" parents="13747 687"/>
    </justification>
  </clause>

  <clause id="13992">
    <literal><![CDATA[
      ((1 / x) * K(y,z)) * K(u,x) = K(y,T(z,x)) / T(x,u)
    ]]></literal>
    <justification jstring="[para(13747(a,1),6322(a,1,1))].">
      <j1 rule="para" parents="13747 6322"/>
    </justification>
  </clause>

  <clause id="13993">
    <literal><![CDATA[
      T(x,(y * z) \ x) = T(x,z \ (y \ x))
    ]]></literal>
    <justification jstring="[hyper(118,a,13804,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 13804 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13994">
    <literal><![CDATA[
      K(x,x \ ((y \ x) * z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(13807(a,1),13127(a,1))].">
      <j1 rule="para" parents="13807 13127"/>
    </justification>
  </clause>

  <clause id="13995">
    <literal><![CDATA[
      T(x,(y * z) \ 1) = T(x,z \ (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(118,a,13808,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 13808 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13996">
    <literal><![CDATA[
      (x \ K(y,T(z,x))) \ 1 = (x \ 1) \ K(z,y)
    ]]></literal>
    <justification jstring="[para(13810(a,2),13773(a,1,1))].">
      <j1 rule="para" parents="13810 13773"/>
    </justification>
  </clause>

  <clause id="13997">
    <literal><![CDATA[
      K(x \ ((y \ x) * z),x) = K(y \ z,x)
    ]]></literal>
    <justification jstring="[hyper(8786,a,13814,a),flip(a)].">
      <j1 rule="hyper" parents="8786 13814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14000">
    <literal><![CDATA[
      (x * y) / (z \ (y * x)) = K(y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(197,a,13816,a)].">
      <j1 rule="hyper" parents="197 13816"/>
    </justification>
  </clause>

  <clause id="14001">
    <literal><![CDATA[
      (K(x,y) * z) \ (x * y) = z \ (y * x)
    ]]></literal>
    <justification jstring="[para(4(a,1),13816(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4 13816"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14002">
    <literal><![CDATA[
      (T(x,y) * z) \ (x * y) = (x * z) \ (y * x)
    ]]></literal>
    <justification jstring="[para(4782(a,1),13816(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4782 13816"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14003">
    <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(13830(a,1),9794(a,1,2,1,1))].">
      <j1 rule="para" parents="13830 9794"/>
    </justification>
  </clause>

  <clause id="14004">
    <literal><![CDATA[
      K(x,y) * (y / (z \ 1)) = y / (z \ K(y,x))
    ]]></literal>
    <justification jstring="[para(13812(a,1),13830(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13812 13830"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14005">
    <literal><![CDATA[
      K((x \ y) \ K(x,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(y \ T(x,z),u) = w
    ]]></literal>
    <justification jstring="[para(13834(a,1),6425(a,1,1))].">
      <j1 rule="para" parents="13834 6425"/>
    </justification>
  </clause>

  <clause id="14006">
    <literal><![CDATA[
      K(x,y * ((z \ u) \ K(z,w))) = K(x,y / (T(z,w) \ u))
    ]]></literal>
    <justification jstring="[para(13834(a,1),13759(a,1,2,2))].">
      <j1 rule="para" parents="13834 13759"/>
    </justification>
  </clause>

  <clause id="14007">
    <literal><![CDATA[
      T(x,y * ((z \ u) \ K(z,w))) = T(x,y / (T(z,w) \ u))
    ]]></literal>
    <justification jstring="[para(13834(a,1),13788(a,1,2,2))].">
      <j1 rule="para" parents="13834 13788"/>
    </justification>
  </clause>

  <clause id="14008">
    <literal><![CDATA[
      K(x,(y \ 1) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = u
    ]]></literal>
    <justification jstring="[para(13852(a,1),12301(a,1))].">
      <j1 rule="para" parents="13852 12301"/>
    </justification>
  </clause>

  <clause id="14009">
    <literal><![CDATA[
      K(x,(y \ x) * (x \ z)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(13127,a,13855,a),flip(a)].">
      <j1 rule="hyper" parents="13127 13855"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14010">
    <literal><![CDATA[
      x * (y * K(x * (z \ y),z)) = (z \ (x * y)) * z
    ]]></literal>
    <justification jstring="[para(13862(a,1),6415(a,1,2,2))].">
      <j1 rule="para" parents="13862 6415"/>
    </justification>
  </clause>

  <clause id="14011">
    <literal><![CDATA[
      (x * K(y,z)) * (y / x) = T(x * (y / x),z)
    ]]></literal>
    <justification jstring="[para(7(a,1),13869(a,1,1,2,1))].">
      <j1 rule="para" parents="7 13869"/>
    </justification>
  </clause>

  <clause id="14014">
    <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(439,a,6477,a,b,13907,a)].">
      <j1 rule="hyper" parents="439 6477 13907"/>
    </justification>
  </clause>

  <clause id="14015">
    <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(439,a,6189,a,b,13907,a)].">
      <j1 rule="hyper" parents="439 6189 13907"/>
    </justification>
  </clause>

  <clause id="14016">
    <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(439,a,3993,a,b,13907,a)].">
      <j1 rule="hyper" parents="439 3993 13907"/>
    </justification>
  </clause>

  <clause id="14017">
    <literal><![CDATA[
      K((1 / x) \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x * y,z) = u
    ]]></literal>
    <justification jstring="[para(13926(a,2),12244(a,1))].">
      <j1 rule="para" parents="13926 12244"/>
    </justification>
  </clause>

  <clause id="14018">
    <literal><![CDATA[
      K(x * (y * (x \ 1)),z) = K(y,T(z,x \ 1))
    ]]></literal>
    <justification jstring="[hyper(320,a,8227,a,b,13944,a),flip(a)].">
      <j1 rule="hyper" parents="320 8227 13944"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14019">
    <literal><![CDATA[
      ((x \ y) / z) \ (y / x) = z * K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(116,a,4776,a(flip),b,13959,a)].">
      <j1 rule="hyper" parents="116 4776 13959"/>
    </justification>
  </clause>

  <clause id="14021">
    <literal><![CDATA[
      (x \ (y * z)) * K(z,y * z) = x \ (L(z,y,z) * y)
    ]]></literal>
    <justification jstring="[para(4373(a,1),13961(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4373 13961"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14023">
    <literal><![CDATA[
      K(x,x \ y) * ((x \ y) / z) = (y / x) / z
    ]]></literal>
    <justification jstring="[hyper(117,a,4776,a(flip),b,13966,a),flip(a)].">
      <j1 rule="hyper" parents="117 4776 13966"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14024">
    <literal><![CDATA[
      T(K(x,y) * (y / T(z,K(x,y))),z) = z \ (y * T(K(x,y),z))
    ]]></literal>
    <justification jstring="[para(13967(a,1),6376(a,1,1))].">
      <j1 rule="para" parents="13967 6376"/>
    </justification>
  </clause>

  <clause id="14025">
    <literal><![CDATA[
      K(x \ (y * z),z) = K((x \ z) * y,z)
    ]]></literal>
    <justification jstring="[hyper(10785,a,13997,a),flip(a)].">
      <j1 rule="hyper" parents="10785 13997"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14026">
    <literal><![CDATA[
      (x * y) / (z \ (y * x)) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(320,a,5130,a(flip),b,14000,a),flip(a)].">
      <j1 rule="hyper" parents="320 5130 14000"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14027">
    <literal><![CDATA[
      K(x,y) * ((1 / x) * (y * x)) = L(y,x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(34,a,11684,a(flip),b,14001,a),flip(a)].">
      <j1 rule="hyper" parents="34 11684 14001"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14028">
    <literal><![CDATA[
      (K(x,x \ y) * z) \ y = z \ ((x \ y) * x)
    ]]></literal>
    <justification jstring="[para(5(a,1),14001(a,1,2))].">
      <j1 rule="para" parents="5 14001"/>
    </justification>
  </clause>

  <clause id="14029">
    <literal><![CDATA[
      K(x,K(y,(z \ y) * u)) = K(x,K(y,z \ u))
    ]]></literal>
    <justification jstring="[para(14009(a,1),10334(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14009 10334"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14030">
    <literal><![CDATA[
      K((x \ y) * z,y) = K(y * (x \ z),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,10492,a(flip),b,14025,a),flip(a)].">
      <j1 rule="hyper" parents="58 10492 14025"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14031">
    <literal><![CDATA[
      K(x,y) * ((y * x) / z) = (x * y) / z
    ]]></literal>
    <justification jstring="[para(75(a,1),14026(a,1,2)),flip(a)].">
      <j1 rule="para" parents="75 14026"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14032">
    <literal><![CDATA[
      K((x / y) * z,x) = K(x * (y \ z),x)
    ]]></literal>
    <justification jstring="[hyper(8787,a,14030,a)].">
      <j1 rule="hyper" parents="8787 14030"/>
    </justification>
  </clause>

  <clause id="14033">
    <literal><![CDATA[
      ((x * y) / z) \ T(x,y) = ((y * x) / z) \ x
    ]]></literal>
    <justification jstring="[para(14031(a,1),13696(a,1,1))].">
      <j1 rule="para" parents="14031 13696"/>
    </justification>
  </clause>

  <clause id="14034">
    <literal><![CDATA[
      ((x * y) / z) \ K(x,y) = ((y * x) / z) \ 1
    ]]></literal>
    <justification jstring="[para(14031(a,1),13756(a,1,1))].">
      <j1 rule="para" parents="14031 13756"/>
    </justification>
  </clause>

  <clause id="14035">
    <literal><![CDATA[
      K((x * y) * (T(x,y) \ z),x * y) = K(y * z,x * y)
    ]]></literal>
    <justification jstring="[para(187(a,1),14032(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="187 14032"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14036">
    <literal><![CDATA[
      L(a(x,y,z),u,K(w,v5)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(13666,a,13405,a)].">
      <j1 rule="hyper" parents="13666 13405"/>
    </justification>
  </clause>

  <clause id="14038">
    <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,10766,a,b,14036,a)].">
      <j1 rule="hyper" parents="58 10766 14036"/>
    </justification>
  </clause>

  <clause id="14039">
    <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,8111,a,b,14036,a)].">
      <j1 rule="hyper" parents="58 8111 14036"/>
    </justification>
  </clause>

  <clause id="14040">
    <literal><![CDATA[
      (T(x,y) * (z * u)) \ (K(x,y) * ((x * z) * u)) = a(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,5123,a,b,14036,a)].">
      <j1 rule="hyper" parents="58 5123 14036"/>
    </justification>
  </clause>

  <clause id="14041">
    <literal><![CDATA[
      (K(x,y) * z) * a(u,w,v5) = K(x,y) * (z * a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(119,a,14036,a(flip),b,4016,a(flip))].">
      <j1 rule="hyper" parents="119 14036 4016"/>
    </justification>
  </clause>

  <clause id="14042">
    <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(14036(a,1),25(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14036 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14043">
    <literal><![CDATA[
      (K(x,y) * z) / a(u,w,v5) = K(x,y) * (z / a(u,w,v5))
    ]]></literal>
    <justification jstring="[para(14036(a,1),544(a,1,2))].">
      <j1 rule="para" parents="14036 544"/>
    </justification>
  </clause>

  <clause id="14045">
    <literal><![CDATA[
      (K(x,y) * z) \ (x \ ((x * y) / x)) = z \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,5397,a(flip),b,13697,a)].">
      <j1 rule="hyper" parents="58 5397 13697"/>
    </justification>
  </clause>

  <clause id="14046">
    <literal><![CDATA[
      L(x \ (T(y,z) \ z),x,K(T(y,z),z)) = x \ (y \ T(z,y))
    ]]></literal>
    <justification jstring="[para(4248(a,1),13697(a,2,2))].">
      <j1 rule="para" parents="4248 13697"/>
    </justification>
  </clause>

  <clause id="14047">
    <literal><![CDATA[
      K(x,y) * (K(z,u) / u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y) / T(u,z) = w
    ]]></literal>
    <justification jstring="[para(4803(a,2),13739(a,1,2))].">
      <j1 rule="para" parents="4803 13739"/>
    </justification>
  </clause>

  <clause id="14048">
    <literal><![CDATA[
      L(K(x,y),z \ 1,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(13813(a,2),287(a,1)),flip(b)].">
      <j1 rule="para" parents="13813 287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14050">
    <literal><![CDATA[
      K(x,L(y,z \ 1,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(10794(a,1),14048(a,1))].">
      <j1 rule="para" parents="10794 14048"/>
    </justification>
  </clause>

  <clause id="14051">
    <literal><![CDATA[
      K(L(x,y \ 1,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) = u
    ]]></literal>
    <justification jstring="[para(10836(a,1),14048(a,1))].">
      <j1 rule="para" parents="10836 14048"/>
    </justification>
  </clause>

  <clause id="14052">
    <literal><![CDATA[
      K(x,L(y,z,z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(2862(a,1),14050(a,1,2))].">
      <j1 rule="para" parents="2862 14050"/>
    </justification>
  </clause>

  <clause id="14053">
    <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(6061(a,1),14050(a,1,2))].">
      <j1 rule="para" parents="6061 14050"/>
    </justification>
  </clause>

  <clause id="14054">
    <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(6061(a,1),14051(a,1,1))].">
      <j1 rule="para" parents="6061 14051"/>
    </justification>
  </clause>

  <clause id="14055">
    <literal><![CDATA[
      K(x,(1 / y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(2815(a,1),14052(a,1,2))].">
      <j1 rule="para" parents="2815 14052"/>
    </justification>
  </clause>

  <clause id="14056">
    <literal><![CDATA[
      K(x,R(y,z,z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(12353(a,2),14052(a,1))].">
      <j1 rule="para" parents="12353 14052"/>
    </justification>
  </clause>

  <clause id="14057">
    <literal><![CDATA[
      K(x,y * (z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y / z) = u
    ]]></literal>
    <justification jstring="[para(12354(a,1),14052(a,1))].">
      <j1 rule="para" parents="12354 14052"/>
    </justification>
  </clause>

  <clause id="14058">
    <literal><![CDATA[
      K(x,T(y * (z \ 1),u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y / z,u)) = w
    ]]></literal>
    <justification jstring="[para(612(a,1),14056(a,1,2))].">
      <j1 rule="para" parents="612 14056"/>
    </justification>
  </clause>

  <clause id="14059">
    <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(4266(a,1),13833(a,1,2))].">
      <j1 rule="para" parents="4266 13833"/>
    </justification>
  </clause>

  <clause id="14060">
    <literal><![CDATA[
      K((1 / x) * y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,z) = u
    ]]></literal>
    <justification jstring="[para(3981(a,2),13868(a,1))].">
      <j1 rule="para" parents="3981 13868"/>
    </justification>
  </clause>

  <clause id="14061">
    <literal><![CDATA[
      K((x \ K(y,z)) * y,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x \ T(y,z),u) = w
    ]]></literal>
    <justification jstring="[para(13892(a,2),13868(a,1,1))].">
      <j1 rule="para" parents="13892 13868"/>
    </justification>
  </clause>

  <clause id="14062">
    <literal><![CDATA[
      (x * (y * z)) / T(x * y,z) != u
    ]]></literal>
    <literal><![CDATA[
      L(z,y,x) = u
    ]]></literal>
    <justification jstring="[para(13954(a,1),330(a,1,2)),flip(b)].">
      <j1 rule="para" parents="13954 330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14064">
    <literal><![CDATA[
      L(x,y,z) * (x \ (z * y)) = (z * (y * x)) / x
    ]]></literal>
    <justification jstring="[hyper(117,a,13955,a(flip),b,10983,a),flip(a)].">
      <j1 rule="hyper" parents="117 13955 10983"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14066">
    <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(6322(a,1),13955(a,2,2))].">
      <j1 rule="para" parents="6322 13955"/>
    </justification>
  </clause>

  <clause id="14067">
    <literal><![CDATA[
      (x * (y * z)) * K(z,x * y) = L(z,y,x) * (x * y)
    ]]></literal>
    <justification jstring="[para(13955(a,1),6331(a,1,1))].">
      <j1 rule="para" parents="13955 6331"/>
    </justification>
  </clause>

  <clause id="14069">
    <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(4393(a,2),14008(a,1,2))].">
      <j1 rule="para" parents="4393 14008"/>
    </justification>
  </clause>

  <clause id="14070">
    <literal><![CDATA[
      K(x,(1 / y) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = u
    ]]></literal>
    <justification jstring="[para(5323(a,2),14008(a,1))].">
      <j1 rule="para" parents="5323 14008"/>
    </justification>
  </clause>

  <clause id="14071">
    <literal><![CDATA[
      K(x,y / T(z \ 1,z * (x * y))) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z * y) = u
    ]]></literal>
    <justification jstring="[para(11232(a,2),14008(a,1))].">
      <j1 rule="para" parents="11232 14008"/>
    </justification>
  </clause>

  <clause id="14072">
    <literal><![CDATA[
      K((x \ 1) \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x * y,z) = u
    ]]></literal>
    <justification jstring="[para(3982(a,1),14017(a,1))].">
      <j1 rule="para" parents="3982 14017"/>
    </justification>
  </clause>

  <clause id="14073">
    <literal><![CDATA[
      K(x,(y \ 1) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(5322(a,1),14055(a,1))].">
      <j1 rule="para" parents="5322 14055"/>
    </justification>
  </clause>

  <clause id="14074">
    <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(13818(a,1),14055(a,1,2,1))].">
      <j1 rule="para" parents="13818 14055"/>
    </justification>
  </clause>

  <clause id="14075">
    <literal><![CDATA[
      K(x,y * (z \ K(u,z))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(4804(a,1),14057(a,1,2,2))].">
      <j1 rule="para" parents="4804 14057"/>
    </justification>
  </clause>

  <clause id="14076">
    <literal><![CDATA[
      K(x,y * (1 / z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y / z) = u
    ]]></literal>
    <justification jstring="[para(5315(a,2),14057(a,1))].">
      <j1 rule="para" parents="5315 14057"/>
    </justification>
  </clause>

  <clause id="14077">
    <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(13834(a,1),14057(a,1,2,2))].">
      <j1 rule="para" parents="13834 14057"/>
    </justification>
  </clause>

  <clause id="14078">
    <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(1953(a,1),14070(a,1,2))].">
      <j1 rule="para" parents="1953 14070"/>
    </justification>
  </clause>

  <clause id="14079">
    <literal><![CDATA[
      K(x / (1 / y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x * y,z) = u
    ]]></literal>
    <justification jstring="[para(13911(a,2),14072(a,1))].">
      <j1 rule="para" parents="13911 14072"/>
    </justification>
  </clause>

  <clause id="14080">
    <literal><![CDATA[
      K(x,((y \ 1) \ 1) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(13775(a,2),14073(a,1))].">
      <j1 rule="para" parents="13775 14073"/>
    </justification>
  </clause>

  <clause id="14081">
    <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(13928(a,1),14073(a,1,2,1))].">
      <j1 rule="para" parents="13928 14073"/>
    </justification>
  </clause>

  <clause id="14082">
    <literal><![CDATA[
      K(x / y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x * (y \ 1),z) = u
    ]]></literal>
    <justification jstring="[para(72(a,1),14079(a,1,1,2))].">
      <j1 rule="para" parents="72 14079"/>
    </justification>
  </clause>

  <clause id="14083">
    <literal><![CDATA[
      K(x * (1 / (1 / y)),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x * y,z) = u
    ]]></literal>
    <justification jstring="[para(13842(a,2),14079(a,1))].">
      <j1 rule="para" parents="13842 14079"/>
    </justification>
  </clause>

  <clause id="14084">
    <literal><![CDATA[
      K(x * (1 / y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x * (y \ 1),z) = u
    ]]></literal>
    <justification jstring="[para(13842(a,2),14082(a,1))].">
      <j1 rule="para" parents="13842 14082"/>
    </justification>
  </clause>

  <clause id="14085">
    <literal><![CDATA[
      T(x,y) * (z * K(x * y,z)) = (y \ T(x * y,z)) * z
    ]]></literal>
    <justification jstring="[para(13705(a,1),6090(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13705 6090"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14086">
    <literal><![CDATA[
      (x \ y) / (x \ T(y,z)) = K(z,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(320,a,8233,a(flip),b,13735,a),flip(a)].">
      <j1 rule="hyper" parents="320 8233 13735"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14087">
    <literal><![CDATA[
      T(1 / (x * K(y,z)),K(z,y)) = (1 / x) * K(z,y)
    ]]></literal>
    <justification jstring="[para(13876(a,2),13751(a,1,1))].">
      <j1 rule="para" parents="13876 13751"/>
    </justification>
  </clause>

  <clause id="14091">
    <literal><![CDATA[
      T(x,T((y \ 1) * z,u)) = T(x,T(y \ z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,4638,a(flip),b,13803,a)].">
      <j1 rule="hyper" parents="58 4638 13803"/>
    </justification>
  </clause>

  <clause id="14092">
    <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,12088,a(flip),b,13811,a)].">
      <j1 rule="hyper" parents="58 12088 13811"/>
    </justification>
  </clause>

  <clause id="14093">
    <literal><![CDATA[
      ((x * K(y,z)) \ u) \ K(x,K(y,z)) = ((K(y,z) * x) \ u) \ 1
    ]]></literal>
    <justification jstring="[para(7796(a,1),13836(a,1,2))].">
      <j1 rule="para" parents="7796 13836"/>
    </justification>
  </clause>

  <clause id="14094">
    <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(4319(a,1),13870(a,1,1,2,1))].">
      <j1 rule="para" parents="4319 13870"/>
    </justification>
  </clause>

  <clause id="14095">
    <literal><![CDATA[
      T(x * K(x * y,z),y) = y \ T(x * y,T(z,x))
    ]]></literal>
    <justification jstring="[para(12230(a,1),13870(a,1,1,2))].">
      <j1 rule="para" parents="12230 13870"/>
    </justification>
  </clause>

  <clause id="14096">
    <literal><![CDATA[
      K(x \ (y / (x \ 1)),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,T(z,x)) = u
    ]]></literal>
    <justification jstring="[para(13924(a,2),8271(a,1))].">
      <j1 rule="para" parents="13924 8271"/>
    </justification>
  </clause>

  <clause id="14098">
    <literal><![CDATA[
      K(x,y / (T(z \ (u \ w),x) * K(u,u \ w))) = K(x,y / (z \ (w / u)))
    ]]></literal>
    <justification jstring="[para(13963(a,1),8872(a,2,2,2))].">
      <j1 rule="para" parents="13963 8872"/>
    </justification>
  </clause>

  <clause id="14100">
    <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(13968(a,1),10874(a,2,2,1))].">
      <j1 rule="para" parents="13968 10874"/>
    </justification>
  </clause>

  <clause id="14102">
    <literal><![CDATA[
      (x \ 1) \ K(y,T(z,x)) = (x \ K(z,y)) \ 1
    ]]></literal>
    <justification jstring="[para(7888(a,1),13996(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7888 13996"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14103">
    <literal><![CDATA[
      K(x * (y * (x \ 1)),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,T(z,x)) = u
    ]]></literal>
    <justification jstring="[para(14018(a,2),8271(a,1))].">
      <j1 rule="para" parents="14018 8271"/>
    </justification>
  </clause>

  <clause id="14105">
    <literal><![CDATA[
      ((x \ y) * z) \ ((x \ y) * x) = ((y / x) * z) \ y
    ]]></literal>
    <justification jstring="[para(5459(a,1),14028(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5459 14028"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14106">
    <literal><![CDATA[
      K(x,((y \ z) * u) \ z) * K(x,K(z,y \ u)) = K(x,z / ((y \ z) * u))
    ]]></literal>
    <justification jstring="[para(14029(a,1),8376(a,1,2))].">
      <j1 rule="para" parents="14029 8376"/>
    </justification>
  </clause>

  <clause id="14107">
    <literal><![CDATA[
      K(x,K(y,z \ u)) * K(x,y \ ((z \ y) * u)) = K(x,((z \ y) * u) / y)
    ]]></literal>
    <justification jstring="[para(14029(a,1),8387(a,1,1))].">
      <j1 rule="para" parents="14029 8387"/>
    </justification>
  </clause>

  <clause id="14108">
    <literal><![CDATA[
      ((x * T(y,x)) / z) \ T(x,T(y,x)) = ((y * ((y * x) / y)) / z) \ x
    ]]></literal>
    <justification jstring="[para(4092(a,1),14033(a,2,1,1))].">
      <j1 rule="para" parents="4092 14033"/>
    </justification>
  </clause>

  <clause id="14109">
    <literal><![CDATA[
      K(x,(((y * z) / u) \ T(K(y,z),x)) \ w) = K(x,(((z * y) / u) \ 1) \ w)
    ]]></literal>
    <justification jstring="[para(14034(a,1),8554(a,2,2,1))].">
      <j1 rule="para" parents="14034 8554"/>
    </justification>
  </clause>

  <clause id="14110">
    <literal><![CDATA[
      T(x,T((y \ 1) * z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(14091(a,2),4374(a,1))].">
      <j1 rule="para" parents="14091 4374"/>
    </justification>
  </clause>

  <clause id="14111">
    <literal><![CDATA[
      ((x \ 1) \ K(y,z)) * K(x,K(y,z)) = (x \ K(z,y)) \ 1
    ]]></literal>
    <justification jstring="[hyper(58,a,12351,a,b,14102,a)].">
      <j1 rule="hyper" parents="58 12351 14102"/>
    </justification>
  </clause>

  <clause id="14112">
    <literal><![CDATA[
      K(x,y * ((1 / y) * z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) = u
    ]]></literal>
    <justification jstring="[para(13945(a,1),6499(a,1))].">
      <j1 rule="para" parents="13945 6499"/>
    </justification>
  </clause>

  <clause id="14113">
    <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(5258(a,1),14112(a,1,2,2))].">
      <j1 rule="para" parents="5258 14112"/>
    </justification>
  </clause>

  <clause id="14114">
    <literal><![CDATA[
      K(x,(y \ z) * K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(11585(a,1),14112(a,1,2,2))].">
      <j1 rule="para" parents="11585 14112"/>
    </justification>
  </clause>

  <clause id="14115">
    <literal><![CDATA[
      L(x,x \ y,z) \ (z * y) = T(z * (y / x),x)
    ]]></literal>
    <justification jstring="[para(10416(a,1),13952(a,1,1))].">
      <j1 rule="para" parents="10416 13952"/>
    </justification>
  </clause>

  <clause id="14116">
    <literal><![CDATA[
      K(x,T(y * z,z \ u)) = K(x,T(y * z,y * u))
    ]]></literal>
    <justification jstring="[para(13953(a,1),7142(a,1,2))].">
      <j1 rule="para" parents="13953 7142"/>
    </justification>
  </clause>

  <clause id="14117">
    <literal><![CDATA[
      K(x,y \ (z * x)) = K(x,(y \ x) * z)
    ]]></literal>
    <justification jstring="[hyper(13994,a,10337,a)].">
      <j1 rule="hyper" parents="13994 10337"/>
    </justification>
  </clause>

  <clause id="14118">
    <literal><![CDATA[
      K(x,(y \ x) * z) = K(x,x * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(10504,a,14117,a),flip(a)].">
      <j1 rule="hyper" parents="10504 14117"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14120">
    <literal><![CDATA[
      T(x,(y \ x) * z) = T(x,x * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(118,a,14118,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 14118 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14122">
    <literal><![CDATA[
      (K(x,y) / x) * (y * x) = L(y,x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(13316,a,14027,a)].">
      <j1 rule="hyper" parents="13316 14027"/>
    </justification>
  </clause>

  <clause id="14123">
    <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(2165(a,1),14080(a,1,2,1))].">
      <j1 rule="para" parents="2165 14080"/>
    </justification>
  </clause>

  <clause id="14124">
    <literal><![CDATA[
      T(x,(y \ 1) * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(4233(a,1),14110(a,1))].">
      <j1 rule="para" parents="4233 14110"/>
    </justification>
  </clause>

  <clause id="14125">
    <literal><![CDATA[
      T(x,((y \ 1) \ 1) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(13802(a,2),14124(a,1))].">
      <j1 rule="para" parents="13802 14124"/>
    </justification>
  </clause>

  <clause id="14126">
    <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(13928(a,1),14124(a,1,2,1))].">
      <j1 rule="para" parents="13928 14124"/>
    </justification>
  </clause>

  <clause id="14127">
    <literal><![CDATA[
      L(x,x \ (x * y),z) \ (z * (x * y)) = T(z * (y * K(x,y)),x)
    ]]></literal>
    <justification jstring="[para(4752(a,1),14115(a,2,1,2))].">
      <j1 rule="para" parents="4752 14115"/>
    </justification>
  </clause>

  <clause id="14128">
    <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(6462(a,1),14115(a,1,2))].">
      <j1 rule="para" parents="6462 14115"/>
    </justification>
  </clause>

  <clause id="14129">
    <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(2648(a,1),14125(a,1,2,1))].">
      <j1 rule="para" parents="2648 14125"/>
    </justification>
  </clause>

  <clause id="14130">
    <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(3071(a,2),14125(a,1,2,1))].">
      <j1 rule="para" parents="3071 14125"/>
    </justification>
  </clause>

  <clause id="14131">
    <literal><![CDATA[
      K(x,y * (z * K(u,y * z))) = K(x,T(y * z,u))
    ]]></literal>
    <justification jstring="[para(13679(a,1),7916(a,1,2))].">
      <j1 rule="para" parents="13679 7916"/>
    </justification>
  </clause>

  <clause id="14132">
    <literal><![CDATA[
      L(x \ y,x,z / T(y,z)) = ((z / y) * x) \ z
    ]]></literal>
    <justification jstring="[hyper(4270,a,13716,a)].">
      <j1 rule="hyper" parents="4270 13716"/>
    </justification>
  </clause>

  <clause id="14133">
    <literal><![CDATA[
      L(x \ y,x,y \ z) = ((z / y) * x) \ z
    ]]></literal>
    <justification jstring="[hyper(58,a,12605,a(flip),b,14132,a)].">
      <j1 rule="hyper" parents="58 12605 14132"/>
    </justification>
  </clause>

  <clause id="14134">
    <literal><![CDATA[
      x / L(y \ z,y,z \ x) = (x / z) * y
    ]]></literal>
    <justification jstring="[hyper(197,a,14133,a(flip))].">
      <j1 rule="hyper" parents="197 14133"/>
    </justification>
  </clause>

  <clause id="14136">
    <literal><![CDATA[
      x / L(y,z,(z * y) \ x) = (x / (z * y)) * z
    ]]></literal>
    <justification jstring="[para(4(a,1),14134(a,1,2,1))].">
      <j1 rule="para" parents="4 14134"/>
    </justification>
  </clause>

  <clause id="14137">
    <literal><![CDATA[
      (x \ y) / (K(z,x) \ y) = ((x \ y) / y) * K(z,x)
    ]]></literal>
    <justification jstring="[para(13313(a,1),14134(a,1,2))].">
      <j1 rule="para" parents="13313 14134"/>
    </justification>
  </clause>

  <clause id="14138">
    <literal><![CDATA[
      x / K(y,L(z,u,(u * K(y,z)) \ x)) = (x / (u * K(y,z))) * u
    ]]></literal>
    <justification jstring="[para(10794(a,1),14136(a,1,2))].">
      <j1 rule="para" parents="10794 14136"/>
    </justification>
  </clause>

  <clause id="14139">
    <literal><![CDATA[
      K(x,L((y \ 1) \ z,u,w)) = K(x,L(y * z,u,w))
    ]]></literal>
    <justification jstring="[para(72(a,1),13776(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="72 13776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14140">
    <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(2166(a,1),13776(a,1,2,1,1))].">
      <j1 rule="para" parents="2166 13776"/>
    </justification>
  </clause>

  <clause id="14141">
    <literal><![CDATA[
      ((x * y) / x) * R(x,z,z \ 1) = R(x,z,z \ 1) * y
    ]]></literal>
    <justification jstring="[para(224(a,1),13787(a,1,2)),flip(a)].">
      <j1 rule="para" parents="224 13787"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14142">
    <literal><![CDATA[
      ((x * y) / x) * L(x,z,z \ 1) = L(x,z,z \ 1) * y
    ]]></literal>
    <justification jstring="[para(224(a,1),13800(a,1,2)),flip(a)].">
      <j1 rule="para" parents="224 13800"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14143">
    <literal><![CDATA[
      T(x,(y / z) \ K(u,y)) = T(x,z / T(y,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,4456,a(flip),b,13831,a),flip(a)].">
      <j1 rule="hyper" parents="58 4456 13831"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14144">
    <literal><![CDATA[
      T(x,(y \ z) / T(z,u)) = T(x,y \ K(u,z))
    ]]></literal>
    <justification jstring="[para(72(a,1),14143(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="72 14143"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14145">
    <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(13856(a,2),10837(a,1))].">
      <j1 rule="para" parents="13856 10837"/>
    </justification>
  </clause>

  <clause id="14146">
    <literal><![CDATA[
      (x \ (y * z)) * K(x * (y \ (x \ (y * z))),y) = x \ (z * y)
    ]]></literal>
    <justification jstring="[hyper(30,a,4662,a(flip),b,13874,a),flip(a)].">
      <j1 rule="hyper" parents="30 4662 13874"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14147">
    <literal><![CDATA[
      (K(x,y) * z) \ K(x,K(y,u)) = z \ K(y,T(x,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,12350,a(flip),b,13898,a),flip(a)].">
      <j1 rule="hyper" parents="320 12350 13898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14148">
    <literal><![CDATA[
      K(x,T(y * (1 / z),u)) = K(x,T(y / z,u))
    ]]></literal>
    <justification jstring="[hyper(7938,a,13904,a),flip(a)].">
      <j1 rule="hyper" parents="7938 13904"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14149">
    <literal><![CDATA[
      K(x,T(y * (1 / z),u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y / z,u)) = w
    ]]></literal>
    <justification jstring="[para(13904(a,1),7938(a,1))].">
      <j1 rule="para" parents="13904 7938"/>
    </justification>
  </clause>

  <clause id="14150">
    <literal><![CDATA[
      K(x,T(y / (z \ 1),u)) = K(x,T(y * z,u))
    ]]></literal>
    <justification jstring="[para(72(a,1),14148(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="72 14148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14151">
    <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(13908(a,2),10837(a,1))].">
      <j1 rule="para" parents="13908 10837"/>
    </justification>
  </clause>

  <clause id="14152">
    <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(13916(a,2),10837(a,1))].">
      <j1 rule="para" parents="13916 10837"/>
    </justification>
  </clause>

  <clause id="14155">
    <literal><![CDATA[
      K(x \ ((x \ 1) \ y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) = u
    ]]></literal>
    <justification jstring="[para(13949(a,2),7357(a,1))].">
      <j1 rule="para" parents="13949 7357"/>
    </justification>
  </clause>

  <clause id="14156">
    <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(6147(a,1),14155(a,1,1,2))].">
      <j1 rule="para" parents="6147 14155"/>
    </justification>
  </clause>

  <clause id="14157">
    <literal><![CDATA[
      (x \ T(y * x,z)) / T(y,x) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(17(a,2),13980(a,1,2))].">
      <j1 rule="para" parents="17 13980"/>
    </justification>
  </clause>

  <clause id="14158">
    <literal><![CDATA[
      K(x * y,z) * T(y,x) = x \ T(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(133,a,14157,a)].">
      <j1 rule="hyper" parents="133 14157"/>
    </justification>
  </clause>

  <clause id="14159">
    <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(14157(a,1),530(a,1,1))].">
      <j1 rule="para" parents="14157 530"/>
    </justification>
  </clause>

  <clause id="14160">
    <literal><![CDATA[
      T(x,y * (T(z,u) \ K(w,u * z))) = T(x,y / (u \ T(z * u,w)))
    ]]></literal>
    <justification jstring="[para(14158(a,1),13859(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="14158 13859"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14161">
    <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(7897(a,1),14062(a,1,1,2))].">
      <j1 rule="para" parents="7897 14062"/>
    </justification>
  </clause>

  <clause id="14162">
    <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(11152(a,1),14062(a,1,2,1))].">
      <j1 rule="para" parents="11152 14062"/>
    </justification>
  </clause>

  <clause id="14163">
    <literal><![CDATA[
      1 / (K(x,y) * z) = (1 / z) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,8226,a(flip),b,14087,a)].">
      <j1 rule="hyper" parents="58 8226 14087"/>
    </justification>
  </clause>

  <clause id="14164">
    <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(14163(a,1),13739(a,1,2))].">
      <j1 rule="para" parents="14163 13739"/>
    </justification>
  </clause>

  <clause id="14165">
    <literal><![CDATA[
      ((x / y) * (y * K(z,u))) \ x = K(u,L(z,y,y \ x))
    ]]></literal>
    <justification jstring="[hyper(10869,a,14105,a),flip(a)].">
      <j1 rule="hyper" parents="10869 14105"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14166">
    <literal><![CDATA[
      K(x,y * (((z * y) \ u) * K(z,z \ u))) = K(x,T(y * ((z * y) \ u),z))
    ]]></literal>
    <justification jstring="[para(12453(a,1),14131(a,1,2,2,2))].">
      <j1 rule="para" parents="12453 14131"/>
    </justification>
  </clause>

  <clause id="14167">
    <literal><![CDATA[
      (x \ y) / (K(x,z) * y) = ((x \ y) / y) * K(z,x)
    ]]></literal>
    <justification jstring="[para(5130(a,1),14137(a,1,2))].">
      <j1 rule="para" parents="5130 14137"/>
    </justification>
  </clause>

  <clause id="14168">
    <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,10833,a(flip),b,14139,a),flip(a)].">
      <j1 rule="hyper" parents="58 10833 14139"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14169">
    <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(3558(a,1),14005(a,1,1,2))].">
      <j1 rule="para" parents="3558 14005"/>
    </justification>
  </clause>

  <clause id="14170">
    <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(4118(a,2),14005(a,1,1,1))].">
      <j1 rule="para" parents="4118 14005"/>
    </justification>
  </clause>

  <clause id="14171">
    <literal><![CDATA[
      L(a(x,y,z),u,K(w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = v6
    ]]></literal>
    <justification jstring="[para(14042(a,1),9901(a,1)),flip(b)].">
      <j1 rule="para" parents="14042 9901"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14172">
    <literal><![CDATA[
      (T(x * y,z) * L(u,y,x)) \ (T(x * y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,u) = w
    ]]></literal>
    <justification jstring="[para(10766(a,2),14171(a,1))].">
      <j1 rule="para" parents="10766 14171"/>
    </justification>
  </clause>

  <clause id="14174">
    <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(14165(a,1),330(a,1,2)),flip(b)].">
      <j1 rule="para" parents="14165 330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14175">
    <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(6153(a,1),13817(a,1,2,1))].">
      <j1 rule="para" parents="6153 13817"/>
    </justification>
  </clause>

  <clause id="14176">
    <literal><![CDATA[
      K(x,(y \ z) * T(u,z \ y)) = K(x,u * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(320,a,13840,a(flip),b,13851,a),flip(a)].">
      <j1 rule="hyper" parents="320 13840 13851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14177">
    <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),14176(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="176 14176"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14178">
    <literal><![CDATA[
      K(x,y * (T(1 / y,z) * u)) = K(x,K(y \ 1,z) * u)
    ]]></literal>
    <justification jstring="[para(3312(a,1),13915(a,2,2,1))].">
      <j1 rule="para" parents="3312 13915"/>
    </justification>
  </clause>

  <clause id="14179">
    <literal><![CDATA[
      (K(x,y) * (z \ 1)) \ K(z,K(y,x)) = (z \ K(x,y)) \ 1
    ]]></literal>
    <justification jstring="[hyper(58,a,13898,a,b,14111,a)].">
      <j1 rule="hyper" parents="58 13898 14111"/>
    </justification>
  </clause>

  <clause id="14180">
    <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,14141,a),flip(a)].">
      <j1 rule="hyper" parents="320 238 14141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14181">
    <literal><![CDATA[
      (L(x,y,y \ 1) * z) / L(x,y,y \ 1) = (x * z) / x
    ]]></literal>
    <justification jstring="[hyper(131,a,14142,a)].">
      <j1 rule="hyper" parents="131 14142"/>
    </justification>
  </clause>

  <clause id="14182">
    <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(13720(a,1),14181(a,2,1))].">
      <j1 rule="para" parents="13720 14181"/>
    </justification>
  </clause>

  <clause id="14184">
    <literal><![CDATA[
      K(x,y) * ((y / z) * (z * x)) = L(x,z,z \ y) * y
    ]]></literal>
    <justification jstring="[hyper(13846,a,13791,a)].">
      <j1 rule="hyper" parents="13846 13791"/>
    </justification>
  </clause>

  <clause id="14187">
    <literal><![CDATA[
      (x * (y * z)) \ (K(x,y) * ((x * T(y,x)) * z)) = a(x,T(y,x),z)
    ]]></literal>
    <justification jstring="[para(4553(a,1),14040(a,1,1))].">
      <j1 rule="para" parents="4553 14040"/>
    </justification>
  </clause>

  <clause id="14188">
    <literal><![CDATA[
      L(x \ (T(y,z) \ z),x,K(y,z)) = x \ (y \ T(z,y))
    ]]></literal>
    <justification jstring="[para(4958(a,1),14046(a,1,3))].">
      <j1 rule="para" parents="4958 14046"/>
    </justification>
  </clause>

  <clause id="14189">
    <literal><![CDATA[
      (K(x,y) * z) \ (x \ y) = z \ (x \ T(y,x))
    ]]></literal>
    <justification jstring="[hyper(58,a,5226,a(flip),b,14188,a)].">
      <j1 rule="hyper" parents="58 5226 14188"/>
    </justification>
  </clause>

  <clause id="14190">
    <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(10143(a,1),14151(a,1,2,1,2))].">
      <j1 rule="para" parents="10143 14151"/>
    </justification>
  </clause>

  <clause id="14191">
    <literal><![CDATA[
      K(x,L(y,z \ u,z) * u) = K(x,z * ((z \ T(u,y)) * y))
    ]]></literal>
    <justification jstring="[para(10960(a,1),13701(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10960 13701"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14192">
    <literal><![CDATA[
      (K(x,y) * (z \ x)) \ K(x,K(y,z \ x)) = (z \ T(x,y)) \ 1
    ]]></literal>
    <justification jstring="[para(7755(a,1),13730(a,1,2))].">
      <j1 rule="para" parents="7755 13730"/>
    </justification>
  </clause>

  <clause id="14193">
    <literal><![CDATA[
      (T(x,y) / z) \ K(x,K(y,x / z)) = ((x / z) * K(x,y)) \ 1
    ]]></literal>
    <justification jstring="[para(7755(a,1),13744(a,1,2))].">
      <j1 rule="para" parents="7755 13744"/>
    </justification>
  </clause>

  <clause id="14194">
    <literal><![CDATA[
      ((K(x,y) * z) / K(x,y)) \ T(y,x) = (z * K(x,y)) \ y
    ]]></literal>
    <justification jstring="[para(7863(a,1),13819(a,2,1))].">
      <j1 rule="para" parents="7863 13819"/>
    </justification>
  </clause>

  <clause id="14195">
    <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(13906(a,2),14149(a,1))].">
      <j1 rule="para" parents="13906 14149"/>
    </justification>
  </clause>

  <clause id="14196">
    <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(13969(a,1),5025(a,1))].">
      <j1 rule="para" parents="13969 5025"/>
    </justification>
  </clause>

  <clause id="14197">
    <literal><![CDATA[
      K(x \ (y * z),T(x,y)) = K(z / (y \ x),x)
    ]]></literal>
    <justification jstring="[hyper(14196,a,8244,a)].">
      <j1 rule="hyper" parents="14196 8244"/>
    </justification>
  </clause>

  <clause id="14198">
    <literal><![CDATA[
      K(x / (y \ z),z) = K(z \ (x * y),z)
    ]]></literal>
    <justification jstring="[hyper(58,a,13148,a(flip),b,14197,a),flip(a)].">
      <j1 rule="hyper" parents="58 13148 14197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14199">
    <literal><![CDATA[
      K(x \ (y * (x / z)),x) = K(y / z,x)
    ]]></literal>
    <justification jstring="[para(75(a,1),14198(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="75 14198"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14200">
    <literal><![CDATA[
      K(x / (y \ z),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x * (z \ y),z) = u
    ]]></literal>
    <justification jstring="[para(14198(a,2),10429(a,1))].">
      <j1 rule="para" parents="14198 10429"/>
    </justification>
  </clause>

  <clause id="14201">
    <literal><![CDATA[
      T(K(x,y) * T(y / z,K(x,y)),z) = z \ (y * T(K(x,y),z))
    ]]></literal>
    <justification jstring="[para(8355(a,1),14024(a,1,1,2))].">
      <j1 rule="para" parents="8355 14024"/>
    </justification>
  </clause>

  <clause id="14203">
    <literal><![CDATA[
      ((x * K(y,z)) \ 1) \ K(x,K(y,z)) = (x \ K(z,y)) \ 1
    ]]></literal>
    <justification jstring="[para(13773(a,1),14093(a,2,1))].">
      <j1 rule="para" parents="13773 14093"/>
    </justification>
  </clause>

  <clause id="14204">
    <literal><![CDATA[
      (x * K(y,z)) \ 1 = K(z,y) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(34,a,14179,a,b,14203,a),flip(a)].">
      <j1 rule="hyper" parents="34 14179 14203"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14205">
    <literal><![CDATA[
      T(K(x,y) / z,z * K(y,x)) = K(x,y) * (z \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,13929,a,b,14204,a)].">
      <j1 rule="hyper" parents="58 13929 14204"/>
    </justification>
  </clause>

  <clause id="14207">
    <literal><![CDATA[
      K(x,y \ (R(x,z,u) * w)) = K(x,y \ (w * R(x,z,u)))
    ]]></literal>
    <justification jstring="[para(14146(a,1),7560(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14146 7560"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14208">
    <literal><![CDATA[
      (x \ (y * z)) * K(y \ (y * z),y) = x \ (z * y)
    ]]></literal>
    <justification jstring="[para(10430(a,1),14146(a,1,2))].">
      <j1 rule="para" parents="10430 14146"/>
    </justification>
  </clause>

  <clause id="14209">
    <literal><![CDATA[
      (x \ (y * z)) * K(z,y) = x \ (z * y)
    ]]></literal>
    <justification jstring="[para(4(a,1),14208(a,1,2,1))].">
      <j1 rule="para" parents="4 14208"/>
    </justification>
  </clause>

  <clause id="14211">
    <literal><![CDATA[
      ((x * y) / z) \ (y * x) = z * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(620,a,14209,a),flip(a)].">
      <j1 rule="hyper" parents="620 14209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14212">
    <literal><![CDATA[
      (x \ (y * z)) / (y * z) = (x \ (z * y)) / (z * y)
    ]]></literal>
    <justification jstring="[hyper(117,a,14209,a(flip),b,10380,a)].">
      <j1 rule="hyper" parents="117 14209 10380"/>
    </justification>
  </clause>

  <clause id="14213">
    <literal><![CDATA[
      (x \ y) * K(z \ y,z) = x \ ((z \ y) * z)
    ]]></literal>
    <justification jstring="[para(5(a,1),14209(a,1,1,2))].">
      <j1 rule="para" parents="5 14209"/>
    </justification>
  </clause>

  <clause id="14215">
    <literal><![CDATA[
      (a(x,y,a(z,u,w)) * (v5 * v6)) \ (v6 * v5) = (a(x,y,a(z,u,w)) \ 1) * K(v6,v5)
    ]]></literal>
    <justification jstring="[para(13455(a,1),14209(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13455 14209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14216">
    <literal><![CDATA[
      (x * y) / (z * K(x,y)) = (y * x) / z
    ]]></literal>
    <justification jstring="[hyper(197,a,14211,a)].">
      <j1 rule="hyper" parents="197 14211"/>
    </justification>
  </clause>

  <clause id="14217">
    <literal><![CDATA[
      x / (y * K(x / z,z)) = (z * (x / z)) / y
    ]]></literal>
    <justification jstring="[para(14211(a,1),324(a,1,2))].">
      <j1 rule="para" parents="14211 324"/>
    </justification>
  </clause>

  <clause id="14218">
    <literal><![CDATA[
      (x * y) / (z * K(y,x)) = K(x,y) * ((x * y) / z)
    ]]></literal>
    <justification jstring="[para(14211(a,1),14026(a,1,2))].">
      <j1 rule="para" parents="14211 14026"/>
    </justification>
  </clause>

  <clause id="14219">
    <literal><![CDATA[
      (x * y) / (z * K(y,T(x,y))) = (T(x,y) * y) / z
    ]]></literal>
    <justification jstring="[para(105(a,1),14216(a,1,1))].">
      <j1 rule="para" parents="105 14216"/>
    </justification>
  </clause>

  <clause id="14220">
    <literal><![CDATA[
      (x * y) / (z * T(x,y)) = (y * x) / (z * x)
    ]]></literal>
    <justification jstring="[para(6116(a,1),14216(a,1,2))].">
      <j1 rule="para" parents="6116 14216"/>
    </justification>
  </clause>

  <clause id="14221">
    <literal><![CDATA[
      x / (y * K(z \ x,z)) = (z * (x / z)) / y
    ]]></literal>
    <justification jstring="[para(4964(a,1),14217(a,1,2,2))].">
      <j1 rule="para" parents="4964 14217"/>
    </justification>
  </clause>

  <clause id="14222">
    <literal><![CDATA[
      R(x,y,z) = (z * (x * y)) / (y * T(z,x * y))
    ]]></literal>
    <justification jstring="[hyper(320,a,15,a,b,14220,a)].">
      <j1 rule="hyper" parents="320 15 14220"/>
    </justification>
  </clause>

  <clause id="14223">
    <literal><![CDATA[
      (x * (y / x)) / (z * (y / x)) = y / (z * (x \ y))
    ]]></literal>
    <justification jstring="[para(6475(a,1),14221(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6475 14221"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14224">
    <literal><![CDATA[
      R(x,y,z) \ (z * (x * y)) = y * T(z,x * y)
    ]]></literal>
    <justification jstring="[hyper(188,a,14222,a(flip))].">
      <j1 rule="hyper" parents="188 14222"/>
    </justification>
  </clause>

  <clause id="14225">
    <literal><![CDATA[
      (x * y) / (z * K(y,x)) = (T(x,y) * y) / z
    ]]></literal>
    <justification jstring="[para(4908(a,1),14219(a,1,2,2))].">
      <j1 rule="para" parents="4908 14219"/>
    </justification>
  </clause>

  <clause id="14226">
    <literal><![CDATA[
      K(x,y) * ((x * y) / z) = (T(x,y) * y) / z
    ]]></literal>
    <justification jstring="[hyper(58,a,14218,a(flip),b,14225,a)].">
      <j1 rule="hyper" parents="58 14218 14225"/>
    </justification>
  </clause>

  <clause id="14227">
    <literal><![CDATA[
      K(x,y \ (R(x,z,u) * w)) = K(x,x * (y \ w))
    ]]></literal>
    <justification jstring="[hyper(320,a,12484,a(flip),b,14207,a),flip(a)].">
      <j1 rule="hyper" parents="320 12484 14207"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14229">
    <literal><![CDATA[
      K(x,(R(x,y,z) \ u) \ w) = K(x,x * (u \ w))
    ]]></literal>
    <justification jstring="[hyper(58,a,8763,a,b,14227,a)].">
      <j1 rule="hyper" parents="58 8763 14227"/>
    </justification>
  </clause>

  <clause id="14230">
    <literal><![CDATA[
      K(x,x * (R(x,y,z) \ u)) = K(x,u)
    ]]></literal>
    <justification jstring="[para(4(a,1),14227(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4 14227"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14232">
    <literal><![CDATA[
      K(x,(x * y) * z) = K(x,x * (y * z))
    ]]></literal>
    <justification jstring="[para(184(a,1),14230(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="184 14230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14233">
    <literal><![CDATA[
      K(x,(y * x) * z) = K(x,x * (y * z))
    ]]></literal>
    <justification jstring="[hyper(11176,a,14232,a)].">
      <j1 rule="hyper" parents="11176 14232"/>
    </justification>
  </clause>

  <clause id="14235">
    <literal><![CDATA[
      K(x,(y / R(x,z,u)) \ w) = K(x,x * (y \ w))
    ]]></literal>
    <justification jstring="[hyper(58,a,7427,a,b,14229,a)].">
      <j1 rule="hyper" parents="58 7427 14229"/>
    </justification>
  </clause>

  <clause id="14237">
    <literal><![CDATA[
      K(x,x * (((y * x) * z) \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * z) \ u) = w
    ]]></literal>
    <justification jstring="[para(14235(a,1),12528(a,1))].">
      <j1 rule="para" parents="14235 12528"/>
    </justification>
  </clause>

  <clause id="14239">
    <literal><![CDATA[
      T(x,y) * a(x,z,z \ 1) = R(T(x,y),z,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(4700,a,14180,a)].">
      <j1 rule="hyper" parents="4700 14180"/>
    </justification>
  </clause>

  <clause id="14240">
    <literal><![CDATA[
      a(T(x,y),z,z \ 1) = a(x,z,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(29,a,706,a,b,14239,a)].">
      <j1 rule="hyper" parents="29 706 14239"/>
    </justification>
  </clause>

  <clause id="14241">
    <literal><![CDATA[
      a(x / y,z,z \ 1) = a(y \ x,z,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,12783,a(flip),b,14240,a),flip(a)].">
      <j1 rule="hyper" parents="58 12783 14240"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14242">
    <literal><![CDATA[
      (K(x,y) * (z \ x)) \ K(x,K(y,z)) = (z \ T(x,y)) \ 1
    ]]></literal>
    <justification jstring="[para(8162(a,1),14192(a,1,2))].">
      <j1 rule="para" parents="8162 14192"/>
    </justification>
  </clause>

  <clause id="14243">
    <literal><![CDATA[
      (x \ y) \ K(z,T(y,x)) = (x \ T(y,z)) \ 1
    ]]></literal>
    <justification jstring="[hyper(58,a,14147,a(flip),b,14242,a)].">
      <j1 rule="hyper" parents="58 14147 14242"/>
    </justification>
  </clause>

  <clause id="14244">
    <literal><![CDATA[
      (T(x,y) / z) \ K(x,K(y,z)) = ((x / z) * K(x,y)) \ 1
    ]]></literal>
    <justification jstring="[para(8156(a,1),14193(a,1,2))].">
      <j1 rule="para" parents="8156 14193"/>
    </justification>
  </clause>

  <clause id="14245">
    <literal><![CDATA[
      (T(x,y) / z) \ K(x,K(y,z)) = K(y,x) * ((x / z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,14204,a(flip),b,14244,a),flip(a)].">
      <j1 rule="hyper" parents="320 14204 14244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14246">
    <literal><![CDATA[
      T((x / y) * K(z,x),y) = y \ (x * T(K(z,x),y))
    ]]></literal>
    <justification jstring="[para(105(a,1),14201(a,1,1))].">
      <j1 rule="para" parents="105 14201"/>
    </justification>
  </clause>

  <clause id="14247">
    <literal><![CDATA[
      T((x / y) * K(z,x),y) = y \ (x * K(z,T(x,y)))
    ]]></literal>
    <justification jstring="[para(7158(a,2),14246(a,2,2,2))].">
      <j1 rule="para" parents="7158 14246"/>
    </justification>
  </clause>

  <clause id="14248">
    <literal><![CDATA[
      L(x,y,z) \ (z * (x * y)) = T(z * (y * K(x,y)),x)
    ]]></literal>
    <justification jstring="[para(4(a,1),14127(a,1,1,2))].">
      <j1 rule="para" parents="4 14127"/>
    </justification>
  </clause>

  <clause id="14249">
    <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(13679(a,2),14248(a,1,2))].">
      <j1 rule="para" parents="13679 14248"/>
    </justification>
  </clause>

  <clause id="14250">
    <literal><![CDATA[
      (x * (y * z)) \ (K(x,y) * ((y * x) * z)) = a(x,T(y,x),z)
    ]]></literal>
    <justification jstring="[para(105(a,1),14187(a,1,2,2,1))].">
      <j1 rule="para" parents="105 14187"/>
    </justification>
  </clause>

  <clause id="14251">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * y) * z) = a(x,T(y,x),z)
    ]]></literal>
    <justification jstring="[para(11157(a,1),14250(a,1,2))].">
      <j1 rule="para" parents="11157 14250"/>
    </justification>
  </clause>

  <clause id="14252">
    <literal><![CDATA[
      a(x,T(y,x),z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(691,a,14251,a),flip(a)].">
      <j1 rule="hyper" parents="691 14251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14253">
    <literal><![CDATA[
      a(x,T(y,x),z) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(14251(a,1),691(a,1))].">
      <j1 rule="para" parents="14251 691"/>
    </justification>
  </clause>

  <clause id="14254">
    <literal><![CDATA[
      a(x,y * x,z) = a(x,x * y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,13330,a(flip),b,14252,a)].">
      <j1 rule="hyper" parents="58 13330 14252"/>
    </justification>
  </clause>

  <clause id="14255">
    <literal><![CDATA[
      a(x / y,y,z) = a(y \ x,y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,4657,a(flip),b,14252,a)].">
      <j1 rule="hyper" parents="58 4657 14252"/>
    </justification>
  </clause>

  <clause id="14256">
    <literal><![CDATA[
      a(x / y,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      a(y \ x,y,z) = u
    ]]></literal>
    <justification jstring="[para(4657(a,1),14253(a,1))].">
      <j1 rule="para" parents="4657 14253"/>
    </justification>
  </clause>

  <clause id="14257">
    <literal><![CDATA[
      a(x,y * x,z) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,x * y,z) = u
    ]]></literal>
    <justification jstring="[para(13330(a,1),14253(a,1))].">
      <j1 rule="para" parents="13330 14253"/>
    </justification>
  </clause>

  <clause id="14258">
    <literal><![CDATA[
      a(K(x,y),z,u) = a(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,9715,a(flip),b,13667,a),flip(a)].">
      <j1 rule="hyper" parents="58 9715 13667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14259">
    <literal><![CDATA[
      a(x,y,K(z,u)) = K(x,a(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(13668,a,14258,a),flip(a)].">
      <j1 rule="hyper" parents="13668 14258"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14260">
    <literal><![CDATA[
      a(K(x,y),z,u) = a(K(u,x),z,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,13661,a,b,14258,a),flip(a)].">
      <j1 rule="hyper" parents="320 13661 14258"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14261">
    <literal><![CDATA[
      a(x,y,K(z,L(u,w,v5))) = a(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,11803,a,b,14258,a)].">
      <j1 rule="hyper" parents="320 11803 14258"/>
    </justification>
  </clause>

  <clause id="14262">
    <literal><![CDATA[
      a(K(x,a(y,z,u)),w,v5) = 1
    ]]></literal>
    <justification jstring="[hyper(320,a,13405,a(flip),b,14258,a),flip(a)].">
      <j1 rule="hyper" parents="320 13405 14258"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14263">
    <literal><![CDATA[
      a(x,y,K(z,u)) = a(u,y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,13661,a(flip),b,14258,a),flip(a)].">
      <j1 rule="hyper" parents="58 13661 14258"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14264">
    <literal><![CDATA[
      (K(x,y) * (z * u)) * a(x,z,K(u,y)) = (K(x,y) * z) * u
    ]]></literal>
    <justification jstring="[hyper(119,a,14258,a(flip),b,9,a(flip))].">
      <j1 rule="hyper" parents="119 14258 9"/>
    </justification>
  </clause>

  <clause id="14265">
    <literal><![CDATA[
      x * a(y,z,K(u,w)) = x * a(w,z,K(y,u))
    ]]></literal>
    <justification jstring="[para(14258(a,1),13664(a,1,2))].">
      <j1 rule="para" parents="14258 13664"/>
    </justification>
  </clause>

  <clause id="14266">
    <literal><![CDATA[
      K(x,a(a(y,z,u),w,v5)) = 1
    ]]></literal>
    <justification jstring="[hyper(13668,a,14262,a)].">
      <j1 rule="hyper" parents="13668 14262"/>
    </justification>
  </clause>

  <clause id="14267">
    <literal><![CDATA[
      a(a(x,y,z),u,K(w,v5)) = 1
    ]]></literal>
    <justification jstring="[hyper(58,a,13661,a(flip),b,14262,a)].">
      <j1 rule="hyper" parents="58 13661 14262"/>
    </justification>
  </clause>

  <clause id="14268">
    <literal><![CDATA[
      a(a(x,y,K(z,u)),w,v5) = 1
    ]]></literal>
    <justification jstring="[para(13400(a,2),14262(a,1,1))].">
      <j1 rule="para" parents="13400 14262"/>
    </justification>
  </clause>

  <clause id="14269">
    <literal><![CDATA[
      a(a(x,y,z),u,w) * v5 = v5 * a(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(5572,a,14266,a),flip(a)].">
      <j1 rule="hyper" parents="5572 14266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14270">
    <literal><![CDATA[
      T(x,a(a(y,z,u),w,v5)) = x
    ]]></literal>
    <justification jstring="[hyper(51,a,14266,a)].">
      <j1 rule="hyper" parents="51 14266"/>
    </justification>
  </clause>

  <clause id="14271">
    <literal><![CDATA[
      x / a(a(y,z,u),w,v5) = a(a(y,z,u),w,v5) \ x
    ]]></literal>
    <justification jstring="[hyper(168,a,5016,a,b,14266,a(flip))].">
      <j1 rule="hyper" parents="168 5016 14266"/>
    </justification>
  </clause>

  <clause id="14272">
    <literal><![CDATA[
      L(K(x,y),z,a(u,w,v5)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(5893,a,14267,a)].">
      <j1 rule="hyper" parents="5893 14267"/>
    </justification>
  </clause>

  <clause id="14273">
    <literal><![CDATA[
      T(x,L(y,z,a(u,w,v5))) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(167,a,10887,a,b,14267,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="167 10887 14267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14274">
    <literal><![CDATA[
      (a(x,y,K(z,u)) * w) * v5 = a(x,y,K(z,u)) * (w * v5)
    ]]></literal>
    <justification jstring="[hyper(6650,a,14268,a)].">
      <j1 rule="hyper" parents="6650 14268"/>
    </justification>
  </clause>

  <clause id="14275">
    <literal><![CDATA[
      L(x,y,a(z,u,K(w,v5))) = x
    ]]></literal>
    <justification jstring="[hyper(47,a,14268,a)].">
      <j1 rule="hyper" parents="47 14268"/>
    </justification>
  </clause>

  <clause id="14276">
    <literal><![CDATA[
      x / a(a(y,z,u),w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(a(y,z,u),w,v5) \ x = v6
    ]]></literal>
    <justification jstring="[para(14270(a,1),420(a,1))].">
      <j1 rule="para" parents="14270 420"/>
    </justification>
  </clause>

  <clause id="14277">
    <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,14275,a)].">
      <j1 rule="hyper" parents="58 298 14275"/>
    </justification>
  </clause>

  <clause id="14278">
    <literal><![CDATA[
      L(x,y,a(z,u,K(w,v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      x = v6
    ]]></literal>
    <justification jstring="[para(14275(a,1),45(a,2))].">
      <j1 rule="para" parents="14275 45"/>
    </justification>
  </clause>

  <clause id="14279">
    <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(14275(a,1),476(a,1,2,2,1))].">
      <j1 rule="para" parents="14275 476"/>
    </justification>
  </clause>

  <clause id="14281">
    <literal><![CDATA[
      K(x,L(y,z,u) \ y) = a(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,13375,a,b,14259,a)].">
      <j1 rule="hyper" parents="320 13375 14259"/>
    </justification>
  </clause>

  <clause id="14282">
    <literal><![CDATA[
      (x * y) * a(y,z,K(u,w)) = x * T(y,a(w,z,u))
    ]]></literal>
    <justification jstring="[hyper(119,a,14259,a,b,6154,a)].">
      <j1 rule="hyper" parents="119 14259 6154"/>
    </justification>
  </clause>

  <clause id="14283">
    <literal><![CDATA[
      x * a(x,y,K(z,u)) = T(x,a(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(119,a,14259,a,b,4729,a(flip))].">
      <j1 rule="hyper" parents="119 14259 4729"/>
    </justification>
  </clause>

  <clause id="14284">
    <literal><![CDATA[
      a(x \ 1,y,K(z,u)) / x = T(1 / x,a(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(117,a,14259,a,b,5047,a)].">
      <j1 rule="hyper" parents="117 14259 5047"/>
    </justification>
  </clause>

  <clause id="14285">
    <literal><![CDATA[
      K(x * y,(x * y) \ (z \ ((z * x) * y))) = a(x * y,x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(10425,a,14259,a(flip))].">
      <j1 rule="hyper" parents="10425 14259"/>
    </justification>
  </clause>

  <clause id="14286">
    <literal><![CDATA[
      a(x,y,K(z,u)) * x = T(x,a(u,y,z))
    ]]></literal>
    <justification jstring="[para(14259(a,2),4770(a,2,1)),flip(a)].">
      <j1 rule="para" parents="14259 4770"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14287">
    <literal><![CDATA[
      x * a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,a(u,y,z)) = w
    ]]></literal>
    <justification jstring="[para(14259(a,2),4766(a,1,2))].">
      <j1 rule="para" parents="14259 4766"/>
    </justification>
  </clause>

  <clause id="14288">
    <literal><![CDATA[
      a(x,y,K(z,u)) * x != w
    ]]></literal>
    <literal><![CDATA[
      T(x,a(u,y,z)) = w
    ]]></literal>
    <justification jstring="[para(14259(a,2),4771(a,1,1))].">
      <j1 rule="para" parents="14259 4771"/>
    </justification>
  </clause>

  <clause id="14289">
    <literal><![CDATA[
      (x / y) \ (x * a(y,z,K(u,w))) = T(y,a(w,z,u))
    ]]></literal>
    <justification jstring="[para(14259(a,2),6149(a,1,2,2))].">
      <j1 rule="para" parents="14259 6149"/>
    </justification>
  </clause>

  <clause id="14290">
    <literal><![CDATA[
      L(a(x,y,K(z,u)),w,v5) = K(x,L(a(u,y,z),w,v5))
    ]]></literal>
    <justification jstring="[para(14259(a,2),10794(a,1,1))].">
      <j1 rule="para" parents="14259 10794"/>
    </justification>
  </clause>

  <clause id="14291">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) = K(z,K(x,a(w,y,u)))
    ]]></literal>
    <justification jstring="[para(14259(a,1),13400(a,2,2))].">
      <j1 rule="para" parents="14259 13400"/>
    </justification>
  </clause>

  <clause id="14292">
    <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(14259(a,2),14010(a,1,2,2))].">
      <j1 rule="para" parents="14259 14010"/>
    </justification>
  </clause>

  <clause id="14293">
    <literal><![CDATA[
      a(K(x,y),z,u) = a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(320,a,14258,a(flip),b,14260,a),flip(a)].">
      <j1 rule="hyper" parents="320 14258 14260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14294">
    <literal><![CDATA[
      a(x \ y,x,K(z,u)) = a(u,x,K(y / x,z))
    ]]></literal>
    <justification jstring="[hyper(14256,a,14263,a)].">
      <j1 rule="hyper" parents="14256 14263"/>
    </justification>
  </clause>

  <clause id="14295">
    <literal><![CDATA[
      a(x \ L(x,y,z),u,K(w,v5)) = 1
    ]]></literal>
    <justification jstring="[hyper(13444,a,14263,a),flip(a)].">
      <j1 rule="hyper" parents="13444 14263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14296">
    <literal><![CDATA[
      a(x,L(x,y,z),K(u,w)) = 1
    ]]></literal>
    <justification jstring="[hyper(13420,a,14263,a),flip(a)].">
      <j1 rule="hyper" parents="13420 14263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14297">
    <literal><![CDATA[
      a(L(x,y,z),x,K(u,w)) = 1
    ]]></literal>
    <justification jstring="[hyper(13419,a,14263,a),flip(a)].">
      <j1 rule="hyper" parents="13419 14263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14298">
    <literal><![CDATA[
      a(x,y,K(z \ u,z)) = a(z,y,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(11029,a,14263,a)].">
      <j1 rule="hyper" parents="11029 14263"/>
    </justification>
  </clause>

  <clause id="14299">
    <literal><![CDATA[
      a(x,y * x,K(z,u)) = a(z,y,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(10935,a,14263,a),flip(a)].">
      <j1 rule="hyper" parents="10935 14263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14300">
    <literal><![CDATA[
      a(x,y * z,K(u,z)) = a(z,y,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(10889,a,14263,a)].">
      <j1 rule="hyper" parents="10889 14263"/>
    </justification>
  </clause>

  <clause id="14301">
    <literal><![CDATA[
      K(x,L(y,z,u)) * K(y,x) = a(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(10880,a,14263,a)].">
      <j1 rule="hyper" parents="10880 14263"/>
    </justification>
  </clause>

  <clause id="14302">
    <literal><![CDATA[
      K(x,y) * K(y,L(x,z,u)) = a(y,z,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(10877,a,14263,a)].">
      <j1 rule="hyper" parents="10877 14263"/>
    </justification>
  </clause>

  <clause id="14303">
    <literal><![CDATA[
      K(x,x * (y \ L(y,z,u))) = a(y,z,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,13390,a,b,14263,a)].">
      <j1 rule="hyper" parents="320 13390 14263"/>
    </justification>
  </clause>

  <clause id="14304">
    <literal><![CDATA[
      a(x,y,K(z,z \ u)) = a(z,y,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(320,a,11031,a,b,14263,a)].">
      <j1 rule="hyper" parents="320 11031 14263"/>
    </justification>
  </clause>

  <clause id="14305">
    <literal><![CDATA[
      x / (a(y,z,K(u,w)) * x) = a(w,z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(320,a,9912,a,b,14263,a)].">
      <j1 rule="hyper" parents="320 9912 14263"/>
    </justification>
  </clause>

  <clause id="14306">
    <literal><![CDATA[
      L(K(x,y),z,u) * K(y,x) = a(y,z,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,5890,a,b,14263,a)].">
      <j1 rule="hyper" parents="320 5890 14263"/>
    </justification>
  </clause>

  <clause id="14307">
    <literal><![CDATA[
      a((x \ y) \ z,u,K(w,v5)) = a(v5,u,K(y \ (x * z),w))
    ]]></literal>
    <justification jstring="[hyper(320,a,11806,a(flip),b,14263,a),flip(a)].">
      <j1 rule="hyper" parents="320 11806 14263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14308">
    <literal><![CDATA[
      a(x,y,K(L(z,u,w),v5)) = a(v5,y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,11803,a(flip),b,14263,a),flip(a)].">
      <j1 rule="hyper" parents="320 11803 14263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14309">
    <literal><![CDATA[
      a(x \ y,z,K(u,w)) = a(w,z,K(u,y \ x))
    ]]></literal>
    <justification jstring="[hyper(320,a,11036,a(flip),b,14263,a),flip(a)].">
      <j1 rule="hyper" parents="320 11036 14263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14310">
    <literal><![CDATA[
      a(x \ 1,y,K(z,u)) = a(u,y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(320,a,11035,a(flip),b,14263,a),flip(a)].">
      <j1 rule="hyper" parents="320 11035 14263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14311">
    <literal><![CDATA[
      K(x,y) * a(y,z,K(x,u)) = L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(119,a,14263,a,b,5895,a)].">
      <j1 rule="hyper" parents="119 14263 5895"/>
    </justification>
  </clause>

  <clause id="14312">
    <literal><![CDATA[
      a(x \ y,z,K(u,w)) = a(u,z,K(y \ x,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,11036,a,b,14263,a),flip(a)].">
      <j1 rule="hyper" parents="58 11036 14263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14313">
    <literal><![CDATA[
      a(x,y,K(z,u \ z)) = a(z,y,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,11033,a,b,14263,a)].">
      <j1 rule="hyper" parents="58 11033 14263"/>
    </justification>
  </clause>

  <clause id="14314">
    <literal><![CDATA[
      a(x,y,K(z,z \ u)) = a(u,y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,11031,a,b,14263,a)].">
      <j1 rule="hyper" parents="58 11031 14263"/>
    </justification>
  </clause>

  <clause id="14315">
    <literal><![CDATA[
      a(x,y,K(z * u,z)) = a(z,y,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,11019,a,b,14263,a)].">
      <j1 rule="hyper" parents="58 11019 14263"/>
    </justification>
  </clause>

  <clause id="14316">
    <literal><![CDATA[
      a((x * y) \ z,u,K(w,v5)) = a(w,u,K(v5,y \ (x \ z)))
    ]]></literal>
    <justification jstring="[hyper(58,a,11805,a(flip),b,14263,a),flip(a)].">
      <j1 rule="hyper" parents="58 11805 14263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14317">
    <literal><![CDATA[
      a(L(x,y,z),u,K(w,v5)) = a(w,u,K(v5,x))
    ]]></literal>
    <justification jstring="[hyper(58,a,11803,a(flip),b,14263,a),flip(a)].">
      <j1 rule="hyper" parents="58 11803 14263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14318">
    <literal><![CDATA[
      a(x * y,z,K(u,x)) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,11030,a(flip),b,14263,a),flip(a)].">
      <j1 rule="hyper" parents="58 11030 14263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14319">
    <literal><![CDATA[
      x * a(y,z,K(u,x)) = T(x,a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(119,a,14263,a(flip),b,13399,a)].">
      <j1 rule="hyper" parents="119 14263 13399"/>
    </justification>
  </clause>

  <clause id="14320">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (a(z,y,K(x,u)) * w) = w
    ]]></literal>
    <justification jstring="[hyper(118,a,14263,a(flip),b,9912,a),flip(a)].">
      <j1 rule="hyper" parents="118 14263 9912"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14321">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) = a(w,y,K(x,K(z,u)))
    ]]></literal>
    <justification jstring="[para(7755(a,1),14263(a,1,3))].">
      <j1 rule="para" parents="7755 14263"/>
    </justification>
  </clause>

  <clause id="14322">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) = a(u,y,K(x,K(w,z)))
    ]]></literal>
    <justification jstring="[para(7780(a,1),14263(a,1,3))].">
      <j1 rule="para" parents="7780 14263"/>
    </justification>
  </clause>

  <clause id="14323">
    <literal><![CDATA[
      a(x,y,K(z,u)) \ w = a(u,y,K(z,x)) * w
    ]]></literal>
    <justification jstring="[para(14263(a,2),9911(a,1,1))].">
      <j1 rule="para" parents="14263 9911"/>
    </justification>
  </clause>

  <clause id="14324">
    <literal><![CDATA[
      a(x,y,K(z,u)) * w != v5
    ]]></literal>
    <literal><![CDATA[
      a(u,y,K(z,x)) * v5 = w
    ]]></literal>
    <justification jstring="[para(14263(a,2),9915(a,1,1))].">
      <j1 rule="para" parents="14263 9915"/>
    </justification>
  </clause>

  <clause id="14325">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(u,y)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(14263(a,1),10807(a,1,2))].">
      <j1 rule="para" parents="14263 10807"/>
    </justification>
  </clause>

  <clause id="14326">
    <literal><![CDATA[
      K(x,y) * a(y,z,K(x,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(14263(a,2),10807(a,1,2))].">
      <j1 rule="para" parents="14263 10807"/>
    </justification>
  </clause>

  <clause id="14327">
    <literal><![CDATA[
      a(x,y,K(z,u)) * K(x,L(z,y,u)) = K(x,z)
    ]]></literal>
    <justification jstring="[para(14263(a,2),10827(a,1,1))].">
      <j1 rule="para" parents="14263 10827"/>
    </justification>
  </clause>

  <clause id="14328">
    <literal><![CDATA[
      a(x,y,K(z,u)) * K(x,u) = K(x,L(u,y,z))
    ]]></literal>
    <justification jstring="[para(14263(a,1),10873(a,1,1))].">
      <j1 rule="para" parents="14263 10873"/>
    </justification>
  </clause>

  <clause id="14329">
    <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(14263(a,1),10866(a,1,2))].">
      <j1 rule="para" parents="14263 10866"/>
    </justification>
  </clause>

  <clause id="14330">
    <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(14263(a,2),10866(a,1,2))].">
      <j1 rule="para" parents="14263 10866"/>
    </justification>
  </clause>

  <clause id="14331">
    <literal><![CDATA[
      a(x,y,K(z,u)) * u = T(u,a(z,y,x))
    ]]></literal>
    <justification jstring="[para(14263(a,1),13407(a,1,1))].">
      <j1 rule="para" parents="14263 13407"/>
    </justification>
  </clause>

  <clause id="14332">
    <literal><![CDATA[
      T(x,a(y,z,u) \ x) = x * a(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[para(14263(a,1),13594(a,2,2))].">
      <j1 rule="para" parents="14263 13594"/>
    </justification>
  </clause>

  <clause id="14333">
    <literal><![CDATA[
      L(K(x,y),L(z,u,w),z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(5893,a,14296,a)].">
      <j1 rule="hyper" parents="5893 14296"/>
    </justification>
  </clause>

  <clause id="14334">
    <literal><![CDATA[
      L(K(x,y),z,L(z,u,w)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(5893,a,14297,a)].">
      <j1 rule="hyper" parents="5893 14297"/>
    </justification>
  </clause>

  <clause id="14335">
    <literal><![CDATA[
      K((a(x,y,z) * u) \ w,v5) = K(u \ (a(x,y,z) \ w),v5)
    ]]></literal>
    <justification jstring="[hyper(10948,a,14272,a)].">
      <j1 rule="hyper" parents="10948 14272"/>
    </justification>
  </clause>

  <clause id="14336">
    <literal><![CDATA[
      K(x,L(y,z,a(u,w,v5))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(10837,a,14272,a)].">
      <j1 rule="hyper" parents="10837 14272"/>
    </justification>
  </clause>

  <clause id="14337">
    <literal><![CDATA[
      K(x,(a(y,z,u) \ w) \ v5) = K(x,w \ (a(y,z,u) * v5))
    ]]></literal>
    <justification jstring="[hyper(58,a,10819,a(flip),b,14272,a),flip(a)].">
      <j1 rule="hyper" parents="58 10819 14272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14338">
    <literal><![CDATA[
      K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,u,a(w,v5,v6))) = z
    ]]></literal>
    <justification jstring="[para(14272(a,1),10432(a,1))].">
      <j1 rule="para" parents="14272 10432"/>
    </justification>
  </clause>

  <clause id="14339">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) * T(v5,x) = v5 * L(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(119,a,14273,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 14273 17"/>
    </justification>
  </clause>

  <clause id="14341">
    <literal><![CDATA[
      L(K(x,y),z,u) \ K(x,y) = a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(320,a,1932,a,b,14293,a)].">
      <j1 rule="hyper" parents="320 1932 14293"/>
    </justification>
  </clause>

  <clause id="14342">
    <literal><![CDATA[
      ((x \ L(x,y,z)) * u) * K(w,v5) = (x \ L(x,y,z)) * (u * K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(977,a,14295,a)].">
      <j1 rule="hyper" parents="977 14295"/>
    </justification>
  </clause>

  <clause id="14343">
    <literal><![CDATA[
      K(x,L(y,L(z,u,w),z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(10837,a,14333,a)].">
      <j1 rule="hyper" parents="10837 14333"/>
    </justification>
  </clause>

  <clause id="14344">
    <literal><![CDATA[
      K(x,L(y,z,L(z,u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(10837,a,14334,a)].">
      <j1 rule="hyper" parents="10837 14334"/>
    </justification>
  </clause>

  <clause id="14345">
    <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(14281(a,1),6404(a,1,1,1))].">
      <j1 rule="para" parents="14281 6404"/>
    </justification>
  </clause>

  <clause id="14346">
    <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(14281(a,1),6799(a,1,1,1))].">
      <j1 rule="para" parents="14281 6799"/>
    </justification>
  </clause>

  <clause id="14347">
    <literal><![CDATA[
      T(x,a(y * z,u,y)) = x * a(x,u,K(y,z))
    ]]></literal>
    <justification jstring="[para(11030(a,1),14283(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11030 14283"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14348">
    <literal><![CDATA[
      a(x,x * y,K(z,u)) = a(z,y,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(14257,a,14299,a)].">
      <j1 rule="hyper" parents="14257 14299"/>
    </justification>
  </clause>

  <clause id="14349">
    <literal><![CDATA[
      a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(z,y,K(u,x)) = w
    ]]></literal>
    <justification jstring="[para(14300(a,1),10935(a,1))].">
      <j1 rule="para" parents="14300 10935"/>
    </justification>
  </clause>

  <clause id="14350">
    <literal><![CDATA[
      T(x,a(y,z * y,u)) = x * a(y,z,K(x,u))
    ]]></literal>
    <justification jstring="[para(14300(a,1),14283(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14300 14283"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14351">
    <literal><![CDATA[
      a(x,y,K(z \ (u * x),w)) = a(w,y,K(x,z \ u))
    ]]></literal>
    <justification jstring="[para(10339(a,1),14304(a,1,3)),flip(a)].">
      <j1 rule="para" parents="10339 14304"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14352">
    <literal><![CDATA[
      a(x \ 1,y,K(z,u)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,14263,a(flip),b,14310,a),flip(a)].">
      <j1 rule="hyper" parents="320 14263 14310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14353">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(y,u)) = K(x,L(y,z,u \ 1))
    ]]></literal>
    <justification jstring="[para(14310(a,1),10807(a,1,2))].">
      <j1 rule="para" parents="14310 10807"/>
    </justification>
  </clause>

  <clause id="14354">
    <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(14310(a,1),10866(a,1,2))].">
      <j1 rule="para" parents="14310 10866"/>
    </justification>
  </clause>

  <clause id="14355">
    <literal><![CDATA[
      a(x,y,K(z,x * u)) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,14263,a(flip),b,14315,a)].">
      <j1 rule="hyper" parents="58 14263 14315"/>
    </justification>
  </clause>

  <clause id="14356">
    <literal><![CDATA[
      a(x * y,z,K(u,x)) = a(y,z,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(320,a,14263,a(flip),b,14318,a),flip(a)].">
      <j1 rule="hyper" parents="320 14263 14318"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14357">
    <literal><![CDATA[
      (x \ y) * a(z,u,K(w,y)) = x \ T(y,a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(116,a,14319,a(flip),b,703,a),flip(a)].">
      <j1 rule="hyper" parents="116 14319 703"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14358">
    <literal><![CDATA[
      T(T(x,a(y,z,u)),y) = T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(14319(a,1),10927(a,1,1))].">
      <j1 rule="para" parents="14319 10927"/>
    </justification>
  </clause>

  <clause id="14359">
    <literal><![CDATA[
      T(x * (y * z),a(x,y,z)) = (x * (y * z)) * 1
    ]]></literal>
    <justification jstring="[para(13690(a,1),14319(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13690 14319"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14360">
    <literal><![CDATA[
      T(x,a(x * y,z,u)) = x * a(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[para(14315(a,1),14319(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14315 14319"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14361">
    <literal><![CDATA[
      T(x,L(y,z,u) \ y) = a(y,z,K(u,x)) * x
    ]]></literal>
    <justification jstring="[hyper(320,a,13376,a,b,14331,a)].">
      <j1 rule="hyper" parents="320 13376 14331"/>
    </justification>
  </clause>

  <clause id="14362">
    <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(11803(a,1),14331(a,1,1))].">
      <j1 rule="para" parents="11803 14331"/>
    </justification>
  </clause>

  <clause id="14363">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (u * w) = T(u,a(z,y,x)) * w
    ]]></literal>
    <justification jstring="[para(14331(a,1),13363(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14331 13363"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14364">
    <literal><![CDATA[
      a(x,y * z,K(u,y)) = a(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,14263,a,b,14348,a)].">
      <j1 rule="hyper" parents="58 14263 14348"/>
    </justification>
  </clause>

  <clause id="14365">
    <literal><![CDATA[
      a(K(x,y) / z,u,K(w,v5)) = a(z * K(y,x),u,K(v5,w))
    ]]></literal>
    <justification jstring="[para(13928(a,1),14352(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13928 14352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14366">
    <literal><![CDATA[
      (x * y) * a(y,z,K(u,x)) = T(x * y,a(x,z,u))
    ]]></literal>
    <justification jstring="[para(14356(a,1),14283(a,1,2))].">
      <j1 rule="para" parents="14356 14283"/>
    </justification>
  </clause>

  <clause id="14367">
    <literal><![CDATA[
      T(T(x,y),a(y,z,u)) = T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(434,a,14358,a)].">
      <j1 rule="hyper" parents="434 14358"/>
    </justification>
  </clause>

  <clause id="14368">
    <literal><![CDATA[
      T(x,a(y,z,u)) * y = y * T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(119,a,14358,a(flip),b,17,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 14358 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14369">
    <literal><![CDATA[
      a(x,y \ z,K(u,y)) = a(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[para(5(a,1),14364(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5 14364"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14370">
    <literal><![CDATA[
      a(x,x \ y,K(z,u)) = a(z,y,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(58,a,14263,a(flip),b,14369,a)].">
      <j1 rule="hyper" parents="58 14263 14369"/>
    </justification>
  </clause>

  <clause id="14371">
    <literal><![CDATA[
      a(x,x \ y,K(z,u)) = a(u,y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,14263,a,b,14370,a),flip(a)].">
      <j1 rule="hyper" parents="320 14263 14370"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14372">
    <literal><![CDATA[
      a(x,x \ y,K(z,u)) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,14263,a(flip),b,14370,a),flip(a)].">
      <j1 rule="hyper" parents="320 14263 14370"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14373">
    <literal><![CDATA[
      a(x,y \ z,K(y,u)) = a(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,14263,a(flip),b,14371,a)].">
      <j1 rule="hyper" parents="58 14263 14371"/>
    </justification>
  </clause>

  <clause id="14374">
    <literal><![CDATA[
      K(x,L(y,z \ u,z)) = K(y,x) \ a(z,u,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(116,a,14372,a(flip),b,10824,a),flip(a)].">
      <j1 rule="hyper" parents="116 14372 10824"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14375">
    <literal><![CDATA[
      K(x,L(y,z \ u,z)) = K(x,y) * a(z,u,K(y,x))
    ]]></literal>
    <justification jstring="[para(14372(a,1),10807(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14372 10807"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14376">
    <literal><![CDATA[
      T(x,a(y,x \ z,u)) = x * a(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[para(14372(a,1),14283(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14372 14283"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14377">
    <literal><![CDATA[
      T(x,a(y,z \ u,z)) = x * a(z,u,K(y,x))
    ]]></literal>
    <justification jstring="[para(14372(a,1),14319(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14372 14319"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14378">
    <literal><![CDATA[
      a(x,y * z,K(y,u)) = a(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[para(4(a,1),14373(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4 14373"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14379">
    <literal><![CDATA[
      a(x,y * z,K(u,K(w,y))) = a(x,z,K(y,K(u,w)))
    ]]></literal>
    <justification jstring="[para(7784(a,2),14378(a,1,3))].">
      <j1 rule="para" parents="7784 14378"/>
    </justification>
  </clause>

  <clause id="14380">
    <literal><![CDATA[
      a(x,y,K(z,u)) * K(x,L(u,w,v5)) = K(x,L(L(u,w,v5),y,z))
    ]]></literal>
    <justification jstring="[para(14308(a,1),10873(a,1,1))].">
      <j1 rule="para" parents="14308 10873"/>
    </justification>
  </clause>

  <clause id="14381">
    <literal><![CDATA[
      a(L(x,y,z),u,K(w,v5)) = a(x,u,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(320,a,14263,a(flip),b,14317,a),flip(a)].">
      <j1 rule="hyper" parents="320 14263 14317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14382">
    <literal><![CDATA[
      K(x,L(y,z,L(u,w,v5))) = K(x,y) * a(y,z,K(x,u))
    ]]></literal>
    <justification jstring="[para(14317(a,1),10807(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14317 10807"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14383">
    <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(11036(a,1),14349(a,1))].">
      <j1 rule="para" parents="11036 14349"/>
    </justification>
  </clause>

  <clause id="14384">
    <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(13302(a,1),14349(a,1))].">
      <j1 rule="para" parents="13302 14349"/>
    </justification>
  </clause>

  <clause id="14385">
    <literal><![CDATA[
      a(K(x,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,z,K(u,y)) = w
    ]]></literal>
    <justification jstring="[para(13661(a,2),14349(a,1))].">
      <j1 rule="para" parents="13661 14349"/>
    </justification>
  </clause>

  <clause id="14386">
    <literal><![CDATA[
      a(K(x,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(u,z,K(y,x)) = w
    ]]></literal>
    <justification jstring="[para(14258(a,2),14349(a,1))].">
      <j1 rule="para" parents="14258 14349"/>
    </justification>
  </clause>

  <clause id="14387">
    <literal><![CDATA[
      a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(u,y,K(x,z)) = w
    ]]></literal>
    <justification jstring="[para(14263(a,1),14349(a,1))].">
      <j1 rule="para" parents="14263 14349"/>
    </justification>
  </clause>

  <clause id="14388">
    <literal><![CDATA[
      a(x,y,K(z \ u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(14298(a,2),14349(a,1))].">
      <j1 rule="para" parents="14298 14349"/>
    </justification>
  </clause>

  <clause id="14389">
    <literal><![CDATA[
      a(x \ 1,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(u,y,K(z,x)) = w
    ]]></literal>
    <justification jstring="[para(14352(a,2),14349(a,1))].">
      <j1 rule="para" parents="14352 14349"/>
    </justification>
  </clause>

  <clause id="14390">
    <literal><![CDATA[
      a(x,x \ y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(u,y,K(x,z)) = w
    ]]></literal>
    <justification jstring="[para(14370(a,2),14349(a,1))].">
      <j1 rule="para" parents="14370 14349"/>
    </justification>
  </clause>

  <clause id="14391">
    <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),14381(a,1,1))].">
      <j1 rule="para" parents="298 14381"/>
    </justification>
  </clause>

  <clause id="14392">
    <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),14381(a,1,1)),flip(a)].">
      <j1 rule="para" parents="490 14381"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14393">
    <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(14261(a,2),14385(a,1))].">
      <j1 rule="para" parents="14261 14385"/>
    </justification>
  </clause>

  <clause id="14394">
    <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(13386(a,2),14387(a,1))].">
      <j1 rule="para" parents="13386 14387"/>
    </justification>
  </clause>

  <clause id="14395">
    <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(14199(a,1),14387(a,1,3))].">
      <j1 rule="para" parents="14199 14387"/>
    </justification>
  </clause>

  <clause id="14396">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) = K(u,K(x,a(w,y,z)))
    ]]></literal>
    <justification jstring="[para(7779(a,1),14291(a,1,3))].">
      <j1 rule="para" parents="7779 14291"/>
    </justification>
  </clause>

  <clause id="14397">
    <literal><![CDATA[
      a(x,y,K((y * z) / y,u)) = a(z,y,K(u,x))
    ]]></literal>
    <justification jstring="[para(4(a,1),14294(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4 14294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14398">
    <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,14303,a(flip),b,8957,a)].">
      <j1 rule="hyper" parents="119 14303 8957"/>
    </justification>
  </clause>

  <clause id="14399">
    <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(14305(a,1),267(a,1,1)),flip(b)].">
      <j1 rule="para" parents="14305 267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14400">
    <literal><![CDATA[
      K(L(x,y,z),u) * K(u,x) = a(u,y,K(x,z))
    ]]></literal>
    <justification jstring="[para(10836(a,1),14306(a,1,1))].">
      <j1 rule="para" parents="10836 14306"/>
    </justification>
  </clause>

  <clause id="14401">
    <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(14309(a,2),14387(a,1))].">
      <j1 rule="para" parents="14309 14387"/>
    </justification>
  </clause>

  <clause id="14402">
    <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(8213(a,1),14311(a,1,2,3))].">
      <j1 rule="para" parents="8213 14311"/>
    </justification>
  </clause>

  <clause id="14403">
    <literal><![CDATA[
      a(x,y,K(z,u)) * K(x,u) = L(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[hyper(5957,a,14320,a),flip(a)].">
      <j1 rule="hyper" parents="5957 14320"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14404">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) = a(w,y,K(z,K(x,u)))
    ]]></literal>
    <justification jstring="[para(7779(a,1),14321(a,2,3))].">
      <j1 rule="para" parents="7779 14321"/>
    </justification>
  </clause>

  <clause id="14405">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) = a(u,y,K(z,K(x,w)))
    ]]></literal>
    <justification jstring="[para(7784(a,1),14322(a,2,3))].">
      <j1 rule="para" parents="7784 14322"/>
    </justification>
  </clause>

  <clause id="14406">
    <literal><![CDATA[
      K(x,L(y,z,(u \ w) / w)) = K(x,y) * a(x,z,K(u \ 1,y))
    ]]></literal>
    <justification jstring="[para(5434(a,1),14325(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="5434 14325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14407">
    <literal><![CDATA[
      K(x,L(y,z,K(y,u) * w)) = K(x,y) * a(x,z,K(w,y))
    ]]></literal>
    <justification jstring="[para(7343(a,1),14325(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="7343 14325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14408">
    <literal><![CDATA[
      K(x,L(y,R(z,u,w),z)) = K(x,y) * 1
    ]]></literal>
    <justification jstring="[para(10732(a,1),14325(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10732 14325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14409">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(y,u)) = K(x,L(y,z,u \ y))
    ]]></literal>
    <justification jstring="[para(11034(a,1),14325(a,1,2))].">
      <j1 rule="para" parents="11034 14325"/>
    </justification>
  </clause>

  <clause id="14410">
    <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(11120(a,1),14325(a,1,2,3))].">
      <j1 rule="para" parents="11120 14325"/>
    </justification>
  </clause>

  <clause id="14411">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(u * w,y)) = K(x,L(y,z,u / (w \ 1)))
    ]]></literal>
    <justification jstring="[para(13843(a,1),14325(a,1,2,3))].">
      <j1 rule="para" parents="13843 14325"/>
    </justification>
  </clause>

  <clause id="14412">
    <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(13734(a,1),14325(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="13734 14325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14413">
    <literal><![CDATA[
      K(x,L(y,R(z,u,w),z)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(14408(a,2),127(a,1)),flip(b)].">
      <j1 rule="para" parents="14408 127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14414">
    <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(8872(a,1),14326(a,1,2,3))].">
      <j1 rule="para" parents="8872 14326"/>
    </justification>
  </clause>

  <clause id="14415">
    <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(14326(a,2),10863(a,1))].">
      <j1 rule="para" parents="14326 10863"/>
    </justification>
  </clause>

  <clause id="14416">
    <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(10919(a,1),14326(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="10919 14326"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14417">
    <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(13938(a,1),14326(a,1,2,3))].">
      <j1 rule="para" parents="13938 14326"/>
    </justification>
  </clause>

  <clause id="14418">
    <literal><![CDATA[
      K(x,a(y,z,u) \ x) = a(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(4837,a,14332,a)].">
      <j1 rule="hyper" parents="4837 14332"/>
    </justification>
  </clause>

  <clause id="14419">
    <literal><![CDATA[
      a(x,y,K(z,a(x,y,z) \ u)) = a(u,y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,13429,a(flip),b,14418,a)].">
      <j1 rule="hyper" parents="58 13429 14418"/>
    </justification>
  </clause>

  <clause id="14420">
    <literal><![CDATA[
      T(x,a(y * z,u,y)) = T(x,a(z,u,y))
    ]]></literal>
    <justification jstring="[hyper(320,a,14283,a(flip),b,14347,a),flip(a)].">
      <j1 rule="hyper" parents="320 14283 14347"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14421">
    <literal><![CDATA[
      T(x,a(y \ z,u,y)) = T(x,a(z,u,y))
    ]]></literal>
    <justification jstring="[para(5(a,1),14420(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 14420"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14422">
    <literal><![CDATA[
      T(x,a(y,z * y,u)) = T(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,13403,a(flip),b,14350,a),flip(a)].">
      <j1 rule="hyper" parents="320 13403 14350"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14423">
    <literal><![CDATA[
      T(x,a(y,y * z,u)) = T(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(14254(a,1),14422(a,1,2))].">
      <j1 rule="para" parents="14254 14422"/>
    </justification>
  </clause>

  <clause id="14424">
    <literal><![CDATA[
      T(x,a(y,(z \ y) * u,z)) = T(x,a(z \ y,u,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,14421,a(flip),b,14423,a)].">
      <j1 rule="hyper" parents="58 14421 14423"/>
    </justification>
  </clause>

  <clause id="14425">
    <literal><![CDATA[
      T(x,a(x * y,z,u)) = T(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,14283,a(flip),b,14360,a),flip(a)].">
      <j1 rule="hyper" parents="320 14283 14360"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14426">
    <literal><![CDATA[
      T(x,a(x \ y,z,u)) = T(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(5(a,1),14425(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 14425"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14427">
    <literal><![CDATA[
      T(x,a(y,x \ z,u)) = T(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,14283,a(flip),b,14376,a),flip(a)].">
      <j1 rule="hyper" parents="320 14283 14376"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14428">
    <literal><![CDATA[
      T(T(x,y),a(z,x \ u,w)) = T(T(x,a(z,u,w)),y)
    ]]></literal>
    <justification jstring="[para(14427(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14427 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14429">
    <literal><![CDATA[
      T(x,a(y,z \ u,z)) = T(x,a(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,14319,a(flip),b,14377,a),flip(a)].">
      <j1 rule="hyper" parents="320 14319 14377"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14430">
    <literal><![CDATA[
      T(x,a(y,z * u,z)) = T(x,a(y,u,z))
    ]]></literal>
    <justification jstring="[para(4(a,1),14429(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 14429"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14431">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) = K(z,K(w,a(u,y,x)))
    ]]></literal>
    <justification jstring="[hyper(58,a,14321,a,b,14396,a)].">
      <j1 rule="hyper" parents="58 14321 14396"/>
    </justification>
  </clause>

  <clause id="14432">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) = K(x,K(z,a(u,y,w)))
    ]]></literal>
    <justification jstring="[hyper(58,a,14322,a(flip),b,14396,a)].">
      <j1 rule="hyper" parents="58 14322 14396"/>
    </justification>
  </clause>

  <clause id="14433">
    <literal><![CDATA[
      a(x,y,K(z,T(u,y))) = a(z,y,K(u,x))
    ]]></literal>
    <justification jstring="[para(7908(a,1),14397(a,1,3))].">
      <j1 rule="para" parents="7908 14397"/>
    </justification>
  </clause>

  <clause id="14434">
    <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(14400(a,1),5148(a,1,2)),flip(b)].">
      <j1 rule="para" parents="14400 5148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14435">
    <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,10839,a(flip),b,14403,a),flip(a)].">
      <j1 rule="hyper" parents="320 10839 14403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14436">
    <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(14403(a,1),39(a,1))].">
      <j1 rule="para" parents="14403 39"/>
    </justification>
  </clause>

  <clause id="14437">
    <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(14403(a,2),10847(a,1))].">
      <j1 rule="para" parents="14403 10847"/>
    </justification>
  </clause>

  <clause id="14438">
    <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(10972,a,14405,a)].">
      <j1 rule="hyper" parents="10972 14405"/>
    </justification>
  </clause>

  <clause id="14439">
    <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,14381,a,b,14431,a)].">
      <j1 rule="hyper" parents="58 14381 14431"/>
    </justification>
  </clause>

  <clause id="14440">
    <literal><![CDATA[
      a(x,y,K(z,u)) * u != w
    ]]></literal>
    <literal><![CDATA[
      T(u,a(z,y,x)) = w
    ]]></literal>
    <justification jstring="[para(14263(a,2),14288(a,1,1))].">
      <j1 rule="para" parents="14263 14288"/>
    </justification>
  </clause>

  <clause id="14441">
    <literal><![CDATA[
      T(x * (y * z),a(x,y,z)) = x * (y * z)
    ]]></literal>
    <justification jstring="[hyper(320,a,3,a(flip),b,14359,a),flip(a)].">
      <j1 rule="hyper" parents="320 3 14359"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14443">
    <literal><![CDATA[
      a(x,y,z) * (x * (y * z)) = (x * y) * z
    ]]></literal>
    <justification jstring="[hyper(119,a,14441,a(flip),b,684,a(flip))].">
      <j1 rule="hyper" parents="119 14441 684"/>
    </justification>
  </clause>

  <clause id="14444">
    <literal><![CDATA[
      a(x,y,z) = ((x * y) * z) / (x * (y * z))
    ]]></literal>
    <justification jstring="[para(14441(a,1),685(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14441 685"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14445">
    <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,14443,a)].">
      <j1 rule="hyper" parents="117 105 14443"/>
    </justification>
  </clause>

  <clause id="14447">
    <literal><![CDATA[
      a(x,y,z) = (z * (x * y)) / ((x * (y * z)) * K(z,x * y))
    ]]></literal>
    <justification jstring="[hyper(320,a,14216,a,b,14444,a),flip(a)].">
      <j1 rule="hyper" parents="320 14216 14444"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14448">
    <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(13515,a,14444,a(flip))].">
      <j1 rule="hyper" parents="13515 14444"/>
    </justification>
  </clause>

  <clause id="14449">
    <literal><![CDATA[
      ((x * y) * z) / (y * (T(x,y) * z)) = a(y,T(x,y),z)
    ]]></literal>
    <justification jstring="[para(105(a,1),14444(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="105 14444"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14451">
    <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(10375(a,2),14388(a,1,3))].">
      <j1 rule="para" parents="10375 14388"/>
    </justification>
  </clause>

  <clause id="14452">
    <literal><![CDATA[
      a(x,y,K(z,x \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(z,y,K(u,x)) = w
    ]]></literal>
    <justification jstring="[para(14263(a,1),14388(a,1))].">
      <j1 rule="para" parents="14263 14388"/>
    </justification>
  </clause>

  <clause id="14453">
    <literal><![CDATA[
      a(x,y \ z,K(y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,z,K(y,u)) = w
    ]]></literal>
    <justification jstring="[para(14263(a,1),14390(a,1))].">
      <j1 rule="para" parents="14263 14390"/>
    </justification>
  </clause>

  <clause id="14454">
    <literal><![CDATA[
      a(x,y,K(z,u)) * x = a(z,y,u) * (x / a(z,y,u))
    ]]></literal>
    <justification jstring="[para(14419(a,1),13432(a,1,1))].">
      <j1 rule="para" parents="14419 13432"/>
    </justification>
  </clause>

  <clause id="14455">
    <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(11032(a,1),14440(a,1,1))].">
      <j1 rule="para" parents="11032 14440"/>
    </justification>
  </clause>

  <clause id="14456">
    <literal><![CDATA[
      T(1 / x,a(y,z,u)) = a(x,z,K(y,u)) / x
    ]]></literal>
    <justification jstring="[para(14352(a,1),14284(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14352 14284"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14457">
    <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,11802,a,b,14290,a)].">
      <j1 rule="hyper" parents="58 11802 14290"/>
    </justification>
  </clause>

  <clause id="14458">
    <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(7058(a,1),14353(a,1,2,3))].">
      <j1 rule="para" parents="7058 14353"/>
    </justification>
  </clause>

  <clause id="14459">
    <literal><![CDATA[
      T(x,a(y,z,u)) * a(u,z,y) = a(u,z,y) * x
    ]]></literal>
    <justification jstring="[hyper(58,a,13430,a(flip),b,14363,a),flip(a)].">
      <j1 rule="hyper" parents="58 13430 14363"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14460">
    <literal><![CDATA[
      T(T(x,a(y,z,u)),a(u,z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(239,a,14363,a(flip),b,13430,a(flip))].">
      <j1 rule="hyper" parents="239 14363 13430"/>
    </justification>
  </clause>

  <clause id="14461">
    <literal><![CDATA[
      T(T(x,a(y,z,u)),L(u,z,y)) = T(x,u)
    ]]></literal>
    <justification jstring="[para(14460(a,1),14358(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14460 14358"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14462">
    <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(14461(a,1),12251(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="14461 12251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14463">
    <literal><![CDATA[
      T(x * y,a(x,z,u)) = x * T(y,a(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,14282,a(flip),b,14366,a),flip(a)].">
      <j1 rule="hyper" parents="58 14282 14366"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14464">
    <literal><![CDATA[
      T(x,a(y,z,u)) / y = T(x / y,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(4584,a,14463,a)].">
      <j1 rule="hyper" parents="4584 14463"/>
    </justification>
  </clause>

  <clause id="14465">
    <literal><![CDATA[
      K(x,L(y,z \ u,z)) = K(x,L(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,10807,a(flip),b,14375,a),flip(a)].">
      <j1 rule="hyper" parents="320 10807 14375"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14466">
    <literal><![CDATA[
      K(x,L(y,z \ u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,u,z)) = w
    ]]></literal>
    <justification jstring="[para(14375(a,2),10866(a,1))].">
      <j1 rule="para" parents="14375 10866"/>
    </justification>
  </clause>

  <clause id="14467">
    <literal><![CDATA[
      K(x,(y * ((y \ z) / u)) \ z) = K(x,L(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(10830,a,14465,a)].">
      <j1 rule="hyper" parents="10830 14465"/>
    </justification>
  </clause>

  <clause id="14468">
    <literal><![CDATA[
      K(x,L(y \ (z \ u),u,z)) = K(x,(z * y) \ u)
    ]]></literal>
    <justification jstring="[hyper(10829,a,14465,a),flip(a)].">
      <j1 rule="hyper" parents="10829 14465"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14469">
    <literal><![CDATA[
      T(x,L(y,z \ u,z)) = T(x,L(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(118,a,14465,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 14465 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14470">
    <literal><![CDATA[
      K(x,L(y,z * u,z)) = K(x,L(y,u,z))
    ]]></literal>
    <justification jstring="[para(4(a,1),14465(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 14465"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14471">
    <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(705(a,1),14465(a,1,2,2))].">
      <j1 rule="para" parents="705 14465"/>
    </justification>
  </clause>

  <clause id="14472">
    <literal><![CDATA[
      K(x,L((y \ z) \ u,z,y)) = K(x,z \ (y * u))
    ]]></literal>
    <justification jstring="[para(490(a,1),14465(a,1,2)),flip(a)].">
      <j1 rule="para" parents="490 14465"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14473">
    <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(4066(a,1),14465(a,1,2,2))].">
      <j1 rule="para" parents="4066 14465"/>
    </justification>
  </clause>

  <clause id="14474">
    <literal><![CDATA[
      K(x,L(y \ z,u,y \ u)) = K(x,u \ ((u / y) * z))
    ]]></literal>
    <justification jstring="[para(7002(a,1),14465(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7002 14465"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14475">
    <literal><![CDATA[
      x * K(y,L(z,x,u)) = u * ((u \ x) * K(y,z))
    ]]></literal>
    <justification jstring="[para(14465(a,1),10814(a,1,2))].">
      <j1 rule="para" parents="14465 10814"/>
    </justification>
  </clause>

  <clause id="14476">
    <literal><![CDATA[
      K(x,L(y,z,u \ z)) = K(x,L(y,u,u \ z))
    ]]></literal>
    <justification jstring="[para(11187(a,1),14465(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11187 14465"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14477">
    <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(13827(a,1),14469(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="13827 14469"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14478">
    <literal><![CDATA[
      K(x,L(y,z * u,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(13269(a,2),14470(a,1,2))].">
      <j1 rule="para" parents="13269 14470"/>
    </justification>
  </clause>

  <clause id="14479">
    <literal><![CDATA[
      K(x,y \ ((y / z) * (u * z))) = K(x,L(T(u,z),y,z \ y))
    ]]></literal>
    <justification jstring="[para(11203(a,1),14476(a,2,2)),flip(a)].">
      <j1 rule="para" parents="11203 14476"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14480">
    <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(14019(a,1),14476(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="14019 14476"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14481">
    <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(11187(a,1),14466(a,1,2))].">
      <j1 rule="para" parents="11187 14466"/>
    </justification>
  </clause>

  <clause id="14482">
    <literal><![CDATA[
      K(x,L(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,u \ z,u)) = w
    ]]></literal>
    <justification jstring="[para(14467(a,1),10868(a,1))].">
      <j1 rule="para" parents="14467 10868"/>
    </justification>
  </clause>

  <clause id="14483">
    <literal><![CDATA[
      K(x,(y * z) \ L(y,u,w)) = K(x,z \ (y \ L(y,u,w)))
    ]]></literal>
    <justification jstring="[hyper(58,a,14343,a(flip),b,14468,a),flip(a)].">
      <j1 rule="hyper" parents="58 14343 14468"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14484">
    <literal><![CDATA[
      K(x,(y \ R(y,z,u)) \ w) = K(x,R(y,z,u) \ (y * w))
    ]]></literal>
    <justification jstring="[hyper(14413,a,14472,a)].">
      <j1 rule="hyper" parents="14413 14472"/>
    </justification>
  </clause>

  <clause id="14485">
    <literal><![CDATA[
      x \ (K(y,L(z,u,x)) * u) = (x \ u) * K(y,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(8529,a,14475,a)].">
      <j1 rule="hyper" parents="8529 14475"/>
    </justification>
  </clause>

  <clause id="14486">
    <literal><![CDATA[
      x \ (y * K(z,L(u,y,x))) = (x \ y) * K(z,u)
    ]]></literal>
    <justification jstring="[hyper(536,a,14475,a)].">
      <j1 rule="hyper" parents="536 14475"/>
    </justification>
  </clause>

  <clause id="14487">
    <literal><![CDATA[
      x \ (y * K(z,T(y,u))) = (x \ y) * K(z,T(y,u))
    ]]></literal>
    <justification jstring="[para(10808(a,1),14486(a,1,2,2))].">
      <j1 rule="para" parents="10808 14486"/>
    </justification>
  </clause>

  <clause id="14488">
    <literal><![CDATA[
      L(x,y,z) \ (x * K(u,w)) = (L(x,y,z) \ x) * K(u,w)
    ]]></literal>
    <justification jstring="[para(14344(a,1),14486(a,1,2,2))].">
      <j1 rule="para" parents="14344 14486"/>
    </justification>
  </clause>

  <clause id="14489">
    <literal><![CDATA[
      a(x,y * z,K(u,K(w,y))) = a(x,z,K(u,K(w,y)))
    ]]></literal>
    <justification jstring="[para(7784(a,2),14379(a,2,3))].">
      <j1 rule="para" parents="7784 14379"/>
    </justification>
  </clause>

  <clause id="14490">
    <literal><![CDATA[
      K(x,L(y,z,u \ 1)) = K(x,L(y,z,u \ y))
    ]]></literal>
    <justification jstring="[hyper(58,a,14353,a(flip),b,14409,a)].">
      <j1 rule="hyper" parents="58 14353 14409"/>
    </justification>
  </clause>

  <clause id="14491">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(u \ w,y)) = K(x,L(y,z,(w \ u) \ y))
    ]]></literal>
    <justification jstring="[para(11036(a,2),14409(a,1,2))].">
      <j1 rule="para" parents="11036 14409"/>
    </justification>
  </clause>

  <clause id="14492">
    <literal><![CDATA[
      T(x,a(y,(z \ y) * u,z)) = T(x,a(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,14421,a(flip),b,14424,a),flip(a)].">
      <j1 rule="hyper" parents="320 14421 14424"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14493">
    <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(14457(a,1),14393(a,1))].">
      <j1 rule="para" parents="14457 14393"/>
    </justification>
  </clause>

  <clause id="14494">
    <literal><![CDATA[
      T((x / y) * K(z,x),y) = (y \ x) * K(z,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,14247,a,b,14487,a)].">
      <j1 rule="hyper" parents="58 14247 14487"/>
    </justification>
  </clause>

  <clause id="14495">
    <literal><![CDATA[
      T((x / y) * K(z,x),y) = K(z,x) * (y \ x)
    ]]></literal>
    <justification jstring="[hyper(320,a,8245,a(flip),b,14494,a),flip(a)].">
      <j1 rule="hyper" parents="320 8245 14494"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14496">
    <literal><![CDATA[
      T(x * K(y,z),x \ z) = K(y,z) * ((x \ z) \ z)
    ]]></literal>
    <justification jstring="[para(72(a,1),14495(a,1,1,1))].">
      <j1 rule="para" parents="72 14495"/>
    </justification>
  </clause>

  <clause id="14497">
    <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(11034(a,1),14329(a,1,2))].">
      <j1 rule="para" parents="11034 14329"/>
    </justification>
  </clause>

  <clause id="14498">
    <literal><![CDATA[
      K(x,L(y,z,L(u,w,v5))) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,14326,a(flip),b,14382,a),flip(a)].">
      <j1 rule="hyper" parents="320 14326 14382"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14499">
    <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(14382(a,2),14330(a,1))].">
      <j1 rule="para" parents="14382 14330"/>
    </justification>
  </clause>

  <clause id="14500">
    <literal><![CDATA[
      K(x,L(y,z \ 1,L(z,u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,13777,a(flip),b,14498,a),flip(a)].">
      <j1 rule="hyper" parents="320 13777 14498"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14501">
    <literal><![CDATA[
      K(x,L(y,z,(u * w) \ u)) = K(x,L(y,z,w \ 1))
    ]]></literal>
    <justification jstring="[para(217(a,1),14498(a,1,2,3))].">
      <j1 rule="para" parents="217 14498"/>
    </justification>
  </clause>

  <clause id="14502">
    <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),14498(a,1,2,3))].">
      <j1 rule="para" parents="298 14498"/>
    </justification>
  </clause>

  <clause id="14503">
    <literal><![CDATA[
      K(x,L(y,z,(u \ w) \ 1)) = K(x,L(y,z,w \ u))
    ]]></literal>
    <justification jstring="[para(390(a,1),14498(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="390 14498"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14504">
    <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(2506(a,1),14500(a,1,2))].">
      <j1 rule="para" parents="2506 14500"/>
    </justification>
  </clause>

  <clause id="14505">
    <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),14499(a,1,2,3))].">
      <j1 rule="para" parents="217 14499"/>
    </justification>
  </clause>

  <clause id="14506">
    <literal><![CDATA[
      K(x,L(y,z,(u \ w) \ y)) = K(x,L(y,z,w \ u))
    ]]></literal>
    <justification jstring="[hyper(58,a,14490,a(flip),b,14503,a)].">
      <j1 rule="hyper" parents="58 14490 14503"/>
    </justification>
  </clause>

  <clause id="14507">
    <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(14394,a,14035,a),flip(a)].">
      <j1 rule="hyper" parents="14394 14035"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14508">
    <literal><![CDATA[
      a(x,y,z) = ((y * x) * z) / (x * (T(y,x) * z))
    ]]></literal>
    <justification jstring="[hyper(320,a,14252,a(flip),b,14449,a)].">
      <j1 rule="hyper" parents="320 14252 14449"/>
    </justification>
  </clause>

  <clause id="14509">
    <literal><![CDATA[
      a(x,y,z) \ ((y * x) * z) = x * (T(y,x) * z)
    ]]></literal>
    <justification jstring="[hyper(188,a,14508,a(flip))].">
      <j1 rule="hyper" parents="188 14508"/>
    </justification>
  </clause>

  <clause id="14510">
    <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,632,a(flip),b,14509,a),flip(a)].">
      <j1 rule="hyper" parents="320 632 14509"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14511">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (K(u,z) * w) = K(u,L(z,y,x)) * w
    ]]></literal>
    <justification jstring="[para(10873(a,1),14274(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10873 14274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14512">
    <literal><![CDATA[
      (a(x,y,K(z,u)) * w) \ v5 = w \ (a(u,y,K(z,x)) * v5)
    ]]></literal>
    <justification jstring="[para(14323(a,1),14277(a,2,2))].">
      <j1 rule="para" parents="14323 14277"/>
    </justification>
  </clause>

  <clause id="14513">
    <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(14307(a,2),14349(a,1))].">
      <j1 rule="para" parents="14307 14349"/>
    </justification>
  </clause>

  <clause id="14514">
    <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(14316(a,2),14387(a,1))].">
      <j1 rule="para" parents="14316 14387"/>
    </justification>
  </clause>

  <clause id="14515">
    <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,14362,a),flip(a)].">
      <j1 rule="hyper" parents="320 20 14362"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14516">
    <literal><![CDATA[
      K(x,L(y,z,K(y,u) * w)) = K(x,L(y,z,w))
    ]]></literal>
    <justification jstring="[hyper(320,a,14325,a(flip),b,14407,a),flip(a)].">
      <j1 rule="hyper" parents="320 14325 14407"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14517">
    <literal><![CDATA[
      K(x,R(y,z,z \ 1) \ (y * u)) = K(x,a(y,z,z \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(705(a,1),14484(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="705 14484"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14518">
    <literal><![CDATA[
      (L(x,y,z) \ x) * K(u,w) = x * (L(x,y,z) \ K(u,w))
    ]]></literal>
    <justification jstring="[hyper(1423,a,14488,a),flip(a)].">
      <j1 rule="hyper" parents="1423 14488"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14519">
    <literal><![CDATA[
      x / K(y,L(z,u,K(y,z) \ (u \ x))) = (x / (u * K(y,z))) * u
    ]]></literal>
    <justification jstring="[para(14502(a,1),14138(a,1,2))].">
      <j1 rule="para" parents="14502 14138"/>
    </justification>
  </clause>

  <clause id="14520">
    <literal><![CDATA[
      K(x,y) / (z * (L(z,u,w) \ K(x,y))) = (L(z,u,w) \ z) \ 1
    ]]></literal>
    <justification jstring="[para(14518(a,1),13875(a,1,2))].">
      <j1 rule="para" parents="14518 13875"/>
    </justification>
  </clause>

  <clause id="14521">
    <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(14264(a,1),327(a,1,1)),flip(b)].">
      <j1 rule="para" parents="14264 327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14522">
    <literal><![CDATA[
      a(x,y,z) = (z * (x * y)) / (L(z,y,x) * (x * y))
    ]]></literal>
    <justification jstring="[para(14067(a,1),14447(a,2,2))].">
      <j1 rule="para" parents="14067 14447"/>
    </justification>
  </clause>

  <clause id="14523">
    <literal><![CDATA[
      a(x,y,z) \ (z * (x * y)) = L(z,y,x) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(188,a,14522,a(flip))].">
      <j1 rule="hyper" parents="188 14522"/>
    </justification>
  </clause>

  <clause id="14524">
    <literal><![CDATA[
      (x * (y * z)) / (L(x,z,y) * (y * z)) != u
    ]]></literal>
    <literal><![CDATA[
      a(y,z,x) = u
    ]]></literal>
    <justification jstring="[para(14523(a,1),330(a,1,2)),flip(b)].">
      <j1 rule="para" parents="14523 330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14525">
    <literal><![CDATA[
      T(x * y,a(y,z,u)) = T(x,a(y,z,u)) * y
    ]]></literal>
    <justification jstring="[hyper(14455,a,14363,a)].">
      <j1 rule="hyper" parents="14455 14363"/>
    </justification>
  </clause>

  <clause id="14526">
    <literal><![CDATA[
      T(x * y,a(y,z,u)) = y * T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,14368,a(flip),b,14525,a),flip(a)].">
      <j1 rule="hyper" parents="320 14368 14525"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14527">
    <literal><![CDATA[
      x * K(y,L(T(z,u),x,u \ x)) = (x / u) * (K(y,z) * u)
    ]]></literal>
    <justification jstring="[para(14479(a,1),11233(a,1,2))].">
      <j1 rule="para" parents="14479 11233"/>
    </justification>
  </clause>

  <clause id="14528">
    <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(14476(a,1),14505(a,1))].">
      <j1 rule="para" parents="14476 14505"/>
    </justification>
  </clause>

  <clause id="14529">
    <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(13746(a,1),14527(a,2,2))].">
      <j1 rule="para" parents="13746 14527"/>
    </justification>
  </clause>

  <clause id="14530">
    <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(14406(a,2),14329(a,1))].">
      <j1 rule="para" parents="14406 14329"/>
    </justification>
  </clause>

  <clause id="14531">
    <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(14411(a,1),14329(a,1))].">
      <j1 rule="para" parents="14411 14329"/>
    </justification>
  </clause>

  <clause id="14532">
    <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),14435(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="91 14435"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14533">
    <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(7779(a,1),14435(a,1,1,3))].">
      <j1 rule="para" parents="7779 14435"/>
    </justification>
  </clause>

  <clause id="14534">
    <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(8175(a,1),14435(a,1,1,3))].">
      <j1 rule="para" parents="8175 14435"/>
    </justification>
  </clause>

  <clause id="14535">
    <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(7797(a,1),14438(a,1,2))].">
      <j1 rule="para" parents="7797 14438"/>
    </justification>
  </clause>

  <clause id="14536">
    <literal><![CDATA[
      K(x,L(y,a(z,u,u \ 1),z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(14413,a,14471,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="14413 14471"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14537">
    <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(10943,a,14536,a)].">
      <j1 rule="hyper" parents="10943 14536"/>
    </justification>
  </clause>

  <clause id="14538">
    <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(14491(a,1),14329(a,1))].">
      <j1 rule="para" parents="14491 14329"/>
    </justification>
  </clause>

  <clause id="14539">
    <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(14490(a,2),14538(a,1))].">
      <j1 rule="para" parents="14490 14538"/>
    </justification>
  </clause>

  <clause id="14540">
    <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),14507(a,1,1)),flip(a)].">
      <j1 rule="para" parents="237 14507"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14541">
    <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,11529,a(flip),b,14535,a)].">
      <j1 rule="hyper" parents="58 11529 14535"/>
    </justification>
  </clause>

  <clause id="14542">
    <literal><![CDATA[
      K(a(x,y * z,K(z,u)),w) = a(z,y,K(w,K(x,u)))
    ]]></literal>
    <justification jstring="[para(6610(a,1),14541(a,1,1))].">
      <j1 rule="para" parents="6610 14541"/>
    </justification>
  </clause>

  <clause id="14543">
    <literal><![CDATA[
      K(a(x,y * z,K(z,u)),w) = a(z,y,K(w,K(u,x)))
    ]]></literal>
    <justification jstring="[para(7797(a,1),14542(a,2,3))].">
      <j1 rule="para" parents="7797 14542"/>
    </justification>
  </clause>

  <clause id="14544">
    <literal><![CDATA[
      K(x * y,(x * y) \ (z \ ((z * x) * y))) = 1
    ]]></literal>
    <justification jstring="[hyper(320,a,13669,a(flip),b,14285,a),flip(a)].">
      <j1 rule="hyper" parents="320 13669 14285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14546">
    <literal><![CDATA[
      K(x * y,z \ R(z,x,y)) = 1
    ]]></literal>
    <justification jstring="[hyper(58,a,10343,a(flip),b,14544,a)].">
      <j1 rule="hyper" parents="58 10343 14544"/>
    </justification>
  </clause>

  <clause id="14547">
    <literal><![CDATA[
      T(x \ R(x,y,z),y * z) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(4953,a,14546,a)].">
      <j1 rule="hyper" parents="4953 14546"/>
    </justification>
  </clause>

  <clause id="14548">
    <literal><![CDATA[
      (x * (y * z)) / (L(x,z,y) * (y * z)) = a(y,z,T(x,y * z))
    ]]></literal>
    <justification jstring="[para(632(a,1),14445(a,1,2))].">
      <j1 rule="para" parents="632 14445"/>
    </justification>
  </clause>

  <clause id="14549">
    <literal><![CDATA[
      a(x,y,T(z,x * y)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(14524,a,14548,a),flip(a)].">
      <j1 rule="hyper" parents="14524 14548"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14550">
    <literal><![CDATA[
      x / K(y,L(z,u,K(z,y) * (u \ x))) = (x / (u * K(y,z))) * u
    ]]></literal>
    <justification jstring="[para(5130(a,1),14519(a,1,2,2,3))].">
      <j1 rule="para" parents="5130 14519"/>
    </justification>
  </clause>

  <clause id="14551">
    <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(14501(a,1),14528(a,1))].">
      <j1 rule="para" parents="14501 14528"/>
    </justification>
  </clause>

  <clause id="14552">
    <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(13290(a,1),14551(a,1,2))].">
      <j1 rule="para" parents="13290 14551"/>
    </justification>
  </clause>

  <clause id="14553">
    <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(14490(a,1),14551(a,1))].">
      <j1 rule="para" parents="14490 14551"/>
    </justification>
  </clause>

  <clause id="14554">
    <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(14501(a,2),14551(a,1))].">
      <j1 rule="para" parents="14501 14551"/>
    </justification>
  </clause>

  <clause id="14555">
    <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(14552,a,13487,a)].">
      <j1 rule="hyper" parents="14552 13487"/>
    </justification>
  </clause>

  <clause id="14556">
    <literal><![CDATA[
      K(x,L((y * z) \ u,u,y \ 1)) = K(x,L((y * z) \ u,z,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(14552,a,10811,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="14552 10811"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14557">
    <literal><![CDATA[
      K(x,L(y,z * u,z \ 1)) = K(x,L(y,u,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(14552,a,xx),flip(a)].">
      <j1 rule="hyper" parents="14552"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14558">
    <literal><![CDATA[
      K(x,L(y,z \ u,z \ 1)) = K(x,L(y,u,z \ 1))
    ]]></literal>
    <justification jstring="[para(5(a,1),14557(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5 14557"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14559">
    <literal><![CDATA[
      K(x,(y * z) \ R(y,u,u \ 1)) = K(x,z \ a(y,u,u \ 1))
    ]]></literal>
    <justification jstring="[para(707(a,1),14537(a,1,2))].">
      <j1 rule="para" parents="707 14537"/>
    </justification>
  </clause>

  <clause id="14560">
    <literal><![CDATA[
      x / K(y,L(z,u,u \ x)) = (x / (u * K(y,z))) * u
    ]]></literal>
    <justification jstring="[para(14516(a,1),14550(a,1,2))].">
      <j1 rule="para" parents="14516 14550"/>
    </justification>
  </clause>

  <clause id="14561">
    <literal><![CDATA[
      (x / (y * K(z,u))) * y = (x / y) * (y * K(u,z))
    ]]></literal>
    <justification jstring="[hyper(14174,a,14560,a),flip(a)].">
      <j1 rule="hyper" parents="14174 14560"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14563">
    <literal><![CDATA[
      ((x * y) / (y * K(z,u))) * y = x * (y * K(u,z))
    ]]></literal>
    <justification jstring="[para(6(a,1),14561(a,2,1))].">
      <j1 rule="para" parents="6 14561"/>
    </justification>
  </clause>

  <clause id="14564">
    <literal><![CDATA[
      (x / y) * (y * K(z,T(u,y))) = (x / (K(u,z) * y)) * y
    ]]></literal>
    <justification jstring="[para(7150(a,1),14561(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7150 14561"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14565">
    <literal><![CDATA[
      (x / ((y \ 1) * K(z,u))) * (y \ 1) = (x / (y \ 1)) * (y \ K(u,z))
    ]]></literal>
    <justification jstring="[para(13812(a,1),14561(a,2,2))].">
      <j1 rule="para" parents="13812 14561"/>
    </justification>
  </clause>

  <clause id="14566">
    <literal><![CDATA[
      (x * (y * K(z,u))) / y = (x * y) / (y * K(u,z))
    ]]></literal>
    <justification jstring="[hyper(131,a,14563,a)].">
      <j1 rule="hyper" parents="131 14563"/>
    </justification>
  </clause>

  <clause id="14567">
    <literal><![CDATA[
      (x * (y * K(z,u))) / y != w
    ]]></literal>
    <literal><![CDATA[
      (x * y) / (y * K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(14563(a,1),327(a,1,1)),flip(b)].">
      <j1 rule="para" parents="14563 327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14568">
    <literal><![CDATA[
      (x / (K(y,z) * u)) * u = (x / u) * (K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(58,a,7301,a(flip),b,14564,a),flip(a)].">
      <j1 rule="hyper" parents="58 7301 14564"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14569">
    <literal><![CDATA[
      (x / (K(y,z) * (1 / u))) * (1 / u) = (x / (1 / u)) * (K(z,y) / u)
    ]]></literal>
    <justification jstring="[para(13712(a,1),14568(a,2,2))].">
      <j1 rule="para" parents="13712 14568"/>
    </justification>
  </clause>

  <clause id="14570">
    <literal><![CDATA[
      K(x,y * (z / (K(u,w) * (v5 \ 1)))) = K(x,y * (z / (K(u,w) / v5)))
    ]]></literal>
    <justification jstring="[para(14204(a,1),13934(a,1,2,2,2))].">
      <j1 rule="para" parents="14204 13934"/>
    </justification>
  </clause>

  <clause id="14571">
    <literal><![CDATA[
      T(x,T((y / z) \ K(y,u),w)) = T(x,T((z / y) * K(y,u),w))
    ]]></literal>
    <justification jstring="[para(13773(a,1),14003(a,1,2,1))].">
      <j1 rule="para" parents="13773 14003"/>
    </justification>
  </clause>

  <clause id="14572">
    <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),14092(a,1,2)),flip(a)].">
      <j1 rule="para" parents="60 14092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14573">
    <literal><![CDATA[
      K(x,T(((y * z) \ y) * x,u)) = K(x,x * ((y * T(z,u)) \ y))
    ]]></literal>
    <justification jstring="[hyper(320,a,5385,a(flip),b,14572,a),flip(a)].">
      <j1 rule="hyper" parents="320 5385 14572"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14574">
    <literal><![CDATA[
      K(x,T(((y * z) \ y) * x,u)) = K(x,T(z,u) \ x)
    ]]></literal>
    <justification jstring="[hyper(320,a,10479,a(flip),b,14573,a),flip(a)].">
      <j1 rule="hyper" parents="320 10479 14573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14576">
    <literal><![CDATA[
      K(x,T(((y * z) \ y) * x,u)) = K(x,T(z \ x,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,8570,a,b,14574,a),flip(a)].">
      <j1 rule="hyper" parents="320 8570 14574"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14577">
    <literal><![CDATA[
      K(x,T((y \ z) \ x,u)) = K(x,T((z \ y) * x,u))
    ]]></literal>
    <justification jstring="[para(5(a,1),14576(a,1,2,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5 14576"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14578">
    <literal><![CDATA[
      K(x,T((y \ z) * x,z)) = K(x,(y / z) \ x)
    ]]></literal>
    <justification jstring="[hyper(9193,a,14577,a),flip(a)].">
      <j1 rule="hyper" parents="9193 14577"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14579">
    <literal><![CDATA[
      K(x,T(x * (y \ z),z)) = K(x,(y / z) \ x)
    ]]></literal>
    <justification jstring="[hyper(12318,a,14578,a)].">
      <j1 rule="hyper" parents="12318 14578"/>
    </justification>
  </clause>

  <clause id="14580">
    <literal><![CDATA[
      K(x,T((y \ z) * x,y)) = K(x,(y / z) \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,9706,a(flip),b,14578,a)].">
      <j1 rule="hyper" parents="58 9706 14578"/>
    </justification>
  </clause>

  <clause id="14581">
    <literal><![CDATA[
      K(x,T(x * T(y,z),z)) = K(x,((y \ z) / z) \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,11479,a(flip),b,14579,a)].">
      <j1 rule="hyper" parents="58 11479 14579"/>
    </justification>
  </clause>

  <clause id="14582">
    <literal><![CDATA[
      K(x,(y / (y * z)) \ x) = K(x,T(z * x,y))
    ]]></literal>
    <justification jstring="[para(4(a,1),14580(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="4 14580"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14583">
    <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(9046,a,14582,a)].">
      <j1 rule="hyper" parents="9046 14582"/>
    </justification>
  </clause>

  <clause id="14584">
    <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(14581(a,2),6743(a,1,1))].">
      <j1 rule="para" parents="14581 6743"/>
    </justification>
  </clause>

  <clause id="14585">
    <literal><![CDATA[
      ((x * ((x * y) / x)) / z) \ y = ((x * y) / z) \ T(y,T(x,y))
    ]]></literal>
    <justification jstring="[para(105(a,1),14108(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="105 14108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14586">
    <literal><![CDATA[
      ((x * ((x * y) / x)) / z) \ y = ((x * y) / z) \ T(y,x)
    ]]></literal>
    <justification jstring="[para(4233(a,1),14585(a,2,2))].">
      <j1 rule="para" parents="4233 14585"/>
    </justification>
  </clause>

  <clause id="14587">
    <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(9566(a,2),14177(a,1,2,2))].">
      <j1 rule="para" parents="9566 14177"/>
    </justification>
  </clause>

  <clause id="14588">
    <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(10142(a,1),14177(a,1,2,1,1))].">
      <j1 rule="para" parents="10142 14177"/>
    </justification>
  </clause>

  <clause id="14589">
    <literal><![CDATA[
      K(x,L(y,z,u \ L(u,w,v5))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(10904,a,14342,a)].">
      <j1 rule="hyper" parents="10904 14342"/>
    </justification>
  </clause>

  <clause id="14590">
    <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(14589(a,2),14338(a,1))].">
      <j1 rule="para" parents="14589 14338"/>
    </justification>
  </clause>

  <clause id="14591">
    <literal><![CDATA[
      K(x,y \ L(y,z,u)) = 1 * a(y,z,K(x,u))
    ]]></literal>
    <justification jstring="[para(13247(a,1),14398(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13247 14398"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14593">
    <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(14402(a,1),14415(a,1))].">
      <j1 rule="para" parents="14402 14415"/>
    </justification>
  </clause>

  <clause id="14594">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(u / w,y)) = K(x,L(y,z,u / (y * w)))
    ]]></literal>
    <justification jstring="[para(11016(a,1),14410(a,1,2))].">
      <j1 rule="para" parents="11016 14410"/>
    </justification>
  </clause>

  <clause id="14595">
    <literal><![CDATA[
      K(x,L(L(y,z,u),z,u \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(14434,a,14458,a),flip(a)].">
      <j1 rule="hyper" parents="14434 14458"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14596">
    <literal><![CDATA[
      K(x,L(L(y,z,u \ 1),z,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(25(a,1),14595(a,1,2))].">
      <j1 rule="para" parents="25 14595"/>
    </justification>
  </clause>

  <clause id="14597">
    <literal><![CDATA[
      K(x,L((y * z) \ u,z,y \ 1)) = K(x,z \ (y \ u))
    ]]></literal>
    <justification jstring="[para(298(a,1),14595(a,1,2,1))].">
      <j1 rule="para" parents="298 14595"/>
    </justification>
  </clause>

  <clause id="14598">
    <literal><![CDATA[
      x * (y * K(z,L(u,y,x \ 1))) = (x * y) * K(z,u)
    ]]></literal>
    <justification jstring="[para(14595(a,1),10903(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14595 10903"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14599">
    <literal><![CDATA[
      (x \ y) * K(z,L(u,y,x \ 1)) = x \ (y * K(z,u))
    ]]></literal>
    <justification jstring="[para(14596(a,1),14486(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="14596 14486"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14600">
    <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),14597(a,1,2,1))].">
      <j1 rule="para" parents="17 14597"/>
    </justification>
  </clause>

  <clause id="14601">
    <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),14597(a,1,2,1))].">
      <j1 rule="para" parents="81 14597"/>
    </justification>
  </clause>

  <clause id="14602">
    <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,7179,a(flip),b,14598,a),flip(a)].">
      <j1 rule="hyper" parents="116 7179 14598"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14604">
    <literal><![CDATA[
      x * (y * K(z,L(u,y,x \ u))) = (x * y) * K(z,u)
    ]]></literal>
    <justification jstring="[para(14490(a,1),14598(a,1,2,2))].">
      <j1 rule="para" parents="14490 14598"/>
    </justification>
  </clause>

  <clause id="14605">
    <literal><![CDATA[
      K(x,L(y \ (z * u),y,z \ 1)) = K(x,(z \ y) \ u)
    ]]></literal>
    <justification jstring="[hyper(29,a,10933,a(flip),b,14599,a),flip(a)].">
      <j1 rule="hyper" parents="29 10933 14599"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14607">
    <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(14122(a,1),14604(a,2,1))].">
      <j1 rule="para" parents="14122 14604"/>
    </justification>
  </clause>

  <clause id="14608">
    <literal><![CDATA[
      x * K(y,x \ (z \ (u * (z * x)))) = z \ (K(y,u) * (z * x))
    ]]></literal>
    <justification jstring="[para(14600(a,1),14602(a,1,2))].">
      <j1 rule="para" parents="14600 14602"/>
    </justification>
  </clause>

  <clause id="14609">
    <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),14608(a,1,2,2,2,2)),flip(a)].">
      <j1 rule="para" parents="101 14608"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14610">
    <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(9713(a,1),14521(a,1))].">
      <j1 rule="para" parents="9713 14521"/>
    </justification>
  </clause>

  <clause id="14611">
    <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,14533,a(flip),b,14534,a),flip(a)].">
      <j1 rule="hyper" parents="58 14533 14534"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14612">
    <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),14611(a,1,2,2,3)),flip(a)].">
      <j1 rule="para" parents="75 14611"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14613">
    <literal><![CDATA[
      K(x,L((y * z) \ u,u,y \ 1)) = K(x,z \ (y \ u))
    ]]></literal>
    <justification jstring="[hyper(320,a,14597,a(flip),b,14556,a),flip(a)].">
      <j1 rule="hyper" parents="320 14597 14556"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14614">
    <literal><![CDATA[
      (x / (K(y,z) / u)) * (1 / u) = (x / (1 / u)) * (K(z,y) / u)
    ]]></literal>
    <justification jstring="[para(13712(a,1),14569(a,1,1,2))].">
      <j1 rule="para" parents="13712 14569"/>
    </justification>
  </clause>

  <clause id="14616">
    <literal><![CDATA[
      ((x * (y * z)) * K(z,u)) \ ((x * y) * T(z,u)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(9225(a,1),14039(a,1,1))].">
      <j1 rule="para" parents="9225 14039"/>
    </justification>
  </clause>

  <clause id="14617">
    <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(10794(a,1),14066(a,1,1))].">
      <j1 rule="para" parents="10794 14066"/>
    </justification>
  </clause>

  <clause id="14618">
    <literal><![CDATA[
      K(x \ ((x \ 1) \ y),T(x,z)) = K(y * K((x \ 1) \ y,z),x)
    ]]></literal>
    <justification jstring="[hyper(14156,a,11255,a),flip(a)].">
      <j1 rule="hyper" parents="14156 11255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14619">
    <literal><![CDATA[
      K(x * K((y \ 1) \ x,z),y) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(14155,a,14618,a),flip(a)].">
      <j1 rule="hyper" parents="14155 14618"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14621">
    <literal><![CDATA[
      K(x * K(y * x,z),y) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(13794(a,1),14619(a,1,1,2))].">
      <j1 rule="para" parents="13794 14619"/>
    </justification>
  </clause>

  <clause id="14622">
    <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,14621,a(flip),b,5285,a(flip))].">
      <j1 rule="hyper" parents="119 14621 5285"/>
    </justification>
  </clause>

  <clause id="14623">
    <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(7779(a,1),14437(a,1,1,3))].">
      <j1 rule="para" parents="7779 14437"/>
    </justification>
  </clause>

  <clause id="14624">
    <literal><![CDATA[
      K(x,(y \ L(y,z,u)) \ w) = K(x,y * (L(y,z,u) \ w))
    ]]></literal>
    <justification jstring="[hyper(14050,a,14504,a)].">
      <j1 rule="hyper" parents="14050 14504"/>
    </justification>
  </clause>

  <clause id="14626">
    <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(3511(a,1),14624(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3511 14624"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14627">
    <literal><![CDATA[
      x * K(y,x \ (z \ ((u * z) * x))) = z \ ((K(y,u) * z) * x)
    ]]></literal>
    <justification jstring="[para(12497(a,1),14609(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12497 14609"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14628">
    <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,14627,a(flip),b,4245,a)].">
      <j1 rule="hyper" parents="116 14627 4245"/>
    </justification>
  </clause>

  <clause id="14629">
    <literal><![CDATA[
      K(x,L(y,z,u)) * T(u * (z / y),K(x,y)) = u * (z / T(y,x))
    ]]></literal>
    <justification jstring="[para(10806(a,1),14617(a,1,1))].">
      <j1 rule="para" parents="10806 14617"/>
    </justification>
  </clause>

  <clause id="14630">
    <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(7439(a,1),13717(a,1,3,2))].">
      <j1 rule="para" parents="7439 13717"/>
    </justification>
  </clause>

  <clause id="14631">
    <literal><![CDATA[
      K(x,(((y * z) / u) \ K(y,T(z,x))) \ w) = K(x,(((z * y) / u) \ 1) \ w)
    ]]></literal>
    <justification jstring="[para(7158(a,2),14109(a,1,2,1,2))].">
      <j1 rule="para" parents="7158 14109"/>
    </justification>
  </clause>

  <clause id="14632">
    <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(14140(a,2),14152(a,1))].">
      <j1 rule="para" parents="14140 14152"/>
    </justification>
  </clause>

  <clause id="14633">
    <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(14314(a,1),14416(a,2,2))].">
      <j1 rule="para" parents="14314 14416"/>
    </justification>
  </clause>

  <clause id="14634">
    <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(14633(a,2),10866(a,1))].">
      <j1 rule="para" parents="14633 10866"/>
    </justification>
  </clause>

  <clause id="14635">
    <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),14634(a,1,2,3,1,2))].">
      <j1 rule="para" parents="104 14634"/>
    </justification>
  </clause>

  <clause id="14636">
    <literal><![CDATA[
      K(x,L(y,z,(u * x) \ w)) = K(x,L(y,z,u \ w))
    ]]></literal>
    <justification jstring="[hyper(14635,a,xx),flip(a)].">
      <j1 rule="hyper" parents="14635"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14637">
    <literal><![CDATA[
      K(x \ 1,L(y,z,x \ u)) = K(x \ 1,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(163(a,1),14636(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="163 14636"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14638">
    <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,9055,a(flip),b,14583,a),flip(a)].">
      <j1 rule="hyper" parents="58 9055 14583"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14639">
    <literal><![CDATA[
      K(x,T(T(y * T(x,z),u),z)) = K(x,T((u / (u * y)) \ x,z))
    ]]></literal>
    <justification jstring="[hyper(7704,a,14638,a)].">
      <j1 rule="hyper" parents="7704 14638"/>
    </justification>
  </clause>

  <clause id="14641">
    <literal><![CDATA[
      K(x,T((y / (y * z)) \ x,u)) = K(x,T(T(x * z,y),u))
    ]]></literal>
    <justification jstring="[hyper(58,a,10310,a(flip),b,14639,a),flip(a)].">
      <j1 rule="hyper" parents="58 10310 14639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14643">
    <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),14641(a,1,2,1,1,2)),flip(a)].">
      <j1 rule="para" parents="105 14641"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14644">
    <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,9196,a(flip),b,14643,a),flip(a)].">
      <j1 rule="hyper" parents="320 9196 14643"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14645">
    <literal><![CDATA[
      K(x,T(x * T(y,z),z)) = K(x,R(1 / (1 / (1 / y)),y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(10308,a,14644,a)].">
      <j1 rule="hyper" parents="10308 14644"/>
    </justification>
  </clause>

  <clause id="14646">
    <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,5344,a(flip),b,14645,a),flip(a)].">
      <j1 rule="hyper" parents="320 5344 14645"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14647">
    <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),14646(a,2,2,1,1))].">
      <j1 rule="para" parents="75 14646"/>
    </justification>
  </clause>

  <clause id="14648">
    <literal><![CDATA[
      R(K(x,x * y),y,z) = K(x,T(x * T(y,z),z))
    ]]></literal>
    <justification jstring="[hyper(320,a,11675,a(flip),b,14647,a)].">
      <j1 rule="hyper" parents="320 11675 14647"/>
    </justification>
  </clause>

  <clause id="14650">
    <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(14648(a,2),6743(a,1,1))].">
      <j1 rule="para" parents="14648 6743"/>
    </justification>
  </clause>

  <clause id="14651">
    <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,6746,a(flip),b,14650,a)].">
      <j1 rule="hyper" parents="58 6746 14650"/>
    </justification>
  </clause>

  <clause id="14652">
    <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,6743,a(flip),b,14584,a)].">
      <j1 rule="hyper" parents="58 6743 14584"/>
    </justification>
  </clause>

  <clause id="14653">
    <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,12701,a(flip),b,14652,a),flip(a)].">
      <j1 rule="hyper" parents="320 12701 14652"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14654">
    <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),14653(a,2,2,2))].">
      <j1 rule="para" parents="72 14653"/>
    </justification>
  </clause>

  <clause id="14656">
    <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,14651,a,b,14654,a)].">
      <j1 rule="hyper" parents="58 14651 14654"/>
    </justification>
  </clause>

  <clause id="14658">
    <literal><![CDATA[
      R(K(x,R(x * y,z,u)),y,w) = K(R(x,z,u),x * y)
    ]]></literal>
    <justification jstring="[para(12496(a,1),14656(a,1,1))].">
      <j1 rule="para" parents="12496 14656"/>
    </justification>
  </clause>

  <clause id="14659">
    <literal><![CDATA[
      K(x,R(R(x * y,z,u),y,w)) = K(R(x,z,u),x * y)
    ]]></literal>
    <justification jstring="[hyper(12504,a,14658,a)].">
      <j1 rule="hyper" parents="12504 14658"/>
    </justification>
  </clause>

  <clause id="14660">
    <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,12496,a(flip),b,14659,a),flip(a)].">
      <j1 rule="hyper" parents="320 12496 14659"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14661">
    <literal><![CDATA[
      K(x,R(x * y,y * z,u)) = K(x,R(x * y,z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,12526,a(flip),b,14660,a),flip(a)].">
      <j1 rule="hyper" parents="58 12526 14660"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14663">
    <literal><![CDATA[
      K(x,R(x * y,z,u)) = K(x,x * R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,12710,a(flip),b,14661,a),flip(a)].">
      <j1 rule="hyper" parents="58 12710 14661"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14664">
    <literal><![CDATA[
      T(x,R(x * y,z,u)) = T(x,x * R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(118,a,14663,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 14663 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14665">
    <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,12562,a,b,14664,a)].">
      <j1 rule="hyper" parents="320 12562 14664"/>
    </justification>
  </clause>

  <clause id="14666">
    <literal><![CDATA[
      L(T(x,R(y,z,u)),y,x) = T(x,R(x * y,z,u))
    ]]></literal>
    <justification jstring="[hyper(11194,a,14665,a)].">
      <j1 rule="hyper" parents="11194 14665"/>
    </justification>
  </clause>

  <clause id="14667">
    <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,12527,a,b,14666,a)].">
      <j1 rule="hyper" parents="58 12527 14666"/>
    </justification>
  </clause>

  <clause id="14668">
    <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(3135(a,2),14666(a,2,2,1))].">
      <j1 rule="para" parents="3135 14666"/>
    </justification>
  </clause>

  <clause id="14669">
    <literal><![CDATA[
      T(x,x * y) * a(x,z,K(u,y)) = T(x,R(x * y,z,u))
    ]]></literal>
    <justification jstring="[para(14258(a,1),14667(a,1,2))].">
      <j1 rule="para" parents="14258 14667"/>
    </justification>
  </clause>

  <clause id="14670">
    <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,13588,a,b,14669,a)].">
      <j1 rule="hyper" parents="58 13588 14669"/>
    </justification>
  </clause>

  <clause id="14671">
    <literal><![CDATA[
      T(x * a(x,y,K(z,u)),u * x) = T(x,R(x * u,y,z))
    ]]></literal>
    <justification jstring="[para(12843(a,1),14670(a,1,1))].">
      <j1 rule="para" parents="12843 14670"/>
    </justification>
  </clause>

  <clause id="14672">
    <literal><![CDATA[
      T(T(x,a(y,z,u) \ x),u * x) = T(x,R(x * u,z,y))
    ]]></literal>
    <justification jstring="[para(14332(a,2),14671(a,1,1))].">
      <j1 rule="para" parents="14332 14671"/>
    </justification>
  </clause>

  <clause id="14673">
    <literal><![CDATA[
      T(T(x,x * y),a(z,u,y) \ x) = T(x,R(x * y,u,z))
    ]]></literal>
    <justification jstring="[hyper(4412,a,14672,a)].">
      <j1 rule="hyper" parents="4412 14672"/>
    </justification>
  </clause>

  <clause id="14674">
    <literal><![CDATA[
      T(x,R(x * y,z,u)) = T(x,L(y * x,z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,13596,a(flip),b,14673,a),flip(a)].">
      <j1 rule="hyper" parents="58 13596 14673"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14675">
    <literal><![CDATA[
      K(x,(y * L(y \ 1,z,u)) \ w) = K(x,y \ (L(y \ 1,z,u) \ w))
    ]]></literal>
    <justification jstring="[hyper(14073,a,14626,a),flip(a)].">
      <j1 rule="hyper" parents="14073 14626"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14676">
    <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(4307(a,1),14094(a,1,1,1))].">
      <j1 rule="para" parents="4307 14094"/>
    </justification>
  </clause>

  <clause id="14677">
    <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,14344,a(flip),b,14473,a),flip(a)].">
      <j1 rule="hyper" parents="320 14344 14473"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14678">
    <literal><![CDATA[
      K(x,L(y,a(z \ 1,z,u),u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(14499,a,14677,a)].">
      <j1 rule="hyper" parents="14499 14677"/>
    </justification>
  </clause>

  <clause id="14680">
    <literal><![CDATA[
      K(x,L(y,z,z \ 1) * (y \ u)) = K(x,a(z \ 1,z,y) \ u)
    ]]></literal>
    <justification jstring="[para(4072(a,1),14677(a,1,2))].">
      <j1 rule="para" parents="4072 14677"/>
    </justification>
  </clause>

  <clause id="14682">
    <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(13706(a,1),14622(a,1,1,2))].">
      <j1 rule="para" parents="13706 14622"/>
    </justification>
  </clause>

  <clause id="14683">
    <literal><![CDATA[
      L(x,T(y,z),x) = L(x,y * K(x * y,u),x)
    ]]></literal>
    <justification jstring="[hyper(13296,a,14682,a)].">
      <j1 rule="hyper" parents="13296 14682"/>
    </justification>
  </clause>

  <clause id="14685">
    <literal><![CDATA[
      L(x,T(y,z),x) = L(x,x \ T(x * y,u),x)
    ]]></literal>
    <justification jstring="[para(13726(a,2),14683(a,2,2))].">
      <j1 rule="para" parents="13726 14683"/>
    </justification>
  </clause>

  <clause id="14686">
    <literal><![CDATA[
      L(x,x \ T(x * y,z),x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(12673,a,14685,a),flip(a)].">
      <j1 rule="hyper" parents="12673 14685"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14687">
    <literal><![CDATA[
      L(x,x \ T(y,z),x) = L(x,x \ y,x)
    ]]></literal>
    <justification jstring="[para(5(a,1),14686(a,1,2,2,1))].">
      <j1 rule="para" parents="5 14686"/>
    </justification>
  </clause>

  <clause id="14689">
    <literal><![CDATA[
      L(x,x \ (y / z),x) = L(x,x \ (z \ y),x)
    ]]></literal>
    <justification jstring="[para(107(a,1),14687(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="107 14687"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14690">
    <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(14689(a,1),12431(a,1,2))].">
      <j1 rule="para" parents="14689 12431"/>
    </justification>
  </clause>

  <clause id="14691">
    <literal><![CDATA[
      T(T(x,x * y) * K(x * y,z),y) = y \ T(T(x,y * x) * y,z)
    ]]></literal>
    <justification jstring="[para(13030(a,1),14676(a,1,1,2))].">
      <j1 rule="para" parents="13030 14676"/>
    </justification>
  </clause>

  <clause id="14692">
    <literal><![CDATA[
      T(T(x * K(x * y,z),x * y),y) = y \ T(T(x,y * x) * y,z)
    ]]></literal>
    <justification jstring="[para(7437(a,2),14691(a,1,1))].">
      <j1 rule="para" parents="7437 14691"/>
    </justification>
  </clause>

  <clause id="14694">
    <literal><![CDATA[
      T(T(x * K(x * y,z),y),x * y) = y \ T(T(x,y * x) * y,z)
    ]]></literal>
    <justification jstring="[hyper(434,a,14692,a)].">
      <j1 rule="hyper" parents="434 14692"/>
    </justification>
  </clause>

  <clause id="14695">
    <literal><![CDATA[
      T(T(x * K(x * y,z),y),x * y) = y \ T(T(x,x * y) * y,z)
    ]]></literal>
    <justification jstring="[para(4307(a,1),14694(a,2,2,1,1))].">
      <j1 rule="para" parents="4307 14694"/>
    </justification>
  </clause>

  <clause id="14696">
    <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),14168(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7 14168"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14697">
    <literal><![CDATA[
      K(x,L(((y / z) \ 1) \ z,z,u)) = K(x,L(y,(y / z) \ 1,u))
    ]]></literal>
    <justification jstring="[para(10414(a,1),14696(a,2,2))].">
      <j1 rule="para" parents="10414 14696"/>
    </justification>
  </clause>

  <clause id="14698">
    <literal><![CDATA[
      K(x,L(((y / z) \ 1) \ z,z,u)) = K(x,L(y,(z \ y) \ 1,u))
    ]]></literal>
    <justification jstring="[para(13292(a,1),14697(a,2,2))].">
      <j1 rule="para" parents="13292 14697"/>
    </justification>
  </clause>

  <clause id="14699">
    <literal><![CDATA[
      K(x,L((y / z) * z,z,u)) = K(x,L(y,(z \ y) \ 1,u))
    ]]></literal>
    <justification jstring="[hyper(14145,a,14698,a)].">
      <j1 rule="hyper" parents="14145 14698"/>
    </justification>
  </clause>

  <clause id="14700">
    <literal><![CDATA[
      K(x,L(y,(z \ y) \ 1,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(7(a,1),14699(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7 14699"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14701">
    <literal><![CDATA[
      (a(x,y,a(z,u,w)) * (v5 * v6)) \ (v6 * v5) = a(x,y,a(z,u,w)) \ K(v6,v5)
    ]]></literal>
    <justification jstring="[hyper(320,a,13812,a(flip),b,14215,a),flip(a)].">
      <j1 rule="hyper" parents="320 13812 14215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14702">
    <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(14255(a,1),13886(a,1,2))].">
      <j1 rule="para" parents="14255 13886"/>
    </justification>
  </clause>

  <clause id="14703">
    <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(14373(a,1),14532(a,2,1))].">
      <j1 rule="para" parents="14373 14532"/>
    </justification>
  </clause>

  <clause id="14704">
    <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,14435,a(flip),b,14703,a),flip(a)].">
      <j1 rule="hyper" parents="320 14435 14703"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14705">
    <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),14704(a,1,2,2))].">
      <j1 rule="para" parents="91 14704"/>
    </justification>
  </clause>

  <clause id="14706">
    <literal><![CDATA[
      K(x,K(y,L(z,u / w,w))) = K(x,K(y,L(z,u,w)))
    ]]></literal>
    <justification jstring="[para(11189(a,2),14705(a,1,2,2))].">
      <j1 rule="para" parents="11189 14705"/>
    </justification>
  </clause>

  <clause id="14707">
    <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(13708(a,1),13989(a,2,1))].">
      <j1 rule="para" parents="13708 13989"/>
    </justification>
  </clause>

  <clause id="14708">
    <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(13743(a,1),14707(a,1,2,2))].">
      <j1 rule="para" parents="13743 14707"/>
    </justification>
  </clause>

  <clause id="14709">
    <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(7779(a,1),14708(a,1,2))].">
      <j1 rule="para" parents="7779 14708"/>
    </justification>
  </clause>

  <clause id="14710">
    <literal><![CDATA[
      (T(x,y) / z) \ K(x,K(z \ x,y)) = (T(x,T(y,z)) / z) \ 1
    ]]></literal>
    <justification jstring="[para(7213(a,1),14709(a,1,2,2))].">
      <j1 rule="para" parents="7213 14709"/>
    </justification>
  </clause>

  <clause id="14711">
    <literal><![CDATA[
      (T(x,y) / z) \ K(x,K(z,y)) = (T(x,T(y,z)) / z) \ 1
    ]]></literal>
    <justification jstring="[para(8167(a,1),14710(a,1,2))].">
      <j1 rule="para" parents="8167 14710"/>
    </justification>
  </clause>

  <clause id="14712">
    <literal><![CDATA[
      (T(x,y) / z) \ K(x,K(y,z)) = (T(x,T(y,z)) / z) \ 1
    ]]></literal>
    <justification jstring="[para(7797(a,1),14711(a,1,2))].">
      <j1 rule="para" parents="7797 14711"/>
    </justification>
  </clause>

  <clause id="14713">
    <literal><![CDATA[
      (T(x,T(y,z)) / z) \ 1 = K(y,x) * ((x / z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,14245,a(flip),b,14712,a),flip(a)].">
      <j1 rule="hyper" parents="58 14245 14712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14714">
    <literal><![CDATA[
      K(x * y,L(z,u,u \ 1)) = (x \ T(y * x,z)) * (T(y,x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(14159,a,13768,a),flip(a)].">
      <j1 rule="hyper" parents="14159 13768"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14715">
    <literal><![CDATA[
      (x \ T(y * x,z)) * (T(y,x) \ 1) = K(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(14159,a,13748,a)].">
      <j1 rule="hyper" parents="14159 13748"/>
    </justification>
  </clause>

  <clause id="14716">
    <literal><![CDATA[
      (x \ T(y * x,z)) * (T(y,x) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      K(x * y,z) = u
    ]]></literal>
    <justification jstring="[para(14714(a,1),6499(a,1))].">
      <j1 rule="para" parents="14714 6499"/>
    </justification>
  </clause>

  <clause id="14717">
    <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(13218,a,14555,a)].">
      <j1 rule="hyper" parents="13218 14555"/>
    </justification>
  </clause>

  <clause id="14718">
    <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(13325,a,14717,a)].">
      <j1 rule="hyper" parents="13325 14717"/>
    </justification>
  </clause>

  <clause id="14719">
    <literal><![CDATA[
      K(x,R(y,z,z \ 1) \ ((z \ 1) * u)) = K(x,y \ (z \ u))
    ]]></literal>
    <justification jstring="[hyper(58,a,14597,a(flip),b,14718,a),flip(a)].">
      <j1 rule="hyper" parents="58 14597 14718"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14720">
    <literal><![CDATA[
      K(x,(y * (z \ 1)) \ ((z \ 1) * u)) = K(x,(y / z) \ (z \ u))
    ]]></literal>
    <justification jstring="[para(523(a,1),14719(a,1,2,1))].">
      <j1 rule="para" parents="523 14719"/>
    </justification>
  </clause>

  <clause id="14721">
    <literal><![CDATA[
      K(x,(y * (z \ 1)) \ ((z \ 1) * (z * u))) = K(x,(y / z) \ u)
    ]]></literal>
    <justification jstring="[para(4(a,1),14720(a,2,2,2))].">
      <j1 rule="para" parents="4 14720"/>
    </justification>
  </clause>

  <clause id="14722">
    <literal><![CDATA[
      K(x,(y * (z \ 1)) \ L(u,z,z \ 1)) = K(x,(y / z) \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,5731,a(flip),b,14721,a)].">
      <j1 rule="hyper" parents="58 5731 14721"/>
    </justification>
  </clause>

  <clause id="14723">
    <literal><![CDATA[
      K(x,((y \ z) * u) \ (y \ (z * u))) = a(x,y \ z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(14493,a,14601,a),flip(a)].">
      <j1 rule="hyper" parents="14493 14601"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14724">
    <literal><![CDATA[
      K(x,((y \ z) * u) \ (y \ (z * u))) = a(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(320,a,14369,a(flip),b,14723,a),flip(a)].">
      <j1 rule="hyper" parents="320 14369 14723"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14725">
    <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(9444(a,1),14724(a,1,2,1))].">
      <j1 rule="para" parents="9444 14724"/>
    </justification>
  </clause>

  <clause id="14726">
    <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(4058(a,1),13991(a,1,2))].">
      <j1 rule="para" parents="4058 13991"/>
    </justification>
  </clause>

  <clause id="14727">
    <literal><![CDATA[
      ((x * ((y * (x / y)) \ y)) / x) \ 1 = x / (x * ((((x / (1 / (x \ y))) / x) \ 1) \ 1))
    ]]></literal>
    <justification jstring="[para(10151(a,1),13950(a,1,1,1,2))].">
      <j1 rule="para" parents="10151 13950"/>
    </justification>
  </clause>

  <clause id="14728">
    <literal><![CDATA[
      x / (x * ((((x / (1 / (x \ y))) / x) \ 1) \ 1)) = ((x / (x / y)) / x) \ 1
    ]]></literal>
    <justification jstring="[para(5395(a,1),14727(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5395 14727"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14729">
    <literal><![CDATA[
      x / (x * ((1 / ((x / ((x \ y) \ 1)) / x)) \ 1)) = ((x / (x / y)) / x) \ 1
    ]]></literal>
    <justification jstring="[para(2646(a,2),14728(a,1,2,2,1))].">
      <j1 rule="para" parents="2646 14728"/>
    </justification>
  </clause>

  <clause id="14730">
    <literal><![CDATA[
      x / (x * ((x / ((x \ y) \ 1)) / x)) = ((x / (x / y)) / x) \ 1
    ]]></literal>
    <justification jstring="[para(75(a,1),14729(a,1,2,2))].">
      <j1 rule="para" parents="75 14729"/>
    </justification>
  </clause>

  <clause id="14732">
    <literal><![CDATA[
      x / (x / ((y / x) \ 1)) = ((x / (x / y)) / x) \ 1
    ]]></literal>
    <justification jstring="[para(11370(a,1),14730(a,1,2))].">
      <j1 rule="para" parents="11370 14730"/>
    </justification>
  </clause>

  <clause id="14733">
    <literal><![CDATA[
      1 / (x / (x / ((y / x) \ 1))) = (x / (x / y)) / x
    ]]></literal>
    <justification jstring="[hyper(197,a,14732,a(flip))].">
      <j1 rule="hyper" parents="197 14732"/>
    </justification>
  </clause>

  <clause id="14734">
    <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(12700(a,1),14480(a,2,2))].">
      <j1 rule="para" parents="12700 14480"/>
    </justification>
  </clause>

  <clause id="14735">
    <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(14019(a,1),14734(a,1,2,3))].">
      <j1 rule="para" parents="14019 14734"/>
    </justification>
  </clause>

  <clause id="14736">
    <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(11180(a,1),14510(a,2,1))].">
      <j1 rule="para" parents="11180 14510"/>
    </justification>
  </clause>

  <clause id="14737">
    <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),14736(a,2,2))].">
      <j1 rule="para" parents="105 14736"/>
    </justification>
  </clause>

  <clause id="14738">
    <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),14737(a,1,1,3,2))].">
      <j1 rule="para" parents="105 14737"/>
    </justification>
  </clause>

  <clause id="14739">
    <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),14690(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="62 14690"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14740">
    <literal><![CDATA[
      ((x * (y * z)) / x) \ L(z,y,z) = T((x * (z * y)) / x,z) \ z
    ]]></literal>
    <justification jstring="[para(5(a,1),14739(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5 14739"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14742">
    <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(13451(a,1),14448(a,1,2))].">
      <j1 rule="para" parents="13451 14448"/>
    </justification>
  </clause>

  <clause id="14743">
    <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(1372(a,1),14742(a,1,2,2))].">
      <j1 rule="para" parents="1372 14742"/>
    </justification>
  </clause>

  <clause id="14744">
    <literal><![CDATA[
      a(x,y,z * a(u,w,a(v5,v6,v7))) = ((x * y) * z) / (x * (y * z))
    ]]></literal>
    <justification jstring="[para(13413(a,1),14743(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="13413 14743"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14745">
    <literal><![CDATA[
      a(x,y,z * a(u,w,a(v5,v6,v7))) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,14444,a,b,14744,a),flip(a)].">
      <j1 rule="hyper" parents="320 14444 14744"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14747">
    <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(14745(a,2),977(a,1))].">
      <j1 rule="para" parents="14745 977"/>
    </justification>
  </clause>

  <clause id="14748">
    <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(6335(a,1),13971(a,1,1,2))].">
      <j1 rule="para" parents="6335 13971"/>
    </justification>
  </clause>

  <clause id="14749">
    <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(11645(a,1),14668(a,1,1))].">
      <j1 rule="para" parents="11645 14668"/>
    </justification>
  </clause>

  <clause id="14750">
    <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),14749(a,1,1,2,1,2,1))].">
      <j1 rule="para" parents="75 14749"/>
    </justification>
  </clause>

  <clause id="14751">
    <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(10296(a,1),14750(a,1,1))].">
      <j1 rule="para" parents="10296 14750"/>
    </justification>
  </clause>

  <clause id="14752">
    <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,4024,a(flip),b,14751,a)].">
      <j1 rule="hyper" parents="58 4024 14751"/>
    </justification>
  </clause>

  <clause id="14754">
    <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),14752(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="75 14752"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14755">
    <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,10583,a(flip),b,14754,a),flip(a)].">
      <j1 rule="hyper" parents="320 10583 14754"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14757">
    <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,14666,a(flip),b,14755,a),flip(a)].">
      <j1 rule="hyper" parents="320 14666 14755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14758">
    <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),14757(a,2,2,1))].">
      <j1 rule="para" parents="5 14757"/>
    </justification>
  </clause>

  <clause id="14759">
    <literal><![CDATA[
      T(x,R(x * (y / T(1 / (1 / x),z)),u,w)) = T(x,R(y,u,w))
    ]]></literal>
    <justification jstring="[para(3135(a,1),14758(a,1,2,1))].">
      <j1 rule="para" parents="3135 14758"/>
    </justification>
  </clause>

  <clause id="14760">
    <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,14674,a(flip),b,14759,a)].">
      <j1 rule="hyper" parents="58 14674 14759"/>
    </justification>
  </clause>

  <clause id="14761">
    <literal><![CDATA[
      T(x,L(y * (x * (1 / T(x,z))),u,w)) = T(x,R(y,u,w))
    ]]></literal>
    <justification jstring="[para(9702(a,1),14760(a,1,2,1))].">
      <j1 rule="para" parents="9702 14760"/>
    </justification>
  </clause>

  <clause id="14762">
    <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,3787,a(flip),b,14761,a)].">
      <j1 rule="hyper" parents="58 3787 14761"/>
    </justification>
  </clause>

  <clause id="14763">
    <literal><![CDATA[
      T(x,L(y * K(z,x),u,w)) = T(x,R(y,u,w))
    ]]></literal>
    <justification jstring="[para(4796(a,2),14762(a,1,2,1,2))].">
      <j1 rule="para" parents="4796 14762"/>
    </justification>
  </clause>

  <clause id="14764">
    <literal><![CDATA[
      T(x,R(y,z,u)) = T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(178(a,1),14763(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="178 14763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14766">
    <literal><![CDATA[
      R(x,y,z) * T(u,L(x,y,z)) = u * R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(119,a,14764,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 14764 17"/>
    </justification>
  </clause>

  <clause id="14767">
    <literal><![CDATA[
      T(x,L(y / z,z,u)) = T(x,(y * u) / (z * u))
    ]]></literal>
    <justification jstring="[para(102(a,1),14764(a,1,2)),flip(a)].">
      <j1 rule="para" parents="102 14764"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14768">
    <literal><![CDATA[
      T(x,L((y / z) / u,u,z)) = T(x,y / (u * z))
    ]]></literal>
    <justification jstring="[para(301(a,1),14764(a,1,2)),flip(a)].">
      <j1 rule="para" parents="301 14764"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14769">
    <literal><![CDATA[
      x / T(x,L(y,z,u)) = K(R(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(14764(a,1),4794(a,2,2)),flip(a)].">
      <j1 rule="para" parents="14764 4794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14770">
    <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(14764(a,1),8290(a,1,2))].">
      <j1 rule="para" parents="14764 8290"/>
    </justification>
  </clause>

  <clause id="14771">
    <literal><![CDATA[
      T(x,L(y / (z / u),u \ z,u)) = T(x,(y * u) / z)
    ]]></literal>
    <justification jstring="[para(10396(a,1),14764(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10396 14764"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14772">
    <literal><![CDATA[
      K(R(x,y,z),u) = K(L(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(4862,a,14769,a),flip(a)].">
      <j1 rule="hyper" parents="4862 14769"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14773">
    <literal><![CDATA[
      K(R(x,y,z),u) = K(x,L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,10840,a(flip),b,14772,a),flip(a)].">
      <j1 rule="hyper" parents="320 10840 14772"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14774">
    <literal><![CDATA[
      K(L(x / y,y,z),u) = K((x * z) / (y * z),u)
    ]]></literal>
    <justification jstring="[para(102(a,1),14772(a,1,1)),flip(a)].">
      <j1 rule="para" parents="102 14772"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14775">
    <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(14772(a,1),7727(a,1))].">
      <j1 rule="para" parents="14772 7727"/>
    </justification>
  </clause>

  <clause id="14776">
    <literal><![CDATA[
      K(x,R(y,z,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(12506,a,14773,a)].">
      <j1 rule="hyper" parents="12506 14773"/>
    </justification>
  </clause>

  <clause id="14777">
    <literal><![CDATA[
      R(K(x,y),z,u) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(12505,a,14773,a)].">
      <j1 rule="hyper" parents="12505 14773"/>
    </justification>
  </clause>

  <clause id="14778">
    <literal><![CDATA[
      L(K(x,y),z,u) = K(x,R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,10794,a,b,14776,a)].">
      <j1 rule="hyper" parents="320 10794 14776"/>
    </justification>
  </clause>

  <clause id="14779">
    <literal><![CDATA[
      ((x * y) * z) / ((T(x,u) * y) * z) = K(u,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,5981,a,b,14776,a)].">
      <j1 rule="hyper" parents="58 5981 14776"/>
    </justification>
  </clause>

  <clause id="14780">
    <literal><![CDATA[
      K(x,L(y / z,z,u)) = K(x,(y * u) / (z * u))
    ]]></literal>
    <justification jstring="[para(102(a,1),14776(a,1,2)),flip(a)].">
      <j1 rule="para" parents="102 14776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14781">
    <literal><![CDATA[
      K(x,L((y / z) / u,u,z)) = K(x,y / (u * z))
    ]]></literal>
    <justification jstring="[para(301(a,1),14776(a,1,2)),flip(a)].">
      <j1 rule="para" parents="301 14776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14782">
    <literal><![CDATA[
      K(x,L(y \ (z / u),y,u)) = K(x,T(z / (y * u),y))
    ]]></literal>
    <justification jstring="[para(649(a,1),14776(a,1,2)),flip(a)].">
      <j1 rule="para" parents="649 14776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14783">
    <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(14776(a,1),9768(a,1,2))].">
      <j1 rule="para" parents="14776 9768"/>
    </justification>
  </clause>

  <clause id="14784">
    <literal><![CDATA[
      K(x,L(y / (z / u),u \ z,u)) = K(x,(y * u) / z)
    ]]></literal>
    <justification jstring="[para(10396(a,1),14776(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10396 14776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14785">
    <literal><![CDATA[
      K(x,L(y,z,u)) * (z * u) = (K(x,y) * z) * u
    ]]></literal>
    <justification jstring="[para(14776(a,1),12497(a,1,1))].">
      <j1 rule="para" parents="14776 12497"/>
    </justification>
  </clause>

  <clause id="14786">
    <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(14776(a,1),14326(a,1,2,3))].">
      <j1 rule="para" parents="14776 14326"/>
    </justification>
  </clause>

  <clause id="14787">
    <literal><![CDATA[
      K(x,(y * z) / ((u \ y) * z)) = K(x,L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(6978,a,14777,a)].">
      <j1 rule="hyper" parents="6978 14777"/>
    </justification>
  </clause>

  <clause id="14788">
    <literal><![CDATA[
      K(x,L(y / z,y,u)) = K(x,(y * u) / (z * u))
    ]]></literal>
    <justification jstring="[hyper(6943,a,14777,a),flip(a)].">
      <j1 rule="hyper" parents="6943 14777"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14789">
    <literal><![CDATA[
      R(K(x,y),z,u) = L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(320,a,10794,a,b,14777,a),flip(a)].">
      <j1 rule="hyper" parents="320 10794 14777"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14790">
    <literal><![CDATA[
      K(x,L(y / (z / u),y,u)) = K(x,(y * u) / z)
    ]]></literal>
    <justification jstring="[hyper(58,a,6945,a(flip),b,14777,a),flip(a)].">
      <j1 rule="hyper" parents="58 6945 14777"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14791">
    <literal><![CDATA[
      K(x,L(y \ 1,z,u)) = K(x,R(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,6921,a(flip),b,14777,a),flip(a)].">
      <j1 rule="hyper" parents="58 6921 14777"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14792">
    <literal><![CDATA[
      K(R(x,y,z) \ 1,u) = K(x \ 1,L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,5703,a(flip),b,14777,a)].">
      <j1 rule="hyper" parents="58 5703 14777"/>
    </justification>
  </clause>

  <clause id="14793">
    <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(14777(a,1),701(a,1,1))].">
      <j1 rule="para" parents="14777 701"/>
    </justification>
  </clause>

  <clause id="14794">
    <literal><![CDATA[
      (K(x,T(y,z * u)) * z) * u = (z * u) * K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(14777(a,1),7903(a,2,2))].">
      <j1 rule="para" parents="14777 7903"/>
    </justification>
  </clause>

  <clause id="14795">
    <literal><![CDATA[
      K(x,L(y,z,u)) * (u * z) = (K(x,y) * z) * T(u,z)
    ]]></literal>
    <justification jstring="[para(14777(a,1),10390(a,1,1))].">
      <j1 rule="para" parents="14777 10390"/>
    </justification>
  </clause>

  <clause id="14796">
    <literal><![CDATA[
      K(x,L(y,z \ u,z)) * u = (K(x,y) * (u / z)) * z
    ]]></literal>
    <justification jstring="[para(14777(a,1),10399(a,1,1))].">
      <j1 rule="para" parents="14777 10399"/>
    </justification>
  </clause>

  <clause id="14797">
    <literal><![CDATA[
      K(x,R(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(14778(a,1),10837(a,1))].">
      <j1 rule="para" parents="14778 10837"/>
    </justification>
  </clause>

  <clause id="14798">
    <literal><![CDATA[
      L(K(x / (y / z),u),x,z) = K((x * z) / y,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,6764,a(flip),b,14789,a),flip(a)].">
      <j1 rule="hyper" parents="58 6764 14789"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14799">
    <literal><![CDATA[
      T(L(K(x,y),z,u),w) * (z * u) = (T(K(x,y),w) * z) * u
    ]]></literal>
    <justification jstring="[para(14789(a,1),512(a,1,1,1))].">
      <j1 rule="para" parents="14789 512"/>
    </justification>
  </clause>

  <clause id="14801">
    <literal><![CDATA[
      R(K(x,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(14789(a,2),10837(a,1))].">
      <j1 rule="para" parents="14789 10837"/>
    </justification>
  </clause>

  <clause id="14802">
    <literal><![CDATA[
      L(K(x,y),z,u) \ (u * (K(x,y) * z)) = z * T(u,K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(14789(a,1),14224(a,1,1))].">
      <j1 rule="para" parents="14789 14224"/>
    </justification>
  </clause>

  <clause id="14803">
    <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),14797(a,1,2))].">
      <j1 rule="para" parents="102 14797"/>
    </justification>
  </clause>

  <clause id="14804">
    <literal><![CDATA[
      K(x,(y * z) / ((u \ y) * z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(u,y,z)) = w
    ]]></literal>
    <justification jstring="[para(6946(a,2),14801(a,1))].">
      <j1 rule="para" parents="6946 14801"/>
    </justification>
  </clause>

  <clause id="14805">
    <literal><![CDATA[
      K(x,R(y,z,u) \ 1) = K(x,L(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,10813,a(flip),b,14791,a),flip(a)].">
      <j1 rule="hyper" parents="58 10813 14791"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14806">
    <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,7568,a(flip),b,14792,a),flip(a)].">
      <j1 rule="hyper" parents="58 7568 14792"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14807">
    <literal><![CDATA[
      K(T(x / y,z) \ 1,L(u,y,y \ z)) = K((z \ (x * (y \ z))) \ 1,u)
    ]]></literal>
    <justification jstring="[para(963(a,1),14792(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="963 14792"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14808">
    <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(769(a,1),14805(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="769 14805"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14810">
    <literal><![CDATA[
      R(x,y,z) * T(y * z,x) = (y * z) * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(13694(a,1),14766(a,1,2))].">
      <j1 rule="para" parents="13694 14766"/>
    </justification>
  </clause>

  <clause id="14811">
    <literal><![CDATA[
      K((x * y) \ z,T(u,y)) = K(((x \ z) * x) / (y * x),u)
    ]]></literal>
    <justification jstring="[hyper(8255,a,14774,a)].">
      <j1 rule="hyper" parents="8255 14774"/>
    </justification>
  </clause>

  <clause id="14812">
    <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(14774(a,1),8255(a,1))].">
      <j1 rule="para" parents="14774 8255"/>
    </justification>
  </clause>

  <clause id="14813">
    <literal><![CDATA[
      K(x,T((y * z) \ u,z)) = K(x,((y \ u) * y) / (z * y))
    ]]></literal>
    <justification jstring="[hyper(58,a,8011,a(flip),b,14780,a)].">
      <j1 rule="hyper" parents="58 8011 14780"/>
    </justification>
  </clause>

  <clause id="14814">
    <literal><![CDATA[
      K(x,K((y / z) / u,L(w,y / z,z))) = K(x,K(w,y / (u * z)))
    ]]></literal>
    <justification jstring="[para(14781(a,1),10895(a,2,2))].">
      <j1 rule="para" parents="14781 10895"/>
    </justification>
  </clause>

  <clause id="14815">
    <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(14785(a,1),6132(a,2,2,1))].">
      <j1 rule="para" parents="14785 6132"/>
    </justification>
  </clause>

  <clause id="14816">
    <literal><![CDATA[
      (K(x,L(y,z,u \ 1)) * z) * u = K(x,y) * (z * u)
    ]]></literal>
    <justification jstring="[para(14596(a,1),14785(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14596 14785"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14817">
    <literal><![CDATA[
      K(x,L((y * z) / u,y,z \ 1)) = K(x,((y * z) * (z \ 1)) / (u * (z \ 1)))
    ]]></literal>
    <justification jstring="[hyper(14551,a,14788,a)].">
      <j1 rule="hyper" parents="14551 14788"/>
    </justification>
  </clause>

  <clause id="14818">
    <literal><![CDATA[
      K(x,(y * (y \ z)) / (u * (y \ z))) = K(x,L(y / u,z,y \ z))
    ]]></literal>
    <justification jstring="[hyper(14481,a,14788,a),flip(a)].">
      <j1 rule="hyper" parents="14481 14788"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14819">
    <literal><![CDATA[
      K(x,L(y * z,y,u)) = K(x,(y * u) / ((z \ 1) * u))
    ]]></literal>
    <justification jstring="[hyper(14151,a,14788,a)].">
      <j1 rule="hyper" parents="14151 14788"/>
    </justification>
  </clause>

  <clause id="14820">
    <literal><![CDATA[
      K(x,(y * z) / (u * z)) != w
    ]]></literal>
    <literal><![CDATA[
      L(K(x,y / u),y,z) = w
    ]]></literal>
    <justification jstring="[para(14788(a,1),10863(a,1))].">
      <j1 rule="para" parents="14788 10863"/>
    </justification>
  </clause>

  <clause id="14821">
    <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,14790,a(flip),b,14328,a)].">
      <j1 rule="hyper" parents="116 14790 14328"/>
    </justification>
  </clause>

  <clause id="14822">
    <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(7735,a,14798,a)].">
      <j1 rule="hyper" parents="7735 14798"/>
    </justification>
  </clause>

  <clause id="14823">
    <literal><![CDATA[
      ((x * y) * z) * a(z,x,y) = (x * y) * R(z,x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,11238,a,b,14810,a)].">
      <j1 rule="hyper" parents="58 11238 14810"/>
    </justification>
  </clause>

  <clause id="14824">
    <literal><![CDATA[
      x * a(x,y,a(z,u,w)) = R(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(899,a,14823,a)].">
      <j1 rule="hyper" parents="899 14823"/>
    </justification>
  </clause>

  <clause id="14825">
    <literal><![CDATA[
      x * a(x,y,K(z,u)) = R(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(831,a,14823,a)].">
      <j1 rule="hyper" parents="831 14823"/>
    </justification>
  </clause>

  <clause id="14826">
    <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(7179(a,1),14823(a,1,1,1))].">
      <j1 rule="para" parents="7179 14823"/>
    </justification>
  </clause>

  <clause id="14827">
    <literal><![CDATA[
      R(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,a(u,y,z)) = w
    ]]></literal>
    <justification jstring="[para(14825(a,1),14287(a,1))].">
      <j1 rule="para" parents="14825 14287"/>
    </justification>
  </clause>

  <clause id="14828">
    <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,3852,a,b,14824,a)].">
      <j1 rule="hyper" parents="29 3852 14824"/>
    </justification>
  </clause>

  <clause id="14829">
    <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(14824(a,1),476(a,1,2,2))].">
      <j1 rule="para" parents="14824 476"/>
    </justification>
  </clause>

  <clause id="14830">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * (v5 * x) = v5 * R(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(14824(a,1),13436(a,2,2))].">
      <j1 rule="para" parents="14824 13436"/>
    </justification>
  </clause>

  <clause id="14831">
    <literal><![CDATA[
      T(x,L(y / (z / u),z,u)) = T(x,(y * u) / z)
    ]]></literal>
    <justification jstring="[hyper(58,a,14469,a(flip),b,14771,a)].">
      <j1 rule="hyper" parents="58 14469 14771"/>
    </justification>
  </clause>

  <clause id="14832">
    <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(14157(a,1),14831(a,1,2,1,2))].">
      <j1 rule="para" parents="14157 14831"/>
    </justification>
  </clause>

  <clause id="14833">
    <literal><![CDATA[
      K(L(x,y,z),u) * ((x * y) * z) = (T(x,u) * y) * z
    ]]></literal>
    <justification jstring="[hyper(31,a,5142,a,b,14779,a)].">
      <j1 rule="hyper" parents="31 5142 14779"/>
    </justification>
  </clause>

  <clause id="14834">
    <literal><![CDATA[
      K(x,L(y,z,(T(y,x) * z) \ u)) * u = (y * z) * ((T(y,x) * z) \ u)
    ]]></literal>
    <justification jstring="[para(14779(a,1),323(a,1,1))].">
      <j1 rule="para" parents="14779 323"/>
    </justification>
  </clause>

  <clause id="14835">
    <literal><![CDATA[
      K(x,T(y / ((z \ u) * z),z \ u)) = K(x,u \ (z * (y / z)))
    ]]></literal>
    <justification jstring="[para(490(a,1),14782(a,1,2)),flip(a)].">
      <j1 rule="para" parents="490 14782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14836">
    <literal><![CDATA[
      K(x,T(1 / (y * z),y)) = K(x,(z * y) \ K(z,1 / z))
    ]]></literal>
    <justification jstring="[para(497(a,1),14782(a,1,2)),flip(a)].">
      <j1 rule="para" parents="497 14782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14837">
    <literal><![CDATA[
      K(x,L(y / (z / u),z,u)) = K(x,(y * u) / z)
    ]]></literal>
    <justification jstring="[hyper(14466,a,14784,a)].">
      <j1 rule="hyper" parents="14466 14784"/>
    </justification>
  </clause>

  <clause id="14838">
    <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,14678,a(flip),b,14837,a),flip(a)].">
      <j1 rule="hyper" parents="58 14678 14837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14839">
    <literal><![CDATA[
      K(x,L(y,z,u)) * z = (K(x,y) * (z / u)) * u
    ]]></literal>
    <justification jstring="[para(14465(a,1),14796(a,1,1))].">
      <j1 rule="para" parents="14465 14796"/>
    </justification>
  </clause>

  <clause id="14840">
    <literal><![CDATA[
      (x * K(y,L(z,x,u))) / u = K(y,T(z,x)) * (x / u)
    ]]></literal>
    <justification jstring="[hyper(8613,a,14839,a)].">
      <j1 rule="hyper" parents="8613 14839"/>
    </justification>
  </clause>

  <clause id="14841">
    <literal><![CDATA[
      (K(x,L(y,z,u)) * z) / u = K(x,y) * (z / u)
    ]]></literal>
    <justification jstring="[hyper(537,a,14839,a)].">
      <j1 rule="hyper" parents="537 14839"/>
    </justification>
  </clause>

  <clause id="14842">
    <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(14839(a,1),537(a,1))].">
      <j1 rule="para" parents="14839 537"/>
    </justification>
  </clause>

  <clause id="14843">
    <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(439,a,14841,a(flip),b,14064,a)].">
      <j1 rule="hyper" parents="439 14841 14064"/>
    </justification>
  </clause>

  <clause id="14844">
    <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(14566(a,1),14841(a,2,2))].">
      <j1 rule="para" parents="14566 14841"/>
    </justification>
  </clause>

  <clause id="14845">
    <literal><![CDATA[
      K(x,L(y,z,u \ 1)) * (z / u) = (K(x,y) * z) / u
    ]]></literal>
    <justification jstring="[para(14596(a,1),14841(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="14596 14841"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14847">
    <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(10114(a,1),14816(a,2,2))].">
      <j1 rule="para" parents="10114 14816"/>
    </justification>
  </clause>

  <clause id="14848">
    <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(5264(a,1),14819(a,2,2,1))].">
      <j1 rule="para" parents="5264 14819"/>
    </justification>
  </clause>

  <clause id="14849">
    <literal><![CDATA[
      a(x,y,K(y * z,u)) * K(x,(y * u) / ((z \ 1) * u)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(14819(a,1),14327(a,1,2))].">
      <j1 rule="para" parents="14819 14327"/>
    </justification>
  </clause>

  <clause id="14850">
    <literal><![CDATA[
      K(x,y) * ((x * y) * z) = (T(x,y) * y) * z
    ]]></literal>
    <justification jstring="[para(10355(a,1),14833(a,1,1))].">
      <j1 rule="para" parents="10355 14833"/>
    </justification>
  </clause>

  <clause id="14851">
    <literal><![CDATA[
      K(x,L(y,z,u)) * ((x * z) * u) = (T(x,y) * z) * u
    ]]></literal>
    <justification jstring="[para(10840(a,1),14833(a,1,1))].">
      <j1 rule="para" parents="10840 14833"/>
    </justification>
  </clause>

  <clause id="14852">
    <literal><![CDATA[
      ((x * y) / x) \ ((y * x) * z) = y \ ((T(y,x) * x) * z)
    ]]></literal>
    <justification jstring="[hyper(116,a,14850,a(flip),b,4814,a),flip(a)].">
      <j1 rule="hyper" parents="116 14850 4814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14853">
    <literal><![CDATA[
      K((x * y) \ z,T(u,y)) = K(T(z,x) / (y * x),u)
    ]]></literal>
    <justification jstring="[hyper(320,a,13147,a(flip),b,14811,a),flip(a)].">
      <j1 rule="hyper" parents="320 13147 14811"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14854">
    <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,13943,a(flip),b,14853,a)].">
      <j1 rule="hyper" parents="58 13943 14853"/>
    </justification>
  </clause>

  <clause id="14855">
    <literal><![CDATA[
      K(T(x,y),(z * y) \ u) = K(x,((z \ u) * z) / (y * z))
    ]]></literal>
    <justification jstring="[hyper(7310,a,14813,a)].">
      <j1 rule="hyper" parents="7310 14813"/>
    </justification>
  </clause>

  <clause id="14856">
    <literal><![CDATA[
      K(x,T((y * z) \ u,z)) = K(x,T(u,y) / (z * y))
    ]]></literal>
    <justification jstring="[hyper(320,a,13139,a(flip),b,14813,a),flip(a)].">
      <j1 rule="hyper" parents="320 13139 14813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14857">
    <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(5601(a,1),14856(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="5601 14856"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14858">
    <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(6919(a,2),14856(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="6919 14856"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14859">
    <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,3603,a(flip),b,14830,a),flip(a)].">
      <j1 rule="hyper" parents="320 3603 14830"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14860">
    <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,14830,a(flip),b,13412,a(flip))].">
      <j1 rule="hyper" parents="116 14830 13412"/>
    </justification>
  </clause>

  <clause id="14861">
    <literal><![CDATA[
      K((x * y) \ T(z,a(y,u,a(w,v5,v6))),L(v7,x * y,a(y,u,a(w,v5,v6)))) = K((x * R(y,u,a(w,v5,v6))) \ (z * a(y,u,a(w,v5,v6))),v7)
    ]]></literal>
    <justification jstring="[para(14830(a,1),10855(a,2,1,1))].">
      <j1 rule="para" parents="14830 10855"/>
    </justification>
  </clause>

  <clause id="14862">
    <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(14855(a,1),7704(a,1))].">
      <j1 rule="para" parents="14855 7704"/>
    </justification>
  </clause>

  <clause id="14863">
    <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(14860(a,1),92(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14860 92"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14864">
    <literal><![CDATA[
      T(K(x,T(y,z * u)) * z,u) = T(z,u) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(239,a,14794,a,b,11210,a(flip))].">
      <j1 rule="hyper" parents="239 14794 11210"/>
    </justification>
  </clause>

  <clause id="14865">
    <literal><![CDATA[
      T(x,y) * K(z,T(u,x * y)) = T(K(z,u) * x,y)
    ]]></literal>
    <justification jstring="[para(7883(a,1),14864(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7883 14864"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14866">
    <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(14864(a,1),7712(a,1,1,1))].">
      <j1 rule="para" parents="14864 7712"/>
    </justification>
  </clause>

  <clause id="14867">
    <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(14865(a,2),770(a,1))].">
      <j1 rule="para" parents="14865 770"/>
    </justification>
  </clause>

  <clause id="14868">
    <literal><![CDATA[
      K(x,y * T(K(x,z) * u,w)) = K(x,y * T(u,w))
    ]]></literal>
    <justification jstring="[para(14865(a,1),7403(a,1,2,2))].">
      <j1 rule="para" parents="14865 7403"/>
    </justification>
  </clause>

  <clause id="14869">
    <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,6545,a(flip),b,14799,a)].">
      <j1 rule="hyper" parents="58 6545 14799"/>
    </justification>
  </clause>

  <clause id="14870">
    <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(14786(a,1),14330(a,1))].">
      <j1 rule="para" parents="14786 14330"/>
    </justification>
  </clause>

  <clause id="14871">
    <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(14870,a,11000,a)].">
      <j1 rule="hyper" parents="14870 11000"/>
    </justification>
  </clause>

  <clause id="14872">
    <literal><![CDATA[
      L(K(x,y),z,u) * (u * (K(y,x) * z)) = z * T(u,K(y,x) * z)
    ]]></literal>
    <justification jstring="[hyper(5894,a,14802,a)].">
      <j1 rule="hyper" parents="5894 14802"/>
    </justification>
  </clause>

  <clause id="14873">
    <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(13147(a,1),14812(a,1))].">
      <j1 rule="para" parents="13147 14812"/>
    </justification>
  </clause>

  <clause id="14874">
    <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(13844(a,1),14814(a,1,2))].">
      <j1 rule="para" parents="13844 14814"/>
    </justification>
  </clause>

  <clause id="14875">
    <literal><![CDATA[
      K(x,L(y / z,u,y \ u)) = K(x,u / (z * (y \ u)))
    ]]></literal>
    <justification jstring="[para(5(a,1),14818(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 14818"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14876">
    <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(4355(a,2),14875(a,2,2,2,2))].">
      <j1 rule="para" parents="4355 14875"/>
    </justification>
  </clause>

  <clause id="14877">
    <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(13139(a,1),14862(a,1))].">
      <j1 rule="para" parents="13139 14862"/>
    </justification>
  </clause>

  <clause id="14878">
    <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,10980,a,b,14872,a)].">
      <j1 rule="hyper" parents="58 10980 14872"/>
    </justification>
  </clause>

  <clause id="14879">
    <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,6259,a(flip),b,14807,a),flip(a)].">
      <j1 rule="hyper" parents="320 6259 14807"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14880">
    <literal><![CDATA[
      K((x / y) \ 1,T(L(z,y,y \ u),u)) = K((x * (y \ u)) \ u,z)
    ]]></literal>
    <justification jstring="[hyper(7712,a,14879,a)].">
      <j1 rule="hyper" parents="7712 14879"/>
    </justification>
  </clause>

  <clause id="14881">
    <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),14880(a,1,2))].">
      <j1 rule="para" parents="20 14880"/>
    </justification>
  </clause>

  <clause id="14882">
    <literal><![CDATA[
      a(x,y,K(z,(u / y) \ z)) \ K(x,(y * z) / u) = K(x,y / (u / z))
    ]]></literal>
    <justification jstring="[para(8484(a,1),14821(a,1,1,3))].">
      <j1 rule="para" parents="8484 14821"/>
    </justification>
  </clause>

  <clause id="14883">
    <literal><![CDATA[
      a(x,y,K(z,u / y)) \ K(z,(y * x) / u) = K(z,y / (u / x))
    ]]></literal>
    <justification jstring="[para(14313(a,1),14882(a,1,1))].">
      <j1 rule="para" parents="14313 14882"/>
    </justification>
  </clause>

  <clause id="14884">
    <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,7169,a,b,14808,a),flip(a)].">
      <j1 rule="hyper" parents="320 7169 14808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14885">
    <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),14817(a,2,2,1))].">
      <j1 rule="para" parents="261 14817"/>
    </justification>
  </clause>

  <clause id="14886">
    <literal><![CDATA[
      T(K(x,y),z) * T(y,x) = T(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(9178,a,14869,a),flip(a)].">
      <j1 rule="hyper" parents="9178 14869"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14887">
    <literal><![CDATA[
      K(x,y / z) * T(z \ y,x) = T(z \ y,K(x,y))
    ]]></literal>
    <justification jstring="[para(7881(a,1),14886(a,1,1))].">
      <j1 rule="para" parents="7881 14886"/>
    </justification>
  </clause>

  <clause id="14889">
    <literal><![CDATA[
      T(x \ y,K(z,y)) = T(y / x,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,7624,a(flip),b,14887,a),flip(a)].">
      <j1 rule="hyper" parents="58 7624 14887"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14890">
    <literal><![CDATA[
      (x \ y) / T(y / x,T(x,z)) = K(K(z,y),x \ y)
    ]]></literal>
    <justification jstring="[para(14889(a,1),4794(a,2,2)),flip(a)].">
      <j1 rule="para" parents="14889 4794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14891">
    <literal><![CDATA[
      (x \ y) / T(y / x,T(x,z)) = K(z,K(y,x \ y))
    ]]></literal>
    <justification jstring="[hyper(320,a,7755,a(flip),b,14890,a),flip(a)].">
      <j1 rule="hyper" parents="320 7755 14890"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14892">
    <literal><![CDATA[
      (x \ y) / T(y / x,T(x,z)) = K(z,K(y,y / x))
    ]]></literal>
    <justification jstring="[para(5197(a,2),14891(a,2,2))].">
      <j1 rule="para" parents="5197 14891"/>
    </justification>
  </clause>

  <clause id="14893">
    <literal><![CDATA[
      (x \ y) / T(y / x,T(x,z)) = K(y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(320,a,8155,a(flip),b,14892,a),flip(a)].">
      <j1 rule="hyper" parents="320 8155 14892"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14894">
    <literal><![CDATA[
      (x \ y) / T(y / x,T(x,z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,7784,a(flip),b,14893,a),flip(a)].">
      <j1 rule="hyper" parents="320 7784 14893"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14895">
    <literal><![CDATA[
      K(x,L((y * z) \ u,u,y \ 1)) = K(x,z \ (R(1 / y,y,z) * u))
    ]]></literal>
    <justification jstring="[hyper(14499,a,14871,a)].">
      <j1 rule="hyper" parents="14499 14871"/>
    </justification>
  </clause>

  <clause id="14897">
    <literal><![CDATA[
      K(x,y \ (R(1 / z,z,y) * u)) = K(x,y \ (z \ u))
    ]]></literal>
    <justification jstring="[hyper(58,a,14613,a(flip),b,14895,a),flip(a)].">
      <j1 rule="hyper" parents="58 14613 14895"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14898">
    <literal><![CDATA[
      K(x,y \ ((y / (z * y)) * u)) = K(x,y \ (z \ u))
    ]]></literal>
    <justification jstring="[para(219(a,1),14897(a,1,2,2,1))].">
      <j1 rule="para" parents="219 14897"/>
    </justification>
  </clause>

  <clause id="14899">
    <literal><![CDATA[
      K(x,y \ ((z / y) \ u)) = K(x,y \ ((y / z) * u))
    ]]></literal>
    <justification jstring="[para(408(a,1),14897(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="408 14897"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14900">
    <literal><![CDATA[
      K(x \ (y / (x \ 1)),z \ ((z / u) * w)) = K(y,T(z \ ((u / z) \ w),x))
    ]]></literal>
    <justification jstring="[hyper(14096,a,14899,a),flip(a)].">
      <j1 rule="hyper" parents="14096 14899"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14901">
    <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(14900(a,1),14096(a,1))].">
      <j1 rule="para" parents="14900 14096"/>
    </justification>
  </clause>

  <clause id="14902">
    <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,9791,a(flip),b,14884,a),flip(a)].">
      <j1 rule="hyper" parents="320 9791 14884"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14903">
    <literal><![CDATA[
      K(x,T(y / (z * u),y / u)) = K(x,(u * z) \ (u * (y / u)))
    ]]></literal>
    <justification jstring="[hyper(6482,a,14902,a),flip(a)].">
      <j1 rule="hyper" parents="6482 14902"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14904">
    <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,13105,a(flip),b,14903,a),flip(a)].">
      <j1 rule="hyper" parents="320 13105 14903"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14905">
    <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(5739(a,1),14903(a,2,2,1))].">
      <j1 rule="para" parents="5739 14903"/>
    </justification>
  </clause>

  <clause id="14906">
    <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,14863,a),flip(a)].">
      <j1 rule="hyper" parents="320 145 14863"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14908">
    <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(1634(a,1),14906(a,1,2))].">
      <j1 rule="para" parents="1634 14906"/>
    </justification>
  </clause>

  <clause id="14909">
    <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(11753(a,1),14878(a,1,1))].">
      <j1 rule="para" parents="11753 14878"/>
    </justification>
  </clause>

  <clause id="14910">
    <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(7832(a,1),14909(a,1,1,2))].">
      <j1 rule="para" parents="7832 14909"/>
    </justification>
  </clause>

  <clause id="14911">
    <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(13557,a,14910,a)].">
      <j1 rule="hyper" parents="13557 14910"/>
    </justification>
  </clause>

  <clause id="14912">
    <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(770,a,14910,a)].">
      <j1 rule="hyper" parents="770 14910"/>
    </justification>
  </clause>

  <clause id="14913">
    <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(8084(a,2),14911(a,1,2,2))].">
      <j1 rule="para" parents="8084 14911"/>
    </justification>
  </clause>

  <clause id="14914">
    <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(8926(a,2),14913(a,1,2))].">
      <j1 rule="para" parents="8926 14913"/>
    </justification>
  </clause>

  <clause id="14915">
    <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(7871(a,2),14914(a,1,2,2,2))].">
      <j1 rule="para" parents="7871 14914"/>
    </justification>
  </clause>

  <clause id="14916">
    <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),14904(a,1,2,1,2))].">
      <j1 rule="para" parents="5 14904"/>
    </justification>
  </clause>

  <clause id="14917">
    <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(3667(a,1),14848(a,1,2))].">
      <j1 rule="para" parents="3667 14848"/>
    </justification>
  </clause>

  <clause id="14918">
    <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(13298(a,1),14917(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13298 14917"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14919">
    <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,5578,a(flip),b,14918,a)].">
      <j1 rule="hyper" parents="58 5578 14918"/>
    </justification>
  </clause>

  <clause id="14920">
    <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(14433(a,1),14826(a,1,2))].">
      <j1 rule="para" parents="14433 14826"/>
    </justification>
  </clause>

  <clause id="14921">
    <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(14610,a,14920,a),flip(a)].">
      <j1 rule="hyper" parents="14610 14920"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14922">
    <literal><![CDATA[
      (K(x,y) * z) * R(u,z,K(x,T(y,z))) = K(x,y) * (z * u)
    ]]></literal>
    <justification jstring="[para(7179(a,1),14921(a,1,1))].">
      <j1 rule="para" parents="7179 14921"/>
    </justification>
  </clause>

  <clause id="14923">
    <literal><![CDATA[
      (K(x,y) * z) * R(u,z,K(x,y)) = K(x,y) * (z * u)
    ]]></literal>
    <justification jstring="[para(10392(a,1),14922(a,1,2))].">
      <j1 rule="para" parents="10392 14922"/>
    </justification>
  </clause>

  <clause id="14924">
    <literal><![CDATA[
      R(x,y,K(z,u)) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(479,a,14923,a),flip(a)].">
      <j1 rule="hyper" parents="479 14923"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14925">
    <literal><![CDATA[
      L(x,y,K(z,u)) = T(x,a(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(14827,a,14924,a),flip(a)].">
      <j1 rule="hyper" parents="14827 14924"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14926">
    <literal><![CDATA[
      L((x * K(y,z)) / u,u,K(z,y)) = x / (u * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(6355,a,14924,a),flip(a)].">
      <j1 rule="hyper" parents="6355 14924"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14927">
    <literal><![CDATA[
      L(x,x \ y,K(z,u)) = (y * K(z,u)) / ((x \ y) * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(879,a,14924,a),flip(a)].">
      <j1 rule="hyper" parents="879 14924"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14928">
    <literal><![CDATA[
      x * a(x,y,K(z,u)) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,14825,a,b,14924,a)].">
      <j1 rule="hyper" parents="58 14825 14924"/>
    </justification>
  </clause>

  <clause id="14929">
    <literal><![CDATA[
      x \ L(x,y,K(z,u)) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(116,a,14924,a(flip),b,14825,a)].">
      <j1 rule="hyper" parents="116 14924 14825"/>
    </justification>
  </clause>

  <clause id="14930">
    <literal><![CDATA[
      L(x,y,K(z,u)) * (y * K(z,u)) = (x * y) * K(z,u)
    ]]></literal>
    <justification jstring="[para(14924(a,1),101(a,1,1))].">
      <j1 rule="para" parents="14924 101"/>
    </justification>
  </clause>

  <clause id="14931">
    <literal><![CDATA[
      L(x,x \ y,K(z,u)) \ (y * K(z,u)) = (x \ y) * K(z,u)
    ]]></literal>
    <justification jstring="[para(14924(a,1),505(a,1,1))].">
      <j1 rule="para" parents="14924 505"/>
    </justification>
  </clause>

  <clause id="14932">
    <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(14924(a,1),6898(a,1))].">
      <j1 rule="para" parents="14924 6898"/>
    </justification>
  </clause>

  <clause id="14933">
    <literal><![CDATA[
      L(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,a(u,y,z)) = w
    ]]></literal>
    <justification jstring="[para(14924(a,1),14827(a,1))].">
      <j1 rule="para" parents="14924 14827"/>
    </justification>
  </clause>

  <clause id="14934">
    <literal><![CDATA[
      T(x,a(y,(z \ y) * u,z)) = L(x,u,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(320,a,14492,a,b,14925,a)].">
      <j1 rule="hyper" parents="320 14492 14925"/>
    </justification>
  </clause>

  <clause id="14935">
    <literal><![CDATA[
      T(x,a(y,z \ u,z)) = L(x,u,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(320,a,14429,a,b,14925,a)].">
      <j1 rule="hyper" parents="320 14429 14925"/>
    </justification>
  </clause>

  <clause id="14936">
    <literal><![CDATA[
      x * a(y,z,K(u,x)) = L(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,14319,a,b,14925,a)].">
      <j1 rule="hyper" parents="320 14319 14925"/>
    </justification>
  </clause>

  <clause id="14937">
    <literal><![CDATA[
      a(x,y,K(z,u)) * x = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,14286,a,b,14925,a)].">
      <j1 rule="hyper" parents="320 14286 14925"/>
    </justification>
  </clause>

  <clause id="14938">
    <literal><![CDATA[
      a(x,y,K(z,u)) * z = L(z,y,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(320,a,13407,a,b,14925,a)].">
      <j1 rule="hyper" parents="320 13407 14925"/>
    </justification>
  </clause>

  <clause id="14939">
    <literal><![CDATA[
      x * a(y,z,K(x,u)) = L(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(320,a,13403,a,b,14925,a)].">
      <j1 rule="hyper" parents="320 13403 14925"/>
    </justification>
  </clause>

  <clause id="14940">
    <literal><![CDATA[
      L(1 / x,y,K(z,u)) = a(x,y,K(u,z)) / x
    ]]></literal>
    <justification jstring="[hyper(320,a,14456,a(flip),b,14925,a),flip(a)].">
      <j1 rule="hyper" parents="320 14456 14925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14941">
    <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,14428,a(flip),b,14925,a),flip(a)].">
      <j1 rule="hyper" parents="320 14428 14925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14942">
    <literal><![CDATA[
      L(T(x,y),z,K(u,y)) = T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,14367,a(flip),b,14925,a),flip(a)].">
      <j1 rule="hyper" parents="320 14367 14925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14943">
    <literal><![CDATA[
      T(x * (a(y,z,u) \ 1),x) = L(x * (a(y,z,u) \ 1),z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(320,a,13951,a(flip),b,14925,a)].">
      <j1 rule="hyper" parents="320 13951 14925"/>
    </justification>
  </clause>

  <clause id="14944">
    <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,14925,a),flip(a)].">
      <j1 rule="hyper" parents="320 107 14925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14945">
    <literal><![CDATA[
      (x / y) * L(y,z,K(u,w)) = x * a(y,z,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(119,a,14925,a,b,14289,a)].">
      <j1 rule="hyper" parents="119 14925 14289"/>
    </justification>
  </clause>

  <clause id="14946">
    <literal><![CDATA[
      x \ L(x,y,K(z,u)) = a(u,y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(116,a,14925,a,b,13403,a)].">
      <j1 rule="hyper" parents="116 14925 13403"/>
    </justification>
  </clause>

  <clause id="14947">
    <literal><![CDATA[
      T(L(x,y,K(z,u)),a(z,y,u)) = x
    ]]></literal>
    <justification jstring="[hyper(36,a,14460,a(flip),b,14925,a),flip(a)].">
      <j1 rule="hyper" parents="36 14460 14925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14948">
    <literal><![CDATA[
      L(x,y,K(L(z,u,w),v5)) = T(x,a(v5,y,z))
    ]]></literal>
    <justification jstring="[hyper(13435,a,14925,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="13435 14925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14949">
    <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(14925(a,2),420(a,1))].">
      <j1 rule="para" parents="14925 420"/>
    </justification>
  </clause>

  <clause id="14950">
    <literal><![CDATA[
      (x * y) * a(z,u,K(y,w)) = x * L(y,u,K(w,z))
    ]]></literal>
    <justification jstring="[para(14925(a,2),13402(a,2,2))].">
      <j1 rule="para" parents="14925 13402"/>
    </justification>
  </clause>

  <clause id="14951">
    <literal><![CDATA[
      (x \ y) * a(z,u,K(w,y)) = x \ L(y,u,K(z,w))
    ]]></literal>
    <justification jstring="[para(14925(a,2),14357(a,2,2))].">
      <j1 rule="para" parents="14925 14357"/>
    </justification>
  </clause>

  <clause id="14952">
    <literal><![CDATA[
      L(x,y,K(z,u)) * a(z,y,u) = a(z,y,u) * x
    ]]></literal>
    <justification jstring="[para(14925(a,2),14459(a,1,1))].">
      <j1 rule="para" parents="14925 14459"/>
    </justification>
  </clause>

  <clause id="14953">
    <literal><![CDATA[
      L(x,y,K(z,u)) / u = T(x / u,a(u,y,z))
    ]]></literal>
    <justification jstring="[para(14925(a,2),14464(a,1,1))].">
      <j1 rule="para" parents="14925 14464"/>
    </justification>
  </clause>

  <clause id="14954">
    <literal><![CDATA[
      L(L(x,y,K(z,u)),y,K(u,z)) = x
    ]]></literal>
    <justification jstring="[hyper(58,a,14925,a,b,14947,a)].">
      <j1 rule="hyper" parents="58 14925 14947"/>
    </justification>
  </clause>

  <clause id="14955">
    <literal><![CDATA[
      T((K(x,y) * z) \ u,a(x,z,y)) = z \ (K(y,x) * u)
    ]]></literal>
    <justification jstring="[para(5153(a,1),14947(a,1,1))].">
      <j1 rule="para" parents="5153 14947"/>
    </justification>
  </clause>

  <clause id="14956">
    <literal><![CDATA[
      L((K(x,y) * z) \ u,z,K(y,x)) = z \ (K(y,x) * u)
    ]]></literal>
    <justification jstring="[hyper(5768,a,14954,a),flip(a)].">
      <j1 rule="hyper" parents="5768 14954"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14957">
    <literal><![CDATA[
      x * a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,K(z,u)) = w
    ]]></literal>
    <justification jstring="[para(14929(a,1),255(a,1,2)),flip(b)].">
      <j1 rule="para" parents="14929 255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14958">
    <literal><![CDATA[
      L(x,y \ z,K(y,u)) = L(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,14925,a,b,14935,a)].">
      <j1 rule="hyper" parents="58 14925 14935"/>
    </justification>
  </clause>

  <clause id="14959">
    <literal><![CDATA[
      a(x,y,z) * (u / a(x,y,z)) = L(u,y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,14454,a(flip),b,14937,a)].">
      <j1 rule="hyper" parents="58 14454 14937"/>
    </justification>
  </clause>

  <clause id="14960">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (z * w) = L(z,y,K(u,x)) * w
    ]]></literal>
    <justification jstring="[para(14938(a,1),14274(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14938 14274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14961">
    <literal><![CDATA[
      L(x,y,K(z,u)) \ x = a(u,y,K(z,x))
    ]]></literal>
    <justification jstring="[para(14939(a,1),9714(a,1,1))].">
      <j1 rule="para" parents="14939 9714"/>
    </justification>
  </clause>

  <clause id="14962">
    <literal><![CDATA[
      L(x,y * z,K(y,u)) = L(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[para(4(a,1),14958(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4 14958"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14963">
    <literal><![CDATA[
      L(L(x,y,z),y,K(z,u)) = L(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(6873,a,14962,a),flip(a)].">
      <j1 rule="hyper" parents="6873 14962"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14964">
    <literal><![CDATA[
      L(L(x,y,K(z,u)),y,z) = L(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[para(14962(a,1),6874(a,1,1))].">
      <j1 rule="para" parents="14962 6874"/>
    </justification>
  </clause>

  <clause id="14965">
    <literal><![CDATA[
      L(x,y,K(z,L(u,w,v5))) = T(x,a(u,y,z))
    ]]></literal>
    <justification jstring="[para(10612(a,1),14948(a,1,3))].">
      <j1 rule="para" parents="10612 14948"/>
    </justification>
  </clause>

  <clause id="14966">
    <literal><![CDATA[
      L(x,T(y,z),T(u,y)) = L(x,T(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(6969,a,14963,a),flip(a)].">
      <j1 rule="hyper" parents="6969 14963"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14968">
    <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(14963(a,1),1406(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="14963 1406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14969">
    <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(14963(a,1),14961(a,1,1))].">
      <j1 rule="para" parents="14963 14961"/>
    </justification>
  </clause>

  <clause id="14970">
    <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(14966(a,1),13276(a,1))].">
      <j1 rule="para" parents="14966 13276"/>
    </justification>
  </clause>

  <clause id="14971">
    <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,12640,a(flip),b,14964,a),flip(a)].">
      <j1 rule="hyper" parents="320 12640 14964"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14972">
    <literal><![CDATA[
      L(x,y,K(z,L(u,w,v5))) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,14925,a,b,14965,a),flip(a)].">
      <j1 rule="hyper" parents="320 14925 14965"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14973">
    <literal><![CDATA[
      L(x,(y \ z) * u,K(y,z)) = L(x,u,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,14925,a,b,14934,a)].">
      <j1 rule="hyper" parents="58 14925 14934"/>
    </justification>
  </clause>

  <clause id="14975">
    <literal><![CDATA[
      L(x / y,z,K(u,y)) = L(x,z,K(u,y)) / y
    ]]></literal>
    <justification jstring="[hyper(320,a,14925,a,b,14953,a)].">
      <j1 rule="hyper" parents="320 14925 14953"/>
    </justification>
  </clause>

  <clause id="14976">
    <literal><![CDATA[
      L(L(x,y,z \ u),y,K(z,u)) = L(x,y,u / z)
    ]]></literal>
    <justification jstring="[hyper(58,a,12750,a(flip),b,14973,a),flip(a)].">
      <j1 rule="hyper" parents="58 12750 14973"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14977">
    <literal><![CDATA[
      L(x * y,z,K(u,x)) = x * L(y,z,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(881,a,14975,a),flip(a)].">
      <j1 rule="hyper" parents="881 14975"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14978">
    <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(439,a,14944,a,b,14486,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="439 14944 14486"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14979">
    <literal><![CDATA[
      x * a(y,z,K(u,x)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,z,K(y,u)) = w
    ]]></literal>
    <justification jstring="[para(14263(a,2),14957(a,1,2))].">
      <j1 rule="para" parents="14263 14957"/>
    </justification>
  </clause>

  <clause id="14980">
    <literal><![CDATA[
      T(x,a(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,z,K(u,y)) = w
    ]]></literal>
    <justification jstring="[para(14283(a,1),14957(a,1))].">
      <j1 rule="para" parents="14283 14957"/>
    </justification>
  </clause>

  <clause id="14981">
    <literal><![CDATA[
      R(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,K(z,u)) = w
    ]]></literal>
    <justification jstring="[para(14825(a,1),14957(a,1))].">
      <j1 rule="para" parents="14825 14957"/>
    </justification>
  </clause>

  <clause id="14982">
    <literal><![CDATA[
      T(x,a(y,z * y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,z,K(u,y)) = w
    ]]></literal>
    <justification jstring="[para(14422(a,2),14980(a,1))].">
      <j1 rule="para" parents="14422 14980"/>
    </justification>
  </clause>

  <clause id="14983">
    <literal><![CDATA[
      L(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,z \ y,K(z,u)) = w
    ]]></literal>
    <justification jstring="[para(14935(a,1),14980(a,1))].">
      <j1 rule="para" parents="14935 14980"/>
    </justification>
  </clause>

  <clause id="14984">
    <literal><![CDATA[
      L(x,y,K(z,u)) / a(u,y,z) = a(u,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(116,a,14954,a(flip),b,14959,a),flip(a)].">
      <j1 rule="hyper" parents="116 14954 14959"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14985">
    <literal><![CDATA[
      x / a(y,z,x) = a(y,z,x) \ x
    ]]></literal>
    <justification jstring="[hyper(116,a,7518,a(flip),b,14959,a),flip(a)].">
      <j1 rule="hyper" parents="116 7518 14959"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14986">
    <literal><![CDATA[
      L(T(x,y),x \ z,K(u,w)) = T(L(x,z,K(u,w)),y)
    ]]></literal>
    <justification jstring="[para(14925(a,2),14941(a,2,1))].">
      <j1 rule="para" parents="14925 14941"/>
    </justification>
  </clause>

  <clause id="14987">
    <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,14986,a),flip(a)].">
      <j1 rule="hyper" parents="320 20 14986"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14988">
    <literal><![CDATA[
      L(x,x \ y,K(z,u)) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(139,a,14986,a(flip))].">
      <j1 rule="hyper" parents="139 14986"/>
    </justification>
  </clause>

  <clause id="14989">
    <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(14988(a,1),14128(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14988 14128"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14990">
    <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(6828(a,1),14930(a,1,2))].">
      <j1 rule="para" parents="6828 14930"/>
    </justification>
  </clause>

  <clause id="14991">
    <literal><![CDATA[
      x \ (K(y,z) * ((K(z,y) * x) * u)) = T(u,a(z,x,y))
    ]]></literal>
    <justification jstring="[para(4(a,1),14955(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4 14955"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14992">
    <literal><![CDATA[
      (K(x,y) * (x * y)) \ z = (x * y) \ (K(y,x) * z)
    ]]></literal>
    <justification jstring="[hyper(11183,a,14956,a)].">
      <j1 rule="hyper" parents="11183 14956"/>
    </justification>
  </clause>

  <clause id="14993">
    <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(705(a,1),14956(a,1,1)),flip(a)].">
      <j1 rule="para" parents="705 14956"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14994">
    <literal><![CDATA[
      (x * y) \ (K(y,x) * z) = (T(x,y) * y) \ z
    ]]></literal>
    <justification jstring="[para(4781(a,1),14992(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4781 14992"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14995">
    <literal><![CDATA[
      K(x,y) * ((K(y,x) * z) * u) = z * L(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(119,a,14925,a,b,14991,a),flip(a)].">
      <j1 rule="hyper" parents="119 14925 14991"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14996">
    <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(439,a,14995,a,b,1644,a)].">
      <j1 rule="hyper" parents="439 14995 1644"/>
    </justification>
  </clause>

  <clause id="14997">
    <literal><![CDATA[
      (x * y) * (z * L(u,z,K(y,x))) = (y * x) * ((K(x,y) * z) * u)
    ]]></literal>
    <justification jstring="[hyper(119,a,14995,a(flip),b,11153,a)].">
      <j1 rule="hyper" parents="119 14995 11153"/>
    </justification>
  </clause>

  <clause id="14998">
    <literal><![CDATA[
      L(x,y,T(z,u)) \ L(x,y,z) = a(u,y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(320,a,11803,a(flip),b,14969,a),flip(a)].">
      <j1 rule="hyper" parents="320 11803 14969"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15000">
    <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(14998(a,1),490(a,1,1,1))].">
      <j1 rule="para" parents="14998 490"/>
    </justification>
  </clause>

  <clause id="15001">
    <literal><![CDATA[
      (x * K(y,z)) / ((u \ x) * K(y,z)) = L(u,x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,14988,a(flip),b,14927,a),flip(a)].">
      <j1 rule="hyper" parents="58 14988 14927"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15002">
    <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(14927(a,2),267(a,1,1)),flip(b)].">
      <j1 rule="para" parents="14927 267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15003">
    <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(5956(a,1),15001(a,1,2,1))].">
      <j1 rule="para" parents="5956 15001"/>
    </justification>
  </clause>

  <clause id="15004">
    <literal><![CDATA[
      L(x,x \ y,K(z,z \ y)) \ (z * (y / z)) = (x \ y) * K(z,z \ y)
    ]]></literal>
    <justification jstring="[para(5013(a,1),14931(a,1,2))].">
      <j1 rule="para" parents="5013 14931"/>
    </justification>
  </clause>

  <clause id="15005">
    <literal><![CDATA[
      L(L(x,y,K(z,u * z)),y,u * z) = L(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(12715(a,1),14971(a,1,1))].">
      <j1 rule="para" parents="12715 14971"/>
    </justification>
  </clause>

  <clause id="15006">
    <literal><![CDATA[
      L(L(x,y,K(z,u)),y,u * z) = L(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(12588(a,1),15005(a,1,1))].">
      <j1 rule="para" parents="12588 15005"/>
    </justification>
  </clause>

  <clause id="15007">
    <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,13956,a(flip),b,15006,a)].">
      <j1 rule="hyper" parents="58 13956 15006"/>
    </justification>
  </clause>

  <clause id="15008">
    <literal><![CDATA[
      L(x * (a(y,z,u) \ 1),z,K(u,y)) = (a(y,z,u) \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(58,a,13486,a(flip),b,14943,a),flip(a)].">
      <j1 rule="hyper" parents="58 13486 14943"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15009">
    <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(14128(a,1),15002(a,1))].">
      <j1 rule="para" parents="14128 15002"/>
    </justification>
  </clause>

  <clause id="15010">
    <literal><![CDATA[
      T(x * a(y,x,K(z,u)),y) = y \ (K(z,u) * ((K(u,z) * x) * y))
    ]]></literal>
    <justification jstring="[para(14945(a,1),14996(a,1,1))].">
      <j1 rule="para" parents="14945 14996"/>
    </justification>
  </clause>

  <clause id="15011">
    <literal><![CDATA[
      (K(x,y) * ((K(y,x) * z) * u)) / u = z * a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(249,a,15010,a)].">
      <j1 rule="hyper" parents="249 15010"/>
    </justification>
  </clause>

  <clause id="15012">
    <literal><![CDATA[
      (K(x,y) * ((K(y,x) * z) * (u \ 1))) / (u \ 1) = z * a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[para(14352(a,1),15011(a,2,2))].">
      <j1 rule="para" parents="14352 15011"/>
    </justification>
  </clause>

  <clause id="15013">
    <literal><![CDATA[
      L(x,x \ y,K(z,y)) \ (z * (y / z)) = (x \ y) * K(z,z \ y)
    ]]></literal>
    <justification jstring="[para(12573(a,1),15004(a,1,1))].">
      <j1 rule="para" parents="12573 15004"/>
    </justification>
  </clause>

  <clause id="15014">
    <literal><![CDATA[
      (x \ y) * K(z,z \ y) = x \ (z * (y / z))
    ]]></literal>
    <justification jstring="[para(13695(a,1),15013(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13695 15013"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15015">
    <literal><![CDATA[
      K(x,y * ((z * y) \ (z * (u / z)))) = K(x,T(y * ((z * y) \ u),z))
    ]]></literal>
    <justification jstring="[para(15014(a,1),14166(a,1,2,2))].">
      <j1 rule="para" parents="15014 14166"/>
    </justification>
  </clause>

  <clause id="15016">
    <literal><![CDATA[
      T(K(x,y) * ((x \ y) / z),z) = z \ ((x \ y) * K(x,y))
    ]]></literal>
    <justification jstring="[para(12590(a,1),14989(a,2,1))].">
      <j1 rule="para" parents="12590 14989"/>
    </justification>
  </clause>

  <clause id="15017">
    <literal><![CDATA[
      T(K(x,y) * ((x \ y) / z),z) = z \ (K(x,y) * (x \ y))
    ]]></literal>
    <justification jstring="[para(6462(a,2),15016(a,2,2))].">
      <j1 rule="para" parents="6462 15016"/>
    </justification>
  </clause>

  <clause id="15018">
    <literal><![CDATA[
      x \ (K(y,z) * (y \ z)) = (x \ (y \ z)) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(15009,a,15017,a),flip(a)].">
      <j1 rule="hyper" parents="15009 15017"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15019">
    <literal><![CDATA[
      x \ (y \ ((y * z) / y)) = (x \ (y \ z)) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,5396,a,b,15018,a)].">
      <j1 rule="hyper" parents="58 5396 15018"/>
    </justification>
  </clause>

  <clause id="15020">
    <literal><![CDATA[
      (K(x,y) * z) \ (x \ ((x * y) / x)) = (z \ (x \ T(y,x))) * K(x,y)
    ]]></literal>
    <justification jstring="[para(14189(a,1),15019(a,2,1))].">
      <j1 rule="para" parents="14189 15019"/>
    </justification>
  </clause>

  <clause id="15021">
    <literal><![CDATA[
      (x \ (y \ T(z,y))) * K(y,z) = x \ (y \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,14045,a(flip),b,15020,a),flip(a)].">
      <j1 rule="hyper" parents="58 14045 15020"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15022">
    <literal><![CDATA[
      (x \ (y \ z)) * K(z,y) = x \ (y \ T(z,y))
    ]]></literal>
    <justification jstring="[hyper(6344,a,15021,a)].">
      <j1 rule="hyper" parents="6344 15021"/>
    </justification>
  </clause>

  <clause id="15023">
    <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(14963(a,1),14968(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14963 14968"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15024">
    <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(4019(a,1),14990(a,1,1))].">
      <j1 rule="para" parents="4019 14990"/>
    </justification>
  </clause>

  <clause id="15025">
    <literal><![CDATA[
      (x * (1 / T(y,z))) * K(y,u) = x * (K(y,u) / T(y,z))
    ]]></literal>
    <justification jstring="[para(10204(a,1),15024(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10204 15024"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15026">
    <literal><![CDATA[
      R(x,T(y,z) \ 1,y) / y = x * (K(y,z) / T(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,6740,a,b,15025,a)].">
      <j1 rule="hyper" parents="58 6740 15025"/>
    </justification>
  </clause>

  <clause id="15027">
    <literal><![CDATA[
      R(x,T(y,z) \ 1,y) / y = x * (1 / y)
    ]]></literal>
    <justification jstring="[para(4756(a,1),15026(a,2,2))].">
      <j1 rule="para" parents="4756 15026"/>
    </justification>
  </clause>

  <clause id="15028">
    <literal><![CDATA[
      R(x,T(y,z) \ 1,y) = R(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(2610,a,15027,a),flip(a)].">
      <j1 rule="hyper" parents="2610 15027"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15030">
    <literal><![CDATA[
      R(x,T(y,z) \ 1,T(y,z)) = R(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(6741,a,15028,a)].">
      <j1 rule="hyper" parents="6741 15028"/>
    </justification>
  </clause>

  <clause id="15031">
    <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(15030(a,1),11498(a,2,2))].">
      <j1 rule="para" parents="15030 11498"/>
    </justification>
  </clause>

  <clause id="15032">
    <literal><![CDATA[
      x / (T(y,z) \ R(x,y \ 1,y)) = (x * (1 / T(T(y,1),z))) \ x
    ]]></literal>
    <justification jstring="[para(15031(a,1),8371(a,1,2))].">
      <j1 rule="para" parents="15031 8371"/>
    </justification>
  </clause>

  <clause id="15034">
    <literal><![CDATA[
      (x * (1 / T(T(y,1),z))) \ x = T((x * (1 / y)) \ x,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,11477,a(flip),b,15032,a),flip(a)].">
      <j1 rule="hyper" parents="58 11477 15032"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15035">
    <literal><![CDATA[
      T((x * (1 / y)) \ x,z) = (x * (1 / T(y,z))) \ x
    ]]></literal>
    <justification jstring="[para(198(a,1),15034(a,1,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="198 15034"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15036">
    <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(15035(a,2),13054(a,1,2,2,1))].">
      <j1 rule="para" parents="15035 13054"/>
    </justification>
  </clause>

  <clause id="15037">
    <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,14036,a(flip),b,14993,a),flip(a)].">
      <j1 rule="hyper" parents="320 14036 14993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15039">
    <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(14997(a,1),15007(a,1,1))].">
      <j1 rule="para" parents="14997 15007"/>
    </justification>
  </clause>

  <clause id="15040">
    <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),14858(a,2,2,1,1))].">
      <j1 rule="para" parents="7 14858"/>
    </justification>
  </clause>

  <clause id="15041">
    <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,13811,a(flip),b,15040,a),flip(a)].">
      <j1 rule="hyper" parents="320 13811 15040"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15043">
    <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(13940(a,1),15041(a,1,2,1))].">
      <j1 rule="para" parents="13940 15041"/>
    </justification>
  </clause>

  <clause id="15044">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ 1)) / (u * ((z \ 1) / u))) = K(x,T(z * y,u))
    ]]></literal>
    <justification jstring="[para(6919(a,1),15043(a,1,2,2))].">
      <j1 rule="para" parents="6919 15043"/>
    </justification>
  </clause>

  <clause id="15045">
    <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(7164(a,2),14915(a,1,2,2))].">
      <j1 rule="para" parents="7164 14915"/>
    </justification>
  </clause>

  <clause id="15046">
    <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(4995(a,2),14847(a,1,1,1,2,3))].">
      <j1 rule="para" parents="4995 14847"/>
    </justification>
  </clause>

  <clause id="15047">
    <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),14908(a,1,1))].">
      <j1 rule="para" parents="68 14908"/>
    </justification>
  </clause>

  <clause id="15048">
    <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(14828(a,1),15047(a,1,2,1))].">
      <j1 rule="para" parents="14828 15047"/>
    </justification>
  </clause>

  <clause id="15049">
    <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,15048,a)].">
      <j1 rule="hyper" parents="288 15048"/>
    </justification>
  </clause>

  <clause id="15050">
    <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,13414,a(flip),b,15049,a),flip(a)].">
      <j1 rule="hyper" parents="58 13414 15049"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15052">
    <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(3691(a,1),15046(a,1,1,1,2))].">
      <j1 rule="para" parents="3691 15046"/>
    </justification>
  </clause>

  <clause id="15053">
    <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(12595(a,1),15052(a,1,1,1,2))].">
      <j1 rule="para" parents="12595 15052"/>
    </justification>
  </clause>

  <clause id="15054">
    <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(14470(a,1),15053(a,1,1,1))].">
      <j1 rule="para" parents="14470 15053"/>
    </justification>
  </clause>

  <clause id="15055">
    <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(14795(a,1),15054(a,1,1))].">
      <j1 rule="para" parents="14795 15054"/>
    </justification>
  </clause>

  <clause id="15056">
    <literal><![CDATA[
      R(K(x,y) * z,u,u \ 1) = K(x,y) * R(z,u,u \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,10106,a(flip),b,15055,a)].">
      <j1 rule="hyper" parents="58 10106 15055"/>
    </justification>
  </clause>

  <clause id="15058">
    <literal><![CDATA[
      R(K(x,y) * (z / u),u,u \ 1) = K(x,y) * (z * (u \ 1))
    ]]></literal>
    <justification jstring="[para(523(a,1),15056(a,2,2))].">
      <j1 rule="para" parents="523 15056"/>
    </justification>
  </clause>

  <clause id="15059">
    <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(15056(a,2),15037(a,1,2))].">
      <j1 rule="para" parents="15056 15037"/>
    </justification>
  </clause>

  <clause id="15060">
    <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(15058(a,1),559(a,1,1))].">
      <j1 rule="para" parents="15058 559"/>
    </justification>
  </clause>

  <clause id="15061">
    <literal><![CDATA[
      (K(x,y) * ((K(y,x) * z) / u)) * u = z * a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(15060,a,15012,a)].">
      <j1 rule="hyper" parents="15060 15012"/>
    </justification>
  </clause>

  <clause id="15062">
    <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(14026(a,1),15061(a,1,1,2))].">
      <j1 rule="para" parents="14026 15061"/>
    </justification>
  </clause>

  <clause id="15063">
    <literal><![CDATA[
      a(K(x,y) * z,u,u \ 1) = z \ R(z,u,u \ 1)
    ]]></literal>
    <justification jstring="[para(5133(a,1),15059(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5133 15059"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15064">
    <literal><![CDATA[
      a(K(x,y) * z,u,u \ 1) = a(z,u,u \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,705,a(flip),b,15063,a),flip(a)].">
      <j1 rule="hyper" parents="320 705 15063"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15065">
    <literal><![CDATA[
      a(x * K(y,z),u,u \ 1) = a(x,u,u \ 1)
    ]]></literal>
    <justification jstring="[para(7288(a,1),15064(a,1,1))].">
      <j1 rule="para" parents="7288 15064"/>
    </justification>
  </clause>

  <clause id="15066">
    <literal><![CDATA[
      a(x \ (y / z),u,u \ 1) = a(x \ (z \ y),u,u \ 1)
    ]]></literal>
    <justification jstring="[para(13963(a,1),15065(a,1,1))].">
      <j1 rule="para" parents="13963 15065"/>
    </justification>
  </clause>

  <clause id="15067">
    <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(7783(a,1),15062(a,1,1,2,1))].">
      <j1 rule="para" parents="7783 15062"/>
    </justification>
  </clause>

  <clause id="15068">
    <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(6335(a,1),14832(a,1,2,1))].">
      <j1 rule="para" parents="6335 14832"/>
    </justification>
  </clause>

  <clause id="15069">
    <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(14840(a,1),14978(a,1,2,1))].">
      <j1 rule="para" parents="14840 14978"/>
    </justification>
  </clause>

  <clause id="15070">
    <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(5163,a,15069,a)].">
      <j1 rule="hyper" parents="5163 15069"/>
    </justification>
  </clause>

  <clause id="15071">
    <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),14829(a,1,2)),flip(a)].">
      <j1 rule="para" parents="447 14829"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15072">
    <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,14906,a(flip),b,15071,a),flip(a)].">
      <j1 rule="hyper" parents="320 14906 15071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15073">
    <literal><![CDATA[
      a(L(x,y,z),u,a(w,v5,v6)) = a(x,u,a(w,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(897,a,15072,a),flip(a)].">
      <j1 rule="hyper" parents="897 15072"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15076">
    <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),15073(a,1,1))].">
      <j1 rule="para" parents="298 15073"/>
    </justification>
  </clause>

  <clause id="15077">
    <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),15073(a,1,1)),flip(a)].">
      <j1 rule="para" parents="390 15073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15078">
    <literal><![CDATA[
      a(x \ ((x / y) * z),u,a(w,v5,v6)) = a(y \ z,u,a(w,v5,v6))
    ]]></literal>
    <justification jstring="[para(493(a,1),15073(a,1,1))].">
      <j1 rule="para" parents="493 15073"/>
    </justification>
  </clause>

  <clause id="15079">
    <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(2548(a,1),15073(a,1,1))].">
      <j1 rule="para" parents="2548 15073"/>
    </justification>
  </clause>

  <clause id="15080">
    <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(14002(a,2),15078(a,1,1))].">
      <j1 rule="para" parents="14002 15078"/>
    </justification>
  </clause>

  <clause id="15081">
    <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,15073,a(flip),b,15079,a),flip(a)].">
      <j1 rule="hyper" parents="58 15073 15079"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15083">
    <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,15076,a(flip),b,15081,a),flip(a)].">
      <j1 rule="hyper" parents="320 15076 15081"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15084">
    <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),15083(a,2,1,2))].">
      <j1 rule="para" parents="4 15083"/>
    </justification>
  </clause>

  <clause id="15085">
    <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,15076,a(flip),b,15084,a),flip(a)].">
      <j1 rule="hyper" parents="320 15076 15084"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15086">
    <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),15085(a,2,1,2))].">
      <j1 rule="para" parents="61 15085"/>
    </justification>
  </clause>

  <clause id="15087">
    <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),15086(a,1,1,1))].">
      <j1 rule="para" parents="2 15086"/>
    </justification>
  </clause>

  <clause id="15089">
    <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(12280(a,1),14857(a,2,2))].">
      <j1 rule="para" parents="12280 14857"/>
    </justification>
  </clause>

  <clause id="15090">
    <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(7679(a,1),15089(a,1,2,1))].">
      <j1 rule="para" parents="7679 15089"/>
    </justification>
  </clause>

  <clause id="15091">
    <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(5600(a,1),15090(a,1,2,2))].">
      <j1 rule="para" parents="5600 15090"/>
    </justification>
  </clause>

  <clause id="15092">
    <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(9446(a,2),15091(a,1,2,2))].">
      <j1 rule="para" parents="9446 15091"/>
    </justification>
  </clause>

  <clause id="15093">
    <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(12229(a,1),15092(a,1,2,2,1))].">
      <j1 rule="para" parents="12229 15092"/>
    </justification>
  </clause>

  <clause id="15094">
    <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(13870(a,1),15093(a,1,2,2))].">
      <j1 rule="para" parents="13870 15093"/>
    </justification>
  </clause>

  <clause id="15095">
    <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(14323(a,1),15000(a,1,1))].">
      <j1 rule="para" parents="14323 15000"/>
    </justification>
  </clause>

  <clause id="15096">
    <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(14998(a,1),15095(a,1,2))].">
      <j1 rule="para" parents="14998 15095"/>
    </justification>
  </clause>

  <clause id="15097">
    <literal><![CDATA[
      L(x,y,z) \ (L(x,y,T(z,u)) * w) = a(x,y,K(z,u)) * w
    ]]></literal>
    <justification jstring="[hyper(13392,a,15096,a),flip(a)].">
      <j1 rule="hyper" parents="13392 15096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15098">
    <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,15023,a(flip),b,15097,a)].">
      <j1 rule="hyper" parents="58 15023 15097"/>
    </justification>
  </clause>

  <clause id="15099">
    <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,14361,a,b,15098,a),flip(a)].">
      <j1 rule="hyper" parents="320 14361 15098"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15100">
    <literal><![CDATA[
      T(L(x,y,z) \ x,u) \ x = L(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(30,a,13973,a,b,15099,a)].">
      <j1 rule="hyper" parents="30 13973 15099"/>
    </justification>
  </clause>

  <clause id="15101">
    <literal><![CDATA[
      T(L(x,y,z) \ x,u) = L(x,y,T(z,u)) \ x
    ]]></literal>
    <justification jstring="[hyper(34,a,5948,a,b,15100,a),flip(a)].">
      <j1 rule="hyper" parents="34 5948 15100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15102">
    <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),14905(a,1,2,1,2))].">
      <j1 rule="para" parents="7 14905"/>
    </justification>
  </clause>

  <clause id="15103">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u)),K(z,u)) = T(y,K(u,z) * x)
    ]]></literal>
    <justification jstring="[para(5599(a,2),15045(a,1,2))].">
      <j1 rule="para" parents="5599 15045"/>
    </justification>
  </clause>

  <clause id="15104">
    <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),15103(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7 15103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15105">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u)),K(u,z)) = T(y,K(z,u) * x)
    ]]></literal>
    <justification jstring="[para(7832(a,1),15103(a,1,2,1,2))].">
      <j1 rule="para" parents="7832 15103"/>
    </justification>
  </clause>

  <clause id="15106">
    <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(8186(a,1),15103(a,1,2,1,2))].">
      <j1 rule="para" parents="8186 15103"/>
    </justification>
  </clause>

  <clause id="15107">
    <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(8208(a,1),15103(a,1,2,1,2))].">
      <j1 rule="para" parents="8208 15103"/>
    </justification>
  </clause>

  <clause id="15108">
    <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(15103(a,1),8647(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15103 8647"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15109">
    <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(15103(a,1),13058(a,2,1,2))].">
      <j1 rule="para" parents="15103 13058"/>
    </justification>
  </clause>

  <clause id="15110">
    <literal><![CDATA[
      T(x / T(y,K(z,u)),K(z,u) \ y) = y \ T(x,K(z,u))
    ]]></literal>
    <justification jstring="[para(5130(a,2),15104(a,1,2))].">
      <j1 rule="para" parents="5130 15104"/>
    </justification>
  </clause>

  <clause id="15111">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u)),K(z,u)) = T(y,K(z,u) * x)
    ]]></literal>
    <justification jstring="[para(7832(a,1),15105(a,1,2))].">
      <j1 rule="para" parents="7832 15105"/>
    </justification>
  </clause>

  <clause id="15112">
    <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(6365(a,2),15110(a,1,1))].">
      <j1 rule="para" parents="6365 15110"/>
    </justification>
  </clause>

  <clause id="15113">
    <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,15111,a),flip(a)].">
      <j1 rule="hyper" parents="134 15111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15114">
    <literal><![CDATA[
      T(x,K(y,z) * u) = T(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(58,a,15103,a(flip),b,15111,a)].">
      <j1 rule="hyper" parents="58 15103 15111"/>
    </justification>
  </clause>

  <clause id="15115">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(y,u)) = T(x,K(y,u) * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(11509,a,15114,a)].">
      <j1 rule="hyper" parents="11509 15114"/>
    </justification>
  </clause>

  <clause id="15116">
    <literal><![CDATA[
      T(x,K(y \ z,y) * u) = T(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(320,a,13064,a,b,15114,a)].">
      <j1 rule="hyper" parents="320 13064 15114"/>
    </justification>
  </clause>

  <clause id="15117">
    <literal><![CDATA[
      T(x,K(y,y * z) * u) = T(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(320,a,13044,a(flip),b,15114,a),flip(a)].">
      <j1 rule="hyper" parents="320 13044 15114"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15118">
    <literal><![CDATA[
      x \ T(x,K(y,z) * u) = K(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(116,a,15114,a,b,4755,a(flip))].">
      <j1 rule="hyper" parents="116 15114 4755"/>
    </justification>
  </clause>

  <clause id="15119">
    <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),15114(a,1,2)),flip(a)].">
      <j1 rule="para" parents="105 15114"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15120">
    <literal><![CDATA[
      T(x,K(y,z) * (z * u)) = T(x,T(z,y) * u)
    ]]></literal>
    <justification jstring="[para(4781(a,1),15114(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4781 15114"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15121">
    <literal><![CDATA[
      T(x,K(y,z) * (K(y,z) * u)) = T(x,u)
    ]]></literal>
    <justification jstring="[para(5133(a,1),15114(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5133 15114"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15122">
    <literal><![CDATA[
      T(x,K(y,z) * (y \ u)) = T(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(5131(a,1),15114(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5131 15114"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15123">
    <literal><![CDATA[
      T(x,K(y \ 1,z) * (((y \ u) / u) \ w)) = T(x,T((y \ u) / u,z) \ w)
    ]]></literal>
    <justification jstring="[para(5352(a,1),15114(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5352 15114"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15124">
    <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(15114(a,1),13133(a,1,2,1))].">
      <j1 rule="para" parents="15114 13133"/>
    </justification>
  </clause>

  <clause id="15125">
    <literal><![CDATA[
      T(x,K(y,z) * (z / u)) = T(x,T(z,y) / u)
    ]]></literal>
    <justification jstring="[para(13708(a,1),15114(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13708 15114"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15126">
    <literal><![CDATA[
      T(x,y * (T(T(y,z),z) \ u)) = T(x,u)
    ]]></literal>
    <justification jstring="[para(5879(a,1),15121(a,1,2))].">
      <j1 rule="para" parents="5879 15121"/>
    </justification>
  </clause>

  <clause id="15127">
    <literal><![CDATA[
      T(x,T(T(y,z),z) * u) = T(x,y * u)
    ]]></literal>
    <justification jstring="[para(4(a,1),15126(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 15126"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15128">
    <literal><![CDATA[
      T(T(x,K(y,z)),z * y) = T(x,y * T(T(z,u),u))
    ]]></literal>
    <justification jstring="[hyper(12326,a,15127,a),flip(a)].">
      <j1 rule="hyper" parents="12326 15127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15129">
    <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(12327,a,15117,a),flip(a)].">
      <j1 rule="hyper" parents="12327 15117"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15130">
    <literal><![CDATA[
      K(x,K(y,z) * u) = K(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(4838,a,15118,a)].">
      <j1 rule="hyper" parents="4838 15118"/>
    </justification>
  </clause>

  <clause id="15131">
    <literal><![CDATA[
      K(x,K(y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y) * u) = w
    ]]></literal>
    <justification jstring="[para(15118(a,1),4838(a,1))].">
      <j1 rule="para" parents="15118 4838"/>
    </justification>
  </clause>

  <clause id="15132">
    <literal><![CDATA[
      K(x,K(y,y \ z) * u) = K(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(13183,a,15130,a),flip(a)].">
      <j1 rule="hyper" parents="13183 15130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15133">
    <literal><![CDATA[
      K(x,K(y * (z \ u),y \ z) * w) = K(x,K(y \ z,u) * w)
    ]]></literal>
    <justification jstring="[hyper(320,a,13104,a(flip),b,15130,a),flip(a)].">
      <j1 rule="hyper" parents="320 13104 15130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15134">
    <literal><![CDATA[
      K(x,K(y,z) * (z * u)) = K(x,T(z,y) * u)
    ]]></literal>
    <justification jstring="[para(4781(a,1),15130(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4781 15130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15135">
    <literal><![CDATA[
      K(x,K(y,z) \ u) = K(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[para(5130(a,2),15130(a,1,2))].">
      <j1 rule="para" parents="5130 15130"/>
    </justification>
  </clause>

  <clause id="15136">
    <literal><![CDATA[
      K(x,K(y,z) * (T(z,y) \ u)) = K(x,z \ u)
    ]]></literal>
    <justification jstring="[para(5081(a,1),15130(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5081 15130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15137">
    <literal><![CDATA[
      K(x,K(y,z) * (y \ u)) = K(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(5131(a,1),15130(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5131 15130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15138">
    <literal><![CDATA[
      K(x,K(y,z \ u) * (u / z)) = K(x,T(u / z,T(y,z)))
    ]]></literal>
    <justification jstring="[para(7317(a,1),15130(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7317 15130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15139">
    <literal><![CDATA[
      K(x,K(y,z) * (z / u)) = K(x,T(z,y) / u)
    ]]></literal>
    <justification jstring="[para(13708(a,1),15130(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13708 15130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15140">
    <literal><![CDATA[
      K(x,K(y,z) \ u) = K(x,K(z,y) \ u)
    ]]></literal>
    <justification jstring="[para(5130(a,2),15135(a,2,2))].">
      <j1 rule="para" parents="5130 15135"/>
    </justification>
  </clause>

  <clause id="15141">
    <literal><![CDATA[
      K(x,K(y,y \ z) \ u) = K(x,K(z,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(320,a,13144,a(flip),b,15140,a),flip(a)].">
      <j1 rule="hyper" parents="320 13144 15140"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15142">
    <literal><![CDATA[
      K(x,L(K(y,z),u,w) \ v5) = K(x,K(L(z,u,w),y) \ v5)
    ]]></literal>
    <justification jstring="[para(10794(a,2),15140(a,1,2,1))].">
      <j1 rule="para" parents="10794 15140"/>
    </justification>
  </clause>

  <clause id="15143">
    <literal><![CDATA[
      T(x,((y * z) / y) \ u) = T(x,T(z,y) \ u)
    ]]></literal>
    <justification jstring="[para(5088(a,2),15122(a,1,2))].">
      <j1 rule="para" parents="5088 15122"/>
    </justification>
  </clause>

  <clause id="15144">
    <literal><![CDATA[
      T(x,T(y \ z,y) \ u) = T(x,(z / y) \ u)
    ]]></literal>
    <justification jstring="[para(5399(a,1),15122(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5399 15122"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15145">
    <literal><![CDATA[
      T(x,T(y \ z,y) / u) = T(x,(z / y) / u)
    ]]></literal>
    <justification jstring="[para(14023(a,1),15125(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14023 15125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15146">
    <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),15132(a,1,2)),flip(a)].">
      <j1 rule="para" parents="105 15132"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15147">
    <literal><![CDATA[
      K(x,y * (K(z,y) * u)) = K(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[para(5256(a,1),15134(a,1,2))].">
      <j1 rule="para" parents="5256 15134"/>
    </justification>
  </clause>

  <clause id="15148">
    <literal><![CDATA[
      K(x,((y * z) / y) * u) = K(x,T(z,y) * u)
    ]]></literal>
    <justification jstring="[para(5442(a,1),15134(a,1,2))].">
      <j1 rule="para" parents="5442 15134"/>
    </justification>
  </clause>

  <clause id="15149">
    <literal><![CDATA[
      K(x,T(y \ z,y) * u) = K(x,(z / y) * u)
    ]]></literal>
    <justification jstring="[para(5459(a,1),15134(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5459 15134"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15150">
    <literal><![CDATA[
      K(x,T(T(y,z),z) \ u) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[para(5238(a,1),15136(a,1,2))].">
      <j1 rule="para" parents="5238 15136"/>
    </justification>
  </clause>

  <clause id="15151">
    <literal><![CDATA[
      K(x,T(y * z,z) \ u) = K(x,(z * y) \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,13154,a(flip),b,15150,a)].">
      <j1 rule="hyper" parents="58 13154 15150"/>
    </justification>
  </clause>

  <clause id="15152">
    <literal><![CDATA[
      K(x,T(y \ z,y) \ u) = K(x,(z / y) \ u)
    ]]></literal>
    <justification jstring="[para(107(a,1),15150(a,1,2,1,1))].">
      <j1 rule="para" parents="107 15150"/>
    </justification>
  </clause>

  <clause id="15153">
    <literal><![CDATA[
      K(x,T(y,y \ z) \ u) = K(x,(z / (z / y)) \ u)
    ]]></literal>
    <justification jstring="[para(4346(a,1),15150(a,1,2,1,1))].">
      <j1 rule="para" parents="4346 15150"/>
    </justification>
  </clause>

  <clause id="15154">
    <literal><![CDATA[
      K(x,(y * K(z,y)) / u) = K(x,T(y,z) / u)
    ]]></literal>
    <justification jstring="[para(13967(a,2),15139(a,1,2))].">
      <j1 rule="para" parents="13967 15139"/>
    </justification>
  </clause>

  <clause id="15155">
    <literal><![CDATA[
      K(x,T(y \ z,y) / u) = K(x,(z / y) / u)
    ]]></literal>
    <justification jstring="[para(14023(a,1),15139(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14023 15139"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15156">
    <literal><![CDATA[
      T(x,K(y,y \ z) \ u) = T(x,K(z,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(118,a,15141,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 15141 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15157">
    <literal><![CDATA[
      K(x,K(y,z \ y) \ u) = K(x,K(y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,13143,a,b,15141,a)].">
      <j1 rule="hyper" parents="58 13143 15141"/>
    </justification>
  </clause>

  <clause id="15158">
    <literal><![CDATA[
      K(x,K(y \ z,z) \ u) = K(x,K(z,y \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(5012(a,1),15141(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5012 15141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15159">
    <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(13832(a,1),15143(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="13832 15143"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15160">
    <literal><![CDATA[
      T(x,T((y / (z \ 1)) / y,y) \ u) = T(x,((y / (z \ K(z,y))) / y) \ u)
    ]]></literal>
    <justification jstring="[para(10134(a,1),15144(a,1,2,1,1))].">
      <j1 rule="para" parents="10134 15144"/>
    </justification>
  </clause>

  <clause id="15161">
    <literal><![CDATA[
      K(x,T(T(y,z),z) * u) = K(x,y * u)
    ]]></literal>
    <justification jstring="[para(225(a,1),15148(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="225 15148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15162">
    <literal><![CDATA[
      K(x,T(L(y \ z,u,w),y) * v5) = K(x,L(z / y,u,w) * v5)
    ]]></literal>
    <justification jstring="[para(644(a,1),15148(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="644 15148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15163">
    <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),15161(a,2,2))].">
      <j1 rule="para" parents="101 15161"/>
    </justification>
  </clause>

  <clause id="15164">
    <literal><![CDATA[
      K(x,T(y,z * u) / (z * u)) = K(x,T(u * z,z) \ y)
    ]]></literal>
    <justification jstring="[hyper(320,a,12994,a,b,15151,a)].">
      <j1 rule="hyper" parents="320 12994 15151"/>
    </justification>
  </clause>

  <clause id="15165">
    <literal><![CDATA[
      K(x,(y * (z / y)) \ u) = K(x,T(z,y) \ u)
    ]]></literal>
    <justification jstring="[para(7(a,1),15151(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="7 15151"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15166">
    <literal><![CDATA[
      K(x,T(T(y,z),z) / u) = K(x,y / u)
    ]]></literal>
    <justification jstring="[para(4751(a,1),15154(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4751 15154"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15167">
    <literal><![CDATA[
      K(x,((y * z) / y) / u) = K(x,T(z,y) / u)
    ]]></literal>
    <justification jstring="[para(4752(a,2),15154(a,1,2,1))].">
      <j1 rule="para" parents="4752 15154"/>
    </justification>
  </clause>

  <clause id="15168">
    <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(12642(a,1),15155(a,1,2,1,1))].">
      <j1 rule="para" parents="12642 15155"/>
    </justification>
  </clause>

  <clause id="15169">
    <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(12737(a,1),15155(a,1,2,1))].">
      <j1 rule="para" parents="12737 15155"/>
    </justification>
  </clause>

  <clause id="15170">
    <literal><![CDATA[
      K(x,K(y \ z,z) \ u) = K(x,K(z,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,15140,a,b,15157,a)].">
      <j1 rule="hyper" parents="58 15140 15157"/>
    </justification>
  </clause>

  <clause id="15171">
    <literal><![CDATA[
      K(x,L((y * (z / y)) \ u,w,v5)) = K(L(x,w,v5),T(z,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(10870,a,15165,a)].">
      <j1 rule="hyper" parents="10870 15165"/>
    </justification>
  </clause>

  <clause id="15172">
    <literal><![CDATA[
      K(x,((y \ z) * y) \ u) = K(x,(y * (z / y)) \ u)
    ]]></literal>
    <justification jstring="[hyper(320,a,13105,a,b,15165,a)].">
      <j1 rule="hyper" parents="320 13105 15165"/>
    </justification>
  </clause>

  <clause id="15173">
    <literal><![CDATA[
      K(x,T(y \ z,z) \ u) = K(x,(y \ T(z,y \ 1)) \ u)
    ]]></literal>
    <justification jstring="[para(3913(a,2),15165(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3913 15165"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15174">
    <literal><![CDATA[
      K(x,K(y,y \ z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z) * u) = w
    ]]></literal>
    <justification jstring="[para(15132(a,2),15131(a,1))].">
      <j1 rule="para" parents="15132 15131"/>
    </justification>
  </clause>

  <clause id="15175">
    <literal><![CDATA[
      T(x,K(y,z) * K(y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(7850,a,15115,a),flip(a)].">
      <j1 rule="hyper" parents="7850 15115"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15176">
    <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(15175(a,1),13069(a,1,2,2))].">
      <j1 rule="para" parents="15175 13069"/>
    </justification>
  </clause>

  <clause id="15177">
    <literal><![CDATA[
      T(x,y * K(z,u)) = T(x,y * K(u,z))
    ]]></literal>
    <justification jstring="[para(7847(a,1),15119(a,1,2))].">
      <j1 rule="para" parents="7847 15119"/>
    </justification>
  </clause>

  <clause id="15178">
    <literal><![CDATA[
      x / T(x,y * K(z,u)) = K(y * K(u,z),x)
    ]]></literal>
    <justification jstring="[para(15177(a,1),4794(a,2,2)),flip(a)].">
      <j1 rule="para" parents="15177 4794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15179">
    <literal><![CDATA[
      T(x,(y / z) * K(z,u)) = T(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[para(6322(a,1),15177(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6322 15177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15180">
    <literal><![CDATA[
      K(x * K(y,z),u) = K(x * K(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(4862,a,15178,a)].">
      <j1 rule="hyper" parents="4862 15178"/>
    </justification>
  </clause>

  <clause id="15181">
    <literal><![CDATA[
      K(x * K(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x * K(z,y),u) = w
    ]]></literal>
    <justification jstring="[para(15178(a,1),4862(a,1))].">
      <j1 rule="para" parents="15178 4862"/>
    </justification>
  </clause>

  <clause id="15182">
    <literal><![CDATA[
      K((1 / x) * K(y,z),u) = K(x \ K(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(14060,a,15180,a),flip(a)].">
      <j1 rule="hyper" parents="14060 15180"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15183">
    <literal><![CDATA[
      K((x * K(y,z)) * K(y,z),u) = K(x,u)
    ]]></literal>
    <justification jstring="[para(6329(a,1),15180(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6329 15180"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15184">
    <literal><![CDATA[
      K((x / y) * K(y,z),u) = K(x / T(y,z),u)
    ]]></literal>
    <justification jstring="[para(6322(a,1),15180(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6322 15180"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15185">
    <literal><![CDATA[
      K((x \ y) * K(z,y),u) = K(x \ T(y,z),u)
    ]]></literal>
    <justification jstring="[para(13699(a,1),15180(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13699 15180"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15186">
    <literal><![CDATA[
      K(x * (K(y,z) * K(y,z)),u) = K(x,u)
    ]]></literal>
    <justification jstring="[para(8992(a,1),15183(a,1,1))].">
      <j1 rule="para" parents="8992 15183"/>
    </justification>
  </clause>

  <clause id="15187">
    <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(15186(a,1),4770(a,2,1)),flip(a)].">
      <j1 rule="para" parents="15186 4770"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15188">
    <literal><![CDATA[
      T(x,y / ((z * u) / z)) = T(x,y / T(u,z))
    ]]></literal>
    <justification jstring="[para(6397(a,2),15179(a,1,2))].">
      <j1 rule="para" parents="6397 15179"/>
    </justification>
  </clause>

  <clause id="15189">
    <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(6194(a,1),15179(a,1,2,1))].">
      <j1 rule="para" parents="6194 15179"/>
    </justification>
  </clause>

  <clause id="15191">
    <literal><![CDATA[
      K(x \ K(y,z),u) = K(x \ K(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(14060,a,15182,a)].">
      <j1 rule="hyper" parents="14060 15182"/>
    </justification>
  </clause>

  <clause id="15192">
    <literal><![CDATA[
      K(x \ K(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x \ K(z,y),u) = w
    ]]></literal>
    <justification jstring="[para(15182(a,1),14060(a,1))].">
      <j1 rule="para" parents="15182 14060"/>
    </justification>
  </clause>

  <clause id="15193">
    <literal><![CDATA[
      K(x \ K(y \ z,y),u) = K(x \ K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(13191,a,15191,a),flip(a)].">
      <j1 rule="hyper" parents="13191 15191"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15194">
    <literal><![CDATA[
      (x \ K(y \ K(z,u),w)) \ (x \ 1) = K(w,y \ K(u,z))
    ]]></literal>
    <justification jstring="[para(15191(a,1),13893(a,1,1,2))].">
      <j1 rule="para" parents="15191 13893"/>
    </justification>
  </clause>

  <clause id="15195">
    <literal><![CDATA[
      K((x \ y) \ K(z,x),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(y \ T(x,z),u) = w
    ]]></literal>
    <justification jstring="[para(15191(a,1),14005(a,1))].">
      <j1 rule="para" parents="15191 14005"/>
    </justification>
  </clause>

  <clause id="15196">
    <literal><![CDATA[
      K(x / ((y * z) / y),u) = K(x / T(z,y),u)
    ]]></literal>
    <justification jstring="[para(6397(a,2),15184(a,1,1))].">
      <j1 rule="para" parents="6397 15184"/>
    </justification>
  </clause>

  <clause id="15198">
    <literal><![CDATA[
      K(x \ (y * K(z,y)),u) = K(x \ T(y,z),u)
    ]]></literal>
    <justification jstring="[para(13960(a,2),15185(a,1,1))].">
      <j1 rule="para" parents="13960 15185"/>
    </justification>
  </clause>

  <clause id="15200">
    <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),15188(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="457 15188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15201">
    <literal><![CDATA[
      T(x,y / ((z * u) / T(z,w))) = T(x,y / T(u * K(w,z),z))
    ]]></literal>
    <justification jstring="[para(7455(a,1),15188(a,1,2,2))].">
      <j1 rule="para" parents="7455 15188"/>
    </justification>
  </clause>

  <clause id="15202">
    <literal><![CDATA[
      T(x,y / (((z * u) / z) * K(z,w))) = T(x,y / T(u * K(z,w),z))
    ]]></literal>
    <justification jstring="[para(7039(a,1),15188(a,1,2,2))].">
      <j1 rule="para" parents="7039 15188"/>
    </justification>
  </clause>

  <clause id="15203">
    <literal><![CDATA[
      K(x \ K(y \ z,z),u) = K(x \ K(y,y \ z),u)
    ]]></literal>
    <justification jstring="[para(4965(a,1),15193(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4965 15193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15206">
    <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(15196(a,1),7438(a,1,2))].">
      <j1 rule="para" parents="15196 7438"/>
    </justification>
  </clause>

  <clause id="15207">
    <literal><![CDATA[
      K(x \ T(T(y,z),z),u) = K(x \ y,u)
    ]]></literal>
    <justification jstring="[para(4751(a,1),15198(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4751 15198"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15208">
    <literal><![CDATA[
      K(x \ T(y * z,z),u) = K(x \ (z * y),u)
    ]]></literal>
    <justification jstring="[hyper(58,a,13158,a(flip),b,15207,a)].">
      <j1 rule="hyper" parents="58 13158 15207"/>
    </justification>
  </clause>

  <clause id="15209">
    <literal><![CDATA[
      K(x,y \ T(T(z,u),u)) = 1 / K(y \ z,x)
    ]]></literal>
    <justification jstring="[para(15207(a,1),4971(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15207 4971"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15210">
    <literal><![CDATA[
      K(x \ (y * (z / y)),u) = K(x \ T(z,y),u)
    ]]></literal>
    <justification jstring="[para(7(a,1),15208(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7 15208"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15211">
    <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(15208(a,1),10807(a,1,2,3))].">
      <j1 rule="para" parents="15208 10807"/>
    </justification>
  </clause>

  <clause id="15212">
    <literal><![CDATA[
      K(x,y \ T(T(z,u),u)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(320,a,4971,a(flip),b,15209,a),flip(a)].">
      <j1 rule="hyper" parents="320 4971 15209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15213">
    <literal><![CDATA[
      T(x,y \ T(T(z,u),u)) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(118,a,15212,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 15212 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15214">
    <literal><![CDATA[
      K(x,y \ T(z \ u,z)) = K(x,y \ (u / z))
    ]]></literal>
    <justification jstring="[para(107(a,1),15212(a,1,2,2,1))].">
      <j1 rule="para" parents="107 15212"/>
    </justification>
  </clause>

  <clause id="15215">
    <literal><![CDATA[
      K(x,y \ T(z * (u / T(z,u)),z)) = K(x,y \ (z * (u / z)))
    ]]></literal>
    <justification jstring="[para(4278(a,1),15212(a,1,2,2,1))].">
      <j1 rule="para" parents="4278 15212"/>
    </justification>
  </clause>

  <clause id="15216">
    <literal><![CDATA[
      K(x,y \ (z * K(u,z))) = K(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[para(4816(a,1),15212(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="4816 15212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15217">
    <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(15212(a,1),12329(a,1,1,2))].">
      <j1 rule="para" parents="15212 12329"/>
    </justification>
  </clause>

  <clause id="15218">
    <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(7563(a,1),15214(a,1,2,2,1))].">
      <j1 rule="para" parents="7563 15214"/>
    </justification>
  </clause>

  <clause id="15219">
    <literal><![CDATA[
      K(x,(y \ z) \ K(u,y)) = K(x,z \ T(y,u))
    ]]></literal>
    <justification jstring="[hyper(6604,a,15216,a)].">
      <j1 rule="hyper" parents="6604 15216"/>
    </justification>
  </clause>

  <clause id="15220">
    <literal><![CDATA[
      K(x,(y \ z) \ K(u \ 1,y)) = K(x,z \ T(y,1 / u))
    ]]></literal>
    <justification jstring="[para(2956(a,2),15219(a,2,2,2))].">
      <j1 rule="para" parents="2956 15219"/>
    </justification>
  </clause>

  <clause id="15221">
    <literal><![CDATA[
      T(x,y * T(T(z,u),u)) = T(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(12300,a,15128,a),flip(a)].">
      <j1 rule="hyper" parents="12300 15128"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15222">
    <literal><![CDATA[
      T(x,y * ((z * u) / z)) = T(x,y * T(u,z))
    ]]></literal>
    <justification jstring="[para(224(a,1),15221(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="224 15221"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15223">
    <literal><![CDATA[
      T(x,y * (z * K(u,z))) = T(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[para(4816(a,1),15221(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="4816 15221"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15224">
    <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(15221(a,1),12290(a,1,2,1))].">
      <j1 rule="para" parents="15221 12290"/>
    </justification>
  </clause>

  <clause id="15225">
    <literal><![CDATA[
      T(x,y * ((z * u) / z)) = x * K(x,y * T(u,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,4755,a(flip),b,15222,a),flip(a)].">
      <j1 rule="hyper" parents="320 4755 15222"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15226">
    <literal><![CDATA[
      K(x * ((y * z) / y),u) = u / T(u,x * T(z,y))
    ]]></literal>
    <justification jstring="[para(15222(a,1),4794(a,2,2))].">
      <j1 rule="para" parents="15222 4794"/>
    </justification>
  </clause>

  <clause id="15227">
    <literal><![CDATA[
      K(x,(y / (y / z)) \ u) = K(x,T(z,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(13213,a,15153,a),flip(a)].">
      <j1 rule="hyper" parents="13213 15153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15228">
    <literal><![CDATA[
      K(x,(y / (y / z)) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z,y) \ u) = w
    ]]></literal>
    <justification jstring="[para(15153(a,1),13213(a,1))].">
      <j1 rule="para" parents="15153 13213"/>
    </justification>
  </clause>

  <clause id="15229">
    <literal><![CDATA[
      T(x,(y / (y / z)) \ u) = T(x,T(z,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(118,a,15227,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 15227 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15230">
    <literal><![CDATA[
      K(x,T(y \ z,z) \ u) = K(x,(z / y) \ u)
    ]]></literal>
    <justification jstring="[para(72(a,1),15227(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="72 15227"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15231">
    <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(15229(a,1),12305(a,1,2,1))].">
      <j1 rule="para" parents="15229 12305"/>
    </justification>
  </clause>

  <clause id="15232">
    <literal><![CDATA[
      K(x,(y / z) \ T(u,y / z)) = K(x,u / T(z \ y,y))
    ]]></literal>
    <justification jstring="[hyper(13135,a,15230,a),flip(a)].">
      <j1 rule="hyper" parents="13135 15230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15233">
    <literal><![CDATA[
      K(x,K(y,z \ 1) \ u) = K(x,K(y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,15170,a(flip),b,15158,a),flip(a)].">
      <j1 rule="hyper" parents="58 15170 15158"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15234">
    <literal><![CDATA[
      K(x,T(y,z \ 1) \ u) = K(x,K(y,z) \ (y \ u))
    ]]></literal>
    <justification jstring="[para(5087(a,1),15233(a,1,2))].">
      <j1 rule="para" parents="5087 15233"/>
    </justification>
  </clause>

  <clause id="15235">
    <literal><![CDATA[
      K(x,(y * (z / y)) \ u) \ 1 = K(((y \ z) * y) \ u,x)
    ]]></literal>
    <justification jstring="[para(15172(a,1),4969(a,1,1))].">
      <j1 rule="para" parents="15172 4969"/>
    </justification>
  </clause>

  <clause id="15236">
    <literal><![CDATA[
      K(x \ K(y \ z,z),u) = K(x \ K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(320,a,13095,a(flip),b,15203,a),flip(a)].">
      <j1 rule="hyper" parents="320 13095 15203"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15237">
    <literal><![CDATA[
      K(x \ K(y,z \ y),u) = K(x \ K(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(15192,a,15236,a)].">
      <j1 rule="hyper" parents="15192 15236"/>
    </justification>
  </clause>

  <clause id="15238">
    <literal><![CDATA[
      K(x \ K(y,z \ 1),u) = K(x \ K(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(58,a,13150,a,b,15237,a)].">
      <j1 rule="hyper" parents="58 13150 15237"/>
    </justification>
  </clause>

  <clause id="15239">
    <literal><![CDATA[
      K((x \ y) \ K(z,x),u) = K(y \ T(x,1 / z),u)
    ]]></literal>
    <justification jstring="[hyper(14169,a,15238,a),flip(a)].">
      <j1 rule="hyper" parents="14169 15238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15240">
    <literal><![CDATA[
      K(x,y * ((z * u) / z)) = K(x,y * T(u,z))
    ]]></literal>
    <justification jstring="[hyper(4837,a,15225,a)].">
      <j1 rule="hyper" parents="4837 15225"/>
    </justification>
  </clause>

  <clause id="15241">
    <literal><![CDATA[
      K(x,y * T(z \ u,z)) = K(x,y * (u / z))
    ]]></literal>
    <justification jstring="[para(5(a,1),15240(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5 15240"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15242">
    <literal><![CDATA[
      K(x,y * T(T(z,u),u)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(225(a,1),15240(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="225 15240"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15243">
    <literal><![CDATA[
      K(x,y * (z * K(u,z))) = K(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[para(4752(a,1),15240(a,1,2,2))].">
      <j1 rule="para" parents="4752 15240"/>
    </justification>
  </clause>

  <clause id="15244">
    <literal><![CDATA[
      K(x,(y / (z * u)) * T(u,z)) = K(x,(y / (u * z)) * u)
    ]]></literal>
    <justification jstring="[para(10656(a,1),15240(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10656 15240"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15245">
    <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(13832(a,1),15240(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="13832 15240"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15246">
    <literal><![CDATA[
      K(x,T(y,z \ u) * (u \ z)) = K(x,(u \ z) * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,14176,a(flip),b,15242,a)].">
      <j1 rule="hyper" parents="58 14176 15242"/>
    </justification>
  </clause>

  <clause id="15247">
    <literal><![CDATA[
      K(x,y * T(z * u,u)) = K(x,y * (u * z))
    ]]></literal>
    <justification jstring="[hyper(58,a,13196,a(flip),b,15242,a)].">
      <j1 rule="hyper" parents="58 13196 15242"/>
    </justification>
  </clause>

  <clause id="15248">
    <literal><![CDATA[
      K(x,y * T(z \ u,u)) = K(x,y * (u / z))
    ]]></literal>
    <justification jstring="[hyper(58,a,13123,a(flip),b,15242,a)].">
      <j1 rule="hyper" parents="58 13123 15242"/>
    </justification>
  </clause>

  <clause id="15249">
    <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),15242(a,2,2))].">
      <j1 rule="para" parents="90 15242"/>
    </justification>
  </clause>

  <clause id="15250">
    <literal><![CDATA[
      K(x,y * (((z \ u) \ u) \ u)) = K(x,y * (u / z))
    ]]></literal>
    <justification jstring="[para(4239(a,1),15241(a,1,2,2))].">
      <j1 rule="para" parents="4239 15241"/>
    </justification>
  </clause>

  <clause id="15251">
    <literal><![CDATA[
      K(x,y * (T(z,u \ 1) \ (u \ z))) = K(x,y * ((u \ z) / z))
    ]]></literal>
    <justification jstring="[para(4355(a,1),15241(a,1,2,2))].">
      <j1 rule="para" parents="4355 15241"/>
    </justification>
  </clause>

  <clause id="15252">
    <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(14526(a,2),15241(a,1,2))].">
      <j1 rule="para" parents="14526 15241"/>
    </justification>
  </clause>

  <clause id="15253">
    <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(4197(a,1),15243(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="4197 15243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15254">
    <literal><![CDATA[
      K(x,y * (z * (u / z))) = K(x,y * T(u,z))
    ]]></literal>
    <justification jstring="[para(7(a,1),15247(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="7 15247"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15255">
    <literal><![CDATA[
      K(x,L(y * T(z \ u,u),w,v5)) = K(L(x,w,v5),y * (u / z))
    ]]></literal>
    <justification jstring="[hyper(10870,a,15248,a)].">
      <j1 rule="hyper" parents="10870 15248"/>
    </justification>
  </clause>

  <clause id="15256">
    <literal><![CDATA[
      K(x,y * (z * ((z * u) / z))) = K(x,y * (u * z))
    ]]></literal>
    <justification jstring="[hyper(320,a,13069,a(flip),b,15254,a),flip(a)].">
      <j1 rule="hyper" parents="320 13069 15254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15257">
    <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),15254(a,2,2,2))].">
      <j1 rule="para" parents="18 15254"/>
    </justification>
  </clause>

  <clause id="15258">
    <literal><![CDATA[
      K(x * ((y * z) / y),u) = K(x * T(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(320,a,4794,a,b,15226,a),flip(a)].">
      <j1 rule="hyper" parents="320 4794 15226"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15259">
    <literal><![CDATA[
      K(x * (y * K(z,y)),u) = K(x * T(y,z),u)
    ]]></literal>
    <justification jstring="[para(4752(a,1),15258(a,1,1,2))].">
      <j1 rule="para" parents="4752 15258"/>
    </justification>
  </clause>

  <clause id="15260">
    <literal><![CDATA[
      K(x,T(y,z \ 1) \ u) = K(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(5087(a,1),15234(a,2,2))].">
      <j1 rule="para" parents="5087 15234"/>
    </justification>
  </clause>

  <clause id="15261">
    <literal><![CDATA[
      K(x,T(y * (z \ 1),z) \ u) = K(x,((z \ 1) * y) \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,15151,a(flip),b,15260,a),flip(a)].">
      <j1 rule="hyper" parents="58 15151 15260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15262">
    <literal><![CDATA[
      K(x,y * (T(z,u) \ u)) = K(x,y * (u / z))
    ]]></literal>
    <justification jstring="[hyper(58,a,13163,a(flip),b,15250,a)].">
      <j1 rule="hyper" parents="58 13163 15250"/>
    </justification>
  </clause>

  <clause id="15263">
    <literal><![CDATA[
      K(x,y * (z \ T(u,z))) = K(x,y * (u / z))
    ]]></literal>
    <justification jstring="[para(4248(a,1),15262(a,1,2,2))].">
      <j1 rule="para" parents="4248 15262"/>
    </justification>
  </clause>

  <clause id="15264">
    <literal><![CDATA[
      K(x,x * (((y * x) * z) \ T(u,(y * x) * z))) = K(x,u / (y * z))
    ]]></literal>
    <justification jstring="[hyper(320,a,12637,a(flip),b,15263,a),flip(a)].">
      <j1 rule="hyper" parents="320 12637 15263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15265">
    <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(5169(a,1),15263(a,2,2,2))].">
      <j1 rule="para" parents="5169 15263"/>
    </justification>
  </clause>

  <clause id="15266">
    <literal><![CDATA[
      K(x,y * (T(z,u) * u)) = K(x,y * (u * z))
    ]]></literal>
    <justification jstring="[para(225(a,1),15256(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="225 15256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15267">
    <literal><![CDATA[
      K(x,T((y * z) * u,y * z)) = K(x,u * (T(z,y) * y))
    ]]></literal>
    <justification jstring="[hyper(320,a,12262,a,b,15266,a)].">
      <j1 rule="hyper" parents="320 12262 15266"/>
    </justification>
  </clause>

  <clause id="15268">
    <literal><![CDATA[
      T(x,y * (T(z,u) * u)) = T(x,y * (u * z))
    ]]></literal>
    <justification jstring="[hyper(118,a,15266,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 15266 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15269">
    <literal><![CDATA[
      K(x,y * (T(z,T(u,w)) * ((w * u) / w))) = K(x,y * (((w * u) / w) * z))
    ]]></literal>
    <justification jstring="[para(7943(a,1),15266(a,1,2,2,1))].">
      <j1 rule="para" parents="7943 15266"/>
    </justification>
  </clause>

  <clause id="15270">
    <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),15268(a,1,2,2,1))].">
      <j1 rule="para" parents="246 15268"/>
    </justification>
  </clause>

  <clause id="15271">
    <literal><![CDATA[
      K(x \ T(y,1 / z),u) = K(x \ T(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(15195,a,15239,a),flip(a)].">
      <j1 rule="hyper" parents="15195 15239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15272">
    <literal><![CDATA[
      K(x \ T(y,z \ 1),u) = K(x \ T(y,z),u)
    ]]></literal>
    <justification jstring="[para(72(a,1),15271(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="72 15271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15273">
    <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(15272(a,1),10807(a,1,2,3))].">
      <j1 rule="para" parents="15272 10807"/>
    </justification>
  </clause>

  <clause id="15274">
    <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(15113(a,2),287(a,1,2)),flip(b)].">
      <j1 rule="para" parents="15113 287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15275">
    <literal><![CDATA[
      K(x,T(y * z,z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z * y) \ u) = w
    ]]></literal>
    <justification jstring="[para(15164(a,1),13061(a,1))].">
      <j1 rule="para" parents="15164 13061"/>
    </justification>
  </clause>

  <clause id="15276">
    <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(13128(a,1),15275(a,1))].">
      <j1 rule="para" parents="13128 15275"/>
    </justification>
  </clause>

  <clause id="15277">
    <literal><![CDATA[
      K(x,(y \ T(z,y \ 1)) \ u) = K(x,(z / y) \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,15230,a(flip),b,15173,a),flip(a)].">
      <j1 rule="hyper" parents="58 15230 15173"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15278">
    <literal><![CDATA[
      K(x,y \ K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(15194(a,1),6394(a,1))].">
      <j1 rule="para" parents="15194 6394"/>
    </justification>
  </clause>

  <clause id="15279">
    <literal><![CDATA[
      T(x,y / T(((z \ u) \ u) \ u,w)) = T(x,y / T(u / z,w))
    ]]></literal>
    <justification jstring="[para(4352(a,1),15200(a,1,2,2))].">
      <j1 rule="para" parents="4352 15200"/>
    </justification>
  </clause>

  <clause id="15280">
    <literal><![CDATA[
      K(x,y / T(z \ u,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (u / z)) = w
    ]]></literal>
    <justification jstring="[para(15232(a,1),13132(a,1))].">
      <j1 rule="para" parents="15232 13132"/>
    </justification>
  </clause>

  <clause id="15281">
    <literal><![CDATA[
      K(((x \ y) * x) \ z,u) = K((x * (y / x)) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(4985,a,15235,a),flip(a)].">
      <j1 rule="hyper" parents="4985 15235"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15282">
    <literal><![CDATA[
      K((x * (y / x)) \ z,u) = K(T(y,x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,13107,a(flip),b,15281,a),flip(a)].">
      <j1 rule="hyper" parents="58 13107 15281"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15283">
    <literal><![CDATA[
      K(K(x,y) * (x \ z),u) = K(T(x,y) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(13198,a,15282,a)].">
      <j1 rule="hyper" parents="13198 15282"/>
    </justification>
  </clause>

  <clause id="15284">
    <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,14854,a(flip),b,15282,a),flip(a)].">
      <j1 rule="hyper" parents="58 14854 15282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15285">
    <literal><![CDATA[
      K(K(x,x \ y) * (x \ z),u) = K(T(x,y) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(320,a,13211,a(flip),b,15283,a),flip(a)].">
      <j1 rule="hyper" parents="320 13211 15283"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15287">
    <literal><![CDATA[
      K((x / (x / y)) \ z,u) = K(T(y,x) \ z,u)
    ]]></literal>
    <justification jstring="[para(5401(a,2),15285(a,1,1))].">
      <j1 rule="para" parents="5401 15285"/>
    </justification>
  </clause>

  <clause id="15288">
    <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,15149,a,b,15244,a)].">
      <j1 rule="hyper" parents="58 15149 15244"/>
    </justification>
  </clause>

  <clause id="15289">
    <literal><![CDATA[
      K(x,y * T(z * (u / z),w)) = K(x,y * T(T(u,z),w))
    ]]></literal>
    <justification jstring="[para(4574(a,2),15257(a,1,2,2))].">
      <j1 rule="para" parents="4574 15257"/>
    </justification>
  </clause>

  <clause id="15290">
    <literal><![CDATA[
      K(x,((y \ 1) * (y * z)) \ u) = K(x,R(z,y,y \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(788(a,1),15261(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="788 15261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15291">
    <literal><![CDATA[
      K(x,y * (T(z,u) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (u * z)) = w
    ]]></literal>
    <justification jstring="[para(15267(a,1),12301(a,1))].">
      <j1 rule="para" parents="15267 12301"/>
    </justification>
  </clause>

  <clause id="15292">
    <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(12281(a,1),15291(a,1,2,2,1))].">
      <j1 rule="para" parents="12281 15291"/>
    </justification>
  </clause>

  <clause id="15293">
    <literal><![CDATA[
      T(x,y * T(z * (u / z),w)) = T(x,y * T(T(u,z),w))
    ]]></literal>
    <justification jstring="[hyper(118,a,15289,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 15289 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15294">
    <literal><![CDATA[
      K(x,R(T(T(y,z),z),u,w) * (u * w)) = K(x,(y * u) * w)
    ]]></literal>
    <justification jstring="[para(823(a,2),15163(a,1,2,1))].">
      <j1 rule="para" parents="823 15163"/>
    </justification>
  </clause>

  <clause id="15295">
    <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),15249(a,1,2,2,1))].">
      <j1 rule="para" parents="20 15249"/>
    </justification>
  </clause>

  <clause id="15296">
    <literal><![CDATA[
      K(x,R(y,z,z \ 1) \ u) = K(x,L(y,z,z \ 1) \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,5574,a(flip),b,15290,a),flip(a)].">
      <j1 rule="hyper" parents="58 5574 15290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15297">
    <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,14517,a(flip),b,15296,a),flip(a)].">
      <j1 rule="hyper" parents="58 14517 15296"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15298">
    <literal><![CDATA[
      K(x,(T(T(y,z),z) * u) * w) = K(x,(y * u) * w)
    ]]></literal>
    <justification jstring="[para(101(a,1),15294(a,1,2))].">
      <j1 rule="para" parents="101 15294"/>
    </justification>
  </clause>

  <clause id="15299">
    <literal><![CDATA[
      K(x,(((y * z) / y) * u) * w) = K(x,(T(z,y) * u) * w)
    ]]></literal>
    <justification jstring="[para(224(a,1),15298(a,1,2,1,1,1)),flip(a)].">
      <j1 rule="para" parents="224 15298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15300">
    <literal><![CDATA[
      K(x,(T(y,z) * z) * u) = K(x,(z * y) * u)
    ]]></literal>
    <justification jstring="[para(7(a,1),15299(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7 15299"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15301">
    <literal><![CDATA[
      K(x,(y * (K(z,y) * u)) * w) = K(x,(T(y,z) * u) * w)
    ]]></literal>
    <justification jstring="[para(5404(a,1),15299(a,1,2,1))].">
      <j1 rule="para" parents="5404 15299"/>
    </justification>
  </clause>

  <clause id="15302">
    <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(7443(a,1),15300(a,1,2,1,1))].">
      <j1 rule="para" parents="7443 15300"/>
    </justification>
  </clause>

  <clause id="15303">
    <literal><![CDATA[
      K(x,(y * (K(z,y) * (u / y))) * w) = K(x,((T(y,z) \ u) * y) * w)
    ]]></literal>
    <justification jstring="[para(7617(a,1),15300(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="7617 15300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15304">
    <literal><![CDATA[
      K(x,((y \ z) * (y * K(u,y))) * w) = K(x,(y * (z / T(y,u))) * w)
    ]]></literal>
    <justification jstring="[para(7601(a,1),15300(a,1,2,1))].">
      <j1 rule="para" parents="7601 15300"/>
    </justification>
  </clause>

  <clause id="15305">
    <literal><![CDATA[
      K(x,y * (z * T(T(u,w),w))) = K(x,y * (z * u))
    ]]></literal>
    <justification jstring="[para(449(a,1),15295(a,1,2))].">
      <j1 rule="para" parents="449 15295"/>
    </justification>
  </clause>

  <clause id="15306">
    <literal><![CDATA[
      K(x,y * (z * T(u \ w,w))) = K(x,y * (z * (w / u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,13217,a(flip),b,15305,a)].">
      <j1 rule="hyper" parents="58 13217 15305"/>
    </justification>
  </clause>

  <clause id="15307">
    <literal><![CDATA[
      K(x,y * (z * ((u * w) / u))) = K(x,y * (z * T(w,u)))
    ]]></literal>
    <justification jstring="[para(224(a,1),15305(a,1,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="224 15305"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15308">
    <literal><![CDATA[
      T(x,y * K(z,z * u)) = T(x,y * K(u,z))
    ]]></literal>
    <justification jstring="[hyper(12325,a,15129,a),flip(a)].">
      <j1 rule="hyper" parents="12325 15129"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15309">
    <literal><![CDATA[
      K(x,K(y,z) * T(u,K(z,y))) = K(x,u * K(z,z \ y))
    ]]></literal>
    <justification jstring="[para(8032(a,1),15146(a,1,2,2))].">
      <j1 rule="para" parents="8032 15146"/>
    </justification>
  </clause>

  <clause id="15310">
    <literal><![CDATA[
      K(x,y * K(z,z \ u)) = K(x,y * K(u,z))
    ]]></literal>
    <justification jstring="[para(7847(a,1),15309(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7847 15309"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15311">
    <literal><![CDATA[
      K(x,y * K(z,u)) = K(x,y * K(u,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,13070,a(flip),b,15310,a)].">
      <j1 rule="hyper" parents="58 13070 15310"/>
    </justification>
  </clause>

  <clause id="15313">
    <literal><![CDATA[
      K(x,(y / z) * K(z,u)) = K(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[para(6322(a,1),15311(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6322 15311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15314">
    <literal><![CDATA[
      K(x,(y \ z) * K(u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(15311(a,1),14114(a,1))].">
      <j1 rule="para" parents="15311 14114"/>
    </justification>
  </clause>

  <clause id="15316">
    <literal><![CDATA[
      K(x,y / T(z \ u,z)) = K(x,y / (u / z))
    ]]></literal>
    <justification jstring="[para(6470(a,1),15313(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6470 15313"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15318">
    <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(3993(a,1),15314(a,1,2,2))].">
      <j1 rule="para" parents="3993 15314"/>
    </justification>
  </clause>

  <clause id="15319">
    <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(15171(a,2),10870(a,1))].">
      <j1 rule="para" parents="15171 10870"/>
    </justification>
  </clause>

  <clause id="15320">
    <literal><![CDATA[
      K(x,y \ ((z / T(u,z)) * u)) = K(x,y \ (u * (z / u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,13076,a(flip),b,15215,a)].">
      <j1 rule="hyper" parents="58 13076 15215"/>
    </justification>
  </clause>

  <clause id="15321">
    <literal><![CDATA[
      K(x,y \ (z * (u / z))) = K(x,y \ T(u,z))
    ]]></literal>
    <justification jstring="[para(4242(a,1),15320(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4242 15320"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15322">
    <literal><![CDATA[
      K(x,T(y / ((z \ u) * z),z \ u)) = K(x,u \ T(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,14835,a,b,15321,a)].">
      <j1 rule="hyper" parents="58 14835 15321"/>
    </justification>
  </clause>

  <clause id="15323">
    <literal><![CDATA[
      K(x,y \ T(z * u,u)) = K(x,y \ (u * z))
    ]]></literal>
    <justification jstring="[para(6(a,1),15321(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="6 15321"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15324">
    <literal><![CDATA[
      K(x,y \ T(z \ u,u)) = K(x,y \ (z \ T(u,z \ 1)))
    ]]></literal>
    <justification jstring="[para(3913(a,2),15321(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3913 15321"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15325">
    <literal><![CDATA[
      K(x,y \ T(z * u,z)) = K(x,y \ (T(z,u) * u))
    ]]></literal>
    <justification jstring="[para(4092(a,2),15321(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4092 15321"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15326">
    <literal><![CDATA[
      K(x,y \ (T(z,u) * u)) = K(x,y \ (u * z))
    ]]></literal>
    <justification jstring="[hyper(58,a,13076,a(flip),b,15325,a),flip(a)].">
      <j1 rule="hyper" parents="58 13076 15325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15327">
    <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(12275(a,1),15326(a,1,2,2,1))].">
      <j1 rule="para" parents="12275 15326"/>
    </justification>
  </clause>

  <clause id="15328">
    <literal><![CDATA[
      K(x,y \ (T(z,u * w) * ((u \ 1) \ w))) = K(x,y \ (((u \ 1) \ w) * z))
    ]]></literal>
    <justification jstring="[para(13802(a,1),15326(a,1,2,2,1))].">
      <j1 rule="para" parents="13802 15326"/>
    </justification>
  </clause>

  <clause id="15329">
    <literal><![CDATA[
      K(x,y \ (T(z,u * w) * ((1 / u) \ w))) = K(x,y \ (((1 / u) \ w) * z))
    ]]></literal>
    <justification jstring="[para(13879(a,1),15326(a,1,2,2,1))].">
      <j1 rule="para" parents="13879 15326"/>
    </justification>
  </clause>

  <clause id="15330">
    <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(15255(a,2),10870(a,1))].">
      <j1 rule="para" parents="15255 10870"/>
    </justification>
  </clause>

  <clause id="15331">
    <literal><![CDATA[
      T(x,y / T(T(z \ u,w),u)) = T(x,y / T(u / z,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,13114,a(flip),b,15279,a)].">
      <j1 rule="hyper" parents="58 13114 15279"/>
    </justification>
  </clause>

  <clause id="15332">
    <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),15331(a,1,2,2))].">
      <j1 rule="para" parents="18 15331"/>
    </justification>
  </clause>

  <clause id="15333">
    <literal><![CDATA[
      K(x,y * (L(y,z,z \ 1) \ u)) = K(x,a(y,z,z \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(1412(a,1),15297(a,1,2))].">
      <j1 rule="para" parents="1412 15297"/>
    </justification>
  </clause>

  <clause id="15334">
    <literal><![CDATA[
      T(x,K(y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(z,y) * u) = w
    ]]></literal>
    <justification jstring="[para(15103(a,1),15274(a,1))].">
      <j1 rule="para" parents="15103 15274"/>
    </justification>
  </clause>

  <clause id="15335">
    <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(15111(a,2),15334(a,1))].">
      <j1 rule="para" parents="15111 15334"/>
    </justification>
  </clause>

  <clause id="15336">
    <literal><![CDATA[
      T(x,K(y \ z,y) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(z,y) * u) = w
    ]]></literal>
    <justification jstring="[para(15116(a,2),15334(a,1))].">
      <j1 rule="para" parents="15116 15334"/>
    </justification>
  </clause>

  <clause id="15338">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u)),K(z,u)) = T(y,K(u \ 1,z) * x)
    ]]></literal>
    <justification jstring="[para(8186(a,1),15106(a,1,2))].">
      <j1 rule="para" parents="8186 15106"/>
    </justification>
  </clause>

  <clause id="15339">
    <literal><![CDATA[
      T(x,K(y \ 1,z) * u) = T(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(15335,a,15338,a),flip(a)].">
      <j1 rule="hyper" parents="15335 15338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15340">
    <literal><![CDATA[
      T(x,K(y \ 1,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,z) * u) = w
    ]]></literal>
    <justification jstring="[para(15338(a,1),15335(a,1))].">
      <j1 rule="para" parents="15338 15335"/>
    </justification>
  </clause>

  <clause id="15341">
    <literal><![CDATA[
      K(x,K(y \ 1,z) * u) = x \ T(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(116,a,15339,a(flip),b,4755,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="116 15339 4755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15342">
    <literal><![CDATA[
      K(K(x \ 1,y) * z,u) = u / T(u,K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(15339(a,1),4794(a,2,2))].">
      <j1 rule="para" parents="15339 4794"/>
    </justification>
  </clause>

  <clause id="15343">
    <literal><![CDATA[
      K(x,K(y \ 1,z) * u) = K(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(320,a,4729,a,b,15341,a),flip(a)].">
      <j1 rule="hyper" parents="320 4729 15341"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15344">
    <literal><![CDATA[
      K(x,K(y \ 1,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z) * u) = w
    ]]></literal>
    <justification jstring="[para(15341(a,2),4838(a,1))].">
      <j1 rule="para" parents="15341 4838"/>
    </justification>
  </clause>

  <clause id="15345">
    <literal><![CDATA[
      K(x,K(y,z \ 1) * u) = K(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(15131,a,15343,a)].">
      <j1 rule="hyper" parents="15131 15343"/>
    </justification>
  </clause>

  <clause id="15346">
    <literal><![CDATA[
      K(x,y * (T(1 / y,z) * u)) = K(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(58,a,14178,a,b,15343,a)].">
      <j1 rule="hyper" parents="58 14178 15343"/>
    </justification>
  </clause>

  <clause id="15347">
    <literal><![CDATA[
      K(x,K(y \ z,u) * w) = K(x,K(z \ y,u) * w)
    ]]></literal>
    <justification jstring="[para(6259(a,1),15343(a,1,2,1))].">
      <j1 rule="para" parents="6259 15343"/>
    </justification>
  </clause>

  <clause id="15348">
    <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(15343(a,1),6726(a,1,1))].">
      <j1 rule="para" parents="15343 6726"/>
    </justification>
  </clause>

  <clause id="15349">
    <literal><![CDATA[
      K(x,K(y,z \ 1) * u) = K(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(320,a,15130,a,b,15345,a),flip(a)].">
      <j1 rule="hyper" parents="320 15130 15345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15350">
    <literal><![CDATA[
      K(x,K(y \ z,u) * w) = K(x,K(u,z \ y) * w)
    ]]></literal>
    <justification jstring="[para(6108(a,1),15345(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6108 15345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15351">
    <literal><![CDATA[
      K(x,K(y,z) * T(u,K(z,y))) = K(x,u * K(z,y \ 1))
    ]]></literal>
    <justification jstring="[para(8207(a,1),15345(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8207 15345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15352">
    <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(15345(a,1),6727(a,1,1))].">
      <j1 rule="para" parents="15345 6727"/>
    </justification>
  </clause>

  <clause id="15353">
    <literal><![CDATA[
      K(x,T(y \ 1,z) \ u) = K(x,K(z,y) * (y * u))
    ]]></literal>
    <justification jstring="[hyper(14053,a,15349,a)].">
      <j1 rule="hyper" parents="14053 15349"/>
    </justification>
  </clause>

  <clause id="15354">
    <literal><![CDATA[
      T(x,K(y,z \ 1) * u) = T(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(118,a,15349,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 15349 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15355">
    <literal><![CDATA[
      K(K(x,y \ 1) * z,u) = u / T(u,K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(15354(a,1),4794(a,2,2))].">
      <j1 rule="para" parents="15354 4794"/>
    </justification>
  </clause>

  <clause id="15356">
    <literal><![CDATA[
      K(K(x \ 1,y) * z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(K(x,y) * z,u) = w
    ]]></literal>
    <justification jstring="[para(15342(a,2),4862(a,1))].">
      <j1 rule="para" parents="15342 4862"/>
    </justification>
  </clause>

  <clause id="15357">
    <literal><![CDATA[
      K(x,y * (K(1 / z,y) * u)) = K(x,K(z,y) * (y * u))
    ]]></literal>
    <justification jstring="[hyper(14113,a,15346,a)].">
      <j1 rule="hyper" parents="14113 15346"/>
    </justification>
  </clause>

  <clause id="15358">
    <literal><![CDATA[
      K(x,K(y \ z,z) * u) = K(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(13183,a,15347,a),flip(a)].">
      <j1 rule="hyper" parents="13183 15347"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15359">
    <literal><![CDATA[
      K(x,K(y * (z \ u),y \ z) * w) = K(x,K(z \ y,u) * w)
    ]]></literal>
    <justification jstring="[hyper(320,a,15133,a,b,15347,a)].">
      <j1 rule="hyper" parents="320 15133 15347"/>
    </justification>
  </clause>

  <clause id="15360">
    <literal><![CDATA[
      K(x,K(y \ z,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z) * u) = w
    ]]></literal>
    <justification jstring="[para(15347(a,1),13183(a,1))].">
      <j1 rule="para" parents="15347 13183"/>
    </justification>
  </clause>

  <clause id="15361">
    <literal><![CDATA[
      T(x,K(y \ z,z) * u) = T(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(118,a,15358,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 15358 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15362">
    <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,15138,a(flip),b,15358,a)].">
      <j1 rule="hyper" parents="58 15138 15358"/>
    </justification>
  </clause>

  <clause id="15363">
    <literal><![CDATA[
      K(x,T(y,z \ y) \ u) = K(x,K(z,y) * (y \ u))
    ]]></literal>
    <justification jstring="[para(5131(a,1),15358(a,1,2))].">
      <j1 rule="para" parents="5131 15358"/>
    </justification>
  </clause>

  <clause id="15364">
    <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(15361(a,1),13133(a,1,2,1))].">
      <j1 rule="para" parents="15361 13133"/>
    </justification>
  </clause>

  <clause id="15365">
    <literal><![CDATA[
      K(x,K(y,z \ y) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y) * u) = w
    ]]></literal>
    <justification jstring="[para(15350(a,1),13183(a,1))].">
      <j1 rule="para" parents="15350 13183"/>
    </justification>
  </clause>

  <clause id="15366">
    <literal><![CDATA[
      K(x,K(y \ (z \ 1),u) * w) = K(x,K(u,z * y) * w)
    ]]></literal>
    <justification jstring="[para(13775(a,1),15350(a,2,2,1))].">
      <j1 rule="para" parents="13775 15350"/>
    </justification>
  </clause>

  <clause id="15367">
    <literal><![CDATA[
      K(x,T(y \ 1,z) \ u) = K(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(320,a,15134,a(flip),b,15353,a),flip(a)].">
      <j1 rule="hyper" parents="320 15134 15353"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15368">
    <literal><![CDATA[
      K(x,T(1 / y,z) \ u) = K(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(14123,a,15367,a)].">
      <j1 rule="hyper" parents="14123 15367"/>
    </justification>
  </clause>

  <clause id="15369">
    <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(10870,a,15367,a)].">
      <j1 rule="hyper" parents="10870 15367"/>
    </justification>
  </clause>

  <clause id="15370">
    <literal><![CDATA[
      T(x,T(y \ 1,z) \ u) = T(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(118,a,15367,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 15367 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15371">
    <literal><![CDATA[
      T(x,T(1 / y,z) \ u) = T(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(118,a,15368,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 15368 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15372">
    <literal><![CDATA[
      K(x,T(y \ 1,z) * u) = K(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(72(a,1),15368(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="72 15368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15373">
    <literal><![CDATA[
      T(x,T(y \ 1,z) * u) = T(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(72(a,1),15371(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="72 15371"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15374">
    <literal><![CDATA[
      T(x,T(K(y,z) * u,w) \ v5) = T(x,T(u \ K(z,y),w) * v5)
    ]]></literal>
    <justification jstring="[para(13818(a,1),15371(a,1,2,1,1))].">
      <j1 rule="para" parents="13818 15371"/>
    </justification>
  </clause>

  <clause id="15375">
    <literal><![CDATA[
      T(x,T(K(y,z) / u,w) \ v5) = T(x,T(u * K(z,y),w) * v5)
    ]]></literal>
    <justification jstring="[para(13876(a,1),15371(a,1,2,1,1))].">
      <j1 rule="para" parents="13876 15371"/>
    </justification>
  </clause>

  <clause id="15376">
    <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(13834(a,1),15373(a,1,2,1,1))].">
      <j1 rule="para" parents="13834 15373"/>
    </justification>
  </clause>

  <clause id="15377">
    <literal><![CDATA[
      K(K(x,y \ 1) * z,u) = K(K(x,y) * z,u)
    ]]></literal>
    <justification jstring="[hyper(320,a,4794,a,b,15355,a),flip(a)].">
      <j1 rule="hyper" parents="320 4794 15355"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15378">
    <literal><![CDATA[
      K(T(x \ 1,y) \ z,u) = K(K(y,x) * (x * z),u)
    ]]></literal>
    <justification jstring="[hyper(14054,a,15377,a)].">
      <j1 rule="hyper" parents="14054 15377"/>
    </justification>
  </clause>

  <clause id="15379">
    <literal><![CDATA[
      K(x,T(y,z \ y) \ u) = K(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(5131(a,1),15363(a,2,2))].">
      <j1 rule="para" parents="5131 15363"/>
    </justification>
  </clause>

  <clause id="15380">
    <literal><![CDATA[
      K(T(x \ 1,y) \ z,u) = K(x * (K(y,x) * z),u)
    ]]></literal>
    <justification jstring="[para(5256(a,1),15378(a,2,1))].">
      <j1 rule="para" parents="5256 15378"/>
    </justification>
  </clause>

  <clause id="15381">
    <literal><![CDATA[
      K(x,y * K(z,u \ 1)) = K(x,y * K(u,z))
    ]]></literal>
    <justification jstring="[para(7847(a,1),15351(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7847 15351"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15382">
    <literal><![CDATA[
      K(x,y * K(z \ 1,u)) = K(x,y * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,15311,a,b,15381,a)].">
      <j1 rule="hyper" parents="58 15311 15381"/>
    </justification>
  </clause>

  <clause id="15383">
    <literal><![CDATA[
      K(x * K(y,z \ 1),u) = 1 / K(u,x * K(z,y))
    ]]></literal>
    <justification jstring="[para(15381(a,1),4971(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15381 4971"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15384">
    <literal><![CDATA[
      T(x,y * K(z \ 1,u)) = T(x,y * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(118,a,15382,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 15382 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15385">
    <literal><![CDATA[
      K(x * K(y,z \ 1),u) = K(x * K(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(320,a,4971,a(flip),b,15383,a),flip(a)].">
      <j1 rule="hyper" parents="320 4971 15383"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15386">
    <literal><![CDATA[
      K(x * K(y \ 1,z),u) = K(x * K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(15181,a,15385,a)].">
      <j1 rule="hyper" parents="15181 15385"/>
    </justification>
  </clause>

  <clause id="15387">
    <literal><![CDATA[
      K(((x * (y \ z)) / x) * y,u) = K(z * K(z \ y,x),T(u,y))
    ]]></literal>
    <justification jstring="[hyper(12297,a,15385,a)].">
      <j1 rule="hyper" parents="12297 15385"/>
    </justification>
  </clause>

  <clause id="15388">
    <literal><![CDATA[
      K(x * K(x \ y,z),T(u,y)) = K(y * T(x / y,z),u)
    ]]></literal>
    <justification jstring="[hyper(58,a,12246,a(flip),b,15386,a),flip(a)].">
      <j1 rule="hyper" parents="58 12246 15386"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15389">
    <literal><![CDATA[
      K(x,y * (K(1 / z,y) * u)) = K(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(320,a,15134,a(flip),b,15357,a),flip(a)].">
      <j1 rule="hyper" parents="320 15134 15357"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15390">
    <literal><![CDATA[
      K(x,y * (K(z \ 1,y) * u)) = K(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[para(3312(a,1),15389(a,1,2,2,1))].">
      <j1 rule="para" parents="3312 15389"/>
    </justification>
  </clause>

  <clause id="15391">
    <literal><![CDATA[
      K(x,T(y,z \ 1) * u) = K(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(58,a,15147,a(flip),b,15390,a)].">
      <j1 rule="hyper" parents="58 15147 15390"/>
    </justification>
  </clause>

  <clause id="15392">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ 1)) * w) = K(x,T(y,u * z) * w)
    ]]></literal>
    <justification jstring="[para(13995(a,1),15391(a,1,2,1))].">
      <j1 rule="para" parents="13995 15391"/>
    </justification>
  </clause>

  <clause id="15393">
    <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,10840,a(flip),b,15369,a),flip(a)].">
      <j1 rule="hyper" parents="320 10840 15369"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15394">
    <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(15369(a,2),10870(a,1))].">
      <j1 rule="para" parents="15369 10870"/>
    </justification>
  </clause>

  <clause id="15395">
    <literal><![CDATA[
      K(((x * (y \ z)) / x) * y,u) = K(y * T(z / y,x),u)
    ]]></literal>
    <justification jstring="[hyper(320,a,15388,a(flip),b,15387,a),flip(a)].">
      <j1 rule="hyper" parents="320 15388 15387"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15396">
    <literal><![CDATA[
      K(((x * y) / x) / z,u) = K((z \ 1) * T((z \ y) / (z \ 1),x),u)
    ]]></literal>
    <justification jstring="[hyper(12812,a,15395,a)].">
      <j1 rule="hyper" parents="12812 15395"/>
    </justification>
  </clause>

  <clause id="15397">
    <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),15393(a,1,2,1,1,1)),flip(a)].">
      <j1 rule="para" parents="75 15393"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15398">
    <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(15397(a,1),14632(a,1))].">
      <j1 rule="para" parents="15397 14632"/>
    </justification>
  </clause>

  <clause id="15399">
    <literal><![CDATA[
      T(x * (K(y,z) * K(y,z)),u) = T(x,u) * (K(y,z) * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(5041,a,15187,a),flip(a)].">
      <j1 rule="hyper" parents="5041 15187"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15400">
    <literal><![CDATA[
      K(x,(y * z) \ T(u,(y * x) * z)) = K(x,u / (y * z))
    ]]></literal>
    <justification jstring="[hyper(14237,a,15264,a)].">
      <j1 rule="hyper" parents="14237 15264"/>
    </justification>
  </clause>

  <clause id="15401">
    <literal><![CDATA[
      K(x,((T(y,z) \ u) * y) * w) = K(x,(T(y,z) * (u / y)) * w)
    ]]></literal>
    <justification jstring="[hyper(58,a,15301,a(flip),b,15303,a),flip(a)].">
      <j1 rule="hyper" parents="58 15301 15303"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15402">
    <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,15138,a(flip),b,15362,a),flip(a)].">
      <j1 rule="hyper" parents="320 15138 15362"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15403">
    <literal><![CDATA[
      K(x,T(y / z,y / (z * u))) = K(x,T(y / z,T(u,z)))
    ]]></literal>
    <justification jstring="[para(9618(a,1),15402(a,1,2))].">
      <j1 rule="para" parents="9618 15402"/>
    </justification>
  </clause>

  <clause id="15404">
    <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,15102,a(flip),b,15403,a)].">
      <j1 rule="hyper" parents="58 15102 15403"/>
    </justification>
  </clause>

  <clause id="15405">
    <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(5910(a,1),15403(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="5910 15403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15406">
    <literal><![CDATA[
      K(x \ T((x \ y) * x,z),u) = K(((z * y) / z) / x,u)
    ]]></literal>
    <justification jstring="[hyper(320,a,12384,a(flip),b,15396,a)].">
      <j1 rule="hyper" parents="320 12384 15396"/>
    </justification>
  </clause>

  <clause id="15407">
    <literal><![CDATA[
      K(T(x \ T(y,z),x),u) = K(((z * y) / z) / x,u)
    ]]></literal>
    <justification jstring="[para(4607(a,1),15406(a,1,1))].">
      <j1 rule="para" parents="4607 15406"/>
    </justification>
  </clause>

  <clause id="15408">
    <literal><![CDATA[
      K(((x * y) / x) / z,u) = K(T(y,x) / z,u)
    ]]></literal>
    <justification jstring="[hyper(8265,a,15407,a),flip(a)].">
      <j1 rule="hyper" parents="8265 15407"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15409">
    <literal><![CDATA[
      K(T(T(x,y),y) / z,u) = K(x / z,u)
    ]]></literal>
    <justification jstring="[para(225(a,1),15408(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="225 15408"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15410">
    <literal><![CDATA[
      K((x * y) \ T(z,x),T(u,y)) = K(z / (y * x),u)
    ]]></literal>
    <justification jstring="[hyper(14873,a,15409,a)].">
      <j1 rule="hyper" parents="14873 15409"/>
    </justification>
  </clause>

  <clause id="15411">
    <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(13988(a,1),15410(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13988 15410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15412">
    <literal><![CDATA[
      T(x,K(y,z) * (((y \ u) / u) \ w)) = T(x,T((y \ u) / u,z) \ w)
    ]]></literal>
    <justification jstring="[hyper(15340,a,15123,a)].">
      <j1 rule="hyper" parents="15340 15123"/>
    </justification>
  </clause>

  <clause id="15413">
    <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),15160(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="107 15160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15414">
    <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,15305,a(flip),b,15224,a)].">
      <j1 rule="hyper" parents="58 15305 15224"/>
    </justification>
  </clause>

  <clause id="15415">
    <literal><![CDATA[
      K(x,(y * T(T(z,u),u)) * w) = K(x,(y * z) * w)
    ]]></literal>
    <justification jstring="[hyper(12305,a,15414,a),flip(a)].">
      <j1 rule="hyper" parents="12305 15414"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15417">
    <literal><![CDATA[
      K(x,(y * (z * K(u,z))) * w) = K(x,(y * T(z,u)) * w)
    ]]></literal>
    <justification jstring="[para(4816(a,1),15415(a,1,2,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4816 15415"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15418">
    <literal><![CDATA[
      T(x,(y * (z * K(u,z))) * w) = T(x,(y * T(z,u)) * w)
    ]]></literal>
    <justification jstring="[hyper(118,a,15417,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 15417 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15419">
    <literal><![CDATA[
      K(x,((y \ z) * T(y,u)) * w) = K(x,(y * (z / T(y,u))) * w)
    ]]></literal>
    <justification jstring="[hyper(58,a,15304,a(flip),b,15417,a),flip(a)].">
      <j1 rule="hyper" parents="58 15304 15417"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15420">
    <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,15307,a(flip),b,15269,a)].">
      <j1 rule="hyper" parents="58 15307 15269"/>
    </justification>
  </clause>

  <clause id="15421">
    <literal><![CDATA[
      K(x,y * (((z * u) / z) * w)) = K(x,y * (T(u,z) * w))
    ]]></literal>
    <justification jstring="[hyper(15291,a,15420,a),flip(a)].">
      <j1 rule="hyper" parents="15291 15420"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15422">
    <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(15420(a,1),15291(a,1))].">
      <j1 rule="para" parents="15420 15291"/>
    </justification>
  </clause>

  <clause id="15423">
    <literal><![CDATA[
      K(x,y * (T(T(z,u),u) * w)) = K(x,y * (z * w))
    ]]></literal>
    <justification jstring="[para(225(a,1),15421(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="225 15421"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15424">
    <literal><![CDATA[
      K(x,y * (z * (T(T(z,u),u) \ w))) = K(x,y * w)
    ]]></literal>
    <justification jstring="[para(5(a,1),15423(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5 15423"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15425">
    <literal><![CDATA[
      K(x,y * (K(z,u) * (K(z,u) * w))) = K(x,y * w)
    ]]></literal>
    <justification jstring="[para(5879(a,2),15424(a,1,2,2))].">
      <j1 rule="para" parents="5879 15424"/>
    </justification>
  </clause>

  <clause id="15426">
    <literal><![CDATA[
      K(x,y * (K(z,u) * (z \ w))) = K(x,y * (T(z,u) \ w))
    ]]></literal>
    <justification jstring="[para(5081(a,1),15425(a,1,2,2,2))].">
      <j1 rule="para" parents="5081 15425"/>
    </justification>
  </clause>

  <clause id="15427">
    <literal><![CDATA[
      K(x,y * ((K(z,u) * K(z,u)) * w)) = K(x,y * w)
    ]]></literal>
    <justification jstring="[para(11439(a,2),15425(a,1,2,2))].">
      <j1 rule="para" parents="11439 15425"/>
    </justification>
  </clause>

  <clause id="15428">
    <literal><![CDATA[
      K(x,y * (z * (K(u,w) * K(u,w)))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,15176,a(flip),b,15427,a)].">
      <j1 rule="hyper" parents="58 15176 15427"/>
    </justification>
  </clause>

  <clause id="15430">
    <literal><![CDATA[
      K(x,y * (z * K(u,w))) = K(x,y * (z * K(w,u)))
    ]]></literal>
    <justification jstring="[para(8998(a,1),15428(a,1,2,2))].">
      <j1 rule="para" parents="8998 15428"/>
    </justification>
  </clause>

  <clause id="15431">
    <literal><![CDATA[
      K(x,y * ((z / u) * K(u,w))) = K(x,y * (z / T(u,w)))
    ]]></literal>
    <justification jstring="[para(6322(a,1),15430(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6322 15430"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15432">
    <literal><![CDATA[
      K(x,y * ((z \ u) * K(w,u))) = K(x,y * (z \ T(u,w)))
    ]]></literal>
    <justification jstring="[para(13699(a,1),15430(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="13699 15430"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15433">
    <literal><![CDATA[
      K(x,y * ((z / (z / u)) \ w)) = K(x,y * (T(u,z) \ w))
    ]]></literal>
    <justification jstring="[hyper(58,a,13203,a,b,15426,a)].">
      <j1 rule="hyper" parents="58 13203 15426"/>
    </justification>
  </clause>

  <clause id="15434">
    <literal><![CDATA[
      K(x,y * (z / T(u,u \ w))) = K(x,y * (z / (w / (w / u))))
    ]]></literal>
    <justification jstring="[para(6473(a,2),15431(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6473 15431"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15435">
    <literal><![CDATA[
      K(x,y * (z \ ((u * w) / u))) = K(x,y * (z \ T(w,u)))
    ]]></literal>
    <justification jstring="[para(13961(a,2),15432(a,1,2,2))].">
      <j1 rule="para" parents="13961 15432"/>
    </justification>
  </clause>

  <clause id="15436">
    <literal><![CDATA[
      K(x,y * (z \ (L(u,w,u) * w))) = K(x,y * (z \ T(w * u,u)))
    ]]></literal>
    <justification jstring="[para(14021(a,1),15432(a,1,2,2))].">
      <j1 rule="para" parents="14021 15432"/>
    </justification>
  </clause>

  <clause id="15437">
    <literal><![CDATA[
      K(x,y * (z \ T(T(u,w),w))) = K(x,y * (z \ u))
    ]]></literal>
    <justification jstring="[para(225(a,1),15435(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="225 15435"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15438">
    <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,12329,a,b,15437,a),flip(a)].">
      <j1 rule="hyper" parents="320 12329 15437"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15439">
    <literal><![CDATA[
      K(x,y * (z \ T(u * w,w))) = K(x,y * (z \ (w * u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,13179,a(flip),b,15436,a),flip(a)].">
      <j1 rule="hyper" parents="58 13179 15436"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15441">
    <literal><![CDATA[
      K(x,y * (z \ (u * (w / u)))) = K(x,y * (z \ T(w,u)))
    ]]></literal>
    <justification jstring="[para(7(a,1),15439(a,1,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="7 15439"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15442">
    <literal><![CDATA[
      K(x,T(y * ((z * y) \ u),z)) = K(x,y * ((z * y) \ T(u,z)))
    ]]></literal>
    <justification jstring="[hyper(58,a,15015,a(flip),b,15441,a)].">
      <j1 rule="hyper" parents="58 15015 15441"/>
    </justification>
  </clause>

  <clause id="15443">
    <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,5339,a(flip),b,15329,a)].">
      <j1 rule="hyper" parents="58 5339 15329"/>
    </justification>
  </clause>

  <clause id="15444">
    <literal><![CDATA[
      K(x,y \ (((1 / z) \ u) * w)) = K(x,y \ (((z \ 1) \ u) * w))
    ]]></literal>
    <justification jstring="[hyper(58,a,15328,a(flip),b,15443,a),flip(a)].">
      <j1 rule="hyper" parents="58 15328 15443"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15445">
    <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(7755(a,1),15112(a,1,1,1,2))].">
      <j1 rule="para" parents="7755 15112"/>
    </justification>
  </clause>

  <clause id="15446">
    <literal><![CDATA[
      K(x,(K(y,z \ K(z,u)) * u) \ w) = K(x,(u * K(y,z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(6866,a,15348,a),flip(a)].">
      <j1 rule="hyper" parents="6866 15348"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15447">
    <literal><![CDATA[
      K(x,(y * K(z,u \ 1)) \ w) = K(x,(y * K(z,u)) \ w)
    ]]></literal>
    <justification jstring="[para(5913(a,1),15446(a,1,2,1))].">
      <j1 rule="para" parents="5913 15446"/>
    </justification>
  </clause>

  <clause id="15448">
    <literal><![CDATA[
      K(x,(K(y \ K(y,z),u) * z) \ w) = K(x,(z * K(u,y)) \ w)
    ]]></literal>
    <justification jstring="[hyper(6866,a,15352,a),flip(a)].">
      <j1 rule="hyper" parents="6866 15352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15449">
    <literal><![CDATA[
      K(x,(y * K(z \ 1,u)) \ w) = K(x,(y * K(u,z)) \ w)
    ]]></literal>
    <justification jstring="[para(6683(a,1),15448(a,1,2,1))].">
      <j1 rule="para" parents="6683 15448"/>
    </justification>
  </clause>

  <clause id="15450">
    <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(7791(a,1),15449(a,2,2))].">
      <j1 rule="para" parents="7791 15449"/>
    </justification>
  </clause>

  <clause id="15451">
    <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(15188(a,1),15206(a,1,1))].">
      <j1 rule="para" parents="15188 15206"/>
    </justification>
  </clause>

  <clause id="15452">
    <literal><![CDATA[
      T(x,T(y / ((z * u) / z),w)) = T(x,T(y / T(u,z),w))
    ]]></literal>
    <justification jstring="[hyper(7703,a,15451,a),flip(a)].">
      <j1 rule="hyper" parents="7703 15451"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15453">
    <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,12377,a(flip),b,15452,a)].">
      <j1 rule="hyper" parents="58 12377 15452"/>
    </justification>
  </clause>

  <clause id="15454">
    <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,14571,a,b,15453,a)].">
      <j1 rule="hyper" parents="58 14571 15453"/>
    </justification>
  </clause>

  <clause id="15455">
    <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(6335(a,1),15159(a,2,2,1))].">
      <j1 rule="para" parents="6335 15159"/>
    </justification>
  </clause>

  <clause id="15456">
    <literal><![CDATA[
      K(x,(y \ T(T(z,u),u)) * w) = K(x,(y \ z) * w)
    ]]></literal>
    <justification jstring="[hyper(29,a,15438,a(flip),b,15217,a),flip(a)].">
      <j1 rule="hyper" parents="29 15438 15217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15457">
    <literal><![CDATA[
      K(x,(y \ ((z * u) / z)) * w) = K(x,(y \ T(u,z)) * w)
    ]]></literal>
    <justification jstring="[para(224(a,1),15456(a,1,2,1,2,1)),flip(a)].">
      <j1 rule="para" parents="224 15456"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15459">
    <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(6335(a,1),15245(a,2,2,2))].">
      <j1 rule="para" parents="6335 15245"/>
    </justification>
  </clause>

  <clause id="15460">
    <literal><![CDATA[
      K(x,y * ((((1 / z) * u) \ u) \ u)) = K(x,y * (((1 / z) * u) * K(z,z \ u)))
    ]]></literal>
    <justification jstring="[para(13774(a,1),15253(a,2,2,2,2))].">
      <j1 rule="para" parents="13774 15253"/>
    </justification>
  </clause>

  <clause id="15461">
    <literal><![CDATA[
      K(x,y * ((((1 / z) * u) \ u) \ u)) = K(x,y * ((1 / z) * (z * (u / z))))
    ]]></literal>
    <justification jstring="[para(10347(a,1),15460(a,2,2,2))].">
      <j1 rule="para" parents="10347 15460"/>
    </justification>
  </clause>

  <clause id="15462">
    <literal><![CDATA[
      K(x,y * L(z / u,u,u \ 1)) = K(x,y * ((((1 / u) * z) \ z) \ z))
    ]]></literal>
    <justification jstring="[para(2820(a,1),15461(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="2820 15461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15463">
    <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,13046,a(flip),b,15462,a)].">
      <j1 rule="hyper" parents="320 13046 15462"/>
    </justification>
  </clause>

  <clause id="15464">
    <literal><![CDATA[
      K(x,y * L(z / u,u,u \ 1)) = K(x,y * (z * (1 / u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,15247,a(flip),b,15463,a),flip(a)].">
      <j1 rule="hyper" parents="58 15247 15463"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15465">
    <literal><![CDATA[
      K(x,y * L(z / u,u,u \ 1)) = K(x,y * (z * (u \ 1)))
    ]]></literal>
    <justification jstring="[hyper(320,a,5334,a(flip),b,15464,a),flip(a)].">
      <j1 rule="hyper" parents="320 5334 15464"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15466">
    <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,15447,a(flip),b,15404,a)].">
      <j1 rule="hyper" parents="58 15447 15404"/>
    </justification>
  </clause>

  <clause id="15467">
    <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,13194,a(flip),b,15466,a)].">
      <j1 rule="hyper" parents="58 13194 15466"/>
    </justification>
  </clause>

  <clause id="15468">
    <literal><![CDATA[
      K(x,T(y,z) \ ((y * z) * (u / (y * z)))) = K(x,T(u / y,T(z,y)))
    ]]></literal>
    <justification jstring="[para(4755(a,2),15467(a,1,2,1))].">
      <j1 rule="para" parents="4755 15467"/>
    </justification>
  </clause>

  <clause id="15469">
    <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(4233(a,1),15468(a,1,2,1))].">
      <j1 rule="para" parents="4233 15468"/>
    </justification>
  </clause>

  <clause id="15470">
    <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(7573(a,1),15411(a,2,1,2))].">
      <j1 rule="para" parents="7573 15411"/>
    </justification>
  </clause>

  <clause id="15472">
    <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),15469(a,1,2,2,1))].">
      <j1 rule="para" parents="105 15469"/>
    </justification>
  </clause>

  <clause id="15473">
    <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),15472(a,1,2,2,2,2))].">
      <j1 rule="para" parents="105 15472"/>
    </justification>
  </clause>

  <clause id="15474">
    <literal><![CDATA[
      K(x,T(y,z) \ ((z * y) * (u / (z * y)))) = K(x,T(u / y,z))
    ]]></literal>
    <justification jstring="[para(7909(a,1),15473(a,2,2))].">
      <j1 rule="para" parents="7909 15473"/>
    </justification>
  </clause>

  <clause id="15475">
    <literal><![CDATA[
      K(x,T(y,z) \ T(u,z * y)) = K(x,T(u / y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,15321,a(flip),b,15474,a)].">
      <j1 rule="hyper" parents="58 15321 15474"/>
    </justification>
  </clause>

  <clause id="15477">
    <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(5842(a,1),15475(a,1,2,2,2))].">
      <j1 rule="para" parents="5842 15475"/>
    </justification>
  </clause>

  <clause id="15478">
    <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(15231,a,15433,a),flip(a)].">
      <j1 rule="hyper" parents="15231 15433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15479">
    <literal><![CDATA[
      K(x,((y / (y / z)) \ u) * w) = K(x,(T(z,y) \ u) * w)
    ]]></literal>
    <justification jstring="[hyper(12305,a,15478,a),flip(a)].">
      <j1 rule="hyper" parents="12305 15478"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15480">
    <literal><![CDATA[
      K(x,(T(y,z) \ z) * u) = K(x,(z / y) * u)
    ]]></literal>
    <justification jstring="[para(75(a,1),15479(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="75 15479"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15481">
    <literal><![CDATA[
      K(x,(y \ T(z,y)) * u) = K(x,(z / y) * u)
    ]]></literal>
    <justification jstring="[para(4248(a,1),15480(a,1,2,1))].">
      <j1 rule="para" parents="4248 15480"/>
    </justification>
  </clause>

  <clause id="15482">
    <literal><![CDATA[
      K(x,(T(y,T(z,u)) \ (u * (z / u))) * w) = K(x,((u * (z / u)) / y) * w)
    ]]></literal>
    <justification jstring="[para(12281(a,1),15480(a,1,2,1,1))].">
      <j1 rule="para" parents="12281 15480"/>
    </justification>
  </clause>

  <clause id="15483">
    <literal><![CDATA[
      K(x,(T(y,z) / z) * u) = K(x,(z \ y) * u)
    ]]></literal>
    <justification jstring="[hyper(58,a,15456,a(flip),b,15481,a),flip(a)].">
      <j1 rule="hyper" parents="58 15456 15481"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15484">
    <literal><![CDATA[
      K(x,(y / T(z,y)) * u) = K(x,(z \ y) * u)
    ]]></literal>
    <justification jstring="[para(4246(a,1),15483(a,1,2,1))].">
      <j1 rule="para" parents="4246 15483"/>
    </justification>
  </clause>

  <clause id="15485">
    <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(13859(a,1),15484(a,1,2,1,2))].">
      <j1 rule="para" parents="13859 15484"/>
    </justification>
  </clause>

  <clause id="15486">
    <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,9342,a(flip),b,15108,a),flip(a)].">
      <j1 rule="hyper" parents="320 9342 15108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15488">
    <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(15114(a,1),15486(a,2,2))].">
      <j1 rule="para" parents="15114 15486"/>
    </justification>
  </clause>

  <clause id="15489">
    <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(15323(a,1),15211(a,1,1))].">
      <j1 rule="para" parents="15323 15211"/>
    </justification>
  </clause>

  <clause id="15490">
    <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(15489(a,1),10866(a,1))].">
      <j1 rule="para" parents="15489 10866"/>
    </justification>
  </clause>

  <clause id="15491">
    <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(9933(a,1),15405(a,2,2))].">
      <j1 rule="para" parents="9933 15405"/>
    </justification>
  </clause>

  <clause id="15492">
    <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(7944(a,1),15491(a,1,2))].">
      <j1 rule="para" parents="7944 15491"/>
    </justification>
  </clause>

  <clause id="15493">
    <literal><![CDATA[
      K(x,T(y / z,y / (u \ z))) = K(x,T(y / z,u \ 1))
    ]]></literal>
    <justification jstring="[para(9626(a,1),15492(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9626 15492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15494">
    <literal><![CDATA[
      K(x,T(y / z,y / (u \ z))) = K(x,T(y / z,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,8227,a(flip),b,15493,a),flip(a)].">
      <j1 rule="hyper" parents="320 8227 15493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15496">
    <literal><![CDATA[
      K(x,T(y,z) \ ((z \ y) * (u / (z \ y)))) = K(x,T(u / y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,14916,a(flip),b,15494,a)].">
      <j1 rule="hyper" parents="58 14916 15494"/>
    </justification>
  </clause>

  <clause id="15497">
    <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(4277(a,1),15496(a,1,2,2,1))].">
      <j1 rule="para" parents="4277 15496"/>
    </justification>
  </clause>

  <clause id="15498">
    <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(7333(a,1),15450(a,1,2,2,2))].">
      <j1 rule="para" parents="7333 15450"/>
    </justification>
  </clause>

  <clause id="15500">
    <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(7784(a,2),15498(a,1,2,2))].">
      <j1 rule="para" parents="7784 15498"/>
    </justification>
  </clause>

  <clause id="15501">
    <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(8193(a,1),15500(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8193 15500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15502">
    <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,6140,a(flip),b,15501,a),flip(a)].">
      <j1 rule="hyper" parents="320 6140 15501"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15503">
    <literal><![CDATA[
      K(x,(K(y,z) * u) \ 1) = K(x,u \ K(y,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(58,a,13081,a(flip),b,15502,a)].">
      <j1 rule="hyper" parents="58 13081 15502"/>
    </justification>
  </clause>

  <clause id="15504">
    <literal><![CDATA[
      K(x,y \ K(z,u \ 1)) = K(x,y \ K(u,z))
    ]]></literal>
    <justification jstring="[hyper(6484,a,15503,a),flip(a)].">
      <j1 rule="hyper" parents="6484 15503"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15508">
    <literal><![CDATA[
      K(x,y \ K(z \ 1,u)) = K(x,y \ K(z,u))
    ]]></literal>
    <justification jstring="[hyper(15278,a,15504,a)].">
      <j1 rule="hyper" parents="15278 15504"/>
    </justification>
  </clause>

  <clause id="15509">
    <literal><![CDATA[
      K(x,y \ K(z \ 1,u)) = K(x,y \ K(u,z))
    ]]></literal>
    <justification jstring="[para(3554(a,1),15504(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3554 15504"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15510">
    <literal><![CDATA[
      K(x,(y \ z) \ K(u,y)) = K(x,z \ T(y,1 / u))
    ]]></literal>
    <justification jstring="[hyper(58,a,15220,a(flip),b,15508,a),flip(a)].">
      <j1 rule="hyper" parents="58 15220 15508"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15511">
    <literal><![CDATA[
      K(x,y \ K(z \ u,u)) = K(x,y \ K(u,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,13090,a(flip),b,15509,a)].">
      <j1 rule="hyper" parents="58 13090 15509"/>
    </justification>
  </clause>

  <clause id="15512">
    <literal><![CDATA[
      K(x,y \ K(z,u \ z)) = K(x,y \ K(z,u))
    ]]></literal>
    <justification jstring="[hyper(15278,a,15511,a)].">
      <j1 rule="hyper" parents="15278 15511"/>
    </justification>
  </clause>

  <clause id="15513">
    <literal><![CDATA[
      K(x,y \ T(z,1 / u)) = K(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,15219,a(flip),b,15510,a),flip(a)].">
      <j1 rule="hyper" parents="58 15219 15510"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15514">
    <literal><![CDATA[
      K(x,y \ T(z,u \ 1)) = K(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[para(72(a,1),15513(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="72 15513"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15515">
    <literal><![CDATA[
      K(x,y \ T(z * (u \ 1),u)) = K(x,y \ ((u \ 1) * z))
    ]]></literal>
    <justification jstring="[hyper(58,a,15323,a(flip),b,15514,a),flip(a)].">
      <j1 rule="hyper" parents="58 15323 15514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15516">
    <literal><![CDATA[
      K(x,y \ T(z,u \ (w \ u))) = K(x,y \ T(z,T(w,u)))
    ]]></literal>
    <justification jstring="[para(7663(a,1),15514(a,1,2,2))].">
      <j1 rule="para" parents="7663 15514"/>
    </justification>
  </clause>

  <clause id="15517">
    <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(15514(a,1),15273(a,1,1))].">
      <j1 rule="para" parents="15514 15273"/>
    </justification>
  </clause>

  <clause id="15518">
    <literal><![CDATA[
      K(x,y \ ((z \ 1) * (z * u))) = K(x,y \ R(u,z,z \ 1))
    ]]></literal>
    <justification jstring="[para(788(a,1),15515(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="788 15515"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15519">
    <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(10901,a,15518,a)].">
      <j1 rule="hyper" parents="10901 15518"/>
    </justification>
  </clause>

  <clause id="15520">
    <literal><![CDATA[
      K(x,y \ R(z,u,u \ 1)) = K(x,y \ L(z,u,u \ 1))
    ]]></literal>
    <justification jstring="[hyper(58,a,5731,a(flip),b,15518,a),flip(a)].">
      <j1 rule="hyper" parents="58 5731 15518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15521">
    <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,14559,a(flip),b,15520,a),flip(a)].">
      <j1 rule="hyper" parents="58 14559 15520"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15522">
    <literal><![CDATA[
      K(x,y \ L(z / u,u,u \ 1)) = K(x,y \ (z * (u \ 1)))
    ]]></literal>
    <justification jstring="[para(523(a,1),15520(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="523 15520"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15523">
    <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,14483,a(flip),b,15521,a)].">
      <j1 rule="hyper" parents="58 14483 15521"/>
    </justification>
  </clause>

  <clause id="15524">
    <literal><![CDATA[
      K(x,(y \ 1) \ a(z,u,u \ 1)) = K(x,y * (z \ L(z,u,u \ 1)))
    ]]></literal>
    <justification jstring="[hyper(14008,a,15523,a),flip(a)].">
      <j1 rule="hyper" parents="14008 15523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15525">
    <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(15524(a,1),14008(a,1))].">
      <j1 rule="para" parents="15524 14008"/>
    </justification>
  </clause>

  <clause id="15526">
    <literal><![CDATA[
      K(x,((y \ 1) * z) \ R(u,y,y \ 1)) = K(x,(y \ z) \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,14605,a(flip),b,15519,a),flip(a)].">
      <j1 rule="hyper" parents="58 14605 15519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15527">
    <literal><![CDATA[
      K(x,((y \ 1) * z) \ L(u,y,y \ 1)) = K(x,(y \ z) \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,15520,a(flip),b,15526,a)].">
      <j1 rule="hyper" parents="58 15520 15526"/>
    </justification>
  </clause>

  <clause id="15528">
    <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(15517(a,1),10866(a,1))].">
      <j1 rule="para" parents="15517 10866"/>
    </justification>
  </clause>

  <clause id="15529">
    <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(8574(a,1),15497(a,1,2,1))].">
      <j1 rule="para" parents="8574 15497"/>
    </justification>
  </clause>

  <clause id="15530">
    <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(4277(a,1),15529(a,1,2,2,2,2))].">
      <j1 rule="para" parents="4277 15529"/>
    </justification>
  </clause>

  <clause id="15532">
    <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,15379,a(flip),b,15530,a)].">
      <j1 rule="hyper" parents="58 15379 15530"/>
    </justification>
  </clause>

  <clause id="15533">
    <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(12743(a,1),15532(a,2,2))].">
      <j1 rule="para" parents="12743 15532"/>
    </justification>
  </clause>

  <clause id="15534">
    <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,15321,a(flip),b,15533,a)].">
      <j1 rule="hyper" parents="58 15321 15533"/>
    </justification>
  </clause>

  <clause id="15535">
    <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,13048,a(flip),b,15477,a)].">
      <j1 rule="hyper" parents="58 13048 15477"/>
    </justification>
  </clause>

  <clause id="15536">
    <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(15384(a,1),15535(a,1,2,2))].">
      <j1 rule="para" parents="15384 15535"/>
    </justification>
  </clause>

  <clause id="15537">
    <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(5385(a,1),15536(a,1,2,2,2,2))].">
      <j1 rule="para" parents="5385 15536"/>
    </justification>
  </clause>

  <clause id="15538">
    <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(15308(a,1),15537(a,1,2,2))].">
      <j1 rule="para" parents="15308 15537"/>
    </justification>
  </clause>

  <clause id="15539">
    <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(4755(a,2),15538(a,1,2,2,2))].">
      <j1 rule="para" parents="4755 15538"/>
    </justification>
  </clause>

  <clause id="15540">
    <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(13212,a,15539,a),flip(a)].">
      <j1 rule="hyper" parents="13212 15539"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15541">
    <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,15151,a(flip),b,15540,a),flip(a)].">
      <j1 rule="hyper" parents="320 15151 15540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15542">
    <literal><![CDATA[
      K(x,T(y / (z * u),u \ (z \ u))) = K(x,(u * z) \ T(y,T(u,z)))
    ]]></literal>
    <justification jstring="[para(7679(a,1),15541(a,1,2))].">
      <j1 rule="para" parents="7679 15541"/>
    </justification>
  </clause>

  <clause id="15543">
    <literal><![CDATA[
      K(x,T(y / (z * u),T(z,u))) = K(x,(u * z) \ T(y,T(u,z)))
    ]]></literal>
    <justification jstring="[hyper(8276,a,15542,a)].">
      <j1 rule="hyper" parents="8276 15542"/>
    </justification>
  </clause>

  <clause id="15544">
    <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(5052(a,1),15543(a,2,2,1))].">
      <j1 rule="para" parents="5052 15543"/>
    </justification>
  </clause>

  <clause id="15545">
    <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(14274(a,1),14279(a,1,2))].">
      <j1 rule="para" parents="14274 14279"/>
    </justification>
  </clause>

  <clause id="15546">
    <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(833,a,15545,a)].">
      <j1 rule="hyper" parents="833 15545"/>
    </justification>
  </clause>

  <clause id="15547">
    <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(14278,a,15546,a),flip(a)].">
      <j1 rule="hyper" parents="14278 15546"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15549">
    <literal><![CDATA[
      L(x,y,a(z,u,K(w,v5)) * v6) = L(x,y,v6)
    ]]></literal>
    <justification jstring="[para(14275(a,1),15547(a,1,2))].">
      <j1 rule="para" parents="14275 15547"/>
    </justification>
  </clause>

  <clause id="15550">
    <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(13233(a,1),14587(a,1,2))].">
      <j1 rule="para" parents="13233 14587"/>
    </justification>
  </clause>

  <clause id="15551">
    <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(14740(a,1),15550(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="14740 15550"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15552">
    <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),15551(a,2,2,1,1,1))].">
      <j1 rule="para" parents="224 15551"/>
    </justification>
  </clause>

  <clause id="15554">
    <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(15552(a,2),14078(a,1))].">
      <j1 rule="para" parents="15552 14078"/>
    </justification>
  </clause>

  <clause id="15555">
    <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),14588(a,1,2,2))].">
      <j1 rule="para" parents="60 14588"/>
    </justification>
  </clause>

  <clause id="15556">
    <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(14972(a,1),14843(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14972 14843"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15557">
    <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(14478(a,1),15556(a,2,2,2,1))].">
      <j1 rule="para" parents="14478 15556"/>
    </justification>
  </clause>

  <clause id="15559">
    <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(14485(a,1),15557(a,2,2))].">
      <j1 rule="para" parents="14485 15557"/>
    </justification>
  </clause>

  <clause id="15560">
    <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(7942(a,1),15544(a,2,2,2))].">
      <j1 rule="para" parents="7942 15544"/>
    </justification>
  </clause>

  <clause id="15561">
    <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(8151(a,1),15560(a,2,2,2))].">
      <j1 rule="para" parents="8151 15560"/>
    </justification>
  </clause>

  <clause id="15562">
    <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,15516,a(flip),b,15561,a),flip(a)].">
      <j1 rule="hyper" parents="320 15516 15561"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15563">
    <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,15449,a(flip),b,15562,a),flip(a)].">
      <j1 rule="hyper" parents="320 15449 15562"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15564">
    <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,13194,a(flip),b,15563,a),flip(a)].">
      <j1 rule="hyper" parents="320 13194 15563"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15565">
    <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(4755(a,2),15564(a,2,2,1))].">
      <j1 rule="para" parents="4755 15564"/>
    </justification>
  </clause>

  <clause id="15566">
    <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,15534,a(flip),b,15565,a),flip(a)].">
      <j1 rule="hyper" parents="320 15534 15565"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15567">
    <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),15566(a,1,2,1,2))].">
      <j1 rule="para" parents="5 15566"/>
    </justification>
  </clause>

  <clause id="15568">
    <literal><![CDATA[
      K(x,T(y / z,T(z * u,z))) = K(x,T(y / z,u \ z))
    ]]></literal>
    <justification jstring="[para(7108(a,1),15567(a,1,2))].">
      <j1 rule="para" parents="7108 15567"/>
    </justification>
  </clause>

  <clause id="15569">
    <literal><![CDATA[
      K(x,T(y / z,u \ z)) = K(x,T(y / z,u * z))
    ]]></literal>
    <justification jstring="[para(12254(a,1),15568(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12254 15568"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15570">
    <literal><![CDATA[
      K(x,T((y * z) / z,u * z)) = K(x,T(y,u \ z))
    ]]></literal>
    <justification jstring="[para(6(a,1),15569(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6 15569"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15571">
    <literal><![CDATA[
      K(x,T(y,z \ u)) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[para(6(a,1),15570(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6 15570"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15572">
    <literal><![CDATA[
      K(x,T(y,z \ u)) = K(x,T(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(8272,a,15571,a)].">
      <j1 rule="hyper" parents="8272 15571"/>
    </justification>
  </clause>

  <clause id="15573">
    <literal><![CDATA[
      K(x \ y,T(z,y * x)) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(8064,a,15571,a),flip(a)].">
      <j1 rule="hyper" parents="8064 15571"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15575">
    <literal><![CDATA[
      K(x,T(y,z * u)) = K(x,T(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(58,a,15571,a(flip),b,15572,a)].">
      <j1 rule="hyper" parents="58 15571 15572"/>
    </justification>
  </clause>

  <clause id="15576">
    <literal><![CDATA[
      K(x,T(y / ((z \ u) * z),u * z)) = K(x,u \ T(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,15322,a(flip),b,15572,a),flip(a)].">
      <j1 rule="hyper" parents="58 15322 15572"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15577">
    <literal><![CDATA[
      T(x * K(y,T(x,z * u)),y) = T(x,K(y,u \ z))
    ]]></literal>
    <justification jstring="[para(15572(a,1),8133(a,1,1,2))].">
      <j1 rule="para" parents="15572 8133"/>
    </justification>
  </clause>

  <clause id="15578">
    <literal><![CDATA[
      K(x,T((y \ z) * u,z * y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u * (y \ z)) = w
    ]]></literal>
    <justification jstring="[para(15572(a,1),12301(a,1))].">
      <j1 rule="para" parents="15572 12301"/>
    </justification>
  </clause>

  <clause id="15579">
    <literal><![CDATA[
      K(x,T(y * (z \ u),u * z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z \ u) * y) = w
    ]]></literal>
    <justification jstring="[para(15572(a,1),12302(a,1))].">
      <j1 rule="para" parents="15572 12302"/>
    </justification>
  </clause>

  <clause id="15580">
    <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(15572(a,1),13941(a,1))].">
      <j1 rule="para" parents="15572 13941"/>
    </justification>
  </clause>

  <clause id="15581">
    <literal><![CDATA[
      K(x * (y * z),T(u,z * y)) = K((y * z) * x,u)
    ]]></literal>
    <justification jstring="[hyper(12244,a,15575,a),flip(a)].">
      <j1 rule="hyper" parents="12244 15575"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15582">
    <literal><![CDATA[
      K(x,T(y,z * (u * y))) = K(x,T(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(320,a,9600,a,b,15575,a)].">
      <j1 rule="hyper" parents="320 9600 15575"/>
    </justification>
  </clause>

  <clause id="15583">
    <literal><![CDATA[
      x * K(y,T(z,u * w)) = x * K(y,T(z,w * u))
    ]]></literal>
    <justification jstring="[hyper(119,a,15575,a,b,4,a)].">
      <j1 rule="hyper" parents="119 15575 4"/>
    </justification>
  </clause>

  <clause id="15586">
    <literal><![CDATA[
      (x * y) * K(z,T(u,y * x)) = K(z,u) * (x * y)
    ]]></literal>
    <justification jstring="[para(15575(a,1),7179(a,1,2))].">
      <j1 rule="para" parents="15575 7179"/>
    </justification>
  </clause>

  <clause id="15588">
    <literal><![CDATA[
      T(x,y) * K(z,T(u,y * x)) = T(K(z,u) * x,y)
    ]]></literal>
    <justification jstring="[para(15575(a,1),14865(a,1,2))].">
      <j1 rule="para" parents="15575 14865"/>
    </justification>
  </clause>

  <clause id="15589">
    <literal><![CDATA[
      T(x * K(y,T(x,z * u)),y) = T(x,K(y,u * (x * z)))
    ]]></literal>
    <justification jstring="[para(15582(a,1),8146(a,1,1,2))].">
      <j1 rule="para" parents="15582 8146"/>
    </justification>
  </clause>

  <clause id="15590">
    <literal><![CDATA[
      T(x,K(y,z \ u)) = T(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(8351,a,15577,a),flip(a)].">
      <j1 rule="hyper" parents="8351 15577"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15591">
    <literal><![CDATA[
      T(x,K(y,z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,u * z)) = w
    ]]></literal>
    <justification jstring="[para(15577(a,1),8351(a,1))].">
      <j1 rule="para" parents="15577 8351"/>
    </justification>
  </clause>

  <clause id="15592">
    <literal><![CDATA[
      T(x,K(y,z \ u)) = T(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[hyper(8219,a,15590,a)].">
      <j1 rule="hyper" parents="8219 15590"/>
    </justification>
  </clause>

  <clause id="15593">
    <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(15590(a,1),15107(a,1,2,1,2))].">
      <j1 rule="para" parents="15590 15107"/>
    </justification>
  </clause>

  <clause id="15594">
    <literal><![CDATA[
      x * K(x,K(y,z * u)) = T(x,K(y,z \ u))
    ]]></literal>
    <justification jstring="[hyper(320,a,4755,a(flip),b,15592,a)].">
      <j1 rule="hyper" parents="320 4755 15592"/>
    </justification>
  </clause>

  <clause id="15595">
    <literal><![CDATA[
      T(x,K(y,z * u)) = T(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(58,a,15590,a(flip),b,15592,a)].">
      <j1 rule="hyper" parents="58 15590 15592"/>
    </justification>
  </clause>

  <clause id="15596">
    <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(15595(a,1),15335(a,1,2,1,2))].">
      <j1 rule="para" parents="15595 15335"/>
    </justification>
  </clause>

  <clause id="15597">
    <literal><![CDATA[
      K(x,K(y,z \ u)) = K(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[hyper(29,a,4755,a(flip),b,15594,a)].">
      <j1 rule="hyper" parents="29 4755 15594"/>
    </justification>
  </clause>

  <clause id="15598">
    <literal><![CDATA[
      K(x,K(y,z \ u)) = K(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(8216,a,15597,a)].">
      <j1 rule="hyper" parents="8216 15597"/>
    </justification>
  </clause>

  <clause id="15599">
    <literal><![CDATA[
      K(x,K(y,z * u)) = K(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(58,a,15597,a(flip),b,15598,a)].">
      <j1 rule="hyper" parents="58 15597 15598"/>
    </justification>
  </clause>

  <clause id="15600">
    <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(15598(a,1),7773(a,1,1))].">
      <j1 rule="para" parents="15598 7773"/>
    </justification>
  </clause>

  <clause id="15601">
    <literal><![CDATA[
      K(x * y,K(z,u)) = K(z,K(u,y * x))
    ]]></literal>
    <justification jstring="[hyper(7799,a,15599,a)].">
      <j1 rule="hyper" parents="7799 15599"/>
    </justification>
  </clause>

  <clause id="15604">
    <literal><![CDATA[
      K(x,K(y,(1 / z) * u)) = K(x,K(y,u / z))
    ]]></literal>
    <justification jstring="[hyper(320,a,11833,a(flip),b,15599,a),flip(a)].">
      <j1 rule="hyper" parents="320 11833 15599"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15605">
    <literal><![CDATA[
      K(x,K(y,z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(y,K(x,u * z)) = w
    ]]></literal>
    <justification jstring="[para(15599(a,1),7781(a,1))].">
      <j1 rule="para" parents="15599 7781"/>
    </justification>
  </clause>

  <clause id="15606">
    <literal><![CDATA[
      x \ T(x * y,K(z,u)) = y * K(z,K(u,y * x))
    ]]></literal>
    <justification jstring="[para(15599(a,1),12314(a,2,2))].">
      <j1 rule="para" parents="15599 12314"/>
    </justification>
  </clause>

  <clause id="15609">
    <literal><![CDATA[
      K(x,K(y,z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,u * z)) = w
    ]]></literal>
    <justification jstring="[para(15601(a,1),7821(a,1))].">
      <j1 rule="para" parents="15601 7821"/>
    </justification>
  </clause>

  <clause id="15610">
    <literal><![CDATA[
      K(x,K(y,z / u)) = K(x,K(y,u \ z))
    ]]></literal>
    <justification jstring="[para(13774(a,1),15604(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13774 15604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15611">
    <literal><![CDATA[
      K(x,K(y,z / u)) = K(x,K(y,z \ u))
    ]]></literal>
    <justification jstring="[hyper(8268,a,15610,a)].">
      <j1 rule="hyper" parents="8268 15610"/>
    </justification>
  </clause>

  <clause id="15612">
    <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,10942,a,b,15610,a)].">
      <j1 rule="hyper" parents="320 10942 15610"/>
    </justification>
  </clause>

  <clause id="15613">
    <literal><![CDATA[
      K(x,K(y \ z,u)) = K(x,K(u,z / y))
    ]]></literal>
    <justification jstring="[hyper(320,a,7797,a,b,15610,a)].">
      <j1 rule="hyper" parents="320 7797 15610"/>
    </justification>
  </clause>

  <clause id="15614">
    <literal><![CDATA[
      T(x,K(y,z / u)) = T(x,K(y,u \ z))
    ]]></literal>
    <justification jstring="[hyper(118,a,15610,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 15610 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15615">
    <literal><![CDATA[
      K(x,K(y,z / u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z \ u)) = w
    ]]></literal>
    <justification jstring="[para(15610(a,2),8216(a,1))].">
      <j1 rule="para" parents="15610 8216"/>
    </justification>
  </clause>

  <clause id="15616">
    <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),15611(a,2,2,2))].">
      <j1 rule="para" parents="13 15611"/>
    </justification>
  </clause>

  <clause id="15617">
    <literal><![CDATA[
      K(x,K(y,z / u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,u \ z)) = w
    ]]></literal>
    <justification jstring="[para(15611(a,2),8216(a,1))].">
      <j1 rule="para" parents="15611 8216"/>
    </justification>
  </clause>

  <clause id="15618">
    <literal><![CDATA[
      K(x,K(y \ z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z / y,u)) = w
    ]]></literal>
    <justification jstring="[para(15613(a,2),7831(a,1))].">
      <j1 rule="para" parents="15613 7831"/>
    </justification>
  </clause>

  <clause id="15619">
    <literal><![CDATA[
      K(x,K(y \ (z \ u),L(w,y,z))) = K(x,K(w,u / (z * y)))
    ]]></literal>
    <justification jstring="[para(10853(a,2),15613(a,1,2))].">
      <j1 rule="para" parents="10853 15613"/>
    </justification>
  </clause>

  <clause id="15621">
    <literal><![CDATA[
      T(x,K(y,(z * u) \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,z)) = w
    ]]></literal>
    <justification jstring="[para(15614(a,1),8269(a,1))].">
      <j1 rule="para" parents="15614 8269"/>
    </justification>
  </clause>

  <clause id="15622">
    <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),15609(a,1,2,2))].">
      <j1 rule="para" parents="101 15609"/>
    </justification>
  </clause>

  <clause id="15623">
    <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),15617(a,1,2,2))].">
      <j1 rule="para" parents="524 15617"/>
    </justification>
  </clause>

  <clause id="15624">
    <literal><![CDATA[
      T(x,K(y,z * (u * z))) = T(x,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(15621,a,15590,a),flip(a)].">
      <j1 rule="hyper" parents="15621 15590"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15625">
    <literal><![CDATA[
      K((x * y) * T(z,y),T(u,y * z)) = K((z * y) * R(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(10390(a,1),15581(a,1,1))].">
      <j1 rule="para" parents="10390 15581"/>
    </justification>
  </clause>

  <clause id="15626">
    <literal><![CDATA[
      T(x,y) \ T(K(z,u) * x,y) = K(z,T(u,y * x))
    ]]></literal>
    <justification jstring="[hyper(14867,a,15583,a)].">
      <j1 rule="hyper" parents="14867 15583"/>
    </justification>
  </clause>

  <clause id="15628">
    <literal><![CDATA[
      (x * (y / x)) * K(z,T(u,y)) = K(z,u) * (x * (y / x))
    ]]></literal>
    <justification jstring="[para(7(a,1),15586(a,1,2,2,2))].">
      <j1 rule="para" parents="7 15586"/>
    </justification>
  </clause>

  <clause id="15629">
    <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(15588(a,1),287(a,1,2)),flip(b)].">
      <j1 rule="para" parents="15588 287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15630">
    <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(14977(a,2),15626(a,2,2,2))].">
      <j1 rule="para" parents="14977 15626"/>
    </justification>
  </clause>

  <clause id="15631">
    <literal><![CDATA[
      T(x,K(y,z * (x * u))) = T(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(8351,a,15589,a),flip(a)].">
      <j1 rule="hyper" parents="8351 15589"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15632">
    <literal><![CDATA[
      T(K(x,y),T(z,u)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(12335,a,15628,a)].">
      <j1 rule="hyper" parents="12335 15628"/>
    </justification>
  </clause>

  <clause id="15633">
    <literal><![CDATA[
      K(x,T(T(y,z) * u,y)) = K(x,u * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(12278,a,15632,a),flip(a)].">
      <j1 rule="hyper" parents="12278 15632"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15634">
    <literal><![CDATA[
      K(x,T(y,T(z,u))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(7708,a,15632,a)].">
      <j1 rule="hyper" parents="7708 15632"/>
    </justification>
  </clause>

  <clause id="15635">
    <literal><![CDATA[
      T(K(x,y),T(z,u)) = T(K(x,y),T(z,w))
    ]]></literal>
    <justification jstring="[hyper(320,a,15632,a,b,15632,a)].">
      <j1 rule="hyper" parents="320 15632 15632"/>
    </justification>
  </clause>

  <clause id="15638">
    <literal><![CDATA[
      T(K(x,y),T(z,u)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(320,a,7158,a(flip),b,15632,a),flip(a)].">
      <j1 rule="hyper" parents="320 7158 15632"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15639">
    <literal><![CDATA[
      K(x,T(y,T(z,u))) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(58,a,7909,a(flip),b,15632,a),flip(a)].">
      <j1 rule="hyper" parents="58 7909 15632"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15640">
    <literal><![CDATA[
      T(x,y) * K(z,T(u,x)) = K(z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,15632,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 15632 17"/>
    </justification>
  </clause>

  <clause id="15641">
    <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(15632(a,1),11661(a,1,2))].">
      <j1 rule="para" parents="15632 11661"/>
    </justification>
  </clause>

  <clause id="15644">
    <literal><![CDATA[
      K(x \ y,T(z,T(y,u))) = K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,7889,a(flip),b,15634,a),flip(a)].">
      <j1 rule="hyper" parents="320 7889 15634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15645">
    <literal><![CDATA[
      T(x,T(y,T(z,u))) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(118,a,15634,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 15634 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15646">
    <literal><![CDATA[
      K(x,T(y,z / u)) = K(x,T(y,u \ z))
    ]]></literal>
    <justification jstring="[para(107(a,1),15634(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="107 15634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15648">
    <literal><![CDATA[
      K(x * y,T(x,z)) * K(x,T(y,T(z,u))) = a(x,y,x)
    ]]></literal>
    <justification jstring="[para(15634(a,1),9656(a,1,1))].">
      <j1 rule="para" parents="15634 9656"/>
    </justification>
  </clause>

  <clause id="15649">
    <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(15634(a,1),12239(a,1))].">
      <j1 rule="para" parents="15634 12239"/>
    </justification>
  </clause>

  <clause id="15650">
    <literal><![CDATA[
      T(K(x,y),K(z,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(7954,a,15638,a)].">
      <j1 rule="hyper" parents="7954 15638"/>
    </justification>
  </clause>

  <clause id="15652">
    <literal><![CDATA[
      T(K(x,y),T(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = w
    ]]></literal>
    <justification jstring="[para(15638(a,2),7708(a,1))].">
      <j1 rule="para" parents="15638 7708"/>
    </justification>
  </clause>

  <clause id="15653">
    <literal><![CDATA[
      K(x,K(y,z) * u) = K(x,u * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(12278,a,15650,a),flip(a)].">
      <j1 rule="hyper" parents="12278 15650"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15654">
    <literal><![CDATA[
      K(x,T(T(y,K(z,u)),w)) = K(x,T(y,w))
    ]]></literal>
    <justification jstring="[hyper(8107,a,15650,a)].">
      <j1 rule="hyper" parents="8107 15650"/>
    </justification>
  </clause>

  <clause id="15655">
    <literal><![CDATA[
      K(x,T(y,K(z,u))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(7982,a,15650,a),flip(a)].">
      <j1 rule="hyper" parents="7982 15650"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15656">
    <literal><![CDATA[
      K(T(x,K(y,z)),u) = K(x,u)
    ]]></literal>
    <justification jstring="[hyper(7410,a,15650,a)].">
      <j1 rule="hyper" parents="7410 15650"/>
    </justification>
  </clause>

  <clause id="15658">
    <literal><![CDATA[
      K(x,K(y,z) / u) = K(x,u \ K(y,z))
    ]]></literal>
    <justification jstring="[hyper(6485,a,15650,a),flip(a)].">
      <j1 rule="hyper" parents="6485 15650"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15662">
    <literal><![CDATA[
      (K(x,y) * K(z,u)) \ K(z,u) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,6456,a,b,15650,a)].">
      <j1 rule="hyper" parents="58 6456 15650"/>
    </justification>
  </clause>

  <clause id="15663">
    <literal><![CDATA[
      K(x,y) \ K(z,u) = K(z,u) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,15650,a(flip),b,5132,a),flip(a)].">
      <j1 rule="hyper" parents="119 15650 5132"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15664">
    <literal><![CDATA[
      K(x,y) * K(z,u) = K(z,u) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,15650,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 15650 17"/>
    </justification>
  </clause>

  <clause id="15665">
    <literal><![CDATA[
      K(x,y) / (K(x,y) * K(z,u)) = K(u,z)
    ]]></literal>
    <justification jstring="[hyper(117,a,15650,a(flip),b,7844,a)].">
      <j1 rule="hyper" parents="117 15650 7844"/>
    </justification>
  </clause>

  <clause id="15666">
    <literal><![CDATA[
      T(x \ K(y,z),K(u,x)) = x \ K(y,z)
    ]]></literal>
    <justification jstring="[hyper(116,a,15650,a(flip),b,8135,a),flip(a)].">
      <j1 rule="hyper" parents="116 15650 8135"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15667">
    <literal><![CDATA[
      K(x,K(y,K(z,u))) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,15650,a(flip),b,10598,a),flip(a)].">
      <j1 rule="hyper" parents="115 15650 10598"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15668">
    <literal><![CDATA[
      K(x,K(K(y,z),u)) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,15650,a(flip),b,7810,a),flip(a)].">
      <j1 rule="hyper" parents="115 15650 7810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15669">
    <literal><![CDATA[
      T(L(K(x,y),z,u),K(w,v5)) = L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(15650(a,1),20(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15650 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15677">
    <literal><![CDATA[
      x * (K(y,z) * K(x,u)) = T(x,u) * K(y,z)
    ]]></literal>
    <justification jstring="[para(15650(a,1),5078(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15650 5078"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15678">
    <literal><![CDATA[
      T(K(x,y),K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = w
    ]]></literal>
    <justification jstring="[para(15650(a,1),5632(a,1,1))].">
      <j1 rule="para" parents="15650 5632"/>
    </justification>
  </clause>

  <clause id="15679">
    <literal><![CDATA[
      T(x * K(y,z),K(x,u)) = x * K(y,z)
    ]]></literal>
    <justification jstring="[para(15650(a,1),7592(a,2,2))].">
      <j1 rule="para" parents="15650 7592"/>
    </justification>
  </clause>

  <clause id="15680">
    <literal><![CDATA[
      K(x,T(y,K(z,u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = w
    ]]></literal>
    <justification jstring="[para(15650(a,1),7982(a,1))].">
      <j1 rule="para" parents="15650 7982"/>
    </justification>
  </clause>

  <clause id="15682">
    <literal><![CDATA[
      K(x,K(y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u * K(y,z)) = w
    ]]></literal>
    <justification jstring="[para(15650(a,1),12278(a,1))].">
      <j1 rule="para" parents="15650 12278"/>
    </justification>
  </clause>

  <clause id="15684">
    <literal><![CDATA[
      K(x,K(y,z)) * u = u * K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(5572,a,15667,a),flip(a)].">
      <j1 rule="hyper" parents="5572 15667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15685">
    <literal><![CDATA[
      T(K(x,K(y,z)),u) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(4953,a,15667,a)].">
      <j1 rule="hyper" parents="4953 15667"/>
    </justification>
  </clause>

  <clause id="15687">
    <literal><![CDATA[
      T(x,K(y,K(z,u))) = x
    ]]></literal>
    <justification jstring="[hyper(51,a,15667,a)].">
      <j1 rule="hyper" parents="51 15667"/>
    </justification>
  </clause>

  <clause id="15688">
    <literal><![CDATA[
      K(x,T(K(y,z),u)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(8070,a,15668,a)].">
      <j1 rule="hyper" parents="8070 15668"/>
    </justification>
  </clause>

  <clause id="15689">
    <literal><![CDATA[
      T(x,K(y,z) * u) = T(x,u * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(12295,a,15687,a)].">
      <j1 rule="hyper" parents="12295 15687"/>
    </justification>
  </clause>

  <clause id="15690">
    <literal><![CDATA[
      T(x,K(y,z) / u) = T(x,u \ K(y,z))
    ]]></literal>
    <justification jstring="[hyper(8320,a,15687,a)].">
      <j1 rule="hyper" parents="8320 15687"/>
    </justification>
  </clause>

  <clause id="15691">
    <literal><![CDATA[
      x * (y * K(x,K(z,u))) = T(x,K(z,u)) * y
    ]]></literal>
    <justification jstring="[hyper(8305,a,15687,a)].">
      <j1 rule="hyper" parents="8305 15687"/>
    </justification>
  </clause>

  <clause id="15692">
    <literal><![CDATA[
      T(x,T(K(y,z),u)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(7858,a,15687,a)].">
      <j1 rule="hyper" parents="7858 15687"/>
    </justification>
  </clause>

  <clause id="15693">
    <literal><![CDATA[
      T(x,T(y,K(z,u))) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(7703,a,15687,a)].">
      <j1 rule="hyper" parents="7703 15687"/>
    </justification>
  </clause>

  <clause id="15694">
    <literal><![CDATA[
      (x * y) * K(x,K(z,u)) = T(x,K(z,u)) * y
    ]]></literal>
    <justification jstring="[hyper(6550,a,15687,a)].">
      <j1 rule="hyper" parents="6550 15687"/>
    </justification>
  </clause>

  <clause id="15695">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * x) = u * T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,8091,a(flip),b,15687,a)].">
      <j1 rule="hyper" parents="58 8091 15687"/>
    </justification>
  </clause>

  <clause id="15696">
    <literal><![CDATA[
      T(x,K(y,K(z,u))) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(15687(a,1),44(a,2))].">
      <j1 rule="para" parents="15687 44"/>
    </justification>
  </clause>

  <clause id="15697">
    <literal><![CDATA[
      K(x,K(y,z)) * u != w
    ]]></literal>
    <literal><![CDATA[
      u * K(x,K(y,z)) = w
    ]]></literal>
    <justification jstring="[para(15687(a,1),284(a,1,2))].">
      <j1 rule="para" parents="15687 284"/>
    </justification>
  </clause>

  <clause id="15698">
    <literal><![CDATA[
      L(x,y,z) * K(u,K(w,v5)) = K(u,K(w,v5)) * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(15687(a,1),237(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="15687 237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15700">
    <literal><![CDATA[
      T(x,K(y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u * K(y,z)) = w
    ]]></literal>
    <justification jstring="[para(15687(a,1),12300(a,1,1))].">
      <j1 rule="para" parents="15687 12300"/>
    </justification>
  </clause>

  <clause id="15701">
    <literal><![CDATA[
      x \ T(y * x,K(z,K(u,w))) = T(y,K(K(u,w),z) * x)
    ]]></literal>
    <justification jstring="[para(15687(a,1),15103(a,1,2,1,2))].">
      <j1 rule="para" parents="15687 15103"/>
    </justification>
  </clause>

  <clause id="15702">
    <literal><![CDATA[
      K((K(x,y) * z) \ 1,u) = K((z * K(x,y)) \ 1,u)
    ]]></literal>
    <justification jstring="[hyper(13108,a,15655,a)].">
      <j1 rule="hyper" parents="13108 15655"/>
    </justification>
  </clause>

  <clause id="15703">
    <literal><![CDATA[
      K(K(x,y) * (z * x),u) = K(z * T(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(12298,a,15655,a)].">
      <j1 rule="hyper" parents="12298 15655"/>
    </justification>
  </clause>

  <clause id="15704">
    <literal><![CDATA[
      K(K(x,y) * z,u) = K(z * K(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(12244,a,15655,a)].">
      <j1 rule="hyper" parents="12244 15655"/>
    </justification>
  </clause>

  <clause id="15708">
    <literal><![CDATA[
      K(x,K(y,z) \ u) = K(x,u * K(z,y))
    ]]></literal>
    <justification jstring="[para(6334(a,1),15655(a,1,2))].">
      <j1 rule="para" parents="6334 15655"/>
    </justification>
  </clause>

  <clause id="15710">
    <literal><![CDATA[
      K(x,y * (z * K(y,u))) = K(x,T(y,u) * z)
    ]]></literal>
    <justification jstring="[para(7036(a,1),15655(a,1,2))].">
      <j1 rule="para" parents="7036 15655"/>
    </justification>
  </clause>

  <clause id="15711">
    <literal><![CDATA[
      x * (K(y,z) * K(u,w)) = x * (K(u,w) * K(y,z))
    ]]></literal>
    <justification jstring="[para(15655(a,1),7301(a,1,2,2))].">
      <j1 rule="para" parents="15655 7301"/>
    </justification>
  </clause>

  <clause id="15712">
    <literal><![CDATA[
      K(T(x,K(y,z)),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u) = w
    ]]></literal>
    <justification jstring="[para(15655(a,1),8056(a,1))].">
      <j1 rule="para" parents="15655 8056"/>
    </justification>
  </clause>

  <clause id="15714">
    <literal><![CDATA[
      K(x,K(y,z) * (u * y)) = K(x,u * T(y,z))
    ]]></literal>
    <justification jstring="[para(8091(a,1),15655(a,1,2))].">
      <j1 rule="para" parents="8091 15655"/>
    </justification>
  </clause>

  <clause id="15717">
    <literal><![CDATA[
      K(K(x,y) * z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(z * K(x,y),u) = w
    ]]></literal>
    <justification jstring="[para(15655(a,1),12239(a,1))].">
      <j1 rule="para" parents="15655 12239"/>
    </justification>
  </clause>

  <clause id="15718">
    <literal><![CDATA[
      K(x * K(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(K(y,z) * x,u) = w
    ]]></literal>
    <justification jstring="[para(15655(a,1),12244(a,1))].">
      <j1 rule="para" parents="15655 12244"/>
    </justification>
  </clause>

  <clause id="15719">
    <literal><![CDATA[
      K(x,y * K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,u) * y) = w
    ]]></literal>
    <justification jstring="[para(15655(a,1),12302(a,1))].">
      <j1 rule="para" parents="15655 12302"/>
    </justification>
  </clause>

  <clause id="15720">
    <literal><![CDATA[
      K(T(1 / x,K(y,z)),u) = K(1 / L(x,w,x),u)
    ]]></literal>
    <justification jstring="[hyper(320,a,8757,a,b,15656,a),flip(a)].">
      <j1 rule="hyper" parents="320 8757 15656"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15722">
    <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(8093(a,2),15656(a,1,1))].">
      <j1 rule="para" parents="8093 15656"/>
    </justification>
  </clause>

  <clause id="15724">
    <literal><![CDATA[
      T(x * K(y,z),T(u,x)) = T(x * K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(8737,a,15693,a)].">
      <j1 rule="hyper" parents="8737 15693"/>
    </justification>
  </clause>

  <clause id="15725">
    <literal><![CDATA[
      T(x,T(T(y,K(z,u)),w)) = T(x,T(y,w))
    ]]></literal>
    <justification jstring="[para(18(a,1),15693(a,1,2))].">
      <j1 rule="para" parents="18 15693"/>
    </justification>
  </clause>

  <clause id="15726">
    <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(648(a,1),15693(a,1,2))].">
      <j1 rule="para" parents="648 15693"/>
    </justification>
  </clause>

  <clause id="15727">
    <literal><![CDATA[
      T(x,K(y,z) \ u) = T(x,u * K(z,y))
    ]]></literal>
    <justification jstring="[para(6334(a,1),15693(a,1,2))].">
      <j1 rule="para" parents="6334 15693"/>
    </justification>
  </clause>

  <clause id="15728">
    <literal><![CDATA[
      T(x,K(y,z) * (u / z)) = T(x,u / T(z,y))
    ]]></literal>
    <justification jstring="[para(6220(a,1),15693(a,1,2))].">
      <j1 rule="para" parents="6220 15693"/>
    </justification>
  </clause>

  <clause id="15729">
    <literal><![CDATA[
      T(x,K(y,z) * (u * y)) = T(x,u * T(y,z))
    ]]></literal>
    <justification jstring="[para(8091(a,1),15693(a,1,2))].">
      <j1 rule="para" parents="8091 15693"/>
    </justification>
  </clause>

  <clause id="15731">
    <literal><![CDATA[
      T(x,(y / z) * K(y,u)) = T(x,T(y,u) / z)
    ]]></literal>
    <justification jstring="[para(13745(a,1),15693(a,1,2))].">
      <j1 rule="para" parents="13745 15693"/>
    </justification>
  </clause>

  <clause id="15732">
    <literal><![CDATA[
      x * K(y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(y,K(z,u)) * x = w
    ]]></literal>
    <justification jstring="[para(6351(a,1),15696(a,1))].">
      <j1 rule="para" parents="6351 15696"/>
    </justification>
  </clause>

  <clause id="15733">
    <literal><![CDATA[
      T(x,T(y,K(z,u))) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = w
    ]]></literal>
    <justification jstring="[para(7438(a,1),15696(a,1))].">
      <j1 rule="para" parents="7438 15696"/>
    </justification>
  </clause>

  <clause id="15735">
    <literal><![CDATA[
      K(x,T(y,T(z,u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = w
    ]]></literal>
    <justification jstring="[para(15639(a,2),7708(a,1))].">
      <j1 rule="para" parents="15639 7708"/>
    </justification>
  </clause>

  <clause id="15736">
    <literal><![CDATA[
      T(x,T(T(y,z) / u,y)) = T(x,u \ T(y,z))
    ]]></literal>
    <justification jstring="[hyper(7256,a,15645,a),flip(a)].">
      <j1 rule="hyper" parents="7256 15645"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15738">
    <literal><![CDATA[
      T(x,T(T(y,z) \ u,y)) = T(x,u / T(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,7942,a(flip),b,15645,a),flip(a)].">
      <j1 rule="hyper" parents="58 7942 15645"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15740">
    <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(15645(a,1),7445(a,1))].">
      <j1 rule="para" parents="15645 7445"/>
    </justification>
  </clause>

  <clause id="15741">
    <literal><![CDATA[
      T(x,y) * K(x / T(y,x),z) = y * T(y \ T(x,y),T(z,x))
    ]]></literal>
    <justification jstring="[para(15645(a,1),8332(a,2,2))].">
      <j1 rule="para" parents="15645 8332"/>
    </justification>
  </clause>

  <clause id="15742">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(8059,a,15685,a)].">
      <j1 rule="hyper" parents="8059 15685"/>
    </justification>
  </clause>

  <clause id="15745">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(8047,a,15688,a)].">
      <j1 rule="hyper" parents="8047 15688"/>
    </justification>
  </clause>

  <clause id="15746">
    <literal><![CDATA[
      K(x,T(K(y,z),u)) = K(y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(320,a,7784,a,b,15688,a),flip(a)].">
      <j1 rule="hyper" parents="320 7784 15688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15747">
    <literal><![CDATA[
      T(K(x,K(y,z)) * u,w) = T(u,w) * K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(119,a,15688,a(flip),b,15626,a),flip(a)].">
      <j1 rule="hyper" parents="119 15688 15626"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15748">
    <literal><![CDATA[
      (T(x,K(y,z)) \ u) * K(x,K(y,z)) = x \ u
    ]]></literal>
    <justification jstring="[hyper(119,a,15688,a(flip),b,7741,a)].">
      <j1 rule="hyper" parents="119 15688 7741"/>
    </justification>
  </clause>

  <clause id="15749">
    <literal><![CDATA[
      K(x,K(T(y,z),u)) = K(x,K(y,u))
    ]]></literal>
    <justification jstring="[para(7145(a,2),15688(a,1,2))].">
      <j1 rule="para" parents="7145 15688"/>
    </justification>
  </clause>

  <clause id="15750">
    <literal><![CDATA[
      K(x,K(y,z)) * (u \ x) = u \ T(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(15688(a,1),13718(a,1,1))].">
      <j1 rule="para" parents="15688 13718"/>
    </justification>
  </clause>

  <clause id="15751">
    <literal><![CDATA[
      T(x,K(y,T(z,u))) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(6218(a,1),15692(a,1,2))].">
      <j1 rule="para" parents="6218 15692"/>
    </justification>
  </clause>

  <clause id="15752">
    <literal><![CDATA[
      T(x,K(T(y,z),u)) = T(x,K(y,u))
    ]]></literal>
    <justification jstring="[para(7145(a,2),15692(a,1,2))].">
      <j1 rule="para" parents="7145 15692"/>
    </justification>
  </clause>

  <clause id="15753">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(7781,a,15742,a)].">
      <j1 rule="hyper" parents="7781 15742"/>
    </justification>
  </clause>

  <clause id="15754">
    <literal><![CDATA[
      K(K(x,y),T(z,u)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(7762,a,15742,a)].">
      <j1 rule="hyper" parents="7762 15742"/>
    </justification>
  </clause>

  <clause id="15756">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(320,a,7784,a(flip),b,15742,a),flip(a)].">
      <j1 rule="hyper" parents="320 7784 15742"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15757">
    <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,8088,a(flip),b,15742,a)].">
      <j1 rule="hyper" parents="58 8088 15742"/>
    </justification>
  </clause>

  <clause id="15758">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(z,K(x,y)) = w
    ]]></literal>
    <justification jstring="[para(15742(a,2),7799(a,1))].">
      <j1 rule="para" parents="15742 7799"/>
    </justification>
  </clause>

  <clause id="15759">
    <literal><![CDATA[
      K(x,K(y,L(z / u,u,w))) = K(x,K(y,(w * u) \ (w * z)))
    ]]></literal>
    <justification jstring="[para(8010(a,1),15742(a,1,2))].">
      <j1 rule="para" parents="8010 15742"/>
    </justification>
  </clause>

  <clause id="15760">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x \ (u * (y / u)),z) = K((u * (y / u)) / x,z)
    ]]></literal>
    <justification jstring="[para(15742(a,1),12248(a,1,1))].">
      <j1 rule="para" parents="15742 12248"/>
    </justification>
  </clause>

  <clause id="15763">
    <literal><![CDATA[
      T(x,K(y,T(z,u))) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(118,a,15745,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 15745 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15764">
    <literal><![CDATA[
      K(x,K(y,z)) * u = u * K(x,K(z,y))
    ]]></literal>
    <justification jstring="[para(15745(a,1),7307(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15745 7307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15765">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) = w
    ]]></literal>
    <justification jstring="[para(15745(a,2),7831(a,1))].">
      <j1 rule="para" parents="15745 7831"/>
    </justification>
  </clause>

  <clause id="15766">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x \ T(y,u),z) = K(T(y,u) / x,z)
    ]]></literal>
    <justification jstring="[para(15745(a,1),8382(a,1,1))].">
      <j1 rule="para" parents="15745 8382"/>
    </justification>
  </clause>

  <clause id="15767">
    <literal><![CDATA[
      K(x,K(y,(z \ u) * z)) = K(x,K(u,y))
    ]]></literal>
    <justification jstring="[para(12272(a,2),15745(a,1,2))].">
      <j1 rule="para" parents="12272 15745"/>
    </justification>
  </clause>

  <clause id="15769">
    <literal><![CDATA[
      (T(x,K(y,z)) \ u) * K(y,K(z,x)) = x \ u
    ]]></literal>
    <justification jstring="[hyper(119,a,15746,a(flip),b,7741,a)].">
      <j1 rule="hyper" parents="119 15746 7741"/>
    </justification>
  </clause>

  <clause id="15771">
    <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(15749(a,1),10672(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="15749 10672"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15774">
    <literal><![CDATA[
      T(T(x,K(y,z)),T(z,u) \ y) = T(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[para(15751(a,1),8321(a,1,1))].">
      <j1 rule="para" parents="15751 8321"/>
    </justification>
  </clause>

  <clause id="15776">
    <literal><![CDATA[
      T(T(x,K(y,z)),T(z,u) * y) = T(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[para(15751(a,1),12257(a,1,1))].">
      <j1 rule="para" parents="15751 12257"/>
    </justification>
  </clause>

  <clause id="15777">
    <literal><![CDATA[
      T(K(x,T(y,z)) * u,K(y,x)) = u * K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(7853,a,15752,a),flip(a)].">
      <j1 rule="hyper" parents="7853 15752"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15778">
    <literal><![CDATA[
      K(x,T(y,z)) * T(u,K(y,x)) = u * K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(15752(a,1),7847(a,1,2))].">
      <j1 rule="para" parents="15752 7847"/>
    </justification>
  </clause>

  <clause id="15780">
    <literal><![CDATA[
      K(x,K(y,z)) * u = u * K(y,K(x,z))
    ]]></literal>
    <justification jstring="[para(15753(a,1),7307(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15753 7307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15781">
    <literal><![CDATA[
      K(x,y) * (K(z,K(y,u)) * w) = y * (T(T(y,K(z,u)),x) \ w)
    ]]></literal>
    <justification jstring="[para(15753(a,1),9931(a,1,2,1))].">
      <j1 rule="para" parents="15753 9931"/>
    </justification>
  </clause>

  <clause id="15784">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * K(y,K(z,x))) = u
    ]]></literal>
    <justification jstring="[para(15754(a,1),7291(a,1,2,2))].">
      <j1 rule="para" parents="15754 7291"/>
    </justification>
  </clause>

  <clause id="15785">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * K(x,y)) = u * T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(15754(a,1),7940(a,1,1))].">
      <j1 rule="para" parents="15754 7940"/>
    </justification>
  </clause>

  <clause id="15786">
    <literal><![CDATA[
      K(x,K(T(y,z),u)) = K(y,K(u,T(x,w)))
    ]]></literal>
    <justification jstring="[hyper(320,a,15749,a,b,15756,a)].">
      <j1 rule="hyper" parents="320 15749 15756"/>
    </justification>
  </clause>

  <clause id="15788">
    <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(15763(a,1),8442(a,1,1))].">
      <j1 rule="para" parents="15763 8442"/>
    </justification>
  </clause>

  <clause id="15789">
    <literal><![CDATA[
      K(x,y / K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,u) \ y) = w
    ]]></literal>
    <justification jstring="[para(7899(a,1),15678(a,1))].">
      <j1 rule="para" parents="7899 15678"/>
    </justification>
  </clause>

  <clause id="15790">
    <literal><![CDATA[
      K(x,K(y,z) * (u / z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u / T(z,y)) = w
    ]]></literal>
    <justification jstring="[para(6220(a,1),15680(a,1,2))].">
      <j1 rule="para" parents="6220 15680"/>
    </justification>
  </clause>

  <clause id="15791">
    <literal><![CDATA[
      K(x,y * (z * K(y,u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u) * z) = w
    ]]></literal>
    <justification jstring="[para(7036(a,1),15680(a,1,2))].">
      <j1 rule="para" parents="7036 15680"/>
    </justification>
  </clause>

  <clause id="15792">
    <literal><![CDATA[
      K(x,y) / (K(x,y) * K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(u,z) = w
    ]]></literal>
    <justification jstring="[para(7997(a,2),15680(a,1))].">
      <j1 rule="para" parents="7997 15680"/>
    </justification>
  </clause>

  <clause id="15793">
    <literal><![CDATA[
      K(x,y * K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(u,z) \ y) = w
    ]]></literal>
    <justification jstring="[para(7859(a,1),15680(a,1,2))].">
      <j1 rule="para" parents="7859 15680"/>
    </justification>
  </clause>

  <clause id="15794">
    <literal><![CDATA[
      K(x,T(y,z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u / z)) = w
    ]]></literal>
    <justification jstring="[para(7948(a,1),15680(a,1,2))].">
      <j1 rule="para" parents="7948 15680"/>
    </justification>
  </clause>

  <clause id="15795">
    <literal><![CDATA[
      K(x,T(y,z / u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u \ z)) = w
    ]]></literal>
    <justification jstring="[para(8317(a,1),15680(a,1,2))].">
      <j1 rule="para" parents="8317 15680"/>
    </justification>
  </clause>

  <clause id="15796">
    <literal><![CDATA[
      K(x,K(y,z) * (u * y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u * T(y,z)) = w
    ]]></literal>
    <justification jstring="[para(8091(a,1),15680(a,1,2))].">
      <j1 rule="para" parents="8091 15680"/>
    </justification>
  </clause>

  <clause id="15797">
    <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(7728(a,1),15680(a,1,2))].">
      <j1 rule="para" parents="7728 15680"/>
    </justification>
  </clause>

  <clause id="15798">
    <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(10544(a,1),15680(a,1,2))].">
      <j1 rule="para" parents="10544 15680"/>
    </justification>
  </clause>

  <clause id="15799">
    <literal><![CDATA[
      K(x,T(y,z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u * z)) = w
    ]]></literal>
    <justification jstring="[para(12286(a,1),15680(a,1,2))].">
      <j1 rule="para" parents="12286 15680"/>
    </justification>
  </clause>

  <clause id="15800">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u \ T(y,z)) = w
    ]]></literal>
    <justification jstring="[para(13733(a,1),15680(a,1,2))].">
      <j1 rule="para" parents="13733 15680"/>
    </justification>
  </clause>

  <clause id="15801">
    <literal><![CDATA[
      K(x,(y / z) * K(y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u) / z) = w
    ]]></literal>
    <justification jstring="[para(13745(a,1),15680(a,1,2))].">
      <j1 rule="para" parents="13745 15680"/>
    </justification>
  </clause>

  <clause id="15802">
    <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(8093(a,2),15712(a,1,1))].">
      <j1 rule="para" parents="8093 15712"/>
    </justification>
  </clause>

  <clause id="15803">
    <literal><![CDATA[
      T(x,K(y,z) * (u / z)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u / T(z,y)) = w
    ]]></literal>
    <justification jstring="[para(6220(a,1),15733(a,1,2))].">
      <j1 rule="para" parents="6220 15733"/>
    </justification>
  </clause>

  <clause id="15804">
    <literal><![CDATA[
      T(x,T(y,T(z,u))) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z)) = w
    ]]></literal>
    <justification jstring="[para(7438(a,1),15733(a,1,2))].">
      <j1 rule="para" parents="7438 15733"/>
    </justification>
  </clause>

  <clause id="15805">
    <literal><![CDATA[
      T(x,K(y,z) * (u * y)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u * T(y,z)) = w
    ]]></literal>
    <justification jstring="[para(8091(a,1),15733(a,1,2))].">
      <j1 rule="para" parents="8091 15733"/>
    </justification>
  </clause>

  <clause id="15806">
    <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(7838(a,1),15733(a,1,2))].">
      <j1 rule="para" parents="7838 15733"/>
    </justification>
  </clause>

  <clause id="15807">
    <literal><![CDATA[
      T(x,K(y,z) * (u \ y)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u \ T(y,z)) = w
    ]]></literal>
    <justification jstring="[para(13733(a,1),15733(a,1,2))].">
      <j1 rule="para" parents="13733 15733"/>
    </justification>
  </clause>

  <clause id="15812">
    <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(15635(a,1),7576(a,1))].">
      <j1 rule="para" parents="15635 7576"/>
    </justification>
  </clause>

  <clause id="15817">
    <literal><![CDATA[
      T(x,y) * K(z \ x,u) = K(x / z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[para(15644(a,1),7897(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15644 7897"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15818">
    <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,14822,a,b,15646,a)].">
      <j1 rule="hyper" parents="320 14822 15646"/>
    </justification>
  </clause>

  <clause id="15819">
    <literal><![CDATA[
      K(x,T(y,z / u)) = K(x,T(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(320,a,15571,a(flip),b,15646,a),flip(a)].">
      <j1 rule="hyper" parents="320 15571 15646"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15821">
    <literal><![CDATA[
      K(x,y * K(z,u \ z)) = K(x,K(u,z) * y)
    ]]></literal>
    <justification jstring="[hyper(15365,a,15653,a),flip(a)].">
      <j1 rule="hyper" parents="15365 15653"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15822">
    <literal><![CDATA[
      K(x,y * K(z \ 1,u)) = K(x,K(z,u) * y)
    ]]></literal>
    <justification jstring="[hyper(15344,a,15653,a),flip(a)].">
      <j1 rule="hyper" parents="15344 15653"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15823">
    <literal><![CDATA[
      K(x,K(y,z) * u) = K(x,u * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(15131,a,15653,a)].">
      <j1 rule="hyper" parents="15131 15653"/>
    </justification>
  </clause>

  <clause id="15824">
    <literal><![CDATA[
      K(x,K(y,z) * (u / y)) = K(x,u / T(y,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,15313,a(flip),b,15653,a),flip(a)].">
      <j1 rule="hyper" parents="320 15313 15653"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15825">
    <literal><![CDATA[
      K(x,K(y,y \ z) * u) = K(x,u * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,13070,a(flip),b,15653,a),flip(a)].">
      <j1 rule="hyper" parents="320 13070 15653"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15826">
    <literal><![CDATA[
      K(x,(y * z) * K(u,y)) = K(x,T(y,u) * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,15134,a(flip),b,15653,a),flip(a)].">
      <j1 rule="hyper" parents="58 15134 15653"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15827">
    <literal><![CDATA[
      K(x,y * K(z * u,z)) = K(x,K(u,z) * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,13056,a(flip),b,15653,a),flip(a)].">
      <j1 rule="hyper" parents="58 13056 15653"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15828">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w)) * (w * u)) = K(x,w * (u * K(y,z)))
    ]]></literal>
    <justification jstring="[para(10815(a,1),15653(a,2,2))].">
      <j1 rule="para" parents="10815 15653"/>
    </justification>
  </clause>

  <clause id="15829">
    <literal><![CDATA[
      K(x,y * K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(u,z) * y) = w
    ]]></literal>
    <justification jstring="[para(15653(a,1),15131(a,1))].">
      <j1 rule="para" parents="15653 15131"/>
    </justification>
  </clause>

  <clause id="15830">
    <literal><![CDATA[
      K(x,T(K(y,z) * (u / z),w)) = K(x,T(u / T(z,y),w))
    ]]></literal>
    <justification jstring="[para(6220(a,1),15654(a,1,2,1))].">
      <j1 rule="para" parents="6220 15654"/>
    </justification>
  </clause>

  <clause id="15831">
    <literal><![CDATA[
      K(x,T(K(y,y \ z) * (u / z),w)) = K(x,T(u / ((y \ z) * y),w))
    ]]></literal>
    <justification jstring="[para(10653(a,1),15654(a,1,2,1))].">
      <j1 rule="para" parents="10653 15654"/>
    </justification>
  </clause>

  <clause id="15832">
    <literal><![CDATA[
      K(x,T(1 / (y * z),y)) = K(x,K(z,1 / z) / (z * y))
    ]]></literal>
    <justification jstring="[hyper(320,a,14836,a,b,15658,a)].">
      <j1 rule="hyper" parents="320 14836 15658"/>
    </justification>
  </clause>

  <clause id="15833">
    <literal><![CDATA[
      (K(x,y) * K(z,u)) \ w != K(y,x)
    ]]></literal>
    <literal><![CDATA[
      K(z,u) = w
    ]]></literal>
    <justification jstring="[para(15662(a,1),42(a,1)),flip(a)].">
      <j1 rule="para" parents="15662 42"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15835">
    <literal><![CDATA[
      K(x,y) \ K(z,u) = K(u,z) \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(320,a,5130,a,b,15663,a)].">
      <j1 rule="hyper" parents="320 5130 15663"/>
    </justification>
  </clause>

  <clause id="15838">
    <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(15664(a,1),649(a,2,1,2))].">
      <j1 rule="para" parents="15664 649"/>
    </justification>
  </clause>

  <clause id="15840">
    <literal><![CDATA[
      K(x,y) * K(z / (z / u),w) = K(u,T(w,z)) * K(x,y)
    ]]></literal>
    <justification jstring="[para(7918(a,1),15664(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7918 15664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15844">
    <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(15666(a,1),15105(a,1,2,1,2))].">
      <j1 rule="para" parents="15666 15105"/>
    </justification>
  </clause>

  <clause id="15845">
    <literal><![CDATA[
      T((x * K(y,z)) * u,K(x,u)) = (x * K(y,z)) * u
    ]]></literal>
    <justification jstring="[para(15679(a,1),8114(a,2,1))].">
      <j1 rule="para" parents="15679 8114"/>
    </justification>
  </clause>

  <clause id="15846">
    <literal><![CDATA[
      (K(x,y) * z) * K(x,K(y,u)) = K(x,T(y,u)) * z
    ]]></literal>
    <justification jstring="[hyper(9161,a,15684,a),flip(a)].">
      <j1 rule="hyper" parents="9161 15684"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15847">
    <literal><![CDATA[
      K(x,K(y,z)) \ u = u * K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(7830,a,15684,a)].">
      <j1 rule="hyper" parents="7830 15684"/>
    </justification>
  </clause>

  <clause id="15848">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) * K(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[hyper(7828,a,15684,a),flip(a)].">
      <j1 rule="hyper" parents="7828 15684"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15849">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * K(x,K(y,z))) = u
    ]]></literal>
    <justification jstring="[hyper(7827,a,15684,a)].">
      <j1 rule="hyper" parents="7827 15684"/>
    </justification>
  </clause>

  <clause id="15850">
    <literal><![CDATA[
      K(x,K(y,z)) * (u \ K(y,z)) = u \ K(y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(320,a,12351,a(flip),b,15684,a),flip(a)].">
      <j1 rule="hyper" parents="320 12351 15684"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15851">
    <literal><![CDATA[
      x \ (y * K(x,K(z,u))) = T(x,K(z,u)) \ y
    ]]></literal>
    <justification jstring="[hyper(116,a,15684,a(flip),b,7825,a)].">
      <j1 rule="hyper" parents="116 15684 7825"/>
    </justification>
  </clause>

  <clause id="15852">
    <literal><![CDATA[
      x * K(y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(y,K(z,u)) * w = x
    ]]></literal>
    <justification jstring="[para(15684(a,1),7827(a,1))].">
      <j1 rule="para" parents="15684 7827"/>
    </justification>
  </clause>

  <clause id="15853">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) * K(x,K(y,z)) != w
    ]]></literal>
    <literal><![CDATA[
      u = w
    ]]></literal>
    <justification jstring="[para(15684(a,1),7828(a,1))].">
      <j1 rule="para" parents="15684 7828"/>
    </justification>
  </clause>

  <clause id="15855">
    <literal><![CDATA[
      T(x,K(y,z) * u) = T(x,u * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(15334,a,15689,a)].">
      <j1 rule="hyper" parents="15334 15689"/>
    </justification>
  </clause>

  <clause id="15856">
    <literal><![CDATA[
      T(x,(y / z) * K(u,y)) = T(x,T(y,u) / z)
    ]]></literal>
    <justification jstring="[hyper(58,a,15125,a(flip),b,15689,a),flip(a)].">
      <j1 rule="hyper" parents="58 15125 15689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15857">
    <literal><![CDATA[
      T(x,(y \ z) * K(y,u)) = T(x,T(y,u) \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,15122,a(flip),b,15689,a),flip(a)].">
      <j1 rule="hyper" parents="58 15122 15689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15858">
    <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,15689,a(flip),b,15111,a),flip(a)].">
      <j1 rule="hyper" parents="119 15689 15111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15859">
    <literal><![CDATA[
      T(x,y * K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(u,z) * y) = w
    ]]></literal>
    <justification jstring="[para(15689(a,1),15334(a,1))].">
      <j1 rule="para" parents="15689 15334"/>
    </justification>
  </clause>

  <clause id="15860">
    <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(15690(a,1),14529(a,1,2,2,1))].">
      <j1 rule="para" parents="15690 14529"/>
    </justification>
  </clause>

  <clause id="15861">
    <literal><![CDATA[
      K(x * K(y \ z,y),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(8781,a,15704,a),flip(a)].">
      <j1 rule="hyper" parents="8781 15704"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15862">
    <literal><![CDATA[
      K(K(x,y) * z,u) = K(z * K(y,x),u)
    ]]></literal>
    <justification jstring="[hyper(320,a,15180,a,b,15704,a),flip(a)].">
      <j1 rule="hyper" parents="320 15180 15704"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15863">
    <literal><![CDATA[
      K(x * K(y * z,y),u) = K(K(z,y) * x,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,13097,a(flip),b,15704,a),flip(a)].">
      <j1 rule="hyper" parents="58 13097 15704"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15864">
    <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(15704(a,1),7714(a,1))].">
      <j1 rule="para" parents="15704 7714"/>
    </justification>
  </clause>

  <clause id="15865">
    <literal><![CDATA[
      K(x * K(y \ z,y),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(K(z,y) * x,u) = w
    ]]></literal>
    <justification jstring="[para(15704(a,1),13184(a,1))].">
      <j1 rule="para" parents="15704 13184"/>
    </justification>
  </clause>

  <clause id="15866">
    <literal><![CDATA[
      K(x * K(y \ 1,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(K(y,z) * x,u) = w
    ]]></literal>
    <justification jstring="[para(15704(a,1),15356(a,1))].">
      <j1 rule="para" parents="15704 15356"/>
    </justification>
  </clause>

  <clause id="15867">
    <literal><![CDATA[
      K(x / (y / z),y) = K(x / (z \ y),y)
    ]]></literal>
    <justification jstring="[para(6470(a,1),15861(a,1,1))].">
      <j1 rule="para" parents="6470 15861"/>
    </justification>
  </clause>

  <clause id="15868">
    <literal><![CDATA[
      K(x * (y / z),y) = K(x * (z \ y),y)
    ]]></literal>
    <justification jstring="[para(6475(a,1),15861(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6475 15861"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15869">
    <literal><![CDATA[
      K(x,K(y,y \ z) \ (u / z)) = K(x,u / (y * (z / y)))
    ]]></literal>
    <justification jstring="[para(10655(a,1),15708(a,2,2))].">
      <j1 rule="para" parents="10655 15708"/>
    </justification>
  </clause>

  <clause id="15870">
    <literal><![CDATA[
      K(x,K(y \ K(z,u),w) * v5) = K(x,K(w,y * K(u,z)) * v5)
    ]]></literal>
    <justification jstring="[para(15708(a,1),15350(a,2,2,1))].">
      <j1 rule="para" parents="15708 15350"/>
    </justification>
  </clause>

  <clause id="15871">
    <literal><![CDATA[
      T(x,T(T(y,T(z,u)) * u,w)) = T(x,T(T(y,z) * u,w))
    ]]></literal>
    <justification jstring="[para(7951(a,1),15725(a,1,2,1))].">
      <j1 rule="para" parents="7951 15725"/>
    </justification>
  </clause>

  <clause id="15872">
    <literal><![CDATA[
      (K(x,y) * z) * K(y,K(x,u)) = K(x,T(y,u)) * z
    ]]></literal>
    <justification jstring="[hyper(9162,a,15764,a),flip(a)].">
      <j1 rule="hyper" parents="9162 15764"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15873">
    <literal><![CDATA[
      K(x,K(y / z,(z \ u) * y)) = K(x,K(u,y / z))
    ]]></literal>
    <justification jstring="[hyper(58,a,10405,a(flip),b,15767,a)].">
      <j1 rule="hyper" parents="58 10405 15767"/>
    </justification>
  </clause>

  <clause id="15874">
    <literal><![CDATA[
      K(x,K(y,z)) * u != w
    ]]></literal>
    <literal><![CDATA[
      u * K(y,K(z,x)) = w
    ]]></literal>
    <justification jstring="[para(15784(a,1),7828(a,1,2))].">
      <j1 rule="para" parents="15784 7828"/>
    </justification>
  </clause>

  <clause id="15875">
    <literal><![CDATA[
      K(x,K(y,z) * (u / (y \ z))) = K(x,u / (z / y))
    ]]></literal>
    <justification jstring="[hyper(320,a,13146,a(flip),b,15823,a),flip(a)].">
      <j1 rule="hyper" parents="320 13146 15823"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15877">
    <literal><![CDATA[
      K(x,K(y,z) * (u * z)) = K(x,u * T(z,y))
    ]]></literal>
    <justification jstring="[para(6116(a,1),15823(a,2,2))].">
      <j1 rule="para" parents="6116 15823"/>
    </justification>
  </clause>

  <clause id="15878">
    <literal><![CDATA[
      L(K(x,y),z,u) \ K(w,v5) = K(v5,w) \ K(L(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(10794(a,2),15835(a,1,1))].">
      <j1 rule="para" parents="10794 15835"/>
    </justification>
  </clause>

  <clause id="15879">
    <literal><![CDATA[
      K(x,K(y,z)) \ T(u,x) = x \ (u * T(x,K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(320,a,7044,a,b,15847,a),flip(a)].">
      <j1 rule="hyper" parents="320 7044 15847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15880">
    <literal><![CDATA[
      K(x,K(y,z)) \ (u / T(x,K(y,z))) != w
    ]]></literal>
    <literal><![CDATA[
      u / x = w
    ]]></literal>
    <justification jstring="[para(15847(a,2),6198(a,1))].">
      <j1 rule="para" parents="15847 6198"/>
    </justification>
  </clause>

  <clause id="15881">
    <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(15847(a,2),15445(a,1,1,1))].">
      <j1 rule="para" parents="15847 15445"/>
    </justification>
  </clause>

  <clause id="15882">
    <literal><![CDATA[
      K(x,K(y,z)) * u != w
    ]]></literal>
    <literal><![CDATA[
      w * K(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(15849(a,1),38(a,1)),flip(a)].">
      <j1 rule="para" parents="15849 38"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15884">
    <literal><![CDATA[
      x \ T(y,K(z,u) * w) = x \ T(y,w * K(u,z))
    ]]></literal>
    <justification jstring="[hyper(116,a,15855,a,b,5,a)].">
      <j1 rule="hyper" parents="116 15855 5"/>
    </justification>
  </clause>

  <clause id="15886">
    <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(15855(a,2),420(a,1))].">
      <j1 rule="para" parents="15855 420"/>
    </justification>
  </clause>

  <clause id="15887">
    <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(6114(a,2),15855(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6114 15855"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15888">
    <literal><![CDATA[
      T(x,K(y,z) * (u \ z)) = T(x,u \ T(z,y))
    ]]></literal>
    <justification jstring="[para(13699(a,1),15855(a,2,2))].">
      <j1 rule="para" parents="13699 15855"/>
    </justification>
  </clause>

  <clause id="15890">
    <literal><![CDATA[
      K(x * K(y,z),x \ z) = K(x,T(x \ z,y))
    ]]></literal>
    <justification jstring="[hyper(11261,a,15862,a),flip(a)].">
      <j1 rule="hyper" parents="11261 15862"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15891">
    <literal><![CDATA[
      K(K(x,y) * z,u) = K(K(y,x) * z,u)
    ]]></literal>
    <justification jstring="[hyper(320,a,15704,a,b,15862,a)].">
      <j1 rule="hyper" parents="320 15704 15862"/>
    </justification>
  </clause>

  <clause id="15892">
    <literal><![CDATA[
      K(K(x \ y,x) * z,u) = K(z * K(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(320,a,13092,a(flip),b,15862,a),flip(a)].">
      <j1 rule="hyper" parents="320 13092 15862"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15893">
    <literal><![CDATA[
      K(K(x,y) * (z * (x * y)),u) = K(z * (y * x),u)
    ]]></literal>
    <justification jstring="[para(10363(a,1),15862(a,2,1))].">
      <j1 rule="para" parents="10363 15862"/>
    </justification>
  </clause>

  <clause id="15894">
    <literal><![CDATA[
      K(x / ((y \ z) \ z),z) = K(x / y,z)
    ]]></literal>
    <justification jstring="[para(72(a,1),15867(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="72 15867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15895">
    <literal><![CDATA[
      K(K(x,y) * (T(x,y) * z),u) = K(x * z,u)
    ]]></literal>
    <justification jstring="[para(4819(a,1),15891(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4819 15891"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15896">
    <literal><![CDATA[
      K(x * (y \ (z \ y)),y) = K(x / z,y)
    ]]></literal>
    <justification jstring="[hyper(14200,a,15894,a)].">
      <j1 rule="hyper" parents="14200 15894"/>
    </justification>
  </clause>

  <clause id="15897">
    <literal><![CDATA[
      x / (K(y / z,u) * x) != w
    ]]></literal>
    <literal><![CDATA[
      K(u,y * (u \ (z \ u))) = w
    ]]></literal>
    <justification jstring="[para(15896(a,1),5150(a,1,2,1))].">
      <j1 rule="para" parents="15896 5150"/>
    </justification>
  </clause>

  <clause id="15898">
    <literal><![CDATA[
      K(x,T(y,(z \ u) * z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u)) = w
    ]]></literal>
    <justification jstring="[para(12253(a,2),15735(a,1,2))].">
      <j1 rule="para" parents="12253 15735"/>
    </justification>
  </clause>

  <clause id="15899">
    <literal><![CDATA[
      K(x,K(T(y,z),u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,u)) = w
    ]]></literal>
    <justification jstring="[para(15786(a,2),15758(a,1))].">
      <j1 rule="para" parents="15786 15758"/>
    </justification>
  </clause>

  <clause id="15900">
    <literal><![CDATA[
      K(x,K(y * z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z * y,u)) = w
    ]]></literal>
    <justification jstring="[para(12230(a,1),15765(a,1,2))].">
      <j1 rule="para" parents="12230 15765"/>
    </justification>
  </clause>

  <clause id="15902">
    <literal><![CDATA[
      T(x,y) * K(z / x,u) = K(x \ z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[para(7907(a,1),15640(a,1,2))].">
      <j1 rule="para" parents="7907 15640"/>
    </justification>
  </clause>

  <clause id="15903">
    <literal><![CDATA[
      K(x,T(T(y,z),u)) * T(z,w) = T(z,w) * K(x,T(y,u))
    ]]></literal>
    <justification jstring="[para(7896(a,1),15640(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7896 15640"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15904">
    <literal><![CDATA[
      T(x,y) * K(z * x,u) = K(x * z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[para(12231(a,1),15640(a,1,2))].">
      <j1 rule="para" parents="12231 15640"/>
    </justification>
  </clause>

  <clause id="15905">
    <literal><![CDATA[
      T(L(K(x,y),z,u),w / v5) = T(L(K(x,y),z,u),v5 \ w)
    ]]></literal>
    <justification jstring="[para(15669(a,1),8318(a,1,1))].">
      <j1 rule="para" parents="15669 8318"/>
    </justification>
  </clause>

  <clause id="15906">
    <literal><![CDATA[
      T(x,K(y,z)) * (u / T(x,K(y,z))) = x * (u / x)
    ]]></literal>
    <justification jstring="[para(6188(a,1),15691(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6188 15691"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15907">
    <literal><![CDATA[
      T(x,K(y,z)) \ (u * x) = x \ (u * T(x,K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(116,a,15695,a(flip),b,7825,a),flip(a)].">
      <j1 rule="hyper" parents="116 15695 7825"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15909">
    <literal><![CDATA[
      K(K(x,y) * (z * (x * y)),u) = K(z * T(x * y,y),u)
    ]]></literal>
    <justification jstring="[hyper(58,a,13152,a(flip),b,15703,a)].">
      <j1 rule="hyper" parents="58 13152 15703"/>
    </justification>
  </clause>

  <clause id="15911">
    <literal><![CDATA[
      K(x,y * (z * K(u,y))) = K(x,T(y,u) * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,15430,a,b,15710,a)].">
      <j1 rule="hyper" parents="58 15430 15710"/>
    </justification>
  </clause>

  <clause id="15912">
    <literal><![CDATA[
      K(x * y,z * T(x,y)) = K(x * y,z * x)
    ]]></literal>
    <justification jstring="[hyper(58,a,8769,a(flip),b,15714,a),flip(a)].">
      <j1 rule="hyper" parents="58 8769 15714"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15913">
    <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(8324(a,1),15714(a,2,2,2))].">
      <j1 rule="para" parents="8324 15714"/>
    </justification>
  </clause>

  <clause id="15915">
    <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,7944,a(flip),b,15724,a)].">
      <j1 rule="hyper" parents="58 7944 15724"/>
    </justification>
  </clause>

  <clause id="15917">
    <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(7243(a,1),15728(a,1,2,1))].">
      <j1 rule="para" parents="7243 15728"/>
    </justification>
  </clause>

  <clause id="15918">
    <literal><![CDATA[
      T(x,K(y,z) \ (z / u)) = T(x,T(z,y) / u)
    ]]></literal>
    <justification jstring="[hyper(58,a,15727,a,b,15731,a)].">
      <j1 rule="hyper" parents="58 15727 15731"/>
    </justification>
  </clause>

  <clause id="15919">
    <literal><![CDATA[
      T(x,T(y * z,u) / T(y,w)) = T(x,T(y,w) \ T(z * y,u))
    ]]></literal>
    <justification jstring="[para(8282(a,1),15738(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8282 15738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15920">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w)) * (w * u)) = K(x,w * (u * K(y \ 1,z)))
    ]]></literal>
    <justification jstring="[para(10815(a,1),15822(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10815 15822"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15921">
    <literal><![CDATA[
      K(x,K(y,z \ (y \ u)) * w) = K(x,w * K(y,z \ u))
    ]]></literal>
    <justification jstring="[para(10340(a,2),15825(a,1,2,1))].">
      <j1 rule="para" parents="10340 15825"/>
    </justification>
  </clause>

  <clause id="15922">
    <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(7455(a,1),15856(a,1,2,1))].">
      <j1 rule="para" parents="7455 15856"/>
    </justification>
  </clause>

  <clause id="15923">
    <literal><![CDATA[
      K(x * K(y * (z * u),z),w) = K(K(y * u,z) * x,w)
    ]]></literal>
    <justification jstring="[para(10540(a,2),15863(a,1,1,2))].">
      <j1 rule="para" parents="10540 15863"/>
    </justification>
  </clause>

  <clause id="15924">
    <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(4913(a,1),15877(a,1,2,1))].">
      <j1 rule="para" parents="4913 15877"/>
    </justification>
  </clause>

  <clause id="15925">
    <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(15890(a,1),15179(a,1,2,2))].">
      <j1 rule="para" parents="15890 15179"/>
    </justification>
  </clause>

  <clause id="15926">
    <literal><![CDATA[
      K(((x \ y) \ z) * K(x,y),u) = K((y / x) \ z,u)
    ]]></literal>
    <justification jstring="[para(5399(a,1),15892(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5399 15892"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15927">
    <literal><![CDATA[
      K(x * K(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(K(z,y) * x,u) = w
    ]]></literal>
    <justification jstring="[para(15892(a,1),13184(a,1))].">
      <j1 rule="para" parents="15892 13184"/>
    </justification>
  </clause>

  <clause id="15928">
    <literal><![CDATA[
      K(T(T(x,y),y) * z,u) = K(x * z,u)
    ]]></literal>
    <justification jstring="[para(5126(a,1),15895(a,1,1))].">
      <j1 rule="para" parents="5126 15895"/>
    </justification>
  </clause>

  <clause id="15929">
    <literal><![CDATA[
      K(((x * y) / x) * z,u) = K(T(y,x) * z,u)
    ]]></literal>
    <justification jstring="[para(224(a,1),15928(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="224 15928"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15930">
    <literal><![CDATA[
      K(x,T(y,z) * (u * z)) = K(x,y * (u * T(z,y)))
    ]]></literal>
    <justification jstring="[para(6116(a,1),15911(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6116 15911"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15931">
    <literal><![CDATA[
      K(x * (y \ z),(1 / (z \ y)) * x) = K(x * (y \ z),x * (1 / (z \ y)))
    ]]></literal>
    <justification jstring="[para(6172(a,1),15912(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6172 15912"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15932">
    <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(7659(a,2),15918(a,2,2,1))].">
      <j1 rule="para" parents="7659 15918"/>
    </justification>
  </clause>

  <clause id="15933">
    <literal><![CDATA[
      K(x * (K(y,x) * z),u) = K(T(x,y) * z,u)
    ]]></literal>
    <justification jstring="[para(5404(a,1),15929(a,1,1))].">
      <j1 rule="para" parents="5404 15929"/>
    </justification>
  </clause>

  <clause id="15934">
    <literal><![CDATA[
      K(T(x \ 1,y) \ z,u) = K(T(x,y) * z,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,15380,a,b,15933,a)].">
      <j1 rule="hyper" parents="58 15380 15933"/>
    </justification>
  </clause>

  <clause id="15935">
    <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,15284,a(flip),b,15934,a)].">
      <j1 rule="hyper" parents="58 15284 15934"/>
    </justification>
  </clause>

  <clause id="15936">
    <literal><![CDATA[
      K(x,y * K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(15823(a,1),15682(a,1))].">
      <j1 rule="para" parents="15823 15682"/>
    </justification>
  </clause>

  <clause id="15937">
    <literal><![CDATA[
      K(x,y * K(z,u \ z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(15821(a,2),15682(a,1))].">
      <j1 rule="para" parents="15821 15682"/>
    </justification>
  </clause>

  <clause id="15938">
    <literal><![CDATA[
      K(x,y * K(z * u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(15827(a,2),15682(a,1))].">
      <j1 rule="para" parents="15827 15682"/>
    </justification>
  </clause>

  <clause id="15939">
    <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(13138(a,1),15700(a,1))].">
      <j1 rule="para" parents="13138 15700"/>
    </justification>
  </clause>

  <clause id="15940">
    <literal><![CDATA[
      T(x,K(y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u * K(z,y)) = w
    ]]></literal>
    <justification jstring="[para(15114(a,1),15700(a,1))].">
      <j1 rule="para" parents="15114 15700"/>
    </justification>
  </clause>

  <clause id="15941">
    <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(15862(a,1),15700(a,1,2,1))].">
      <j1 rule="para" parents="15862 15700"/>
    </justification>
  </clause>

  <clause id="15942">
    <literal><![CDATA[
      K(K(x,y) * z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(K(y,x) * z,u) = w
    ]]></literal>
    <justification jstring="[para(15862(a,2),15718(a,1))].">
      <j1 rule="para" parents="15862 15718"/>
    </justification>
  </clause>

  <clause id="15943">
    <literal><![CDATA[
      K(T(1 / (x \ y),K(z,u)),w) = K(1 / L(x \ y,v5,y / x),w)
    ]]></literal>
    <justification jstring="[para(9064(a,2),15720(a,2,1,2))].">
      <j1 rule="para" parents="9064 15720"/>
    </justification>
  </clause>

  <clause id="15944">
    <literal><![CDATA[
      x * K(y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(z,K(y,u)) * x = w
    ]]></literal>
    <justification jstring="[para(7779(a,1),15732(a,1,2))].">
      <j1 rule="para" parents="7779 15732"/>
    </justification>
  </clause>

  <clause id="15945">
    <literal><![CDATA[
      K(x,K(y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z) \ u) = w
    ]]></literal>
    <justification jstring="[para(15823(a,2),15793(a,1))].">
      <j1 rule="para" parents="15823 15793"/>
    </justification>
  </clause>

  <clause id="15946">
    <literal><![CDATA[
      K(x,T(y,z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u / z)) = w
    ]]></literal>
    <justification jstring="[para(15571(a,1),15794(a,1))].">
      <j1 rule="para" parents="15571 15794"/>
    </justification>
  </clause>

  <clause id="15947">
    <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(11204(a,1),15799(a,1,2,2))].">
      <j1 rule="para" parents="11204 15799"/>
    </justification>
  </clause>

  <clause id="15948">
    <literal><![CDATA[
      K(x,T(y,z / (1 / u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u * z)) = w
    ]]></literal>
    <justification jstring="[para(13815(a,2),15799(a,1,2))].">
      <j1 rule="para" parents="13815 15799"/>
    </justification>
  </clause>

  <clause id="15949">
    <literal><![CDATA[
      K(x,T(y,z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z * u)) = w
    ]]></literal>
    <justification jstring="[para(15572(a,2),15799(a,1))].">
      <j1 rule="para" parents="15572 15799"/>
    </justification>
  </clause>

  <clause id="15950">
    <literal><![CDATA[
      K(x,T(y,z / u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z * u)) = w
    ]]></literal>
    <justification jstring="[para(15819(a,2),15799(a,1))].">
      <j1 rule="para" parents="15819 15799"/>
    </justification>
  </clause>

  <clause id="15954">
    <literal><![CDATA[
      K(x,y * K(z,z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(13068(a,2),15936(a,1))].">
      <j1 rule="para" parents="13068 15936"/>
    </justification>
  </clause>

  <clause id="15955">
    <literal><![CDATA[
      K((x * K(y,z)) \ 1,u) = K(x \ K(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(6503,a,15702,a),flip(a)].">
      <j1 rule="hyper" parents="6503 15702"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15956">
    <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(14866,a,15955,a)].">
      <j1 rule="hyper" parents="14866 15955"/>
    </justification>
  </clause>

  <clause id="15957">
    <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(14842,a,15711,a)].">
      <j1 rule="hyper" parents="14842 15711"/>
    </justification>
  </clause>

  <clause id="15958">
    <literal><![CDATA[
      T(K(x,K(y,z)) * u,w) = K(x,K(y,z)) * T(u,w)
    ]]></literal>
    <justification jstring="[hyper(320,a,15684,a,b,15747,a),flip(a)].">
      <j1 rule="hyper" parents="320 15684 15747"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15959">
    <literal><![CDATA[
      T(x * K(y,K(z,u)),w) = T(x,w) * K(y,K(z,u))
    ]]></literal>
    <justification jstring="[para(15684(a,1),15747(a,1,1))].">
      <j1 rule="para" parents="15684 15747"/>
    </justification>
  </clause>

  <clause id="15960">
    <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(7628(a,1),15774(a,2,2))].">
      <j1 rule="para" parents="7628 15774"/>
    </justification>
  </clause>

  <clause id="15961">
    <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,12293,a(flip),b,15776,a)].">
      <j1 rule="hyper" parents="58 12293 15776"/>
    </justification>
  </clause>

  <clause id="15962">
    <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(15777(a,1),236(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="15777 236"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15963">
    <literal><![CDATA[
      K(x,T(y,z)) * (u * K(y,T(x,z))) = T(u,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(119,a,15778,a(flip),b,7224,a)].">
      <j1 rule="hyper" parents="119 15778 7224"/>
    </justification>
  </clause>

  <clause id="15964">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * K(x,y)) = u * K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,7178,a,b,15785,a),flip(a)].">
      <j1 rule="hyper" parents="320 7178 15785"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15965">
    <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(439,a,15845,a,b,13907,a)].">
      <j1 rule="hyper" parents="439 15845 13907"/>
    </justification>
  </clause>

  <clause id="15966">
    <literal><![CDATA[
      (K(x,y) * (z \ x)) * K(y,K(x,z)) = z \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,13718,a(flip),b,15872,a),flip(a)].">
      <j1 rule="hyper" parents="320 13718 15872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15967">
    <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),15879(a,2,2,2))].">
      <j1 rule="para" parents="107 15879"/>
    </justification>
  </clause>

  <clause id="15968">
    <literal><![CDATA[
      K(x,K(y,z)) \ T(u,z) = z \ (u * T(z,K(x,y)))
    ]]></literal>
    <justification jstring="[para(7784(a,2),15879(a,1,1))].">
      <j1 rule="para" parents="7784 15879"/>
    </justification>
  </clause>

  <clause id="15969">
    <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(15884(a,1),7558(a,2,2,1))].">
      <j1 rule="para" parents="15884 7558"/>
    </justification>
  </clause>

  <clause id="15970">
    <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(15902(a,2),14767(a,2,2,2))].">
      <j1 rule="para" parents="15902 14767"/>
    </justification>
  </clause>

  <clause id="15971">
    <literal><![CDATA[
      T(x * T(y,K(z,u)),w) / y = y \ T(T(y,K(z,u)) * x,w)
    ]]></literal>
    <justification jstring="[hyper(4604,a,15906,a),flip(a)].">
      <j1 rule="hyper" parents="4604 15906"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15972">
    <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(7859(a,1),15907(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7859 15907"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15973">
    <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(15930(a,2),7402(a,1))].">
      <j1 rule="para" parents="15930 7402"/>
    </justification>
  </clause>

  <clause id="15975">
    <literal><![CDATA[
      T(x * K(y,K(z,u)),w) = K(y,K(z,u)) * T(x,w)
    ]]></literal>
    <justification jstring="[para(15684(a,1),15958(a,1,1))].">
      <j1 rule="para" parents="15684 15958"/>
    </justification>
  </clause>

  <clause id="15976">
    <literal><![CDATA[
      T(K(x,K(y,z)) \ u,w) = K(x,K(y,z)) \ T(u,w)
    ]]></literal>
    <justification jstring="[hyper(4618,a,15959,a),flip(a)].">
      <j1 rule="hyper" parents="4618 15959"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15977">
    <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(15959(a,2),7813(a,1,1))].">
      <j1 rule="para" parents="15959 7813"/>
    </justification>
  </clause>

  <clause id="15978">
    <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(15963(a,1),11213(a,1,2,2))].">
      <j1 rule="para" parents="15963 11213"/>
    </justification>
  </clause>

  <clause id="15979">
    <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(15964(a,2),38(a,1))].">
      <j1 rule="para" parents="15964 38"/>
    </justification>
  </clause>

  <clause id="15980">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * K(y,z)) = u * K(y,T(z,x))
    ]]></literal>
    <justification jstring="[para(7784(a,1),15964(a,1,1))].">
      <j1 rule="para" parents="7784 15964"/>
    </justification>
  </clause>

  <clause id="15981">
    <literal><![CDATA[
      T(x,K(y,z)) \ T(z,y) = K(z,y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(30,a,15769,a,b,15966,a)].">
      <j1 rule="hyper" parents="30 15769 15966"/>
    </justification>
  </clause>

  <clause id="15982">
    <literal><![CDATA[
      ((K(x,y) * z) / K(x,y)) \ T(y,x) = K(y,x) * (z \ y)
    ]]></literal>
    <justification jstring="[para(7861(a,2),15981(a,1,1))].">
      <j1 rule="para" parents="7861 15981"/>
    </justification>
  </clause>

  <clause id="15983">
    <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(15980(a,2),38(a,1))].">
      <j1 rule="para" parents="15980 38"/>
    </justification>
  </clause>

  <clause id="15984">
    <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(7891(a,1),15648(a,1,1))].">
      <j1 rule="para" parents="7891 15648"/>
    </justification>
  </clause>

  <clause id="15985">
    <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),15649(a,1,2))].">
      <j1 rule="para" parents="18 15649"/>
    </justification>
  </clause>

  <clause id="15986">
    <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(15740,a,14091,a)].">
      <j1 rule="hyper" parents="15740 14091"/>
    </justification>
  </clause>

  <clause id="15987">
    <literal><![CDATA[
      K(x,K(y,z) \ (u / y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u / T(y,z)) = w
    ]]></literal>
    <justification jstring="[para(5130(a,2),15790(a,1,2))].">
      <j1 rule="para" parents="5130 15790"/>
    </justification>
  </clause>

  <clause id="15988">
    <literal><![CDATA[
      K(x,K(y,z) * (u / y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u / T(y,z)) = w
    ]]></literal>
    <justification jstring="[para(15130(a,1),15790(a,1))].">
      <j1 rule="para" parents="15130 15790"/>
    </justification>
  </clause>

  <clause id="15989">
    <literal><![CDATA[
      K(x,(y / z) * K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(15823(a,1),15790(a,1))].">
      <j1 rule="para" parents="15823 15790"/>
    </justification>
  </clause>

  <clause id="15990">
    <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(7345(a,1),15796(a,1,2,1))].">
      <j1 rule="para" parents="7345 15796"/>
    </justification>
  </clause>

  <clause id="15991">
    <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(9415(a,1),15796(a,1,2,1))].">
      <j1 rule="para" parents="9415 15796"/>
    </justification>
  </clause>

  <clause id="15992">
    <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(14011(a,1),15805(a,1,2,2))].">
      <j1 rule="para" parents="14011 15805"/>
    </justification>
  </clause>

  <clause id="15993">
    <literal><![CDATA[
      T(x,K(y,z) * (u \ z)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u \ T(z,y)) = w
    ]]></literal>
    <justification jstring="[para(15114(a,1),15807(a,1))].">
      <j1 rule="para" parents="15114 15807"/>
    </justification>
  </clause>

  <clause id="15994">
    <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(13804(a,1),15937(a,1,2,2))].">
      <j1 rule="para" parents="13804 15937"/>
    </justification>
  </clause>

  <clause id="15995">
    <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(13323(a,2),15938(a,1))].">
      <j1 rule="para" parents="13323 15938"/>
    </justification>
  </clause>

  <clause id="15996">
    <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(14233(a,2),15954(a,1,2,2))].">
      <j1 rule="para" parents="14233 15954"/>
    </justification>
  </clause>

  <clause id="15997">
    <literal><![CDATA[
      K(x,y / ((z * u) / z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / T(u,z)) = w
    ]]></literal>
    <justification jstring="[para(6397(a,2),15989(a,1,2))].">
      <j1 rule="para" parents="6397 15989"/>
    </justification>
  </clause>

  <clause id="15998">
    <literal><![CDATA[
      T(x,K(K(y,z),u) * w) = w \ (x * w)
    ]]></literal>
    <justification jstring="[para(15687(a,1),15701(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15687 15701"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15999">
    <literal><![CDATA[
      T(x,K(K(y,z),u) * w) = T(x,w)
    ]]></literal>
    <justification jstring="[hyper(320,a,17,a,b,15998,a),flip(a)].">
      <j1 rule="hyper" parents="320 17 15998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16001">
    <literal><![CDATA[
      T(x,y \ T(z,K(u,w))) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(15993,a,15999,a)].">
      <j1 rule="hyper" parents="15993 15999"/>
    </justification>
  </clause>

  <clause id="16002">
    <literal><![CDATA[
      T(x,y * K(z,K(u,w))) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(15940,a,15999,a)].">
      <j1 rule="hyper" parents="15940 15999"/>
    </justification>
  </clause>

  <clause id="16003">
    <literal><![CDATA[
      T(x,y / T(z,K(u,w))) = T(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(15803,a,15999,a)].">
      <j1 rule="hyper" parents="15803 15999"/>
    </justification>
  </clause>

  <clause id="16004">
    <literal><![CDATA[
      T(x,K(y,K(z,u)) * w) = T(x,w)
    ]]></literal>
    <justification jstring="[hyper(15334,a,15999,a)].">
      <j1 rule="hyper" parents="15334 15999"/>
    </justification>
  </clause>

  <clause id="16005">
    <literal><![CDATA[
      T(x,T(y,K(z,u)) / w) = T(x,y / w)
    ]]></literal>
    <justification jstring="[hyper(58,a,15125,a(flip),b,15999,a)].">
      <j1 rule="hyper" parents="58 15125 15999"/>
    </justification>
  </clause>

  <clause id="16006">
    <literal><![CDATA[
      T(x,T(y,K(z,u)) * w) = T(x,y * w)
    ]]></literal>
    <justification jstring="[hyper(58,a,15120,a(flip),b,15999,a)].">
      <j1 rule="hyper" parents="58 15120 15999"/>
    </justification>
  </clause>

  <clause id="16007">
    <literal><![CDATA[
      T(x,T(y,K(z,u)) \ w) = T(x,y \ w)
    ]]></literal>
    <justification jstring="[para(5131(a,1),15999(a,1,2))].">
      <j1 rule="para" parents="5131 15999"/>
    </justification>
  </clause>

  <clause id="16008">
    <literal><![CDATA[
      T(x,y * (K(z,u) * w)) = T(x,y * (w * K(z,u)))
    ]]></literal>
    <justification jstring="[para(10381(a,1),15999(a,1,2))].">
      <j1 rule="para" parents="10381 15999"/>
    </justification>
  </clause>

  <clause id="16009">
    <literal><![CDATA[
      T(x,(K(y,z) * u) * w) = T(x,(u * K(y,z)) * w)
    ]]></literal>
    <justification jstring="[para(11157(a,1),15999(a,1,2))].">
      <j1 rule="para" parents="11157 15999"/>
    </justification>
  </clause>

  <clause id="16010">
    <literal><![CDATA[
      K(x,K(y,K(z,u)) * w) = x \ T(x,w)
    ]]></literal>
    <justification jstring="[para(15999(a,1),15118(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15999 15118"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16011">
    <literal><![CDATA[
      T(x,y * T(z,K(u,w))) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(1433(a,1),16002(a,1,2))].">
      <j1 rule="para" parents="1433 16002"/>
    </justification>
  </clause>

  <clause id="16012">
    <literal><![CDATA[
      K(x * K(y,K(z,u)),w) = w / T(w,x)
    ]]></literal>
    <justification jstring="[para(16002(a,1),4794(a,2,2))].">
      <j1 rule="para" parents="16002 4794"/>
    </justification>
  </clause>

  <clause id="16013">
    <literal><![CDATA[
      T(x,y * (z * T(u,K(w,v5)))) = T(x,y * (z * u))
    ]]></literal>
    <justification jstring="[para(5990(a,1),16002(a,1,2))].">
      <j1 rule="para" parents="5990 16002"/>
    </justification>
  </clause>

  <clause id="16014">
    <literal><![CDATA[
      T(x,y / (K(z,u) * w)) = T(x,y / (w * K(z,u)))
    ]]></literal>
    <justification jstring="[para(10644(a,1),16002(a,1,2))].">
      <j1 rule="para" parents="10644 16002"/>
    </justification>
  </clause>

  <clause id="16015">
    <literal><![CDATA[
      T(x,y * (z * K(u,K(w,v5)))) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(10883(a,1),16002(a,1,2))].">
      <j1 rule="para" parents="10883 16002"/>
    </justification>
  </clause>

  <clause id="16016">
    <literal><![CDATA[
      T(x,K(y,T(z,u)) * w) = T(x,K(y,z) * w)
    ]]></literal>
    <justification jstring="[para(15846(a,1),16002(a,1,2))].">
      <j1 rule="para" parents="15846 16002"/>
    </justification>
  </clause>

  <clause id="16017">
    <literal><![CDATA[
      K(K(x,K(y,z)) * u,w) = w / T(w,u)
    ]]></literal>
    <justification jstring="[para(16004(a,1),4794(a,2,2))].">
      <j1 rule="para" parents="16004 4794"/>
    </justification>
  </clause>

  <clause id="16018">
    <literal><![CDATA[
      T(x,y * K(z,T(u,w))) = T(x,y * K(z,u))
    ]]></literal>
    <justification jstring="[para(15964(a,1),16004(a,1,2))].">
      <j1 rule="para" parents="15964 16004"/>
    </justification>
  </clause>

  <clause id="16019">
    <literal><![CDATA[
      T(x,y \ T(z,T(u,w))) = T(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[para(7438(a,1),16001(a,1,2,2))].">
      <j1 rule="para" parents="7438 16001"/>
    </justification>
  </clause>

  <clause id="16020">
    <literal><![CDATA[
      T(x,y / T(z,T(u,w))) = T(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[para(7438(a,1),16003(a,1,2,2))].">
      <j1 rule="para" parents="7438 16003"/>
    </justification>
  </clause>

  <clause id="16021">
    <literal><![CDATA[
      T(x,y / T(T(z,T(u,w)),v5)) = T(x,y / T(T(z,u),v5))
    ]]></literal>
    <justification jstring="[para(7442(a,1),16003(a,1,2,2))].">
      <j1 rule="para" parents="7442 16003"/>
    </justification>
  </clause>

  <clause id="16022">
    <literal><![CDATA[
      T(x,T(y,T(z,u)) / w) = T(x,T(y,z) / w)
    ]]></literal>
    <justification jstring="[para(7438(a,1),16005(a,1,2,1))].">
      <j1 rule="para" parents="7438 16005"/>
    </justification>
  </clause>

  <clause id="16024">
    <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,13206,a(flip),b,16006,a),flip(a)].">
      <j1 rule="hyper" parents="58 13206 16006"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16025">
    <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,14175,a(flip),b,16007,a),flip(a)].">
      <j1 rule="hyper" parents="58 14175 16007"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16026">
    <literal><![CDATA[
      T(x,T(y,T(z,u)) \ w) = T(x,T(y,z) \ w)
    ]]></literal>
    <justification jstring="[para(7438(a,1),16007(a,1,2,1))].">
      <j1 rule="para" parents="7438 16007"/>
    </justification>
  </clause>

  <clause id="16027">
    <literal><![CDATA[
      K(x,K(y,K(z,u)) * w) = K(x,w)
    ]]></literal>
    <justification jstring="[hyper(320,a,4729,a,b,16010,a),flip(a)].">
      <j1 rule="hyper" parents="320 4729 16010"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16028">
    <literal><![CDATA[
      K(x,K(y,K(z,u)) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,w) = v5
    ]]></literal>
    <justification jstring="[para(16010(a,2),4838(a,1))].">
      <j1 rule="para" parents="16010 4838"/>
    </justification>
  </clause>

  <clause id="16029">
    <literal><![CDATA[
      K(x,y / T(z,K(u,w))) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(15988,a,16027,a)].">
      <j1 rule="hyper" parents="15988 16027"/>
    </justification>
  </clause>

  <clause id="16030">
    <literal><![CDATA[
      K(x,K(y,K(z,u)) \ w) = K(x,w)
    ]]></literal>
    <justification jstring="[hyper(15945,a,16027,a)].">
      <j1 rule="hyper" parents="15945 16027"/>
    </justification>
  </clause>

  <clause id="16031">
    <literal><![CDATA[
      K(x,y \ T(z,K(u,w))) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(15800,a,16027,a)].">
      <j1 rule="hyper" parents="15800 16027"/>
    </justification>
  </clause>

  <clause id="16032">
    <literal><![CDATA[
      K(x,y * T(z,K(u,w))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(15796,a,16027,a)].">
      <j1 rule="hyper" parents="15796 16027"/>
    </justification>
  </clause>

  <clause id="16033">
    <literal><![CDATA[
      K(x,y * K(z,K(u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(15682,a,16027,a)].">
      <j1 rule="hyper" parents="15682 16027"/>
    </justification>
  </clause>

  <clause id="16034">
    <literal><![CDATA[
      K(x,T(y,K(z,u)) \ w) = K(x,y \ w)
    ]]></literal>
    <justification jstring="[hyper(58,a,15137,a(flip),b,16027,a)].">
      <j1 rule="hyper" parents="58 15137 16027"/>
    </justification>
  </clause>

  <clause id="16035">
    <literal><![CDATA[
      K(x,T(y,K(z,u)) * w) = K(x,y * w)
    ]]></literal>
    <justification jstring="[para(4781(a,1),16027(a,1,2))].">
      <j1 rule="para" parents="4781 16027"/>
    </justification>
  </clause>

  <clause id="16036">
    <literal><![CDATA[
      K(x,T(y,K(z,u)) / w) = K(x,y / w)
    ]]></literal>
    <justification jstring="[para(5738(a,1),16027(a,1,2))].">
      <j1 rule="para" parents="5738 16027"/>
    </justification>
  </clause>

  <clause id="16037">
    <literal><![CDATA[
      K(x,(K(y,z) * u) \ w) = K(x,(u * K(y,z)) \ w)
    ]]></literal>
    <justification jstring="[para(9628(a,1),16027(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9628 16027"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16038">
    <literal><![CDATA[
      K(x,(K(y,z) * u) * w) = K(x,(u * K(y,z)) * w)
    ]]></literal>
    <justification jstring="[para(11157(a,1),16027(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11157 16027"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16039">
    <literal><![CDATA[
      K(x,(K(y,z) * u) / w) = K(x,(u * K(y,z)) / w)
    ]]></literal>
    <justification jstring="[para(14031(a,1),16027(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14031 16027"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16040">
    <literal><![CDATA[
      K(x,y \ K(z,T(u,w))) = K(x,y \ K(z,u))
    ]]></literal>
    <justification jstring="[para(15850(a,1),16027(a,1,2))].">
      <j1 rule="para" parents="15850 16027"/>
    </justification>
  </clause>

  <clause id="16041">
    <literal><![CDATA[
      K(x,y * K(z,T(u,w))) = K(x,y * K(z,u))
    ]]></literal>
    <justification jstring="[para(15964(a,1),16027(a,1,2))].">
      <j1 rule="para" parents="15964 16027"/>
    </justification>
  </clause>

  <clause id="16042">
    <literal><![CDATA[
      K(x,y * (z * T(u,K(w,v5)))) = K(x,y * (z * u))
    ]]></literal>
    <justification jstring="[para(5990(a,1),16033(a,1,2))].">
      <j1 rule="para" parents="5990 16033"/>
    </justification>
  </clause>

  <clause id="16043">
    <literal><![CDATA[
      K(x,y * (K(z,u) * w)) = K(x,y * (w * K(z,u)))
    ]]></literal>
    <justification jstring="[para(8130(a,1),16033(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8130 16033"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16044">
    <literal><![CDATA[
      K(x,y / (K(z,u) * w)) = K(x,y / (w * K(z,u)))
    ]]></literal>
    <justification jstring="[para(10644(a,1),16033(a,1,2))].">
      <j1 rule="para" parents="10644 16033"/>
    </justification>
  </clause>

  <clause id="16045">
    <literal><![CDATA[
      K(x,y * (z * K(u,K(w,v5)))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(10883(a,1),16033(a,1,2))].">
      <j1 rule="para" parents="10883 16033"/>
    </justification>
  </clause>

  <clause id="16046">
    <literal><![CDATA[
      K(x,y \ (K(z,u) * w)) = K(x,y \ (w * K(z,u)))
    ]]></literal>
    <justification jstring="[para(14146(a,1),16033(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14146 16033"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16047">
    <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,13110,a(flip),b,16011,a),flip(a)].">
      <j1 rule="hyper" parents="58 13110 16011"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16050">
    <literal><![CDATA[
      K(x * K(y,K(z,u)),w) = K(x,w)
    ]]></literal>
    <justification jstring="[hyper(320,a,4794,a,b,16012,a),flip(a)].">
      <j1 rule="hyper" parents="320 4794 16012"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16051">
    <literal><![CDATA[
      K(x * K(y,K(z,u)),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,w) = v5
    ]]></literal>
    <justification jstring="[para(16012(a,2),4862(a,1))].">
      <j1 rule="para" parents="16012 4862"/>
    </justification>
  </clause>

  <clause id="16052">
    <literal><![CDATA[
      K(K(x,K(y,z)) * u,w) = K(u,w)
    ]]></literal>
    <justification jstring="[hyper(15866,a,16050,a)].">
      <j1 rule="hyper" parents="15866 16050"/>
    </justification>
  </clause>

  <clause id="16053">
    <literal><![CDATA[
      K(x \ T(y,K(z,u)),w) = K(x \ y,w)
    ]]></literal>
    <justification jstring="[para(1430(a,1),16050(a,1,1))].">
      <j1 rule="para" parents="1430 16050"/>
    </justification>
  </clause>

  <clause id="16054">
    <literal><![CDATA[
      K(x * (K(y,z) * u),w) = K(x * (u * K(y,z)),w)
    ]]></literal>
    <justification jstring="[para(8130(a,1),16050(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8130 16050"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16055">
    <literal><![CDATA[
      K(x \ K(y,T(z,u)),w) = K(x \ K(y,z),w)
    ]]></literal>
    <justification jstring="[para(12343(a,1),16050(a,1,1))].">
      <j1 rule="para" parents="12343 16050"/>
    </justification>
  </clause>

  <clause id="16056">
    <literal><![CDATA[
      K(x \ (K(y,z) * u),w) = K(x \ (u * K(y,z)),w)
    ]]></literal>
    <justification jstring="[para(14146(a,1),16050(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14146 16050"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16058">
    <literal><![CDATA[
      K(x * K(y,T(z,u)),w) = K(x * K(y,z),w)
    ]]></literal>
    <justification jstring="[para(15964(a,1),16052(a,1,1))].">
      <j1 rule="para" parents="15964 16052"/>
    </justification>
  </clause>

  <clause id="16059">
    <literal><![CDATA[
      K(K(x,K(y,z)) * u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(u,w) = v5
    ]]></literal>
    <justification jstring="[para(16017(a,2),4862(a,1))].">
      <j1 rule="para" parents="16017 4862"/>
    </justification>
  </clause>

  <clause id="16060">
    <literal><![CDATA[
      K(x,y \ T(z,y)) = K(x,z / T(y,K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(320,a,13131,a,b,16029,a)].">
      <j1 rule="hyper" parents="320 13131 16029"/>
    </justification>
  </clause>

  <clause id="16061">
    <literal><![CDATA[
      K(x,y / T(z,u / w)) = K(x,y / T(z,w \ u))
    ]]></literal>
    <justification jstring="[para(7948(a,1),16029(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7948 16029"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16062">
    <literal><![CDATA[
      K(x,y \ T(z,u / w)) = K(x,y \ T(z,w \ u))
    ]]></literal>
    <justification jstring="[para(7948(a,1),16031(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7948 16031"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16064">
    <literal><![CDATA[
      K(x,y * T(z,T(u,w))) = K(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[para(7438(a,1),16032(a,1,2,2))].">
      <j1 rule="para" parents="7438 16032"/>
    </justification>
  </clause>

  <clause id="16065">
    <literal><![CDATA[
      K(x,y * T(z,u / w)) = K(x,y * T(z,w \ u))
    ]]></literal>
    <justification jstring="[para(7948(a,1),16032(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7948 16032"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16066">
    <literal><![CDATA[
      K(x,y * (K(z,u) * (w \ z))) = K(x,y * (w \ T(z,u)))
    ]]></literal>
    <justification jstring="[para(13733(a,1),16032(a,1,2,2))].">
      <j1 rule="para" parents="13733 16032"/>
    </justification>
  </clause>

  <clause id="16067">
    <literal><![CDATA[
      K(x,y * ((z / u) * K(z,w))) = K(x,y * (T(z,w) / u))
    ]]></literal>
    <justification jstring="[para(13745(a,1),16032(a,1,2,2))].">
      <j1 rule="para" parents="13745 16032"/>
    </justification>
  </clause>

  <clause id="16068">
    <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(16034(a,1),15275(a,1))].">
      <j1 rule="para" parents="16034 15275"/>
    </justification>
  </clause>

  <clause id="16069">
    <literal><![CDATA[
      K(x,T(y,T(z,u)) * w) = K(x,T(y,z) * w)
    ]]></literal>
    <justification jstring="[para(7438(a,1),16035(a,1,2,1))].">
      <j1 rule="para" parents="7438 16035"/>
    </justification>
  </clause>

  <clause id="16070">
    <literal><![CDATA[
      K(x,T(y,T(z,u)) / w) = K(x,T(y,z) / w)
    ]]></literal>
    <justification jstring="[para(7438(a,1),16036(a,1,2,1))].">
      <j1 rule="para" parents="7438 16036"/>
    </justification>
  </clause>

  <clause id="16071">
    <literal><![CDATA[
      K(x,T(y,z / u) / w) = K(x,T(y,u \ z) / w)
    ]]></literal>
    <justification jstring="[para(7948(a,1),16036(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7948 16036"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16072">
    <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,15488,a(flip),b,16053,a),flip(a)].">
      <j1 rule="hyper" parents="58 15488 16053"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16073">
    <literal><![CDATA[
      K(x \ T(y,T(z,u)),w) = K(x \ T(y,z),w)
    ]]></literal>
    <justification jstring="[para(7438(a,1),16053(a,1,1,2))].">
      <j1 rule="para" parents="7438 16053"/>
    </justification>
  </clause>

  <clause id="16074">
    <literal><![CDATA[
      K(x \ T(y,z * u),w) = K(x \ T(y,u * z),w)
    ]]></literal>
    <justification jstring="[para(12286(a,1),16053(a,1,1,2))].">
      <j1 rule="para" parents="12286 16053"/>
    </justification>
  </clause>

  <clause id="16075">
    <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(16053(a,1),13927(a,1,1,1,2))].">
      <j1 rule="para" parents="16053 13927"/>
    </justification>
  </clause>

  <clause id="16076">
    <literal><![CDATA[
      K(x,T(y,K(z,u)) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * w) = v5
    ]]></literal>
    <justification jstring="[para(4781(a,1),16028(a,1,2))].">
      <j1 rule="para" parents="4781 16028"/>
    </justification>
  </clause>

  <clause id="16077">
    <literal><![CDATA[
      K(x,y \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,K(w,v5)) \ z) = u
    ]]></literal>
    <justification jstring="[para(5081(a,1),16028(a,1,2))].">
      <j1 rule="para" parents="5081 16028"/>
    </justification>
  </clause>

  <clause id="16078">
    <literal><![CDATA[
      K(x,K(K(y,z),u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,w) = v5
    ]]></literal>
    <justification jstring="[para(5621(a,2),16028(a,1,2,1))].">
      <j1 rule="para" parents="5621 16028"/>
    </justification>
  </clause>

  <clause id="16079">
    <literal><![CDATA[
      K(x,y * T(z,K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = v5
    ]]></literal>
    <justification jstring="[para(5555(a,1),16028(a,1,2))].">
      <j1 rule="para" parents="5555 16028"/>
    </justification>
  </clause>

  <clause id="16080">
    <literal><![CDATA[
      K(x,y \ T(z,K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = v5
    ]]></literal>
    <justification jstring="[para(5553(a,1),16028(a,1,2))].">
      <j1 rule="para" parents="5553 16028"/>
    </justification>
  </clause>

  <clause id="16081">
    <literal><![CDATA[
      K(x,y * K(z,K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(7288(a,1),16028(a,1,2))].">
      <j1 rule="para" parents="7288 16028"/>
    </justification>
  </clause>

  <clause id="16082">
    <literal><![CDATA[
      K(x,T(y,K(z,u)) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ w) = v5
    ]]></literal>
    <justification jstring="[para(7772(a,1),16028(a,1,2))].">
      <j1 rule="para" parents="7772 16028"/>
    </justification>
  </clause>

  <clause id="16083">
    <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(14031(a,1),16028(a,1,2))].">
      <j1 rule="para" parents="14031 16028"/>
    </justification>
  </clause>

  <clause id="16084">
    <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(14833(a,1),16028(a,1,2))].">
      <j1 rule="para" parents="14833 16028"/>
    </justification>
  </clause>

  <clause id="16085">
    <literal><![CDATA[
      K(x,y / T(z,K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y / z) = v5
    ]]></literal>
    <justification jstring="[para(15824(a,1),16028(a,1))].">
      <j1 rule="para" parents="15824 16028"/>
    </justification>
  </clause>

  <clause id="16086">
    <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(15850(a,1),16028(a,1,2))].">
      <j1 rule="para" parents="15850 16028"/>
    </justification>
  </clause>

  <clause id="16087">
    <literal><![CDATA[
      K(x \ T(y,K(z,u)),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,w) = v5
    ]]></literal>
    <justification jstring="[para(1430(a,1),16051(a,1,1))].">
      <j1 rule="para" parents="1430 16051"/>
    </justification>
  </clause>

  <clause id="16088">
    <literal><![CDATA[
      K(T(x,K(y,z)) / u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x / u,w) = v5
    ]]></literal>
    <justification jstring="[para(1439(a,1),16051(a,1,1))].">
      <j1 rule="para" parents="1439 16051"/>
    </justification>
  </clause>

  <clause id="16089">
    <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(12343(a,1),16051(a,1,1))].">
      <j1 rule="para" parents="12343 16051"/>
    </justification>
  </clause>

  <clause id="16090">
    <literal><![CDATA[
      K((x * K(y,z)) \ u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K((K(y,z) * x) \ u,w) = v5
    ]]></literal>
    <justification jstring="[para(9628(a,1),16059(a,1,1))].">
      <j1 rule="para" parents="9628 16059"/>
    </justification>
  </clause>

  <clause id="16091">
    <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(11156(a,1),16059(a,1,1))].">
      <j1 rule="para" parents="11156 16059"/>
    </justification>
  </clause>

  <clause id="16092">
    <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(15893(a,1),16059(a,1))].">
      <j1 rule="para" parents="15893 16059"/>
    </justification>
  </clause>

  <clause id="16093">
    <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(10381(a,1),16078(a,1,2))].">
      <j1 rule="para" parents="10381 16078"/>
    </justification>
  </clause>

  <clause id="16094">
    <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(11157(a,1),16078(a,1,2))].">
      <j1 rule="para" parents="11157 16078"/>
    </justification>
  </clause>

  <clause id="16095">
    <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(5990(a,1),16081(a,1,2))].">
      <j1 rule="para" parents="5990 16081"/>
    </justification>
  </clause>

  <clause id="16096">
    <literal><![CDATA[
      K(x,y * (z * K(u,K(w,v5)))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = v6
    ]]></literal>
    <justification jstring="[para(10883(a,1),16081(a,1,2))].">
      <j1 rule="para" parents="10883 16081"/>
    </justification>
  </clause>

  <clause id="16097">
    <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(14146(a,1),16081(a,1,2))].">
      <j1 rule="para" parents="14146 16081"/>
    </justification>
  </clause>

  <clause id="16098">
    <literal><![CDATA[
      T(x,y * K(z / u,w)) = T(x,y * K(u \ z,w))
    ]]></literal>
    <justification jstring="[para(8392(a,1),16015(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="8392 16015"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16099">
    <literal><![CDATA[
      T(x,K(y,T(z,u)) * w) = T(x,K(z,y) * w)
    ]]></literal>
    <justification jstring="[hyper(320,a,15114,a,b,16016,a),flip(a)].">
      <j1 rule="hyper" parents="320 15114 16016"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16100">
    <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(16016(a,1),15993(a,1))].">
      <j1 rule="para" parents="16016 15993"/>
    </justification>
  </clause>

  <clause id="16101">
    <literal><![CDATA[
      T(x,y * K(z,T(u,w))) = T(x,K(u,z) * y)
    ]]></literal>
    <justification jstring="[hyper(320,a,15855,a,b,16018,a),flip(a)].">
      <j1 rule="hyper" parents="320 15855 16018"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16102">
    <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(16018(a,2),15859(a,1))].">
      <j1 rule="para" parents="16018 15859"/>
    </justification>
  </clause>

  <clause id="16103">
    <literal><![CDATA[
      T(x,T(y * K(y * z,u),z)) = T(x,z \ T(y * z,u))
    ]]></literal>
    <justification jstring="[para(14095(a,2),16019(a,1,2))].">
      <j1 rule="para" parents="14095 16019"/>
    </justification>
  </clause>

  <clause id="16104">
    <literal><![CDATA[
      T(x,y / T(z,T(u,w))) = T(x,y / T(z,z \ u))
    ]]></literal>
    <justification jstring="[hyper(320,a,13038,a,b,16020,a),flip(a)].">
      <j1 rule="hyper" parents="320 13038 16020"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16105">
    <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(16020(a,1),12742(a,1))].">
      <j1 rule="para" parents="16020 12742"/>
    </justification>
  </clause>

  <clause id="16106">
    <literal><![CDATA[
      T(x,T(T(y,z) \ u,y) / w) = T(x,(u / T(y,z)) / w)
    ]]></literal>
    <justification jstring="[hyper(58,a,15145,a(flip),b,16022,a),flip(a)].">
      <j1 rule="hyper" parents="58 15145 16022"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16107">
    <literal><![CDATA[
      K(x,y \ K(z / u,w)) = K(x,y \ K(u \ z,w))
    ]]></literal>
    <justification jstring="[para(7171(a,1),16040(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7171 16040"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16108">
    <literal><![CDATA[
      K(x,K(y,T(z,u)) * w) = K(x,w * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(15719,a,16041,a)].">
      <j1 rule="hyper" parents="15719 16041"/>
    </justification>
  </clause>

  <clause id="16109">
    <literal><![CDATA[
      K(x,y * K(z,u / w)) = K(x,y * K(z,w \ u))
    ]]></literal>
    <justification jstring="[para(107(a,1),16041(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="107 16041"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16110">
    <literal><![CDATA[
      K(x,y * K(z,u * w)) = K(x,y * K(z,w * u))
    ]]></literal>
    <justification jstring="[para(12262(a,1),16041(a,1,2,2))].">
      <j1 rule="para" parents="12262 16041"/>
    </justification>
  </clause>

  <clause id="16111">
    <literal><![CDATA[
      K(x,T(K(y,z) * u,w)) = K(x,T(u,w) * K(y,z))
    ]]></literal>
    <justification jstring="[para(14865(a,1),16041(a,1,2))].">
      <j1 rule="para" parents="14865 16041"/>
    </justification>
  </clause>

  <clause id="16112">
    <literal><![CDATA[
      K(x,y * (z / T(u,K(w,v5)))) = K(x,y * (z / u))
    ]]></literal>
    <justification jstring="[hyper(58,a,15431,a(flip),b,16045,a)].">
      <j1 rule="hyper" parents="58 15431 16045"/>
    </justification>
  </clause>

  <clause id="16113">
    <literal><![CDATA[
      K(x,y * (z \ T(u,K(w,v5)))) = K(x,y * (z \ u))
    ]]></literal>
    <justification jstring="[para(1430(a,1),16045(a,1,2,2))].">
      <j1 rule="para" parents="1430 16045"/>
    </justification>
  </clause>

  <clause id="16114">
    <literal><![CDATA[
      K(x,y * (T(z,K(u,w)) / v5)) = K(x,y * (z / v5))
    ]]></literal>
    <justification jstring="[para(1439(a,1),16045(a,1,2,2))].">
      <j1 rule="para" parents="1439 16045"/>
    </justification>
  </clause>

  <clause id="16115">
    <literal><![CDATA[
      K(x,y * (T(z,K(u,w)) * v5)) = K(x,y * (z * v5))
    ]]></literal>
    <justification jstring="[para(5539(a,1),16045(a,1,2,2))].">
      <j1 rule="para" parents="5539 16045"/>
    </justification>
  </clause>

  <clause id="16117">
    <literal><![CDATA[
      K(x,y * (K(z,T(u,w)) * v5)) = K(x,y * (K(z,u) * v5))
    ]]></literal>
    <justification jstring="[para(15846(a,1),16045(a,1,2,2))].">
      <j1 rule="para" parents="15846 16045"/>
    </justification>
  </clause>

  <clause id="16118">
    <literal><![CDATA[
      K(x \ K(y,z * u),w) = K(x \ K(y,u * z),w)
    ]]></literal>
    <justification jstring="[para(12262(a,1),16055(a,1,1,2))].">
      <j1 rule="para" parents="12262 16055"/>
    </justification>
  </clause>

  <clause id="16119">
    <literal><![CDATA[
      K(x * K(y,T(z,u)),w) = K(K(z,y) * x,w)
    ]]></literal>
    <justification jstring="[hyper(320,a,15862,a,b,16058,a),flip(a)].">
      <j1 rule="hyper" parents="320 15862 16058"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16120">
    <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,13513,a(flip),b,16064,a),flip(a)].">
      <j1 rule="hyper" parents="58 13513 16064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16121">
    <literal><![CDATA[
      K(x,T(y,T(z,u)) * z) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(320,a,12290,a(flip),b,16069,a),flip(a)].">
      <j1 rule="hyper" parents="320 12290 16069"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16122">
    <literal><![CDATA[
      K(x,T(T(y,z) / u,y) * w) = K(x,(u \ T(y,z)) * w)
    ]]></literal>
    <justification jstring="[hyper(58,a,13055,a(flip),b,16069,a),flip(a)].">
      <j1 rule="hyper" parents="58 13055 16069"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16123">
    <literal><![CDATA[
      K(x,T(y,z * u) * (u * z)) = K(x,(u * z) * y)
    ]]></literal>
    <justification jstring="[para(12254(a,1),16121(a,1,2,1))].">
      <j1 rule="para" parents="12254 16121"/>
    </justification>
  </clause>

  <clause id="16124">
    <literal><![CDATA[
      K(x,T(T(y,z) / u,y) / w) = K(x,(u \ T(y,z)) / w)
    ]]></literal>
    <justification jstring="[hyper(58,a,13057,a(flip),b,16070,a),flip(a)].">
      <j1 rule="hyper" parents="58 13057 16070"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16125">
    <literal><![CDATA[
      K(T(x * K(x * y,z),y),u) = K(y \ T(x * y,z),u)
    ]]></literal>
    <justification jstring="[para(14095(a,2),16073(a,1,1))].">
      <j1 rule="para" parents="14095 16073"/>
    </justification>
  </clause>

  <clause id="16126">
    <literal><![CDATA[
      T(x,K(y * z,u) * w) = T(x,K(u,z * y) * w)
    ]]></literal>
    <justification jstring="[para(12230(a,1),16099(a,1,2,1))].">
      <j1 rule="para" parents="12230 16099"/>
    </justification>
  </clause>

  <clause id="16127">
    <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,15559,a,b,16101,a)].">
      <j1 rule="hyper" parents="58 15559 16101"/>
    </justification>
  </clause>

  <clause id="16128">
    <literal><![CDATA[
      K(x,K(y * z,u) * w) = K(x,w * K(z * y,u))
    ]]></literal>
    <justification jstring="[para(12230(a,1),16108(a,1,2,1))].">
      <j1 rule="para" parents="12230 16108"/>
    </justification>
  </clause>

  <clause id="16129">
    <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(16108(a,2),15829(a,1))].">
      <j1 rule="para" parents="16108 15829"/>
    </justification>
  </clause>

  <clause id="16130">
    <literal><![CDATA[
      K(K(x * y,z) * u,w) = K(u * K(z,y * x),w)
    ]]></literal>
    <justification jstring="[para(12262(a,1),16119(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="12262 16119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16131">
    <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(7948(a,1),16076(a,1,2,1))].">
      <j1 rule="para" parents="7948 16076"/>
    </justification>
  </clause>

  <clause id="16132">
    <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(8317(a,1),16079(a,1,2,2))].">
      <j1 rule="para" parents="8317 16079"/>
    </justification>
  </clause>

  <clause id="16133">
    <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(8091(a,1),16079(a,1,2,2))].">
      <j1 rule="para" parents="8091 16079"/>
    </justification>
  </clause>

  <clause id="16134">
    <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(13733(a,1),16079(a,1,2,2))].">
      <j1 rule="para" parents="13733 16079"/>
    </justification>
  </clause>

  <clause id="16135">
    <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(13745(a,1),16079(a,1,2,2))].">
      <j1 rule="para" parents="13745 16079"/>
    </justification>
  </clause>

  <clause id="16136">
    <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(15248(a,1),16079(a,1))].">
      <j1 rule="para" parents="15248 16079"/>
    </justification>
  </clause>

  <clause id="16137">
    <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(8317(a,1),16080(a,1,2,2))].">
      <j1 rule="para" parents="8317 16080"/>
    </justification>
  </clause>

  <clause id="16138">
    <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(12286(a,1),16080(a,1,2,2))].">
      <j1 rule="para" parents="12286 16080"/>
    </justification>
  </clause>

  <clause id="16139">
    <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),16085(a,1,2,2))].">
      <j1 rule="para" parents="20 16085"/>
    </justification>
  </clause>

  <clause id="16140">
    <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(13733(a,1),16085(a,1,2,2))].">
      <j1 rule="para" parents="13733 16085"/>
    </justification>
  </clause>

  <clause id="16141">
    <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(6337(a,1),16087(a,1,1,2))].">
      <j1 rule="para" parents="6337 16087"/>
    </justification>
  </clause>

  <clause id="16142">
    <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(7438(a,1),16087(a,1,1,2))].">
      <j1 rule="para" parents="7438 16087"/>
    </justification>
  </clause>

  <clause id="16143">
    <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(8317(a,1),16088(a,1,1,1))].">
      <j1 rule="para" parents="8317 16088"/>
    </justification>
  </clause>

  <clause id="16144">
    <literal><![CDATA[
      T(x,y * (z * T(u,w / v5))) = T(x,y * (z * T(u,v5 \ w)))
    ]]></literal>
    <justification jstring="[para(7948(a,1),16013(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="7948 16013"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16145">
    <literal><![CDATA[
      T(x,y / (z * K(u,w))) = T(x,y * (z \ K(w,u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,13859,a(flip),b,16014,a),flip(a)].">
      <j1 rule="hyper" parents="58 13859 16014"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16147">
    <literal><![CDATA[
      K(x,(y * K(z,u)) \ 1) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(16037(a,1),6484(a,1))].">
      <j1 rule="para" parents="16037 6484"/>
    </justification>
  </clause>

  <clause id="16148">
    <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(14785(a,1),16039(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="14785 16039"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16149">
    <literal><![CDATA[
      K(x,y * (z * (K(u,w) / v5))) = K(x,y * (z * (v5 \ K(u,w))))
    ]]></literal>
    <justification jstring="[hyper(58,a,15306,a(flip),b,16042,a)].">
      <j1 rule="hyper" parents="58 15306 16042"/>
    </justification>
  </clause>

  <clause id="16150">
    <literal><![CDATA[
      K(x,y * (K(z,u) * w)) = K(x,y * (w * K(u,z)))
    ]]></literal>
    <justification jstring="[hyper(320,a,15430,a,b,16043,a),flip(a)].">
      <j1 rule="hyper" parents="320 15430 16043"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16151">
    <literal><![CDATA[
      K(x,y * (K(z,u) * (w / z))) = K(x,y * (w / T(z,u)))
    ]]></literal>
    <justification jstring="[hyper(320,a,15431,a(flip),b,16043,a),flip(a)].">
      <j1 rule="hyper" parents="320 15431 16043"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16152">
    <literal><![CDATA[
      K(x,y * (z * K(u,u \ w))) = K(x,y * (K(u,w) * z))
    ]]></literal>
    <justification jstring="[hyper(58,a,13086,a(flip),b,16043,a),flip(a)].">
      <j1 rule="hyper" parents="58 13086 16043"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16153">
    <literal><![CDATA[
      K(x,y / (z * K(u,w))) = K(x,y * (z \ K(w,u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,13849,a(flip),b,16044,a),flip(a)].">
      <j1 rule="hyper" parents="58 13849 16044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16154">
    <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(14785(a,1),16046(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="14785 16046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16155">
    <literal><![CDATA[
      K(x * (((y * z) / y) \ u),w) = K(x * ((z \ u) * K(z,y)),w)
    ]]></literal>
    <justification jstring="[para(5088(a,2),16054(a,1,1,2))].">
      <j1 rule="para" parents="5088 16054"/>
    </justification>
  </clause>

  <clause id="16156">
    <literal><![CDATA[
      K(x,(y / z) / T(u,z \ y)) = K(x,u \ (y / z))
    ]]></literal>
    <justification jstring="[hyper(13063,a,16061,a),flip(a)].">
      <j1 rule="hyper" parents="13063 16061"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16157">
    <literal><![CDATA[
      K(x,(y / z) / T(u,z \ y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u \ (y / z)) = w
    ]]></literal>
    <justification jstring="[para(16061(a,1),13063(a,1))].">
      <j1 rule="para" parents="16061 13063"/>
    </justification>
  </clause>

  <clause id="16159">
    <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,15169,a(flip),b,16071,a),flip(a)].">
      <j1 rule="hyper" parents="58 15169 16071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16160">
    <literal><![CDATA[
      K(x,T(y,z \ u) / (u / z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(u / z) \ y) = w
    ]]></literal>
    <justification jstring="[para(16071(a,1),13061(a,1))].">
      <j1 rule="para" parents="16071 13061"/>
    </justification>
  </clause>

  <clause id="16161">
    <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(16074(a,1),6712(a,1))].">
      <j1 rule="para" parents="16074 6712"/>
    </justification>
  </clause>

  <clause id="16162">
    <literal><![CDATA[
      T(x,((y / z) \ u) * K(z \ y,w)) = T(x,T(y / z,w) \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,15857,a(flip),b,16098,a),flip(a)].">
      <j1 rule="hyper" parents="58 15857 16098"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16163">
    <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,15189,a(flip),b,16098,a),flip(a)].">
      <j1 rule="hyper" parents="58 15189 16098"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16164">
    <literal><![CDATA[
      T(x,y \ K(z / u,w)) = T(x,y \ K(u \ z,w))
    ]]></literal>
    <justification jstring="[hyper(118,a,16107,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 16107 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16165">
    <literal><![CDATA[
      K(x,(y * z) * K(u,z * y)) = K(x,T(y * z,u))
    ]]></literal>
    <justification jstring="[hyper(8023,a,16110,a),flip(a)].">
      <j1 rule="hyper" parents="8023 16110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16166">
    <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(16110(a,1),15829(a,1))].">
      <j1 rule="para" parents="16110 15829"/>
    </justification>
  </clause>

  <clause id="16167">
    <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(16110(a,1),15936(a,1))].">
      <j1 rule="para" parents="16110 15936"/>
    </justification>
  </clause>

  <clause id="16168">
    <literal><![CDATA[
      K(x,T(K(y,z) * u,w)) = K(x,K(y,z) * T(u,w))
    ]]></literal>
    <justification jstring="[hyper(320,a,15653,a,b,16111,a),flip(a)].">
      <j1 rule="hyper" parents="320 15653 16111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16169">
    <literal><![CDATA[
      K(x,y * (z / T(u,u \ w))) = K(x,y * (z / ((u \ w) \ w)))
    ]]></literal>
    <justification jstring="[para(3338(a,1),16112(a,1,2,2,2))].">
      <j1 rule="para" parents="3338 16112"/>
    </justification>
  </clause>

  <clause id="16170">
    <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(14912(a,1),16113(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="14912 16113"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16171">
    <literal><![CDATA[
      K(x,y * (T(z,u / w) / v5)) = K(x,y * (T(z,w \ u) / v5))
    ]]></literal>
    <justification jstring="[para(7948(a,1),16114(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="7948 16114"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16172">
    <literal><![CDATA[
      K(x,y * (T(z,T(u,w)) * v5)) = K(x,y * (T(z,u) * v5))
    ]]></literal>
    <justification jstring="[para(7438(a,1),16115(a,1,2,2,1))].">
      <j1 rule="para" parents="7438 16115"/>
    </justification>
  </clause>

  <clause id="16173">
    <literal><![CDATA[
      K(x,y * (T(z,u / w) * v5)) = K(x,y * (T(z,w \ u) * v5))
    ]]></literal>
    <justification jstring="[para(7948(a,1),16115(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="7948 16115"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16174">
    <literal><![CDATA[
      K(x \ K(y,z * (u * y)),w) = K(x \ K(y,u * z),w)
    ]]></literal>
    <justification jstring="[hyper(320,a,13151,a(flip),b,16118,a),flip(a)].">
      <j1 rule="hyper" parents="320 13151 16118"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16175">
    <literal><![CDATA[
      K(x,T(y,(z / y) * u) * (u * (z / y))) = K(x,R(u,y \ z,y) * z)
    ]]></literal>
    <justification jstring="[para(10399(a,2),16123(a,2,2))].">
      <j1 rule="para" parents="10399 16123"/>
    </justification>
  </clause>

  <clause id="16176">
    <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(16126(a,2),15334(a,1))].">
      <j1 rule="para" parents="16126 15334"/>
    </justification>
  </clause>

  <clause id="16177">
    <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(16128(a,2),15829(a,1))].">
      <j1 rule="para" parents="16128 15829"/>
    </justification>
  </clause>

  <clause id="16178">
    <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(16130(a,1),15717(a,1))].">
      <j1 rule="para" parents="16130 15717"/>
    </justification>
  </clause>

  <clause id="16179">
    <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,15202,a(flip),b,16145,a),flip(a)].">
      <j1 rule="hyper" parents="58 15202 16145"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16180">
    <literal><![CDATA[
      T(x,y * (z \ K(y,u))) = T(x,T(y,u) / z)
    ]]></literal>
    <justification jstring="[para(13736(a,1),16145(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13736 16145"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16181">
    <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(15259(a,1),16180(a,1,2,2,2))].">
      <j1 rule="para" parents="15259 16180"/>
    </justification>
  </clause>

  <clause id="16182">
    <literal><![CDATA[
      K(x,y * (K(z,u) * (w * u))) = K(x,y * (w * T(u,z)))
    ]]></literal>
    <justification jstring="[para(6116(a,1),16150(a,2,2,2))].">
      <j1 rule="para" parents="6116 16150"/>
    </justification>
  </clause>

  <clause id="16183">
    <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,14098,a(flip),b,16153,a),flip(a)].">
      <j1 rule="hyper" parents="58 14098 16153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16184">
    <literal><![CDATA[
      K(x,y * ((z * u) \ K(w,u))) = K(x,y / (z * T(u,w)))
    ]]></literal>
    <justification jstring="[para(6116(a,1),16153(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6116 16153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16185">
    <literal><![CDATA[
      K(x,y * ((z / u) \ K(u,w))) = K(x,y / (z / T(u,w)))
    ]]></literal>
    <justification jstring="[para(6322(a,1),16153(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6322 16153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16186">
    <literal><![CDATA[
      K(x,y / (z * ((u * w) / u))) = K(x,y * ((z * w) \ K(w,u)))
    ]]></literal>
    <justification jstring="[para(6097(a,1),16153(a,1,2,2))].">
      <j1 rule="para" parents="6097 16153"/>
    </justification>
  </clause>

  <clause id="16187">
    <literal><![CDATA[
      K(x,y * ((z \ (u \ w)) \ K(u,w))) = K(x,y / (z \ (u \ T(w,u))))
    ]]></literal>
    <justification jstring="[para(15022(a,1),16153(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="15022 16153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16188">
    <literal><![CDATA[
      K(x,y * (z * K(u,z * y))) = K(x,T(y * z,u))
    ]]></literal>
    <justification jstring="[para(13689(a,1),16165(a,1,2))].">
      <j1 rule="para" parents="13689 16165"/>
    </justification>
  </clause>

  <clause id="16189">
    <literal><![CDATA[
      T(x,T(K(y,z) * u,w)) = T(x,K(y,z) * T(u,w))
    ]]></literal>
    <justification jstring="[hyper(118,a,16168,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 16168 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16190">
    <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(14213(a,1),16188(a,1,2,2))].">
      <j1 rule="para" parents="14213 16188"/>
    </justification>
  </clause>

  <clause id="16191">
    <literal><![CDATA[
      T(x,T(K(y,z) * u,w)) = T(x,T(u,w) * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(320,a,15855,a(flip),b,16189,a),flip(a)].">
      <j1 rule="hyper" parents="320 15855 16189"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16192">
    <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(7890(a,1),16086(a,1,2,2))].">
      <j1 rule="para" parents="7890 16086"/>
    </justification>
  </clause>

  <clause id="16193">
    <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(1430(a,1),16096(a,1,2,2))].">
      <j1 rule="para" parents="1430 16096"/>
    </justification>
  </clause>

  <clause id="16194">
    <literal><![CDATA[
      K(x,y * (K(z,K(u,w)) * v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * v5) = v6
    ]]></literal>
    <justification jstring="[para(7150(a,1),16096(a,1,2,2))].">
      <j1 rule="para" parents="7150 16096"/>
    </justification>
  </clause>

  <clause id="16195">
    <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(7769(a,1),16096(a,1,2,2))].">
      <j1 rule="para" parents="7769 16096"/>
    </justification>
  </clause>

  <clause id="16196">
    <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(12343(a,1),16096(a,1,2,2))].">
      <j1 rule="para" parents="12343 16096"/>
    </justification>
  </clause>

  <clause id="16197">
    <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(15959(a,2),16096(a,1,2,2))].">
      <j1 rule="para" parents="15959 16096"/>
    </justification>
  </clause>

  <clause id="16198">
    <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(15223(a,1),16105(a,1,2,2))].">
      <j1 rule="para" parents="15223 16105"/>
    </justification>
  </clause>

  <clause id="16199">
    <literal><![CDATA[
      K(x,((y * z) / y) / u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(u / z) \ K(y,z)) = w
    ]]></literal>
    <justification jstring="[para(6474(a,1),16147(a,1))].">
      <j1 rule="para" parents="6474 16147"/>
    </justification>
  </clause>

  <clause id="16200">
    <literal><![CDATA[
      K(x,T(1 / (y * z),y)) = K(x,1 / (z * y))
    ]]></literal>
    <justification jstring="[hyper(320,a,5345,a(flip),b,15832,a),flip(a)].">
      <j1 rule="hyper" parents="320 5345 15832"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16202">
    <literal><![CDATA[
      K(x,y / (y * (y * z))) = K(x,1 / (z * y))
    ]]></literal>
    <justification jstring="[hyper(58,a,8140,a(flip),b,16200,a)].">
      <j1 rule="hyper" parents="58 8140 16200"/>
    </justification>
  </clause>

  <clause id="16203">
    <literal><![CDATA[
      K(x / (x / y),z * ((x / y) / x)) = K(y,T(((x / y) / x) * z,x))
    ]]></literal>
    <justification jstring="[hyper(12373,a,15840,a)].">
      <j1 rule="hyper" parents="12373 15840"/>
    </justification>
  </clause>

  <clause id="16204">
    <literal><![CDATA[
      T(x * T(y,x * K(z,u)),K(z,u)) = y * T(x,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(7851,a,15858,a)].">
      <j1 rule="hyper" parents="7851 15858"/>
    </justification>
  </clause>

  <clause id="16206">
    <literal><![CDATA[
      K(x,K(y,z) \ (u / y)) = K(x,u / (z * (y / z)))
    ]]></literal>
    <justification jstring="[hyper(58,a,15141,a(flip),b,15869,a)].">
      <j1 rule="hyper" parents="58 15141 15869"/>
    </justification>
  </clause>

  <clause id="16207">
    <literal><![CDATA[
      K(x,y / (z * (u / z))) = K(x,y / T(u,z))
    ]]></literal>
    <justification jstring="[hyper(15987,a,16206,a),flip(a)].">
      <j1 rule="hyper" parents="15987 16206"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16208">
    <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,15044,a(flip),b,16207,a),flip(a)].">
      <j1 rule="hyper" parents="58 15044 16207"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16209">
    <literal><![CDATA[
      K(x,y / T(z * u,u)) = K(x,y / (u * z))
    ]]></literal>
    <justification jstring="[para(6(a,1),16207(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="6 16207"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16210">
    <literal><![CDATA[
      K(x,y / T(z \ u,u)) = K(x,y / (z \ T(u,z \ 1)))
    ]]></literal>
    <justification jstring="[para(3913(a,2),16207(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3913 16207"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16211">
    <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,12321,a,b,15871,a)].">
      <j1 rule="hyper" parents="58 12321 15871"/>
    </justification>
  </clause>

  <clause id="16212">
    <literal><![CDATA[
      K(x,y) \ K(L(x,z,u),y) = a(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,14341,a(flip),b,15878,a),flip(a)].">
      <j1 rule="hyper" parents="58 14341 15878"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16213">
    <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,15583,a,b,15903,a),flip(a)].">
      <j1 rule="hyper" parents="320 15583 15903"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16214">
    <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,795,a(flip),b,15905,a),flip(a)].">
      <j1 rule="hyper" parents="320 795 15905"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16215">
    <literal><![CDATA[
      K(x * T(y * z,z),u) = K(x * (z * y),u)
    ]]></literal>
    <justification jstring="[hyper(58,a,15893,a(flip),b,15909,a),flip(a)].">
      <j1 rule="hyper" parents="58 15893 15909"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16216">
    <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,15470,a,b,15923,a)].">
      <j1 rule="hyper" parents="58 15470 15923"/>
    </justification>
  </clause>

  <clause id="16217">
    <literal><![CDATA[
      (x * K(y,z)) \ z = K(z,y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,14194,a(flip),b,15982,a)].">
      <j1 rule="hyper" parents="58 14194 15982"/>
    </justification>
  </clause>

  <clause id="16218">
    <literal><![CDATA[
      (x * K(y,T(z,u))) \ z = K(z,T(y,u)) * (x \ z)
    ]]></literal>
    <justification jstring="[para(7160(a,1),16217(a,1,1,2))].">
      <j1 rule="para" parents="7160 16217"/>
    </justification>
  </clause>

  <clause id="16219">
    <literal><![CDATA[
      K(x,y) * ((z \ T(x,y)) \ x) = (z \ x) \ x
    ]]></literal>
    <justification jstring="[para(13720(a,1),16217(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13720 16217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16220">
    <literal><![CDATA[
      K(x,y) * ((z \ y) \ y) = (z \ T(y,x)) \ y
    ]]></literal>
    <justification jstring="[hyper(5147,a,16219,a)].">
      <j1 rule="hyper" parents="5147 16219"/>
    </justification>
  </clause>

  <clause id="16221">
    <literal><![CDATA[
      T(x * K(y,z),x \ z) = (x \ T(z,y)) \ z
    ]]></literal>
    <justification jstring="[hyper(58,a,14496,a,b,16220,a)].">
      <j1 rule="hyper" parents="58 14496 16220"/>
    </justification>
  </clause>

  <clause id="16222">
    <literal><![CDATA[
      (x * K(y,T(z \ u,z))) \ (z \ u) = K(u / z,y) * (x \ (z \ u))
    ]]></literal>
    <justification jstring="[para(7907(a,1),16218(a,2,1))].">
      <j1 rule="para" parents="7907 16218"/>
    </justification>
  </clause>

  <clause id="16223">
    <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,12746,a(flip),b,16021,a),flip(a)].">
      <j1 rule="hyper" parents="58 12746 16021"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16224">
    <literal><![CDATA[
      K(x,y * (K(z / u,w) * v5)) = K(x,y * (K(u \ z,w) * v5))
    ]]></literal>
    <justification jstring="[para(7171(a,1),16117(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="7171 16117"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16225">
    <literal><![CDATA[
      K(x,T(y * ((y / z) / y),y) / u) = K(x,(z \ T(y,z \ 1)) / u)
    ]]></literal>
    <justification jstring="[para(3910(a,1),16124(a,1,2,1,1))].">
      <j1 rule="para" parents="3910 16124"/>
    </justification>
  </clause>

  <clause id="16226">
    <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(16125(a,1),7704(a,1))].">
      <j1 rule="para" parents="16125 7704"/>
    </justification>
  </clause>

  <clause id="16227">
    <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,15459,a,b,16152,a)].">
      <j1 rule="hyper" parents="58 15459 16152"/>
    </justification>
  </clause>

  <clause id="16228">
    <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,13823,a,b,16152,a)].">
      <j1 rule="hyper" parents="58 13823 16152"/>
    </justification>
  </clause>

  <clause id="16229">
    <literal><![CDATA[
      K(x,y * (z / (u / (u / w)))) = K(x,y * (K(w,u) * (z / w)))
    ]]></literal>
    <justification jstring="[para(6473(a,2),16152(a,1,2,2))].">
      <j1 rule="para" parents="6473 16152"/>
    </justification>
  </clause>

  <clause id="16230">
    <literal><![CDATA[
      K(x,y * (K(z,u) * (w * u))) = K(x,y * (w * (z * (u / z))))
    ]]></literal>
    <justification jstring="[para(10347(a,1),16152(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10347 16152"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16231">
    <literal><![CDATA[
      K(x,y * (T(z,u) * (w * (u / w)))) = K(x,y * ((w * (u / w)) * z))
    ]]></literal>
    <justification jstring="[hyper(15292,a,16172,a),flip(a)].">
      <j1 rule="hyper" parents="15292 16172"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16232">
    <literal><![CDATA[
      K(x,y * (T(z,u) * T(u,w))) = K(x,y * (T(u,w) * z))
    ]]></literal>
    <justification jstring="[hyper(15291,a,16172,a),flip(a)].">
      <j1 rule="hyper" parents="15291 16172"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16233">
    <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(16172(a,1),15291(a,1))].">
      <j1 rule="para" parents="16172 15291"/>
    </justification>
  </clause>

  <clause id="16234">
    <literal><![CDATA[
      K(x,y * T((z / u) \ 1,z)) = K(x,y / (z / T(u,z)))
    ]]></literal>
    <justification jstring="[hyper(58,a,13216,a,b,16185,a)].">
      <j1 rule="hyper" parents="58 13216 16185"/>
    </justification>
  </clause>

  <clause id="16235">
    <literal><![CDATA[
      K(x,y / (z \ T(u,z \ 1))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (u / z)) = w
    ]]></literal>
    <justification jstring="[para(16210(a,1),15280(a,1))].">
      <j1 rule="para" parents="16210 15280"/>
    </justification>
  </clause>

  <clause id="16236">
    <literal><![CDATA[
      K(x,K((y \ z) / u,L(w,u,y))) = K(x,K(w,z / (y * u)))
    ]]></literal>
    <justification jstring="[hyper(15618,a,15619,a)].">
      <j1 rule="hyper" parents="15618 15619"/>
    </justification>
  </clause>

  <clause id="16237">
    <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,15610,a,b,15759,a),flip(a)].">
      <j1 rule="hyper" parents="320 15610 15759"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16238">
    <literal><![CDATA[
      K(x,y * (x \ (z \ x))) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(15897,a,15665,a)].">
      <j1 rule="hyper" parents="15897 15665"/>
    </justification>
  </clause>

  <clause id="16239">
    <literal><![CDATA[
      K(x,(y * x) / z) = K(x,y * (z \ x))
    ]]></literal>
    <justification jstring="[hyper(12463,a,16238,a),flip(a)].">
      <j1 rule="hyper" parents="12463 16238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16240">
    <literal><![CDATA[
      K(x,y / (x \ z)) = K(x,y * (z \ x))
    ]]></literal>
    <justification jstring="[hyper(8446,a,16239,a)].">
      <j1 rule="hyper" parents="8446 16239"/>
    </justification>
  </clause>

  <clause id="16241">
    <literal><![CDATA[
      T(x,y / (x \ z)) = T(x,y * (z \ x))
    ]]></literal>
    <justification jstring="[hyper(118,a,16240,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 16240 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16242">
    <literal><![CDATA[
      x / (K(y,z * (u \ y)) * x) = K(z / (y \ u),y)
    ]]></literal>
    <justification jstring="[para(16240(a,1),5142(a,1,2,1))].">
      <j1 rule="para" parents="16240 5142"/>
    </justification>
  </clause>

  <clause id="16243">
    <literal><![CDATA[
      T(x,(x * y) / z) = T(x,y * (z \ x))
    ]]></literal>
    <justification jstring="[hyper(58,a,8490,a,b,16241,a)].">
      <j1 rule="hyper" parents="58 8490 16241"/>
    </justification>
  </clause>

  <clause id="16244">
    <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(16243(a,1),15080(a,1,1,1,1))].">
      <j1 rule="para" parents="16243 15080"/>
    </justification>
  </clause>

  <clause id="16245">
    <literal><![CDATA[
      K(x / (y \ z),y) = K(x * (z \ y),y)
    ]]></literal>
    <justification jstring="[hyper(15792,a,16242,a),flip(a)].">
      <j1 rule="hyper" parents="15792 16242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16246">
    <literal><![CDATA[
      K(x * (y \ z),z) * ((z * x) / y) = T((z * x) / y,z)
    ]]></literal>
    <justification jstring="[para(16245(a,1),8547(a,1,1))].">
      <j1 rule="para" parents="16245 8547"/>
    </justification>
  </clause>

  <clause id="16247">
    <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(6337(a,1),16084(a,1,2,1,1))].">
      <j1 rule="para" parents="6337 16084"/>
    </justification>
  </clause>

  <clause id="16248">
    <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(15302(a,1),16084(a,1))].">
      <j1 rule="para" parents="15302 16084"/>
    </justification>
  </clause>

  <clause id="16249">
    <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(16150(a,1),16093(a,1))].">
      <j1 rule="para" parents="16150 16093"/>
    </justification>
  </clause>

  <clause id="16250">
    <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(7948(a,1),16095(a,1,2,2,2))].">
      <j1 rule="para" parents="7948 16095"/>
    </justification>
  </clause>

  <clause id="16251">
    <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(13937(a,2),16136(a,1))].">
      <j1 rule="para" parents="13937 16136"/>
    </justification>
  </clause>

  <clause id="16252">
    <literal><![CDATA[
      K(x,(y * z) \ T(u,z * (y * x))) = K(x,u / (y * z))
    ]]></literal>
    <justification jstring="[hyper(16138,a,15400,a)].">
      <j1 rule="hyper" parents="16138 15400"/>
    </justification>
  </clause>

  <clause id="16253">
    <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(16026(a,1),16157(a,1,2,2))].">
      <j1 rule="para" parents="16026 16157"/>
    </justification>
  </clause>

  <clause id="16254">
    <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(6337(a,1),16193(a,1,2,2,2))].">
      <j1 rule="para" parents="6337 16193"/>
    </justification>
  </clause>

  <clause id="16255">
    <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(7438(a,1),16193(a,1,2,2,2))].">
      <j1 rule="para" parents="7438 16193"/>
    </justification>
  </clause>

  <clause id="16256">
    <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(13895(a,1),16193(a,1,2,2,2))].">
      <j1 rule="para" parents="13895 16193"/>
    </justification>
  </clause>

  <clause id="16257">
    <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(7438(a,1),16195(a,1,2,2,2))].">
      <j1 rule="para" parents="7438 16195"/>
    </justification>
  </clause>

  <clause id="16258">
    <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(13895(a,1),16195(a,1,2,2,2))].">
      <j1 rule="para" parents="13895 16195"/>
    </justification>
  </clause>

  <clause id="16259">
    <literal><![CDATA[
      K(x,(y / z) \ K(u,z)) = K(x,T(z,u) / y)
    ]]></literal>
    <justification jstring="[hyper(16199,a,15167,a)].">
      <j1 rule="hyper" parents="16199 15167"/>
    </justification>
  </clause>

  <clause id="16260">
    <literal><![CDATA[
      K(x,(y / z) \ K(z,u)) = K(x,T(z,u) / y)
    ]]></literal>
    <justification jstring="[hyper(15278,a,16259,a)].">
      <j1 rule="hyper" parents="15278 16259"/>
    </justification>
  </clause>

  <clause id="16261">
    <literal><![CDATA[
      K(x,(y / z) \ K(z,u \ w)) = K(x,T(z,w / u) / y)
    ]]></literal>
    <justification jstring="[hyper(16192,a,16260,a)].">
      <j1 rule="hyper" parents="16192 16260"/>
    </justification>
  </clause>

  <clause id="16262">
    <literal><![CDATA[
      K(x,T(y,y / z) / u) = K(x,(u / y) \ K(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,15512,a(flip),b,16261,a),flip(a)].">
      <j1 rule="hyper" parents="58 15512 16261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16263">
    <literal><![CDATA[
      K(x,T(y,y / z) / u) = K(x,T(y,z) / u)
    ]]></literal>
    <justification jstring="[hyper(320,a,16260,a(flip),b,16262,a),flip(a)].">
      <j1 rule="hyper" parents="320 16260 16262"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16264">
    <literal><![CDATA[
      K(x,T(((y / z) * u) \ y,u)) = K(x,T(y,z) / (u * (y / z)))
    ]]></literal>
    <justification jstring="[hyper(14877,a,16263,a)].">
      <j1 rule="hyper" parents="14877 16263"/>
    </justification>
  </clause>

  <clause id="16265">
    <literal><![CDATA[
      K(x,T(y,z \ y) / u) = K(x,T(y,z) / u)
    ]]></literal>
    <justification jstring="[hyper(58,a,16071,a(flip),b,16263,a)].">
      <j1 rule="hyper" parents="58 16071 16263"/>
    </justification>
  </clause>

  <clause id="16266">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ y)) / w) = K(x,T(y,u * z) / w)
    ]]></literal>
    <justification jstring="[para(13993(a,1),16265(a,1,2,1))].">
      <j1 rule="para" parents="13993 16265"/>
    </justification>
  </clause>

  <clause id="16267">
    <literal><![CDATA[
      K(x,T(y,z \ (y / u)) / w) = K(x,T(y,u * z) / w)
    ]]></literal>
    <justification jstring="[para(10710(a,2),16266(a,1,2,1))].">
      <j1 rule="para" parents="10710 16266"/>
    </justification>
  </clause>

  <clause id="16268">
    <literal><![CDATA[
      K(x,T(y,z * u) / ((y / z) / u)) = K(x,((y / z) / u) \ y)
    ]]></literal>
    <justification jstring="[hyper(16160,a,16267,a),flip(a)].">
      <j1 rule="hyper" parents="16160 16267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16269">
    <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(16235,a,15094,a)].">
      <j1 rule="hyper" parents="16235 15094"/>
    </justification>
  </clause>

  <clause id="16270">
    <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),16236(a,1,2,1,1))].">
      <j1 rule="para" parents="17 16236"/>
    </justification>
  </clause>

  <clause id="16271">
    <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),16237(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="6 16237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16272">
    <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(8012(a,2),16237(a,1,2))].">
      <j1 rule="para" parents="8012 16237"/>
    </justification>
  </clause>

  <clause id="16273">
    <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(16044(a,2),16251(a,1))].">
      <j1 rule="para" parents="16044 16251"/>
    </justification>
  </clause>

  <clause id="16274">
    <literal><![CDATA[
      K(x,K(y * z,y * (u * z))) = K(x,K(y * z,L(u,z,y)))
    ]]></literal>
    <justification jstring="[hyper(13100,a,16271,a)].">
      <j1 rule="hyper" parents="13100 16271"/>
    </justification>
  </clause>

  <clause id="16275">
    <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(16274(a,1),8393(a,1,1))].">
      <j1 rule="para" parents="16274 8393"/>
    </justification>
  </clause>

  <clause id="16276">
    <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,1546,a,b,15741,a)].">
      <j1 rule="hyper" parents="320 1546 15741"/>
    </justification>
  </clause>

  <clause id="16279">
    <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(5691(a,1),15757(a,2,2))].">
      <j1 rule="para" parents="5691 15757"/>
    </justification>
  </clause>

  <clause id="16280">
    <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,10925,a(flip),b,16279,a),flip(a)].">
      <j1 rule="hyper" parents="320 10925 16279"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16281">
    <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(16280(a,2),10848(a,1))].">
      <j1 rule="para" parents="16280 10848"/>
    </justification>
  </clause>

  <clause id="16282">
    <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(15781(a,1),15067(a,1,1))].">
      <j1 rule="para" parents="15781 15067"/>
    </justification>
  </clause>

  <clause id="16284">
    <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(15915(a,1),15218(a,1,2,2))].">
      <j1 rule="para" parents="15915 15218"/>
    </justification>
  </clause>

  <clause id="16285">
    <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(15971(a,1),15109(a,1,1,2,1))].">
      <j1 rule="para" parents="15971 15109"/>
    </justification>
  </clause>

  <clause id="16286">
    <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(15846(a,1),15977(a,1,1,1))].">
      <j1 rule="para" parents="15846 15977"/>
    </justification>
  </clause>

  <clause id="16287">
    <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,13752,a,b,16149,a)].">
      <j1 rule="hyper" parents="58 13752 16149"/>
    </justification>
  </clause>

  <clause id="16288">
    <literal><![CDATA[
      K(x * (((y * z) / y) \ u),w) = K(x * (K(z,y) * (z \ u)),w)
    ]]></literal>
    <justification jstring="[hyper(320,a,16054,a,b,16155,a),flip(a)].">
      <j1 rule="hyper" parents="320 16054 16155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16289">
    <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(16173(a,1),15291(a,1))].">
      <j1 rule="para" parents="16173 15291"/>
    </justification>
  </clause>

  <clause id="16290">
    <literal><![CDATA[
      K(x,y * (z / (u / (u / w)))) = K(x,y * (z / T(w,u)))
    ]]></literal>
    <justification jstring="[hyper(320,a,16151,a(flip),b,16229,a),flip(a)].">
      <j1 rule="hyper" parents="320 16151 16229"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16291">
    <literal><![CDATA[
      K(x,y * (z / T(u,u \ w))) = K(x,y * (z / T(u,w)))
    ]]></literal>
    <justification jstring="[hyper(58,a,15434,a,b,16290,a)].">
      <j1 rule="hyper" parents="58 15434 16290"/>
    </justification>
  </clause>

  <clause id="16292">
    <literal><![CDATA[
      K(x,y * (z / ((u \ w) \ w))) = K(x,y * (z / T(u,w)))
    ]]></literal>
    <justification jstring="[hyper(58,a,16169,a(flip),b,16291,a)].">
      <j1 rule="hyper" parents="58 16169 16291"/>
    </justification>
  </clause>

  <clause id="16293">
    <literal><![CDATA[
      T(x,y * (z / ((u \ w) \ w))) = T(x,y * (z / T(u,w)))
    ]]></literal>
    <justification jstring="[hyper(118,a,16292,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 16292 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16294">
    <literal><![CDATA[
      K(x,y * (z * (u * (w / u)))) = K(x,y * (z * T(w,u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,16182,a(flip),b,16230,a),flip(a)].">
      <j1 rule="hyper" parents="58 16182 16230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16295">
    <literal><![CDATA[
      K(x,y * (z * T(u * w,w))) = K(x,y * (z * (w * u)))
    ]]></literal>
    <justification jstring="[para(6(a,1),16294(a,1,2,2,2,2)),flip(a)].">
      <j1 rule="para" parents="6 16294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16296">
    <literal><![CDATA[
      K(x,y * ((z * u) * u)) = K(x,y * (u * (u * z)))
    ]]></literal>
    <justification jstring="[para(105(a,1),16295(a,1,2,2))].">
      <j1 rule="para" parents="105 16295"/>
    </justification>
  </clause>

  <clause id="16297">
    <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(7525(a,2),16296(a,2,2,2,2))].">
      <j1 rule="para" parents="7525 16296"/>
    </justification>
  </clause>

  <clause id="16298">
    <literal><![CDATA[
      T(x,y) * K(x / T(y,x),z) = T(x * K(x / y,z),y)
    ]]></literal>
    <justification jstring="[para(7975(a,1),16276(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7975 16276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16299">
    <literal><![CDATA[
      T(x * K(x / y,z),y) = T(x,y) * K(y \ x,z)
    ]]></literal>
    <justification jstring="[para(12722(a,1),16298(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12722 16298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16300">
    <literal><![CDATA[
      T(x * K(x / y,z),y) = K(x / y,z) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,15817,a(flip),b,16299,a),flip(a)].">
      <j1 rule="hyper" parents="320 15817 16299"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16301">
    <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(5130(a,1),15726(a,1,2,1))].">
      <j1 rule="para" parents="5130 15726"/>
    </justification>
  </clause>

  <clause id="16302">
    <literal><![CDATA[
      K(x,y * (z * K(u \ 1,w))) = K(x,y * (z * K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(58,a,15828,a(flip),b,15920,a),flip(a)].">
      <j1 rule="hyper" parents="58 15828 15920"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16303">
    <literal><![CDATA[
      K(x,y * (((z * (u \ 1)) / z) \ 1)) = K(x,y * (u * K(u,z)))
    ]]></literal>
    <justification jstring="[hyper(58,a,7731,a,b,16302,a)].">
      <j1 rule="hyper" parents="58 7731 16302"/>
    </justification>
  </clause>

  <clause id="16304">
    <literal><![CDATA[
      K(x,y * (((z * (u \ 1)) / z) \ 1)) = K(x,y * T(u,z))
    ]]></literal>
    <justification jstring="[para(4755(a,2),16303(a,2,2,2))].">
      <j1 rule="para" parents="4755 16303"/>
    </justification>
  </clause>

  <clause id="16305">
    <literal><![CDATA[
      K(x,y / ((z * (u \ 1)) / z)) = K(x,y * T(u,z))
    ]]></literal>
    <justification jstring="[hyper(14057,a,16304,a)].">
      <j1 rule="hyper" parents="14057 16304"/>
    </justification>
  </clause>

  <clause id="16306">
    <literal><![CDATA[
      K(x,y / T(z \ 1,u)) = K(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[hyper(15997,a,16305,a)].">
      <j1 rule="hyper" parents="15997 16305"/>
    </justification>
  </clause>

  <clause id="16307">
    <literal><![CDATA[
      K(x,y * T(z,z * (x * y))) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(14071,a,16306,a),flip(a)].">
      <j1 rule="hyper" parents="14071 16306"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16308">
    <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(10870,a,16306,a)].">
      <j1 rule="hyper" parents="10870 16306"/>
    </justification>
  </clause>

  <clause id="16309">
    <literal><![CDATA[
      T(x,y / T(z \ 1,u)) = T(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[hyper(118,a,16306,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 16306 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16310">
    <literal><![CDATA[
      K(x,y / T(1 / z,u)) = K(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,5331,a,b,16306,a)].">
      <j1 rule="hyper" parents="58 5331 16306"/>
    </justification>
  </clause>

  <clause id="16311">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ 1)) * T(z,u)) = K(x,T(z * y,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,16208,a(flip),b,16306,a),flip(a)].">
      <j1 rule="hyper" parents="58 16208 16306"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16312">
    <literal><![CDATA[
      K(x,y * T(1 / z,u)) = K(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[para(75(a,1),16306(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="75 16306"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16313">
    <literal><![CDATA[
      K(x,y * T(z,x * y)) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(13181,a,16307,a)].">
      <j1 rule="hyper" parents="13181 16307"/>
    </justification>
  </clause>

  <clause id="16314">
    <literal><![CDATA[
      T(x,y * T(z,x * y)) = T(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(118,a,16313,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 16313 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16315">
    <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,15105,a,b,16314,a)].">
      <j1 rule="hyper" parents="58 15105 16314"/>
    </justification>
  </clause>

  <clause id="16316">
    <literal><![CDATA[
      T(x,y / T(1 / z,u)) = T(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,3816,a,b,16309,a)].">
      <j1 rule="hyper" parents="58 3816 16309"/>
    </justification>
  </clause>

  <clause id="16317">
    <literal><![CDATA[
      T(x,y / T(z * K(u,w),v5)) = T(x,y * T(K(w,u) / z,v5))
    ]]></literal>
    <justification jstring="[para(13928(a,1),16309(a,1,2,2,1))].">
      <j1 rule="para" parents="13928 16309"/>
    </justification>
  </clause>

  <clause id="16318">
    <literal><![CDATA[
      K(x,y * T(z \ 1,u)) = K(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[para(72(a,1),16310(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="72 16310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16319">
    <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,15555,a(flip),b,16312,a),flip(a)].">
      <j1 rule="hyper" parents="58 15555 16312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16320">
    <literal><![CDATA[
      T(x,y / T(K(z,u) * w,v5)) = T(x,y * T(w \ K(u,z),v5))
    ]]></literal>
    <justification jstring="[para(13818(a,1),16316(a,1,2,2,1))].">
      <j1 rule="para" parents="13818 16316"/>
    </justification>
  </clause>

  <clause id="16321">
    <literal><![CDATA[
      K(x,y / (z / T(u,z))) = K(x,y / T(z / u,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,16234,a(flip),b,16318,a)].">
      <j1 rule="hyper" parents="58 16234 16318"/>
    </justification>
  </clause>

  <clause id="16322">
    <literal><![CDATA[
      K(x,y / (z / T(u,z))) = K(x,y / (u \ z))
    ]]></literal>
    <justification jstring="[hyper(320,a,13045,a(flip),b,16321,a),flip(a)].">
      <j1 rule="hyper" parents="320 13045 16321"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16323">
    <literal><![CDATA[
      K(x,y / (T(z,u) / u)) = K(x,y / (u \ z))
    ]]></literal>
    <justification jstring="[hyper(58,a,8791,a,b,16322,a)].">
      <j1 rule="hyper" parents="58 8791 16322"/>
    </justification>
  </clause>

  <clause id="16324">
    <literal><![CDATA[
      K(x,T(y,z * u) * T(u,z)) = K(x,T(u * y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,15392,a(flip),b,16311,a)].">
      <j1 rule="hyper" parents="58 15392 16311"/>
    </justification>
  </clause>

  <clause id="16325">
    <literal><![CDATA[
      K(x,T(y * ((z * y) \ u),z)) = K(x,(u / (y * z)) * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,15288,a(flip),b,16324,a),flip(a)].">
      <j1 rule="hyper" parents="58 15288 16324"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16326">
    <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(5846(a,1),16324(a,1,2,1))].">
      <j1 rule="para" parents="5846 16324"/>
    </justification>
  </clause>

  <clause id="16327">
    <literal><![CDATA[
      K(x,y * ((z * y) \ T(u,z))) = K(x,(u / (y * z)) * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,15442,a(flip),b,16325,a)].">
      <j1 rule="hyper" parents="58 15442 16325"/>
    </justification>
  </clause>

  <clause id="16328">
    <literal><![CDATA[
      K(x,y * ((T(z,u) * y) \ u)) = K(x,(u / (y * z)) * y)
    ]]></literal>
    <justification jstring="[para(13715(a,2),16327(a,1,2,2))].">
      <j1 rule="para" parents="13715 16327"/>
    </justification>
  </clause>

  <clause id="16329">
    <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,10840,a(flip),b,16308,a),flip(a)].">
      <j1 rule="hyper" parents="320 10840 16308"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16330">
    <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,16047,a(flip),b,16317,a),flip(a)].">
      <j1 rule="hyper" parents="320 16047 16317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16331">
    <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(14190,a,16329,a)].">
      <j1 rule="hyper" parents="14190 16329"/>
    </justification>
  </clause>

  <clause id="16332">
    <literal><![CDATA[
      T(x,((y \ z) * y) * K(u,w)) = T(x,T(K(u,w) * z,y))
    ]]></literal>
    <justification jstring="[hyper(15939,a,16189,a(flip))].">
      <j1 rule="hyper" parents="15939 16189"/>
    </justification>
  </clause>

  <clause id="16333">
    <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,6286,a(flip),b,15943,a)].">
      <j1 rule="hyper" parents="320 6286 15943"/>
    </justification>
  </clause>

  <clause id="16334">
    <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),16333(a,1,1,1))].">
      <j1 rule="para" parents="4 16333"/>
    </justification>
  </clause>

  <clause id="16335">
    <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(16224(a,1),16133(a,1))].">
      <j1 rule="para" parents="16224 16133"/>
    </justification>
  </clause>

  <clause id="16336">
    <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(16150(a,1),16134(a,1))].">
      <j1 rule="para" parents="16150 16134"/>
    </justification>
  </clause>

  <clause id="16337">
    <literal><![CDATA[
      T(L(K(x,y),z / u,u),z / u) = z \ (u * (K(x,y) * (u \ z)))
    ]]></literal>
    <justification jstring="[para(11189(a,2),16214(a,1,1))].">
      <j1 rule="para" parents="11189 16214"/>
    </justification>
  </clause>

  <clause id="16338">
    <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(7942(a,1),16233(a,1,2,2,2))].">
      <j1 rule="para" parents="7942 16233"/>
    </justification>
  </clause>

  <clause id="16339">
    <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(16294(a,2),16233(a,1))].">
      <j1 rule="para" parents="16294 16233"/>
    </justification>
  </clause>

  <clause id="16340">
    <literal><![CDATA[
      K(x,y * (T(z,u \ 1) \ T(z / u,z))) = K(x,y * (z \ (z / u)))
    ]]></literal>
    <justification jstring="[hyper(16255,a,15265,a)].">
      <j1 rule="hyper" parents="16255 15265"/>
    </justification>
  </clause>

  <clause id="16341">
    <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(13988(a,1),16255(a,1,2,2))].">
      <j1 rule="para" parents="13988 16255"/>
    </justification>
  </clause>

  <clause id="16342">
    <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,14764,a(flip),b,16301,a)].">
      <j1 rule="hyper" parents="58 14764 16301"/>
    </justification>
  </clause>

  <clause id="16343">
    <literal><![CDATA[
      L(K(x,y),z,u / (u * x)) = K(1 / ((u * x) \ u),y)
    ]]></literal>
    <justification jstring="[hyper(320,a,15656,a(flip),b,16334,a),flip(a)].">
      <j1 rule="hyper" parents="320 15656 16334"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16344">
    <literal><![CDATA[
      L(K(x,y),z,u / (u * x)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = w
    ]]></literal>
    <justification jstring="[para(16343(a,2),6304(a,1))].">
      <j1 rule="para" parents="16343 6304"/>
    </justification>
  </clause>

  <clause id="16345">
    <literal><![CDATA[
      K((x * (y / x)) / z,u) = K(z,K(y,u)) * K(z \ T(y,x),u)
    ]]></literal>
    <justification jstring="[para(15210(a,1),15760(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15210 15760"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16347">
    <literal><![CDATA[
      K((x * (y / x)) / z,u) = K(T(y,x) / z,u)
    ]]></literal>
    <justification jstring="[hyper(320,a,15766,a(flip),b,16345,a),flip(a)].">
      <j1 rule="hyper" parents="320 15766 16345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16348">
    <literal><![CDATA[
      K(T(x * y,y) / z,u) = K((y * x) / z,u)
    ]]></literal>
    <justification jstring="[para(6(a,1),16347(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6 16347"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16349">
    <literal><![CDATA[
      K(x,T(y * z,z) / u) = (w * K((z * y) / u,x)) \ w
    ]]></literal>
    <justification jstring="[para(16348(a,1),6338(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="16348 6338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16350">
    <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(14122(a,1),16348(a,2,1,1))].">
      <j1 rule="para" parents="14122 16348"/>
    </justification>
  </clause>

  <clause id="16351">
    <literal><![CDATA[
      K(x,T(y * z,z) / u) = K(x,(z * y) / u)
    ]]></literal>
    <justification jstring="[hyper(320,a,15662,a(flip),b,16349,a),flip(a)].">
      <j1 rule="hyper" parents="320 15662 16349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16352">
    <literal><![CDATA[
      K(x,T(y * z,z) / u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z * y) / u) = w
    ]]></literal>
    <justification jstring="[para(16349(a,2),6345(a,1))].">
      <j1 rule="para" parents="16349 6345"/>
    </justification>
  </clause>

  <clause id="16353">
    <literal><![CDATA[
      K(x,(y * (z / y)) / u) = K(x,T(z,y) / u)
    ]]></literal>
    <justification jstring="[para(7(a,1),16351(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="7 16351"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16354">
    <literal><![CDATA[
      K(x,(y * ((y * z) / y)) / u) = K(x,(z * y) / u)
    ]]></literal>
    <justification jstring="[hyper(320,a,13066,a(flip),b,16353,a),flip(a)].">
      <j1 rule="hyper" parents="320 13066 16353"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16355">
    <literal><![CDATA[
      K(x,T(y,z) / (u * (y / z))) = K(x,y / (u * (z \ y)))
    ]]></literal>
    <justification jstring="[para(14223(a,1),16353(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14223 16353"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16356">
    <literal><![CDATA[
      K(x,(T(y,z) * z) / u) = K(x,(z * y) / u)
    ]]></literal>
    <justification jstring="[para(225(a,1),16354(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="225 16354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16357">
    <literal><![CDATA[
      K(x,L(T(y,z) / u,u,z)) = K(x,(z * y) / (u * z))
    ]]></literal>
    <justification jstring="[hyper(14803,a,16356,a)].">
      <j1 rule="hyper" parents="14803 16356"/>
    </justification>
  </clause>

  <clause id="16358">
    <literal><![CDATA[
      K(x,T(((y / z) * u) \ y,u)) = K(x,y / (u * (z \ y)))
    ]]></literal>
    <justification jstring="[hyper(58,a,16264,a,b,16355,a)].">
      <j1 rule="hyper" parents="58 16264 16355"/>
    </justification>
  </clause>

  <clause id="16359">
    <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,13178,a(flip),b,15831,a),flip(a)].">
      <j1 rule="hyper" parents="58 13178 15831"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16360">
    <literal><![CDATA[
      K(x,T(y / ((z \ u) * z),w)) = K(x,T(y / T(u,z),w))
    ]]></literal>
    <justification jstring="[hyper(320,a,15830,a(flip),b,16359,a),flip(a)].">
      <j1 rule="hyper" parents="320 15830 16359"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16361">
    <literal><![CDATA[
      K(x,T(y / T(z,u),z * u)) = K(x,z \ T(y,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,15576,a(flip),b,16360,a),flip(a)].">
      <j1 rule="hyper" parents="58 15576 16360"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16362">
    <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),15935(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7 15935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16363">
    <literal><![CDATA[
      K(T(x,y) * z,T(u,y * x)) = K(T(z,y) * x,u)
    ]]></literal>
    <justification jstring="[hyper(320,a,13843,a(flip),b,16362,a),flip(a)].">
      <j1 rule="hyper" parents="320 13843 16362"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16365">
    <literal><![CDATA[
      K(x * T(y,z),T(u,z * y)) = K(T(x,z) * y,T(u,y))
    ]]></literal>
    <justification jstring="[hyper(15985,a,16363,a)].">
      <j1 rule="hyper" parents="15985 16363"/>
    </justification>
  </clause>

  <clause id="16366">
    <literal><![CDATA[
      K(x * T(y,z),T(u,z * y)) = K(y * T(x,z),u)
    ]]></literal>
    <justification jstring="[hyper(320,a,12230,a(flip),b,16365,a),flip(a)].">
      <j1 rule="hyper" parents="320 12230 16365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16367">
    <literal><![CDATA[
      K((x * y) * R(z,y,x),u) = K(x * T(z * y,y),u)
    ]]></literal>
    <justification jstring="[hyper(58,a,15625,a(flip),b,16366,a)].">
      <j1 rule="hyper" parents="58 15625 16366"/>
    </justification>
  </clause>

  <clause id="16368">
    <literal><![CDATA[
      K((x * y) * R(z,y,x),u) = K(x * (y * z),u)
    ]]></literal>
    <justification jstring="[hyper(320,a,16215,a(flip),b,16367,a),flip(a)].">
      <j1 rule="hyper" parents="320 16215 16367"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16369">
    <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,16368,a(flip),b,8069,a)].">
      <j1 rule="hyper" parents="116 16368 8069"/>
    </justification>
  </clause>

  <clause id="16370">
    <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),16368(a,1,1,2))].">
      <j1 rule="para" parents="99 16368"/>
    </justification>
  </clause>

  <clause id="16371">
    <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(6503,a,15956,a)].">
      <j1 rule="hyper" parents="6503 15956"/>
    </justification>
  </clause>

  <clause id="16372">
    <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(7160(a,1),16371(a,1,1,2))].">
      <j1 rule="para" parents="7160 16371"/>
    </justification>
  </clause>

  <clause id="16373">
    <literal><![CDATA[
      K(T(x,y) \ K(z,u),w) = K(x \ K(z,u),T(w,y))
    ]]></literal>
    <justification jstring="[hyper(16089,a,16372,a),flip(a)].">
      <j1 rule="hyper" parents="16089 16372"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16375">
    <literal><![CDATA[
      K(T(x,y) \ K(z,u),w) = T(K(x \ K(z,u),w),y)
    ]]></literal>
    <justification jstring="[hyper(320,a,7158,a(flip),b,16373,a),flip(a)].">
      <j1 rule="hyper" parents="320 7158 16373"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16376">
    <literal><![CDATA[
      T(K((x / y) \ K(y,z),u),T(y,x)) = K(x \ T(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(14170,a,16375,a),flip(a)].">
      <j1 rule="hyper" parents="14170 16375"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16378">
    <literal><![CDATA[
      T(K(x \ T(y,z),u),T(y,x)) = K((x / y) \ K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(7884,a,16376,a)].">
      <j1 rule="hyper" parents="7884 16376"/>
    </justification>
  </clause>

  <clause id="16379">
    <literal><![CDATA[
      T(K(x \ T(y,z),u),T(y,w)) = K((x / y) \ K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(15812,a,16378,a)].">
      <j1 rule="hyper" parents="15812 16378"/>
    </justification>
  </clause>

  <clause id="16380">
    <literal><![CDATA[
      K((x / y) \ K(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(T(y,z) / x,u) = w
    ]]></literal>
    <justification jstring="[para(16379(a,1),8057(a,1))].">
      <j1 rule="para" parents="16379 8057"/>
    </justification>
  </clause>

  <clause id="16381">
    <literal><![CDATA[
      K((x / y) \ K(z,y),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(T(y,z) / x,u) = w
    ]]></literal>
    <justification jstring="[para(15191(a,1),16380(a,1))].">
      <j1 rule="para" parents="15191 16380"/>
    </justification>
  </clause>

  <clause id="16382">
    <literal><![CDATA[
      T(T(x,K(y,z)),T(z \ y,u) \ y) = T(x,T(y / z,u) \ y)
    ]]></literal>
    <justification jstring="[para(8172(a,1),15960(a,1,1))].">
      <j1 rule="para" parents="8172 15960"/>
    </justification>
  </clause>

  <clause id="16383">
    <literal><![CDATA[
      T(T(x,K(y,z)),T(y \ z,u) \ z) = T(x,T(z / y,u) \ z)
    ]]></literal>
    <justification jstring="[para(7832(a,1),16382(a,1,1))].">
      <j1 rule="para" parents="7832 16382"/>
    </justification>
  </clause>

  <clause id="16384">
    <literal><![CDATA[
      T(T(x,K(y,z)),y * T(z / y,u)) = T(x,y * T(y \ z,u))
    ]]></literal>
    <justification jstring="[para(8032(a,1),15961(a,1,1))].">
      <j1 rule="para" parents="8032 15961"/>
    </justification>
  </clause>

  <clause id="16385">
    <literal><![CDATA[
      T(T(x,K(y,z)),z * T(y / z,u)) = T(x,z * T(z \ y,u))
    ]]></literal>
    <justification jstring="[para(7832(a,1),16384(a,1,1))].">
      <j1 rule="para" parents="7832 16384"/>
    </justification>
  </clause>

  <clause id="16387">
    <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,10322,a(flip),b,16072,a)].">
      <j1 rule="hyper" parents="58 10322 16072"/>
    </justification>
  </clause>

  <clause id="16388">
    <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(6197(a,2),16170(a,1,2,2))].">
      <j1 rule="para" parents="6197 16170"/>
    </justification>
  </clause>

  <clause id="16389">
    <literal><![CDATA[
      K(x,T(((y / x) / y) * z,y)) = K(x,T(z * ((y / x) / y),y))
    ]]></literal>
    <justification jstring="[hyper(7938,a,16203,a),flip(a)].">
      <j1 rule="hyper" parents="7938 16203"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16390">
    <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,12370,a(flip),b,16211,a),flip(a)].">
      <j1 rule="hyper" parents="320 12370 16211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16391">
    <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(7915(a,1),16213(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7915 16213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16392">
    <literal><![CDATA[
      (x * K(y,z / u)) \ (u \ z) = K(z / u,y) * (x \ (u \ z))
    ]]></literal>
    <justification jstring="[para(7913(a,1),16222(a,1,1,2))].">
      <j1 rule="para" parents="7913 16222"/>
    </justification>
  </clause>

  <clause id="16393">
    <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(16392(a,1),13115(a,1,2,2,1))].">
      <j1 rule="para" parents="16392 13115"/>
    </justification>
  </clause>

  <clause id="16394">
    <literal><![CDATA[
      K(x,(y \ T(z,y \ 1)) / u) = K(x,(((z / y) / z) * z) / u)
    ]]></literal>
    <justification jstring="[hyper(58,a,13066,a(flip),b,16225,a),flip(a)].">
      <j1 rule="hyper" parents="58 13066 16225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16395">
    <literal><![CDATA[
      K(x,(y \ T(z,y \ 1)) / u) = K(x,(z / y) / u)
    ]]></literal>
    <justification jstring="[para(7(a,1),16394(a,2,2,1))].">
      <j1 rule="para" parents="7 16394"/>
    </justification>
  </clause>

  <clause id="16397">
    <literal><![CDATA[
      K(x,y * (T(z,u \ 1) \ (u \ z))) = K(x,y * (z \ (z / u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,13169,a(flip),b,16340,a)].">
      <j1 rule="hyper" parents="58 13169 16340"/>
    </justification>
  </clause>

  <clause id="16398">
    <literal><![CDATA[
      K(x,y * ((z \ u) / u)) = K(x,y * (u \ (u / z)))
    ]]></literal>
    <justification jstring="[hyper(58,a,15251,a(flip),b,16397,a)].">
      <j1 rule="hyper" parents="58 15251 16397"/>
    </justification>
  </clause>

  <clause id="16399">
    <literal><![CDATA[
      K(x,T(y,K(z,u) * w)) = K(x,T(y,w))
    ]]></literal>
    <justification jstring="[hyper(16051,a,16387,a),flip(a)].">
      <j1 rule="hyper" parents="16051 16387"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16400">
    <literal><![CDATA[
      K(x,T(y,K(z,u) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,w)) = v5
    ]]></literal>
    <justification jstring="[para(16387(a,1),16051(a,1))].">
      <j1 rule="para" parents="16387 16051"/>
    </justification>
  </clause>

  <clause id="16402">
    <literal><![CDATA[
      K(x,T(y,z / K(u,w))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(15946,a,16399,a)].">
      <j1 rule="hyper" parents="15946 16399"/>
    </justification>
  </clause>

  <clause id="16403">
    <literal><![CDATA[
      K(x,T(y,z * K(u,w))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(15799,a,16399,a)].">
      <j1 rule="hyper" parents="15799 16399"/>
    </justification>
  </clause>

  <clause id="16407">
    <literal><![CDATA[
      K(x,T(y,K(z,u) * w)) = T(K(x,y),w)
    ]]></literal>
    <justification jstring="[hyper(320,a,7158,a(flip),b,16399,a),flip(a)].">
      <j1 rule="hyper" parents="320 7158 16399"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16408">
    <literal><![CDATA[
      T(x,T(y,K(z,u) * w)) = T(x,T(y,w))
    ]]></literal>
    <justification jstring="[hyper(118,a,16399,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 16399 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16409">
    <literal><![CDATA[
      K(x,T(y,T(z,u) * w)) = K(x,T(y,z * w))
    ]]></literal>
    <justification jstring="[para(4781(a,1),16399(a,1,2,2))].">
      <j1 rule="para" parents="4781 16399"/>
    </justification>
  </clause>

  <clause id="16410">
    <literal><![CDATA[
      K(x,T(y,T(z,u) \ w)) = K(x,T(y,z \ w))
    ]]></literal>
    <justification jstring="[para(5081(a,1),16399(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5081 16399"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16411">
    <literal><![CDATA[
      K(x,T(y,(z / u) * w)) = K(x,T(y,(u \ z) * w))
    ]]></literal>
    <justification jstring="[para(5443(a,1),16399(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5443 16399"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16412">
    <literal><![CDATA[
      K(x,T(y,z \ T(u,w))) = K(x,T(y,z \ u))
    ]]></literal>
    <justification jstring="[para(5408(a,1),16399(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5408 16399"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16413">
    <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(16399(a,1),7184(a,1,2))].">
      <j1 rule="para" parents="16399 7184"/>
    </justification>
  </clause>

  <clause id="16417">
    <literal><![CDATA[
      K(x,T(y,K(z,u) / w)) = K(x,T(y,w))
    ]]></literal>
    <justification jstring="[hyper(8275,a,16402,a)].">
      <j1 rule="hyper" parents="8275 16402"/>
    </justification>
  </clause>

  <clause id="16418">
    <literal><![CDATA[
      T(x,T(y,z / K(u,w))) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(118,a,16402,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 16402 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16419">
    <literal><![CDATA[
      T(K(x,y),z * K(u,w)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(8433,a,16403,a)].">
      <j1 rule="hyper" parents="8433 16403"/>
    </justification>
  </clause>

  <clause id="16423">
    <literal><![CDATA[
      K(x,T(y,z / (u / w))) = K(x,T(y,z / (w \ u)))
    ]]></literal>
    <justification jstring="[para(6221(a,1),16403(a,1,2,2))].">
      <j1 rule="para" parents="6221 16403"/>
    </justification>
  </clause>

  <clause id="16424">
    <literal><![CDATA[
      K(x,T(y,(z * K(u,w)) * v5)) = K(x,T(y,z * v5))
    ]]></literal>
    <justification jstring="[para(6818(a,1),16403(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6818 16403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16425">
    <literal><![CDATA[
      K(x,T(y,z)) * (z * K(u,w)) = (z * K(u,w)) * K(x,y)
    ]]></literal>
    <justification jstring="[para(16403(a,1),7897(a,1,1))].">
      <j1 rule="para" parents="16403 7897"/>
    </justification>
  </clause>

  <clause id="16429">
    <literal><![CDATA[
      K(x,T(y,z \ (u / w))) = K(x,T(y,z \ (w \ u)))
    ]]></literal>
    <justification jstring="[para(13963(a,1),16403(a,1,2,2))].">
      <j1 rule="para" parents="13963 16403"/>
    </justification>
  </clause>

  <clause id="16430">
    <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(16403(a,1),14775(a,1))].">
      <j1 rule="para" parents="16403 14775"/>
    </justification>
  </clause>

  <clause id="16431">
    <literal><![CDATA[
      K(x,T(y,K(z,u) \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,w)) = v5
    ]]></literal>
    <justification jstring="[para(16403(a,1),15898(a,1))].">
      <j1 rule="para" parents="16403 15898"/>
    </justification>
  </clause>

  <clause id="16432">
    <literal><![CDATA[
      T(K(x,y),K(z,u) * w) = T(K(x,y),w)
    ]]></literal>
    <justification jstring="[hyper(8433,a,16407,a)].">
      <j1 rule="hyper" parents="8433 16407"/>
    </justification>
  </clause>

  <clause id="16433">
    <literal><![CDATA[
      T(x,T(y,K(z,u) \ w)) = T(x,T(y,w))
    ]]></literal>
    <justification jstring="[para(5(a,1),16408(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5 16408"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16434">
    <literal><![CDATA[
      T(x,T(y,T(z,u) * w)) = T(x,T(y,z * w))
    ]]></literal>
    <justification jstring="[para(4781(a,1),16408(a,1,2,2))].">
      <j1 rule="para" parents="4781 16408"/>
    </justification>
  </clause>

  <clause id="16435">
    <literal><![CDATA[
      T(x,T(y,(z * u) * w)) = T(x,T(y,(u * z) * w))
    ]]></literal>
    <justification jstring="[para(11157(a,1),16408(a,1,2,2))].">
      <j1 rule="para" parents="11157 16408"/>
    </justification>
  </clause>

  <clause id="16436">
    <literal><![CDATA[
      T(x,T(y,(T(z,u) * w) * v5)) = T(x,T(y,(z * w) * v5))
    ]]></literal>
    <justification jstring="[para(14833(a,1),16408(a,1,2,2))].">
      <j1 rule="para" parents="14833 16408"/>
    </justification>
  </clause>

  <clause id="16437">
    <literal><![CDATA[
      K(x,T(y,z)) * (K(u,w) / z) = (K(u,w) / z) * K(x,y)
    ]]></literal>
    <justification jstring="[para(16417(a,1),7897(a,1,1))].">
      <j1 rule="para" parents="16417 7897"/>
    </justification>
  </clause>

  <clause id="16438">
    <literal><![CDATA[
      K(x,K(y,z / K(u,w))) = (x \ y) / T(y / x,T(x,z))
    ]]></literal>
    <justification jstring="[para(16418(a,1),14894(a,1,2)),flip(a)].">
      <j1 rule="para" parents="16418 14894"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16439">
    <literal><![CDATA[
      T(K(x,y),z * K(u,w)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(320,a,7158,a(flip),b,16419,a),flip(a)].">
      <j1 rule="hyper" parents="320 7158 16419"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16441">
    <literal><![CDATA[
      (K(x,T(y,z)) * z) * K(x,y) = (x * y) * ((y * x) \ (K(x,y) * z))
    ]]></literal>
    <justification jstring="[para(16419(a,1),11209(a,1,1,1))].">
      <j1 rule="para" parents="16419 11209"/>
    </justification>
  </clause>

  <clause id="16443">
    <literal><![CDATA[
      (K(x,T(y,z)) * u) \ (z * K(x,y)) = (K(x,y) * u) \ (K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(16419(a,1),13976(a,1,1,1))].">
      <j1 rule="para" parents="16419 13976"/>
    </justification>
  </clause>

  <clause id="16444">
    <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(16419(a,1),14748(a,1,2,2))].">
      <j1 rule="para" parents="16419 14748"/>
    </justification>
  </clause>

  <clause id="16447">
    <literal><![CDATA[
      T(K(x,y),K(z,u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,w)) = v5
    ]]></literal>
    <justification jstring="[para(16432(a,2),7708(a,1))].">
      <j1 rule="para" parents="16432 7708"/>
    </justification>
  </clause>

  <clause id="16449">
    <literal><![CDATA[
      T(x,T((K(y,z) \ u) \ w,u)) = T(x,w / (K(y,z) \ u))
    ]]></literal>
    <justification jstring="[hyper(58,a,7942,a(flip),b,16433,a),flip(a)].">
      <j1 rule="hyper" parents="58 7942 16433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16452">
    <literal><![CDATA[
      T(K(x,y),z * K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = v5
    ]]></literal>
    <justification jstring="[para(16439(a,2),7708(a,1))].">
      <j1 rule="para" parents="16439 7708"/>
    </justification>
  </clause>

  <clause id="16455">
    <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(16410(a,1),12239(a,1))].">
      <j1 rule="para" parents="16410 12239"/>
    </justification>
  </clause>

  <clause id="16456">
    <literal><![CDATA[
      K(x,T(y,z \ (u / (u / w)))) = K(x,T(y,z \ w))
    ]]></literal>
    <justification jstring="[para(244(a,1),16412(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="244 16412"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16457">
    <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(1587(a,1),16400(a,1,2,2))].">
      <j1 rule="para" parents="1587 16400"/>
    </justification>
  </clause>

  <clause id="16458">
    <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(4781(a,1),16400(a,1,2,2))].">
      <j1 rule="para" parents="4781 16400"/>
    </justification>
  </clause>

  <clause id="16459">
    <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(5555(a,1),16400(a,1,2,2))].">
      <j1 rule="para" parents="5555 16400"/>
    </justification>
  </clause>

  <clause id="16460">
    <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(5553(a,1),16400(a,1,2,2))].">
      <j1 rule="para" parents="5553 16400"/>
    </justification>
  </clause>

  <clause id="16461">
    <literal><![CDATA[
      K(x,T(y,z * K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = v5
    ]]></literal>
    <justification jstring="[para(7288(a,1),16400(a,1,2,2))].">
      <j1 rule="para" parents="7288 16400"/>
    </justification>
  </clause>

  <clause id="16462">
    <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(11157(a,1),16400(a,1,2,2))].">
      <j1 rule="para" parents="11157 16400"/>
    </justification>
  </clause>

  <clause id="16463">
    <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(12230(a,1),16400(a,1))].">
      <j1 rule="para" parents="12230 16400"/>
    </justification>
  </clause>

  <clause id="16464">
    <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(6221(a,1),16461(a,1,2,2))].">
      <j1 rule="para" parents="6221 16461"/>
    </justification>
  </clause>

  <clause id="16465">
    <literal><![CDATA[
      K(x,y) * K(x,K(y,z / (u / w))) = K(x,T(y,z / (w \ u)))
    ]]></literal>
    <justification jstring="[hyper(8075,a,16423,a)].">
      <j1 rule="hyper" parents="8075 16423"/>
    </justification>
  </clause>

  <clause id="16466">
    <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,16425,a(flip),b,9838,a),flip(a)].">
      <j1 rule="hyper" parents="239 16425 9838"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16467">
    <literal><![CDATA[
      K(x,y) * ((1 / y) * K(z,u)) = ((1 / y) * K(z,u)) * K(x,y)
    ]]></literal>
    <justification jstring="[para(3560(a,1),16425(a,1,1))].">
      <j1 rule="para" parents="3560 16425"/>
    </justification>
  </clause>

  <clause id="16468">
    <literal><![CDATA[
      T(x,T(y,(z * T(u,w)) * v5)) = T(x,T(y,(u * z) * v5))
    ]]></literal>
    <justification jstring="[hyper(58,a,16435,a,b,16436,a)].">
      <j1 rule="hyper" parents="58 16435 16436"/>
    </justification>
  </clause>

  <clause id="16469">
    <literal><![CDATA[
      K(x,T(y,z)) / T(z,u) = (K(u,z) / z) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(14047,a,16437,a)].">
      <j1 rule="hyper" parents="14047 16437"/>
    </justification>
  </clause>

  <clause id="16470">
    <literal><![CDATA[
      ((1 / x) * K(y,z)) * K(u,x) = (K(u,x) / x) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,13992,a,b,16469,a)].">
      <j1 rule="hyper" parents="58 13992 16469"/>
    </justification>
  </clause>

  <clause id="16471">
    <literal><![CDATA[
      K(x,K(y,z / K(u,w))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,14894,a(flip),b,16438,a),flip(a)].">
      <j1 rule="hyper" parents="320 14894 16438"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16472">
    <literal><![CDATA[
      K(x,K(y,K(z,u) \ w)) = K(x,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(15617,a,16471,a)].">
      <j1 rule="hyper" parents="15617 16471"/>
    </justification>
  </clause>

  <clause id="16473">
    <literal><![CDATA[
      K(x,K(y,z \ K(u,w))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(15615,a,16471,a)].">
      <j1 rule="hyper" parents="15615 16471"/>
    </justification>
  </clause>

  <clause id="16474">
    <literal><![CDATA[
      K(x,K(y,K(z,u) / w)) = K(x,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(8268,a,16471,a)].">
      <j1 rule="hyper" parents="8268 16471"/>
    </justification>
  </clause>

  <clause id="16475">
    <literal><![CDATA[
      K(x,K(y,z * K(u,w))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(6(a,1),16471(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6 16471"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16476">
    <literal><![CDATA[
      K(x,K(y,z / T(u,w))) = K(x,K(y,z / u))
    ]]></literal>
    <justification jstring="[para(6326(a,1),16471(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6326 16471"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16477">
    <literal><![CDATA[
      K(x,K(y,K(z,u) * w)) = K(x,K(y,w))
    ]]></literal>
    <justification jstring="[para(7285(a,1),16471(a,1,2,2))].">
      <j1 rule="para" parents="7285 16471"/>
    </justification>
  </clause>

  <clause id="16480">
    <literal><![CDATA[
      K(x,K(y,(z * u) * w)) = K(x,K(y,(u * z) * w))
    ]]></literal>
    <justification jstring="[para(11158(a,1),16472(a,1,2,2))].">
      <j1 rule="para" parents="11158 16472"/>
    </justification>
  </clause>

  <clause id="16481">
    <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(16472(a,1),15968(a,1,1)),flip(a)].">
      <j1 rule="para" parents="16472 15968"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16482">
    <literal><![CDATA[
      T(x,K(y,z \ K(u,w))) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(118,a,16473,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 16473 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16483">
    <literal><![CDATA[
      K(x,K(y,K(z,u) / w)) = K(x,K(w,y))
    ]]></literal>
    <justification jstring="[hyper(320,a,7797,a,b,16474,a),flip(a)].">
      <j1 rule="hyper" parents="320 7797 16474"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16485">
    <literal><![CDATA[
      T(x,K(y,z * K(u,w))) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(118,a,16475,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 16475 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16487">
    <literal><![CDATA[
      K(x,K(y,z / ((u * w) / u))) = K(x,K(y,z / w))
    ]]></literal>
    <justification jstring="[para(6093(a,1),16475(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6093 16475"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16488">
    <literal><![CDATA[
      K(x,K(y,z / (u / w))) = K(x,K(y,z / (w \ u)))
    ]]></literal>
    <justification jstring="[para(6221(a,1),16475(a,1,2,2))].">
      <j1 rule="para" parents="6221 16475"/>
    </justification>
  </clause>

  <clause id="16489">
    <literal><![CDATA[
      K(x,K(y,z / (u / (u / w)))) = K(x,K(y,z / w))
    ]]></literal>
    <justification jstring="[para(6472(a,2),16475(a,1,2,2))].">
      <j1 rule="para" parents="6472 16475"/>
    </justification>
  </clause>

  <clause id="16490">
    <literal><![CDATA[
      K(x,K(y,(z * K(u,w)) * v5)) = K(x,K(y,z * v5))
    ]]></literal>
    <justification jstring="[para(6818(a,1),16475(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6818 16475"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16491">
    <literal><![CDATA[
      K(x,K(y,z / (u * w))) = K(x,K(y,z / (w * u)))
    ]]></literal>
    <justification jstring="[para(10644(a,1),16475(a,1,2,2))].">
      <j1 rule="para" parents="10644 16475"/>
    </justification>
  </clause>

  <clause id="16492">
    <literal><![CDATA[
      K(x,K(y,z \ (u / w))) = K(x,K(y,z \ (w \ u)))
    ]]></literal>
    <justification jstring="[para(13963(a,1),16475(a,1,2,2))].">
      <j1 rule="para" parents="13963 16475"/>
    </justification>
  </clause>

  <clause id="16493">
    <literal><![CDATA[
      T(x,K(y,K(z,u) * w)) = T(x,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(118,a,16477,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 16477 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16494">
    <literal><![CDATA[
      K(x,K(y,((z * u) / z) * w)) = K(x,K(y,u * w))
    ]]></literal>
    <justification jstring="[para(5371(a,1),16477(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5371 16477"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16496">
    <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(16477(a,1),12331(a,1,1))].">
      <j1 rule="para" parents="16477 12331"/>
    </justification>
  </clause>

  <clause id="16497">
    <literal><![CDATA[
      K(x,K(y,(z * u) / w)) = K(x,K(y,(u * z) / w))
    ]]></literal>
    <justification jstring="[para(14031(a,1),16477(a,1,2,2))].">
      <j1 rule="para" parents="14031 16477"/>
    </justification>
  </clause>

  <clause id="16498">
    <literal><![CDATA[
      K(x,K(y,(T(z,u) * w) * v5)) = K(x,K(y,(z * w) * v5))
    ]]></literal>
    <justification jstring="[para(14833(a,1),16477(a,1,2,2))].">
      <j1 rule="para" parents="14833 16477"/>
    </justification>
  </clause>

  <clause id="16499">
    <literal><![CDATA[
      K(x,K(y,(K(z,u) * w) / v5)) = K(x,K(y,w / v5))
    ]]></literal>
    <justification jstring="[para(14845(a,1),16477(a,1,2,2))].">
      <j1 rule="para" parents="14845 16477"/>
    </justification>
  </clause>

  <clause id="16500">
    <literal><![CDATA[
      T(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,K(w,v5) * z)) = u
    ]]></literal>
    <justification jstring="[para(16482(a,1),15591(a,1))].">
      <j1 rule="para" parents="16482 15591"/>
    </justification>
  </clause>

  <clause id="16501">
    <literal><![CDATA[
      K(x,K(y * K(z,u),w)) = K(x,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(8217,a,16483,a),flip(a)].">
      <j1 rule="hyper" parents="8217 16483"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16502">
    <literal><![CDATA[
      K(x,K(K(y,z) / u,w)) = K(x,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(7831,a,16483,a)].">
      <j1 rule="hyper" parents="7831 16483"/>
    </justification>
  </clause>

  <clause id="16503">
    <literal><![CDATA[
      K(x,K(y * K(z,u),w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,w)) = v5
    ]]></literal>
    <justification jstring="[para(16483(a,1),8217(a,1))].">
      <j1 rule="para" parents="16483 8217"/>
    </justification>
  </clause>

  <clause id="16504">
    <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(10840(a,1),16483(a,1,2))].">
      <j1 rule="para" parents="10840 16483"/>
    </justification>
  </clause>

  <clause id="16506">
    <literal><![CDATA[
      T(x,K(y,z * (u * K(w,v5)))) = T(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[para(10815(a,1),16485(a,1,2,2))].">
      <j1 rule="para" parents="10815 16485"/>
    </justification>
  </clause>

  <clause id="16507">
    <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(16485(a,1),15103(a,1,2,1,2))].">
      <j1 rule="para" parents="16485 15103"/>
    </justification>
  </clause>

  <clause id="16508">
    <literal><![CDATA[
      T(x,K(y,z \ K(u,w))) = T(x,K(y,K(v5,v6) * z))
    ]]></literal>
    <justification jstring="[hyper(320,a,16482,a,b,16493,a)].">
      <j1 rule="hyper" parents="320 16482 16493"/>
    </justification>
  </clause>

  <clause id="16509">
    <literal><![CDATA[
      T(x,K(y,K(z,u) * w)) = T(x,K(w,y))
    ]]></literal>
    <justification jstring="[hyper(320,a,7832,a,b,16493,a),flip(a)].">
      <j1 rule="hyper" parents="320 7832 16493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16510">
    <literal><![CDATA[
      T(x,K(y,(z / u) \ w)) = T(x,K(y,(u \ z) \ w))
    ]]></literal>
    <justification jstring="[para(5399(a,1),16493(a,1,2,2))].">
      <j1 rule="para" parents="5399 16493"/>
    </justification>
  </clause>

  <clause id="16511">
    <literal><![CDATA[
      T(x,K(y,K(z,u) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,K(w,y)) = v5
    ]]></literal>
    <justification jstring="[para(16493(a,2),7866(a,1))].">
      <j1 rule="para" parents="16493 7866"/>
    </justification>
  </clause>

  <clause id="16512">
    <literal><![CDATA[
      K(x,K(K(y,z) * u,w)) = K(x,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(15900,a,16501,a)].">
      <j1 rule="hyper" parents="15900 16501"/>
    </justification>
  </clause>

  <clause id="16513">
    <literal><![CDATA[
      K(x,K(T(y,z) / u,w)) = K(x,K(y / u,w))
    ]]></literal>
    <justification jstring="[para(1439(a,1),16501(a,1,2,1))].">
      <j1 rule="para" parents="1439 16501"/>
    </justification>
  </clause>

  <clause id="16516">
    <literal><![CDATA[
      K(x,K(K(y,z) / u,w)) = K(x,K(u * K(v5,v6),w))
    ]]></literal>
    <justification jstring="[hyper(320,a,16501,a,b,16502,a),flip(a)].">
      <j1 rule="hyper" parents="320 16501 16502"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16517">
    <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(10862,a,16512,a)].">
      <j1 rule="hyper" parents="10862 16512"/>
    </justification>
  </clause>

  <clause id="16518">
    <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,16270,a(flip),b,16513,a),flip(a)].">
      <j1 rule="hyper" parents="58 16270 16513"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16519">
    <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(16482(a,2),16500(a,1))].">
      <j1 rule="para" parents="16482 16500"/>
    </justification>
  </clause>

  <clause id="16520">
    <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(16488(a,2),10839(a,1,1))].">
      <j1 rule="para" parents="16488 10839"/>
    </justification>
  </clause>

  <clause id="16521">
    <literal><![CDATA[
      K(x,K(y,(T(z,u) / w) * v5)) = K(x,K(y,(z / w) * v5))
    ]]></literal>
    <justification jstring="[para(1439(a,1),16490(a,1,2,2,1))].">
      <j1 rule="para" parents="1439 16490"/>
    </justification>
  </clause>

  <clause id="16522">
    <literal><![CDATA[
      K(x,K(y,((z / u) * w) * v5)) = K(x,K(y,((u \ z) * w) * v5))
    ]]></literal>
    <justification jstring="[para(6524(a,1),16490(a,1,2,2,1))].">
      <j1 rule="para" parents="6524 16490"/>
    </justification>
  </clause>

  <clause id="16523">
    <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(16490(a,2),15609(a,1))].">
      <j1 rule="para" parents="16490 15609"/>
    </justification>
  </clause>

  <clause id="16524">
    <literal><![CDATA[
      K(x,K(y,(z * u) / w)) = K(x,K(y,w / (u * z)))
    ]]></literal>
    <justification jstring="[hyper(8268,a,16491,a)].">
      <j1 rule="hyper" parents="8268 16491"/>
    </justification>
  </clause>

  <clause id="16525">
    <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,16271,a(flip),b,16497,a),flip(a)].">
      <j1 rule="hyper" parents="320 16271 16497"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16526">
    <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(956(a,1),16497(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="956 16497"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16527">
    <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(16497(a,1),8268(a,1))].">
      <j1 rule="para" parents="16497 8268"/>
    </justification>
  </clause>

  <clause id="16528">
    <literal><![CDATA[
      K(x,K(y,z / (K(u,w) * v5))) = K(x,K(y,v5 / z))
    ]]></literal>
    <justification jstring="[hyper(8268,a,16499,a)].">
      <j1 rule="hyper" parents="8268 16499"/>
    </justification>
  </clause>

  <clause id="16529">
    <literal><![CDATA[
      K(x,K(y,(z * T(u,w)) / v5)) = K(x,K(y,(z * u) / v5))
    ]]></literal>
    <justification jstring="[para(5555(a,1),16499(a,1,2,2,1))].">
      <j1 rule="para" parents="5555 16499"/>
    </justification>
  </clause>

  <clause id="16530">
    <literal><![CDATA[
      T(x,K(y,z * (u \ T(w,v5)))) = T(x,K(y,z * (u \ w)))
    ]]></literal>
    <justification jstring="[para(1430(a,1),16506(a,1,2,2,2))].">
      <j1 rule="para" parents="1430 16506"/>
    </justification>
  </clause>

  <clause id="16531">
    <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,16508,a(flip),b,8135,a),flip(a)].">
      <j1 rule="hyper" parents="116 16508 8135"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16532">
    <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(16508(a,1),7858(a,1))].">
      <j1 rule="para" parents="16508 7858"/>
    </justification>
  </clause>

  <clause id="16533">
    <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,10895,a(flip),b,16516,a),flip(a)].">
      <j1 rule="hyper" parents="58 10895 16516"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16534">
    <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(16524(a,1),8268(a,1))].">
      <j1 rule="para" parents="16524 8268"/>
    </justification>
  </clause>

  <clause id="16535">
    <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(16524(a,2),8268(a,1))].">
      <j1 rule="para" parents="16524 8268"/>
    </justification>
  </clause>

  <clause id="16536">
    <literal><![CDATA[
      K(x,K(y,z / ((K(u,w) * v5) * v6))) = K(x,K(y,(v5 * v6) / z))
    ]]></literal>
    <justification jstring="[para(6751(a,1),16528(a,1,2,2,2))].">
      <j1 rule="para" parents="6751 16528"/>
    </justification>
  </clause>

  <clause id="16537">
    <literal><![CDATA[
      K(x,K(y,(z * K(u,w)) / v5)) = K(x,K(y,v5 / z))
    ]]></literal>
    <justification jstring="[para(7937(a,1),16528(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="7937 16528"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16538">
    <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(16537(a,1),15964(a,1,1))].">
      <j1 rule="para" parents="16537 15964"/>
    </justification>
  </clause>

  <clause id="16539">
    <literal><![CDATA[
      T(x * K(y,z),K(u,w)) = T(x,K(u,w)) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(7809,a,16466,a),flip(a)].">
      <j1 rule="hyper" parents="7809 16466"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16540">
    <literal><![CDATA[
      T(K(x,y) * z,K(u,w)) = K(x,y) * T(z,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(6035,a,16539,a),flip(a)].">
      <j1 rule="hyper" parents="6035 16539"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16546">
    <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,8294,a(flip),b,16468,a),flip(a)].">
      <j1 rule="hyper" parents="58 8294 16468"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16547">
    <literal><![CDATA[
      K(x,K(y,z * (T(u,w) * v5))) = K(x,K(y,(u * v5) * z))
    ]]></literal>
    <justification jstring="[hyper(15609,a,16498,a)].">
      <j1 rule="hyper" parents="15609 16498"/>
    </justification>
  </clause>

  <clause id="16548">
    <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,10860,a,b,16504,a),flip(a)].">
      <j1 rule="hyper" parents="320 10860 16504"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16549">
    <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),16521(a,1,2,2,1,1)),flip(a)].">
      <j1 rule="para" parents="244 16521"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16550">
    <literal><![CDATA[
      K(x,K(y,z / (T(u,w) * v5))) = K(x,K(y,(v5 * u) / z))
    ]]></literal>
    <justification jstring="[hyper(58,a,16524,a(flip),b,16529,a)].">
      <j1 rule="hyper" parents="58 16524 16529"/>
    </justification>
  </clause>

  <clause id="16551">
    <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),16550(a,1,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="107 16550"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16552">
    <literal><![CDATA[
      K(x,T(y,T(z * u,w) * v5)) = K(x,T(y,(u * z) * v5))
    ]]></literal>
    <justification jstring="[hyper(16462,a,16409,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="16462 16409"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16554">
    <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,14705,a(flip),b,16518,a)].">
      <j1 rule="hyper" parents="58 14705 16518"/>
    </justification>
  </clause>

  <clause id="16555">
    <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(7860(a,1),16518(a,1,2,1))].">
      <j1 rule="para" parents="7860 16518"/>
    </justification>
  </clause>

  <clause id="16556">
    <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(6196(a,1),16523(a,1,2,2))].">
      <j1 rule="para" parents="6196 16523"/>
    </justification>
  </clause>

  <clause id="16557">
    <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(6322(a,1),16523(a,1,2,2,1))].">
      <j1 rule="para" parents="6322 16523"/>
    </justification>
  </clause>

  <clause id="16558">
    <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(15599(a,1),16523(a,1))].">
      <j1 rule="para" parents="15599 16523"/>
    </justification>
  </clause>

  <clause id="16559">
    <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),16558(a,1,2,2,2))].">
      <j1 rule="para" parents="84 16558"/>
    </justification>
  </clause>

  <clause id="16560">
    <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(8537(a,1),16558(a,1,2,2,2))].">
      <j1 rule="para" parents="8537 16558"/>
    </justification>
  </clause>

  <clause id="16561">
    <literal><![CDATA[
      ((1 / x) * K(y,z)) * K(u,x) = K(u,x) / (K(z,y) * x)
    ]]></literal>
    <justification jstring="[hyper(14164,a,16467,a),flip(a)].">
      <j1 rule="hyper" parents="14164 16467"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16562">
    <literal><![CDATA[
      K(x,y) / (K(z,u) * y) = (K(x,y) / y) * K(u,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,16470,a(flip),b,16561,a),flip(a)].">
      <j1 rule="hyper" parents="58 16470 16561"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16563">
    <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(16562(a,2),6610(a,2,2))].">
      <j1 rule="para" parents="16562 6610"/>
    </justification>
  </clause>

  <clause id="16564">
    <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(863(a,1),16522(a,1,2,2,1,1)),flip(a)].">
      <j1 rule="para" parents="863 16522"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16565">
    <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,8189,a,b,16536,a),flip(a)].">
      <j1 rule="hyper" parents="320 8189 16536"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16566">
    <literal><![CDATA[
      K(x,K(y,z * ((u / (u / w)) / v5))) = K(x,K(y,(w / v5) * z))
    ]]></literal>
    <justification jstring="[hyper(15609,a,16549,a)].">
      <j1 rule="hyper" parents="15609 16549"/>
    </justification>
  </clause>

  <clause id="16567">
    <literal><![CDATA[
      K(x,K(y,z / (u * (K(w,v5) * v6)))) = K(x,K(y,z / (v6 * u)))
    ]]></literal>
    <justification jstring="[hyper(16534,a,16565,a)].">
      <j1 rule="hyper" parents="16534 16565"/>
    </justification>
  </clause>

  <clause id="16568">
    <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),16566(a,1,2,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="72 16566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16569">
    <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(16566(a,1),15609(a,1))].">
      <j1 rule="para" parents="16566 15609"/>
    </justification>
  </clause>

  <clause id="16570">
    <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(16567(a,2),16534(a,1))].">
      <j1 rule="para" parents="16567 16534"/>
    </justification>
  </clause>

  <clause id="16571">
    <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(16388(a,1),16197(a,1))].">
      <j1 rule="para" parents="16388 16197"/>
    </justification>
  </clause>

  <clause id="16572">
    <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(5555(a,1),16571(a,1,2,2,2))].">
      <j1 rule="para" parents="5555 16571"/>
    </justification>
  </clause>

  <clause id="16573">
    <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(7288(a,1),16571(a,1,2,2,2))].">
      <j1 rule="para" parents="7288 16571"/>
    </justification>
  </clause>

  <clause id="16574">
    <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(13963(a,1),16573(a,1,2,2,2))].">
      <j1 rule="para" parents="13963 16573"/>
    </justification>
  </clause>

  <clause id="16575">
    <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,14865,a(flip),b,16391,a),flip(a)].">
      <j1 rule="hyper" parents="58 14865 16391"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16576">
    <literal><![CDATA[
      K(x,T(y,z * u)) * T(u,z) = T(u * K(x,y),z)
    ]]></literal>
    <justification jstring="[para(7897(a,1),16575(a,2,1))].">
      <j1 rule="para" parents="7897 16575"/>
    </justification>
  </clause>

  <clause id="16577">
    <literal><![CDATA[
      T(x * K(x \ y,z),y) = K(x \ y,z) * T(x,y)
    ]]></literal>
    <justification jstring="[para(15573(a,1),16576(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15573 16576"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16578">
    <literal><![CDATA[
      K(x,T(y,z * u)) * T(z,u) = T(z * K(x,y),u)
    ]]></literal>
    <justification jstring="[para(15575(a,1),16576(a,1,1))].">
      <j1 rule="para" parents="15575 16576"/>
    </justification>
  </clause>

  <clause id="16579">
    <literal><![CDATA[
      T(x * K(x \ y,z),y) = T(x,y) * K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,15902,a,b,16577,a),flip(a)].">
      <j1 rule="hyper" parents="320 15902 16577"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16580">
    <literal><![CDATA[
      T(x * K(x * y,z),y) = K(x * y,z) * T(x,y)
    ]]></literal>
    <justification jstring="[para(4908(a,1),16578(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4908 16578"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16581">
    <literal><![CDATA[
      T(x * K(x * y,z),y) = T(x,y) * K(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,15904,a,b,16580,a),flip(a)].">
      <j1 rule="hyper" parents="320 15904 16580"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16582">
    <literal><![CDATA[
      T(x * y,z) / T(y,x) = T(x * K(x * y,z),y)
    ]]></literal>
    <justification jstring="[hyper(14059,a,16580,a(flip))].">
      <j1 rule="hyper" parents="14059 16580"/>
    </justification>
  </clause>

  <clause id="16583">
    <literal><![CDATA[
      T(x * K(x * y,y \ 1),y) = (x * y) * (x / (y * x))
    ]]></literal>
    <justification jstring="[hyper(320,a,12310,a(flip),b,16581,a),flip(a)].">
      <j1 rule="hyper" parents="320 12310 16581"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16584">
    <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(16582(a,2),7225(a,2,2))].">
      <j1 rule="para" parents="16582 7225"/>
    </justification>
  </clause>

  <clause id="16585">
    <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(16582(a,1),15736(a,1,2,1))].">
      <j1 rule="para" parents="16582 15736"/>
    </justification>
  </clause>

  <clause id="16586">
    <literal><![CDATA[
      x \ T(y * x,x \ 1) = (y * x) * (y / (x * y))
    ]]></literal>
    <justification jstring="[hyper(58,a,6579,a(flip),b,16583,a)].">
      <j1 rule="hyper" parents="58 6579 16583"/>
    </justification>
  </clause>

  <clause id="16587">
    <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(16586(a,2),14788(a,2,2,1))].">
      <j1 rule="para" parents="16586 14788"/>
    </justification>
  </clause>

  <clause id="16588">
    <literal><![CDATA[
      (x * y) * ((y * x) \ (K(x,y) * z)) = (z * K(x,y)) * K(x,y)
    ]]></literal>
    <justification jstring="[para(7897(a,1),16441(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7897 16441"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16590">
    <literal><![CDATA[
      (x * y) * ((y * x) \ (K(x,y) * z)) = z * (K(x,y) * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(320,a,8992,a(flip),b,16588,a),flip(a)].">
      <j1 rule="hyper" parents="320 8992 16588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16591">
    <literal><![CDATA[
      (x * y) * ((T(y,x) * x) \ z) = z * (K(x,y) * K(x,y))
    ]]></literal>
    <justification jstring="[para(14994(a,1),16590(a,1,2))].">
      <j1 rule="para" parents="14994 16590"/>
    </justification>
  </clause>

  <clause id="16592">
    <literal><![CDATA[
      (x * (K(y,z) * K(y,z))) / (y * z) = x / (T(z,y) * y)
    ]]></literal>
    <justification jstring="[para(16591(a,1),12376(a,1,1))].">
      <j1 rule="para" parents="16591 12376"/>
    </justification>
  </clause>

  <clause id="16594">
    <literal><![CDATA[
      K(x,(y * (T(z,y) * K(u,w))) / v5) = K(x,((K(u,w) * z) * y) / v5)
    ]]></literal>
    <justification jstring="[para(11210(a,1),16148(a,1,2,1))].">
      <j1 rule="para" parents="11210 16148"/>
    </justification>
  </clause>

  <clause id="16595">
    <literal><![CDATA[
      K(x,y \ (z * (T(u,z) * K(w,v5)))) = K(x,y \ ((K(w,v5) * u) * z))
    ]]></literal>
    <justification jstring="[para(11210(a,1),16154(a,1,2,2))].">
      <j1 rule="para" parents="11210 16154"/>
    </justification>
  </clause>

  <clause id="16596">
    <literal><![CDATA[
      K(x,T(y,z * (y \ u)) * (u * (z / y))) = K(x,R(u,y \ z,y) * z)
    ]]></literal>
    <justification jstring="[para(12461(a,1),16175(a,1,2,1))].">
      <j1 rule="para" parents="12461 16175"/>
    </justification>
  </clause>

  <clause id="16597">
    <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(16231(a,1),16339(a,1))].">
      <j1 rule="para" parents="16231 16339"/>
    </justification>
  </clause>

  <clause id="16598">
    <literal><![CDATA[
      K(x,T(y,z * u) * z) = K(x,y * (u \ T(u * z,y)))
    ]]></literal>
    <justification jstring="[hyper(16341,a,15911,a),flip(a)].">
      <j1 rule="hyper" parents="16341 15911"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16599">
    <literal><![CDATA[
      K(x,T(y,z * x) * z) = K(x,(x \ (x * z)) * y)
    ]]></literal>
    <justification jstring="[hyper(320,a,12464,a(flip),b,16598,a),flip(a)].">
      <j1 rule="hyper" parents="320 12464 16598"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16600">
    <literal><![CDATA[
      K(x,T(y,z * x) * z) = K(x,z * y)
    ]]></literal>
    <justification jstring="[para(4(a,1),16599(a,2,2,1))].">
      <j1 rule="para" parents="4 16599"/>
    </justification>
  </clause>

  <clause id="16601">
    <literal><![CDATA[
      K(x,y * T(z,y * x)) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,15161,a(flip),b,16600,a),flip(a)].">
      <j1 rule="hyper" parents="58 15161 16600"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16602">
    <literal><![CDATA[
      K(T(x,y),z * T(u,z * x)) = K(T(x,y),u * z)
    ]]></literal>
    <justification jstring="[hyper(16572,a,16601,a)].">
      <j1 rule="hyper" parents="16572 16601"/>
    </justification>
  </clause>

  <clause id="16603">
    <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(4997(a,1),16570(a,1,2,2,2,2))].">
      <j1 rule="para" parents="4997 16570"/>
    </justification>
  </clause>

  <clause id="16604">
    <literal><![CDATA[
      K(x,T(y,z * u) * (u * (z / y))) = K(x,R(u,y \ z,y) * z)
    ]]></literal>
    <justification jstring="[hyper(13197,a,16596,a)].">
      <j1 rule="hyper" parents="13197 16596"/>
    </justification>
  </clause>

  <clause id="16605">
    <literal><![CDATA[
      K(x,T(y,z * u) * (u * (z / y))) = K(x,(u * (z / y)) * y)
    ]]></literal>
    <justification jstring="[para(10399(a,1),16604(a,2,2))].">
      <j1 rule="para" parents="10399 16604"/>
    </justification>
  </clause>

  <clause id="16606">
    <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(15590(a,1),15593(a,1,2))].">
      <j1 rule="para" parents="15590 15593"/>
    </justification>
  </clause>

  <clause id="16607">
    <literal><![CDATA[
      K(x * (y \ z),x * (1 / (z \ y))) = K(x * (y \ z),(z \ y) \ x)
    ]]></literal>
    <justification jstring="[hyper(14055,a,15931,a),flip(a)].">
      <j1 rule="hyper" parents="14055 15931"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16608">
    <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(16607(a,1),14076(a,1))].">
      <j1 rule="para" parents="16607 14076"/>
    </justification>
  </clause>

  <clause id="16609">
    <literal><![CDATA[
      K(x,T(y,L(z,u,u \ w) * w)) = K(x,T(y,(u \ w) * (u * z)))
    ]]></literal>
    <justification jstring="[hyper(15947,a,16411,a)].">
      <j1 rule="hyper" parents="15947 16411"/>
    </justification>
  </clause>

  <clause id="16611">
    <literal><![CDATA[
      T((x * T(y,z)) \ T(y,z),(x * y) \ y) = T(x * y,K(y,z)) \ y
    ]]></literal>
    <justification jstring="[para(6153(a,1),16025(a,2,1))].">
      <j1 rule="para" parents="6153 16025"/>
    </justification>
  </clause>

  <clause id="16612">
    <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,8358,a,b,16611,a),flip(a)].">
      <j1 rule="hyper" parents="320 8358 16611"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16613">
    <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,15168,a(flip),b,16159,a)].">
      <j1 rule="hyper" parents="58 15168 16159"/>
    </justification>
  </clause>

  <clause id="16614">
    <literal><![CDATA[
      K(x,(K(y,z) * (u / (y \ z))) / w) = K(x,(u / (T(y,z) \ z)) / w)
    ]]></literal>
    <justification jstring="[para(12594(a,1),16613(a,1,2,1))].">
      <j1 rule="para" parents="12594 16613"/>
    </justification>
  </clause>

  <clause id="16615">
    <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(12229(a,1),16216(a,2,1))].">
      <j1 rule="para" parents="12229 16216"/>
    </justification>
  </clause>

  <clause id="16616">
    <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),16269(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6 16269"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16617">
    <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(6346,a,16286,a),flip(a)].">
      <j1 rule="hyper" parents="6346 16286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16618">
    <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(16331(a,2),15330(a,1))].">
      <j1 rule="para" parents="16331 15330"/>
    </justification>
  </clause>

  <clause id="16619">
    <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,16548,a(flip),b,16533,a),flip(a)].">
      <j1 rule="hyper" parents="320 16548 16533"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16621">
    <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,10894,a(flip),b,16619,a),flip(a)].">
      <j1 rule="hyper" parents="320 10894 16619"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16622">
    <literal><![CDATA[
      K(x,K(y,L(z,K(u,w),v5))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(16503,a,16621,a)].">
      <j1 rule="hyper" parents="16503 16621"/>
    </justification>
  </clause>

  <clause id="16624">
    <literal><![CDATA[
      K(x,T(y,(z * K(u,w)) / v5)) = K(x,T(y,v5 / z))
    ]]></literal>
    <justification jstring="[hyper(15979,a,16538,a),flip(a)].">
      <j1 rule="hyper" parents="15979 16538"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16625">
    <literal><![CDATA[
      K(x,T(y,(z / T(u,w)) / v5)) = K(x,T(y,v5 / (z / u)))
    ]]></literal>
    <justification jstring="[para(6322(a,1),16624(a,1,2,2,1))].">
      <j1 rule="para" parents="6322 16624"/>
    </justification>
  </clause>

  <clause id="16626">
    <literal><![CDATA[
      K(x,T(y,z / (u / T(w,v5)))) = K(x,T(y,z / (u / w)))
    ]]></literal>
    <justification jstring="[hyper(8275,a,16625,a)].">
      <j1 rule="hyper" parents="8275 16625"/>
    </justification>
  </clause>

  <clause id="16627">
    <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,8480,a(flip),b,16626,a),flip(a)].">
      <j1 rule="hyper" parents="320 8480 16626"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16628">
    <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),16626(a,1,2,2,2,2)),flip(a)].">
      <j1 rule="para" parents="107 16626"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16629">
    <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(16626(a,1),4904(a,1,1)),flip(a)].">
      <j1 rule="para" parents="16626 4904"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16630">
    <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(13205(a,1),16546(a,1,2))].">
      <j1 rule="para" parents="13205 16546"/>
    </justification>
  </clause>

  <clause id="16631">
    <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(14695(a,1),16585(a,1,2))].">
      <j1 rule="para" parents="14695 16585"/>
    </justification>
  </clause>

  <clause id="16632">
    <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,13986,a(flip),b,16615,a),flip(a)].">
      <j1 rule="hyper" parents="320 13986 16615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16633">
    <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(11161,a,16632,a)].">
      <j1 rule="hyper" parents="11161 16632"/>
    </justification>
  </clause>

  <clause id="16634">
    <literal><![CDATA[
      K(x * K(y,z),T(u,z * T(y,x))) = K(z \ T(x * z,y),u)
    ]]></literal>
    <justification jstring="[para(7936(a,1),16633(a,1,1))].">
      <j1 rule="para" parents="7936 16633"/>
    </justification>
  </clause>

  <clause id="16635">
    <literal><![CDATA[
      K(x * K(y,z),T(u,z * y)) = K(z \ T(x * z,y),u)
    ]]></literal>
    <justification jstring="[hyper(16459,a,16634,a)].">
      <j1 rule="hyper" parents="16459 16634"/>
    </justification>
  </clause>

  <clause id="16636">
    <literal><![CDATA[
      K(T(K(x,y) * z,x * y),u) = K(y \ T(z * y,x),u)
    ]]></literal>
    <justification jstring="[hyper(58,a,12336,a,b,16635,a)].">
      <j1 rule="hyper" parents="58 12336 16635"/>
    </justification>
  </clause>

  <clause id="16637">
    <literal><![CDATA[
      K(K(x,y) * z,T(u,x * y)) = K(y \ T(z * y,x),u)
    ]]></literal>
    <justification jstring="[hyper(7704,a,16636,a)].">
      <j1 rule="hyper" parents="7704 16636"/>
    </justification>
  </clause>

  <clause id="16638">
    <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(7158(a,2),16617(a,1,2))].">
      <j1 rule="para" parents="7158 16617"/>
    </justification>
  </clause>

  <clause id="16639">
    <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(7232,a,16638,a),flip(a)].">
      <j1 rule="hyper" parents="7232 16638"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16640">
    <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,15962,a(flip),b,16639,a),flip(a)].">
      <j1 rule="hyper" parents="58 15962 16639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16641">
    <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,15641,a(flip),b,16640,a)].">
      <j1 rule="hyper" parents="58 15641 16640"/>
    </justification>
  </clause>

  <clause id="16642">
    <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),15881(a,1,1))].">
      <j1 rule="para" parents="383 15881"/>
    </justification>
  </clause>

  <clause id="16643">
    <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,15976,a(flip),b,16642,a)].">
      <j1 rule="hyper" parents="58 15976 16642"/>
    </justification>
  </clause>

  <clause id="16644">
    <literal><![CDATA[
      K(x,y * (z / (K(u,w) / v5))) = K(x,y * (z / (v5 \ K(u,w))))
    ]]></literal>
    <justification jstring="[hyper(16258,a,14570,a),flip(a)].">
      <j1 rule="hyper" parents="16258 14570"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16645">
    <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(3516(a,2),16644(a,1,2))].">
      <j1 rule="para" parents="3516 16644"/>
    </justification>
  </clause>

  <clause id="16646">
    <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(7196(a,1),16272(a,1,2))].">
      <j1 rule="para" parents="7196 16272"/>
    </justification>
  </clause>

  <clause id="16647">
    <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(16646(a,1),16281(a,1))].">
      <j1 rule="para" parents="16646 16281"/>
    </justification>
  </clause>

  <clause id="16648">
    <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(16509(a,1),16532(a,1))].">
      <j1 rule="para" parents="16509 16532"/>
    </justification>
  </clause>

  <clause id="16649">
    <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(5131(a,1),15844(a,2,2))].">
      <j1 rule="para" parents="5131 15844"/>
    </justification>
  </clause>

  <clause id="16650">
    <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,7558,a(flip),b,15969,a)].">
      <j1 rule="hyper" parents="58 7558 15969"/>
    </justification>
  </clause>

  <clause id="16651">
    <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,16191,a,b,16163,a)].">
      <j1 rule="hyper" parents="58 16191 16163"/>
    </justification>
  </clause>

  <clause id="16653">
    <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,15332,a(flip),b,16223,a)].">
      <j1 rule="hyper" parents="58 15332 16223"/>
    </justification>
  </clause>

  <clause id="16654">
    <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(13708(a,1),16227(a,2,2,2))].">
      <j1 rule="para" parents="13708 16227"/>
    </justification>
  </clause>

  <clause id="16655">
    <literal><![CDATA[
      K(x,y * (((z \ u) \ u) / w)) = K(x,y * (T(z,u) / w))
    ]]></literal>
    <justification jstring="[hyper(16079,a,16654,a)].">
      <j1 rule="hyper" parents="16079 16654"/>
    </justification>
  </clause>

  <clause id="16656">
    <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(13116,a,16655,a),flip(a)].">
      <j1 rule="hyper" parents="13116 16655"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16658">
    <literal><![CDATA[
      K(x,(((y \ z) \ z) / u) * w) = K(x,(T(y,z) / u) * w)
    ]]></literal>
    <justification jstring="[hyper(12305,a,16656,a),flip(a)].">
      <j1 rule="hyper" parents="12305 16656"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16659">
    <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(7449(a,1),16284(a,1,2,2))].">
      <j1 rule="para" parents="7449 16284"/>
    </justification>
  </clause>

  <clause id="16660">
    <literal><![CDATA[
      K(x,y \ (z / T(z / u,w))) = K(x,y \ (T(u \ z,w) \ z))
    ]]></literal>
    <justification jstring="[para(7614(a,1),16659(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7614 16659"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16661">
    <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(16485(a,1),16507(a,1,2)),flip(a)].">
      <j1 rule="para" parents="16485 16507"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16662">
    <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(16176,a,16661,a)].">
      <j1 rule="hyper" parents="16176 16661"/>
    </justification>
  </clause>

  <clause id="16663">
    <literal><![CDATA[
      T(x,K(y * K(z,u),w) * v5) = T(x,K(y,w) * v5)
    ]]></literal>
    <justification jstring="[hyper(320,a,15103,a(flip),b,16661,a),flip(a)].">
      <j1 rule="hyper" parents="320 15103 16661"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16665">
    <literal><![CDATA[
      T(x,K(K(y,z) * u,w) * v5) = T(x,K(u,w) * v5)
    ]]></literal>
    <justification jstring="[hyper(16176,a,16663,a)].">
      <j1 rule="hyper" parents="16176 16663"/>
    </justification>
  </clause>

  <clause id="16666">
    <literal><![CDATA[
      T(x,y * K(K(z,u) * w,v5)) = T(x,K(w,v5) * y)
    ]]></literal>
    <justification jstring="[hyper(15941,a,16663,a)].">
      <j1 rule="hyper" parents="15941 16663"/>
    </justification>
  </clause>

  <clause id="16667">
    <literal><![CDATA[
      T(x,y * K(z,u * K(w,v5))) = T(x,K(u,z) * y)
    ]]></literal>
    <justification jstring="[hyper(15940,a,16663,a)].">
      <j1 rule="hyper" parents="15940 16663"/>
    </justification>
  </clause>

  <clause id="16669">
    <literal><![CDATA[
      T(x,K(T(y,z) \ u,w) * v5) = T(x,K(y \ u,w) * v5)
    ]]></literal>
    <justification jstring="[para(7298(a,1),16663(a,1,2,1,1))].">
      <j1 rule="para" parents="7298 16663"/>
    </justification>
  </clause>

  <clause id="16670">
    <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,15122,a(flip),b,16665,a),flip(a)].">
      <j1 rule="hyper" parents="58 15122 16665"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16671">
    <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,16666,a(flip),b,14547,a(flip))].">
      <j1 rule="hyper" parents="119 16666 14547"/>
    </justification>
  </clause>

  <clause id="16672">
    <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(16667(a,1),4838(a,1,2))].">
      <j1 rule="para" parents="16667 4838"/>
    </justification>
  </clause>

  <clause id="16673">
    <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(16667(a,1),4862(a,1,2))].">
      <j1 rule="para" parents="16667 4862"/>
    </justification>
  </clause>

  <clause id="16674">
    <literal><![CDATA[
      T(x,y * K(z,T(u,w) * v5)) = T(x,K(u * v5,z) * y)
    ]]></literal>
    <justification jstring="[para(5539(a,1),16667(a,1,2,2,2))].">
      <j1 rule="para" parents="5539 16667"/>
    </justification>
  </clause>

  <clause id="16675">
    <literal><![CDATA[
      T(x,y \ T(z,T(u,w) \ v5)) = T(x,K(u \ v5,z) * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(15993,a,16669,a)].">
      <j1 rule="hyper" parents="15993 16669"/>
    </justification>
  </clause>

  <clause id="16676">
    <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(16669(a,1),15993(a,1))].">
      <j1 rule="para" parents="16669 15993"/>
    </justification>
  </clause>

  <clause id="16677">
    <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(16675(a,2),15993(a,1))].">
      <j1 rule="para" parents="16675 15993"/>
    </justification>
  </clause>

  <clause id="16678">
    <literal><![CDATA[
      K(x,y * K(z,u * K(w,v5))) = K(x,K(z,u) * y)
    ]]></literal>
    <justification jstring="[hyper(16672,a,15118,a)].">
      <j1 rule="hyper" parents="16672 15118"/>
    </justification>
  </clause>

  <clause id="16679">
    <literal><![CDATA[
      K(x,y * K(z,u * K(w,v5))) = K(x,K(u,z) * y)
    ]]></literal>
    <justification jstring="[hyper(16672,a,4729,a(flip))].">
      <j1 rule="hyper" parents="16672 4729"/>
    </justification>
  </clause>

  <clause id="16680">
    <literal><![CDATA[
      K(x,y * K(K(z,u) * w,v5)) = K(x,K(v5,w) * y)
    ]]></literal>
    <justification jstring="[hyper(16167,a,16678,a)].">
      <j1 rule="hyper" parents="16167 16678"/>
    </justification>
  </clause>

  <clause id="16681">
    <literal><![CDATA[
      K(x,K(K(y,z) * u,w) * v5) = K(x,K(w,u) * v5)
    ]]></literal>
    <justification jstring="[hyper(16166,a,16678,a)].">
      <j1 rule="hyper" parents="16166 16678"/>
    </justification>
  </clause>

  <clause id="16682">
    <literal><![CDATA[
      K(x,K(y,z * K(u,w)) * v5) = K(x,K(y,z) * v5)
    ]]></literal>
    <justification jstring="[hyper(15719,a,16678,a)].">
      <j1 rule="hyper" parents="15719 16678"/>
    </justification>
  </clause>

  <clause id="16683">
    <literal><![CDATA[
      K(x,y * K(K(z,u) * w,v5)) = K(x,K(w,v5) * y)
    ]]></literal>
    <justification jstring="[hyper(16167,a,16679,a)].">
      <j1 rule="hyper" parents="16167 16679"/>
    </justification>
  </clause>

  <clause id="16684">
    <literal><![CDATA[
      K(x,K(K(y,z) * u,w) * v5) = K(x,K(u,w) * v5)
    ]]></literal>
    <justification jstring="[hyper(16166,a,16679,a)].">
      <j1 rule="hyper" parents="16166 16679"/>
    </justification>
  </clause>

  <clause id="16685">
    <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(16679(a,1),15719(a,1))].">
      <j1 rule="para" parents="16679 15719"/>
    </justification>
  </clause>

  <clause id="16686">
    <literal><![CDATA[
      K(x,K(y,K(z,u) * w) * v5) = K(x,v5 * K(w,y))
    ]]></literal>
    <justification jstring="[para(5133(a,1),16680(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5133 16680"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16687">
    <literal><![CDATA[
      K(x,K(y,z * K(u,w)) * v5) = K(x,v5 * K(z,y))
    ]]></literal>
    <justification jstring="[para(7937(a,1),16680(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="7937 16680"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16688">
    <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(16681(a,2),15131(a,1))].">
      <j1 rule="para" parents="16681 15131"/>
    </justification>
  </clause>

  <clause id="16689">
    <literal><![CDATA[
      K(x,K(y \ K(z,u),w) * v5) = K(x,K(w,y) * v5)
    ]]></literal>
    <justification jstring="[hyper(58,a,15870,a,b,16682,a)].">
      <j1 rule="hyper" parents="58 15870 16682"/>
    </justification>
  </clause>

  <clause id="16691">
    <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(16686(a,2),15829(a,1))].">
      <j1 rule="para" parents="16686 15829"/>
    </justification>
  </clause>

  <clause id="16692">
    <literal><![CDATA[
      K(x,K(y,z \ K(u,w)) * v5) = K(x,K(y,z) * v5)
    ]]></literal>
    <justification jstring="[hyper(15131,a,16689,a)].">
      <j1 rule="hyper" parents="15131 16689"/>
    </justification>
  </clause>

  <clause id="16694">
    <literal><![CDATA[
      T(x,K(y,z \ K(u,w)) * v5) = T(x,K(y,z) * v5)
    ]]></literal>
    <justification jstring="[hyper(118,a,16692,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 16692 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16695">
    <literal><![CDATA[
      T(x,y * K(z \ K(u,w),v5)) = T(x,K(v5,z) * y)
    ]]></literal>
    <justification jstring="[hyper(15940,a,16694,a)].">
      <j1 rule="hyper" parents="15940 16694"/>
    </justification>
  </clause>

  <clause id="16696">
    <literal><![CDATA[
      T(x,y * K(z \ K(u,w),v5)) = T(x,K(z,v5) * y)
    ]]></literal>
    <justification jstring="[hyper(320,a,15114,a,b,16695,a),flip(a)].">
      <j1 rule="hyper" parents="320 15114 16695"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16697">
    <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,16665,a,b,16696,a)].">
      <j1 rule="hyper" parents="320 16665 16696"/>
    </justification>
  </clause>

  <clause id="16698">
    <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,16162,a(flip),b,16696,a),flip(a)].">
      <j1 rule="hyper" parents="58 16162 16696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16699">
    <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(4859(a,1),16688(a,1,2,1,1))].">
      <j1 rule="para" parents="4859 16688"/>
    </justification>
  </clause>

  <clause id="16700">
    <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(5130(a,2),16699(a,1,2))].">
      <j1 rule="para" parents="5130 16699"/>
    </justification>
  </clause>

  <clause id="16701">
    <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,15689,a,b,16697,a)].">
      <j1 rule="hyper" parents="320 15689 16697"/>
    </justification>
  </clause>

  <clause id="16702">
    <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,15887,a(flip),b,16701,a),flip(a)].">
      <j1 rule="hyper" parents="58 15887 16701"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16703">
    <literal><![CDATA[
      K(x * K(y,z * K(u,w)),v5) = K(K(z,y) * x,v5)
    ]]></literal>
    <justification jstring="[hyper(16673,a,4794,a(flip))].">
      <j1 rule="hyper" parents="16673 4794"/>
    </justification>
  </clause>

  <clause id="16704">
    <literal><![CDATA[
      K(x * K(y,z * K(u,w)),v5) = K(x * K(y,z),v5)
    ]]></literal>
    <justification jstring="[hyper(320,a,15862,a(flip),b,16703,a),flip(a)].">
      <j1 rule="hyper" parents="320 15862 16703"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16705">
    <literal><![CDATA[
      K(x * K(y,T(z,u) * w),v5) = K(x * K(y,z * w),v5)
    ]]></literal>
    <justification jstring="[para(5539(a,1),16704(a,1,1,2,2))].">
      <j1 rule="para" parents="5539 16704"/>
    </justification>
  </clause>

  <clause id="16706">
    <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(16662(a,2),15335(a,1))].">
      <j1 rule="para" parents="16662 15335"/>
    </justification>
  </clause>

  <clause id="16707">
    <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,15374,a(flip),b,16670,a),flip(a)].">
      <j1 rule="hyper" parents="320 15374 16670"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16709">
    <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(16702(a,1),16706(a,1))].">
      <j1 rule="para" parents="16702 16706"/>
    </justification>
  </clause>

  <clause id="16710">
    <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(8335(a,1),16651(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="8335 16651"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16711">
    <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,11066,a(flip),b,16710,a),flip(a)].">
      <j1 rule="hyper" parents="320 11066 16710"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16712">
    <literal><![CDATA[
      T(x,K(y \ z,u) * w) = T(x,K(z * y,u) * w)
    ]]></literal>
    <justification jstring="[hyper(15596,a,16606,a),flip(a)].">
      <j1 rule="hyper" parents="15596 16606"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16713">
    <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(16606(a,1),15596(a,1))].">
      <j1 rule="para" parents="16606 15596"/>
    </justification>
  </clause>

  <clause id="16714">
    <literal><![CDATA[
      T(x,y \ T(z,T(u,w) \ v5)) = T(x,K(v5 * u,z) * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(16676,a,16712,a)].">
      <j1 rule="hyper" parents="16676 16712"/>
    </justification>
  </clause>

  <clause id="16715">
    <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(16712(a,1),14715(a,1,1,2))].">
      <j1 rule="para" parents="16712 14715"/>
    </justification>
  </clause>

  <clause id="16716">
    <literal><![CDATA[
      T(x,y \ T(z,T(u,w) \ v5)) = T(x,y \ T(z,v5 * u))
    ]]></literal>
    <justification jstring="[hyper(320,a,15888,a(flip),b,16714,a),flip(a)].">
      <j1 rule="hyper" parents="320 15888 16714"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16717">
    <literal><![CDATA[
      T(x,y \ T(z,u \ w)) = T(x,y \ T(z,w * u))
    ]]></literal>
    <justification jstring="[hyper(16677,a,16716,a)].">
      <j1 rule="hyper" parents="16677 16716"/>
    </justification>
  </clause>

  <clause id="16718">
    <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(16717(a,1),14715(a,1,1,2))].">
      <j1 rule="para" parents="16717 14715"/>
    </justification>
  </clause>

  <clause id="16719">
    <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,16483,a(flip),b,15612,a),flip(a)].">
      <j1 rule="hyper" parents="320 16483 15612"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16720">
    <literal><![CDATA[
      K(x,K((1 / y) / z,L(z / u,u,y))) = K(x,K(y * z,z / u))
    ]]></literal>
    <justification jstring="[hyper(15618,a,16719,a)].">
      <j1 rule="hyper" parents="15618 16719"/>
    </justification>
  </clause>

  <clause id="16722">
    <literal><![CDATA[
      K(x,K((y \ z) * u,u / y)) = K(x,K(z,(1 / (y \ z)) / u))
    ]]></literal>
    <justification jstring="[hyper(58,a,14783,a(flip),b,16720,a),flip(a)].">
      <j1 rule="hyper" parents="58 14783 16720"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16723">
    <literal><![CDATA[
      K(x,K(y / z,(z \ u) * y)) = K(x,K(u,(1 / (z \ u)) / y))
    ]]></literal>
    <justification jstring="[hyper(7831,a,16722,a)].">
      <j1 rule="hyper" parents="7831 16722"/>
    </justification>
  </clause>

  <clause id="16724">
    <literal><![CDATA[
      K(x,K(y,(1 / (z \ y)) / u)) = K(x,K(y,u / z))
    ]]></literal>
    <justification jstring="[hyper(58,a,15873,a(flip),b,16723,a),flip(a)].">
      <j1 rule="hyper" parents="58 15873 16723"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16725">
    <literal><![CDATA[
      K(x,K(y,(1 / z) / u)) = K(x,K(y,u / (y / z)))
    ]]></literal>
    <justification jstring="[para(75(a,1),16724(a,1,2,2,1,2))].">
      <j1 rule="para" parents="75 16724"/>
    </justification>
  </clause>

  <clause id="16726">
    <literal><![CDATA[
      K(x,K(y,z / (y / u))) = K(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,11837,a(flip),b,16725,a),flip(a)].">
      <j1 rule="hyper" parents="58 11837 16725"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16727">
    <literal><![CDATA[
      K(x,K(y,z * (y / u))) = K(x,K(y,z / u))
    ]]></literal>
    <justification jstring="[hyper(58,a,16489,a(flip),b,16726,a),flip(a)].">
      <j1 rule="hyper" parents="58 16489 16726"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16728">
    <literal><![CDATA[
      K(x,K(y,z * x)) * K(y / x,(y / x) \ z) = K(x \ y,z / (y / x))
    ]]></literal>
    <justification jstring="[para(16726(a,1),8375(a,1,1))].">
      <j1 rule="para" parents="16726 8375"/>
    </justification>
  </clause>

  <clause id="16729">
    <literal><![CDATA[
      K(x,K(y,z * (x / u))) = K(y,K(x,z / u))
    ]]></literal>
    <justification jstring="[hyper(7781,a,16727,a)].">
      <j1 rule="hyper" parents="7781 16727"/>
    </justification>
  </clause>

  <clause id="16730">
    <literal><![CDATA[
      K(x,K(y,z * (x / u))) = K(x,K(y,z / u))
    ]]></literal>
    <justification jstring="[hyper(320,a,7779,a,b,16729,a),flip(a)].">
      <j1 rule="hyper" parents="320 7779 16729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16731">
    <literal><![CDATA[
      K(x,K(y,z / y)) * K(y / x,(x / y) * z) = K(x \ y,z * (x / y))
    ]]></literal>
    <justification jstring="[para(16730(a,1),12372(a,1,1))].">
      <j1 rule="para" parents="16730 12372"/>
    </justification>
  </clause>

  <clause id="16732">
    <literal><![CDATA[
      K(x,K(y,z)) * K(z / x,(z / x) \ y) = K(x \ z,y / (z / x))
    ]]></literal>
    <justification jstring="[para(7877(a,1),16728(a,1,1))].">
      <j1 rule="para" parents="7877 16728"/>
    </justification>
  </clause>

  <clause id="16733">
    <literal><![CDATA[
      K(x,K(y,z)) * K(z / x,y / (z / x)) = K(x \ z,y / (z / x))
    ]]></literal>
    <justification jstring="[para(4912(a,2),16732(a,1,2))].">
      <j1 rule="para" parents="4912 16732"/>
    </justification>
  </clause>

  <clause id="16734">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y / x,(x / y) * z) = K(x \ y,z * (x / y))
    ]]></literal>
    <justification jstring="[para(7868(a,1),16731(a,1,1))].">
      <j1 rule="para" parents="7868 16731"/>
    </justification>
  </clause>

  <clause id="16735">
    <literal><![CDATA[
      K(x,K(y,z)) * K(z / x,(x / z) * y) = K(x \ z,y * (x / z))
    ]]></literal>
    <justification jstring="[para(7797(a,1),16734(a,1,1))].">
      <j1 rule="para" parents="7797 16734"/>
    </justification>
  </clause>

  <clause id="16737">
    <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(6335(a,1),15838(a,1,1,2))].">
      <j1 rule="para" parents="6335 15838"/>
    </justification>
  </clause>

  <clause id="16738">
    <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(13749(a,1),16350(a,1,1,1,1))].">
      <j1 rule="para" parents="13749 16350"/>
    </justification>
  </clause>

  <clause id="16739">
    <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(16143,a,16738,a)].">
      <j1 rule="hyper" parents="16143 16738"/>
    </justification>
  </clause>

  <clause id="16740">
    <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(5130(a,1),16737(a,1,1))].">
      <j1 rule="para" parents="5130 16737"/>
    </justification>
  </clause>

  <clause id="16741">
    <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(6290(a,1),15818(a,1,2,2))].">
      <j1 rule="para" parents="6290 15818"/>
    </justification>
  </clause>

  <clause id="16742">
    <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(16102,a,15925,a)].">
      <j1 rule="hyper" parents="16102 15925"/>
    </justification>
  </clause>

  <clause id="16743">
    <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(15336,a,16742,a),flip(a)].">
      <j1 rule="hyper" parents="15336 16742"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16745">
    <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(7278(a,1),15932(a,1,2,1))].">
      <j1 rule="para" parents="7278 15932"/>
    </justification>
  </clause>

  <clause id="16746">
    <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,15156,a(flip),b,16745,a),flip(a)].">
      <j1 rule="hyper" parents="58 15156 16745"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16748">
    <literal><![CDATA[
      (K(x,y) \ z) \ (u * (z * K(y,x))) = (z * K(y,x)) \ (u * (K(x,y) \ z))
    ]]></literal>
    <justification jstring="[para(7859(a,1),15972(a,1,2,2))].">
      <j1 rule="para" parents="7859 15972"/>
    </justification>
  </clause>

  <clause id="16749">
    <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,7942,a(flip),b,15986,a),flip(a)].">
      <j1 rule="hyper" parents="320 7942 15986"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16750">
    <literal><![CDATA[
      T(((x \ 1) * y) \ z,K(y * (x \ 1),x)) = T(z / ((x \ 1) * y),y / x)
    ]]></literal>
    <justification jstring="[para(12230(a,1),16749(a,1,2))].">
      <j1 rule="para" parents="12230 16749"/>
    </justification>
  </clause>

  <clause id="16751">
    <literal><![CDATA[
      T(((x \ 1) * y) \ z,K(x \ y,x)) = T(z / ((x \ 1) * y),y / x)
    ]]></literal>
    <justification jstring="[para(5861(a,1),16750(a,1,2))].">
      <j1 rule="para" parents="5861 16750"/>
    </justification>
  </clause>

  <clause id="16752">
    <literal><![CDATA[
      T(x / ((y \ 1) * z),z / y) = T(((y \ 1) * z) \ x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(13099,a,16751,a),flip(a)].">
      <j1 rule="hyper" parents="13099 16751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16753">
    <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(6189(a,2),16228(a,1,2))].">
      <j1 rule="para" parents="6189 16228"/>
    </justification>
  </clause>

  <clause id="16754">
    <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,13193,a(flip),b,16287,a),flip(a)].">
      <j1 rule="hyper" parents="320 13193 16287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16755">
    <literal><![CDATA[
      K(x,y * (T(z / u,u) * (w \ 1))) = K(x,y * ((z / u) * (w \ K(u,z))))
    ]]></literal>
    <justification jstring="[hyper(15422,a,16754,a)].">
      <j1 rule="hyper" parents="15422 16754"/>
    </justification>
  </clause>

  <clause id="16756">
    <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),16755(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="107 16755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16757">
    <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(13182,a,16326,a)].">
      <j1 rule="hyper" parents="13182 16326"/>
    </justification>
  </clause>

  <clause id="16758">
    <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,15372,a(flip),b,16757,a),flip(a)].">
      <j1 rule="hyper" parents="58 15372 16757"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16759">
    <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,15152,a(flip),b,16758,a),flip(a)].">
      <j1 rule="hyper" parents="320 15152 16758"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16760">
    <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(16759(a,1),14058(a,1))].">
      <j1 rule="para" parents="16759 14058"/>
    </justification>
  </clause>

  <clause id="16761">
    <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,12240,a(flip),b,16370,a)].">
      <j1 rule="hyper" parents="58 12240 16370"/>
    </justification>
  </clause>

  <clause id="16762">
    <literal><![CDATA[
      T(x,y / ((z \ T(z \ u,w)) \ (z \ u))) = T(x,y / (T(z \ u,w) \ u))
    ]]></literal>
    <justification jstring="[para(13977(a,1),16393(a,1,2,2,1))].">
      <j1 rule="para" parents="13977 16393"/>
    </justification>
  </clause>

  <clause id="16763">
    <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(7859(a,1),16481(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7859 16481"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16764">
    <literal><![CDATA[
      (K(x,y) \ z) \ (u * (z * K(y,x))) = z \ T(u * z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,16643,a(flip),b,16763,a),flip(a)].">
      <j1 rule="hyper" parents="58 16643 16763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16765">
    <literal><![CDATA[
      (x * K(y,z)) \ (u * (K(z,y) \ x)) = x \ T(u * x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,16748,a(flip),b,16764,a)].">
      <j1 rule="hyper" parents="58 16748 16764"/>
    </justification>
  </clause>

  <clause id="16766">
    <literal><![CDATA[
      (x * K(y,z)) \ (u * (K(z,y) \ x)) = x \ T(u * x,K(y,z))
    ]]></literal>
    <justification jstring="[para(7832(a,1),16765(a,2,2))].">
      <j1 rule="para" parents="7832 16765"/>
    </justification>
  </clause>

  <clause id="16767">
    <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(16519,a,16531,a)].">
      <j1 rule="hyper" parents="16519 16531"/>
    </justification>
  </clause>

  <clause id="16768">
    <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,16434,a(flip),b,16630,a)].">
      <j1 rule="hyper" parents="58 16434 16630"/>
    </justification>
  </clause>

  <clause id="16770">
    <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,12323,a(flip),b,16768,a),flip(a)].">
      <j1 rule="hyper" parents="58 12323 16768"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16771">
    <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(14924(a,1),16671(a,1,2,1,2))].">
      <j1 rule="para" parents="14924 16671"/>
    </justification>
  </clause>

  <clause id="16772">
    <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(16715(a,1),14716(a,1))].">
      <j1 rule="para" parents="16715 14716"/>
    </justification>
  </clause>

  <clause id="16773">
    <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(16718(a,1),14716(a,1))].">
      <j1 rule="para" parents="16718 14716"/>
    </justification>
  </clause>

  <clause id="16774">
    <literal><![CDATA[
      K(((x \ y) * x) / z,T(u,y / x)) = y \ (y * K((x * (z / x)) \ y,u))
    ]]></literal>
    <justification jstring="[para(6655(a,1),16741(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6655 16741"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16775">
    <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,16774,a),flip(a)].">
      <j1 rule="hyper" parents="320 4 16774"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16776">
    <literal><![CDATA[
      K((x * ((y * ((x \ z) * x)) / x)) \ z,u) = K(1 / y,T(u,z / x))
    ]]></literal>
    <justification jstring="[hyper(5440,a,16775,a),flip(a)].">
      <j1 rule="hyper" parents="5440 16775"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16778">
    <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(16775(a,1),5440(a,1))].">
      <j1 rule="para" parents="16775 5440"/>
    </justification>
  </clause>

  <clause id="16779">
    <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(10351(a,1),16761(a,1,1,2))].">
      <j1 rule="para" parents="10351 16761"/>
    </justification>
  </clause>

  <clause id="16781">
    <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(16509(a,1),16767(a,2,2))].">
      <j1 rule="para" parents="16509 16767"/>
    </justification>
  </clause>

  <clause id="16782">
    <literal><![CDATA[
      T((x \ K(y,z)) \ u,K(x,w)) = (x \ K(y,z)) \ T(u,K(x,w))
    ]]></literal>
    <justification jstring="[hyper(16511,a,16781,a)].">
      <j1 rule="hyper" parents="16511 16781"/>
    </justification>
  </clause>

  <clause id="16783">
    <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,16649,a(flip),b,16782,a),flip(a)].">
      <j1 rule="hyper" parents="320 16649 16782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16784">
    <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),16783(a,1,1))].">
      <j1 rule="para" parents="17 16783"/>
    </justification>
  </clause>

  <clause id="16785">
    <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(16784(a,1),16648(a,1))].">
      <j1 rule="para" parents="16784 16648"/>
    </justification>
  </clause>

  <clause id="16786">
    <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(14946(a,1),16771(a,1,2,1))].">
      <j1 rule="para" parents="14946 16771"/>
    </justification>
  </clause>

  <clause id="16787">
    <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(8568(a,1),15860(a,1,2,2,1))].">
      <j1 rule="para" parents="8568 15860"/>
    </justification>
  </clause>

  <clause id="16789">
    <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),15924(a,2,2,2))].">
      <j1 rule="para" parents="247 15924"/>
    </justification>
  </clause>

  <clause id="16790">
    <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(15991,a,15349,a),flip(a)].">
      <j1 rule="hyper" parents="15991 15349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16791">
    <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(15990,a,16790,a),flip(a)].">
      <j1 rule="hyper" parents="15990 16790"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16792">
    <literal><![CDATA[
      K(x,y * T(K(x,z) * u,z)) = K(x,y * T(u,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(58,a,14868,a(flip),b,16791,a),flip(a)].">
      <j1 rule="hyper" parents="58 14868 16791"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16793">
    <literal><![CDATA[
      K(x,y * T(z,u \ 1)) = K(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,14868,a(flip),b,16792,a),flip(a)].">
      <j1 rule="hyper" parents="58 14868 16792"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16795">
    <literal><![CDATA[
      T(x,y * T(z,u \ 1)) = T(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[hyper(118,a,16793,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 16793 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16796">
    <literal><![CDATA[
      K(x,y * T((z \ 1) \ u,z)) = K(x,y * (u / (z \ 1)))
    ]]></literal>
    <justification jstring="[hyper(58,a,15241,a(flip),b,16793,a),flip(a)].">
      <j1 rule="hyper" parents="58 15241 16793"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16797">
    <literal><![CDATA[
      T(x,(y * ((z \ 1) * K(u,z \ 1))) * u) = T(x,(y * (z \ 1)) * T(u,z))
    ]]></literal>
    <justification jstring="[para(6243(a,2),16795(a,1,2))].">
      <j1 rule="para" parents="6243 16795"/>
    </justification>
  </clause>

  <clause id="16798">
    <literal><![CDATA[
      K(x,y * ((z \ K(z,u)) \ u)) = K(x,y * (u / (z \ 1)))
    ]]></literal>
    <justification jstring="[hyper(58,a,13157,a(flip),b,16796,a)].">
      <j1 rule="hyper" parents="58 13157 16796"/>
    </justification>
  </clause>

  <clause id="16799">
    <literal><![CDATA[
      T(x,(y * (z \ K(u,z \ 1))) * u) = T(x,(y * (z \ 1)) * T(u,z))
    ]]></literal>
    <justification jstring="[para(2930(a,1),16797(a,1,2,1,2))].">
      <j1 rule="para" parents="2930 16797"/>
    </justification>
  </clause>

  <clause id="16800">
    <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(15992,a,15293,a),flip(a)].">
      <j1 rule="hyper" parents="15992 15293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16801">
    <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,16189,a,b,16800,a)].">
      <j1 rule="hyper" parents="58 16189 16800"/>
    </justification>
  </clause>

  <clause id="16802">
    <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(16300(a,2),16801(a,1,2,1))].">
      <j1 rule="para" parents="16300 16801"/>
    </justification>
  </clause>

  <clause id="16803">
    <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,16390,a(flip),b,16802,a),flip(a)].">
      <j1 rule="hyper" parents="58 16390 16802"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16804">
    <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(12473(a,1),15913(a,1,2,1))].">
      <j1 rule="para" parents="12473 15913"/>
    </justification>
  </clause>

  <clause id="16805">
    <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(15911(a,1),15922(a,1,2,2))].">
      <j1 rule="para" parents="15911 15922"/>
    </justification>
  </clause>

  <clause id="16806">
    <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,16674,a(flip),b,16805,a)].">
      <j1 rule="hyper" parents="58 16674 16805"/>
    </justification>
  </clause>

  <clause id="16808">
    <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(13708(a,1),16806(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13708 16806"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16809">
    <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,15919,a(flip),b,16808,a),flip(a)].">
      <j1 rule="hyper" parents="320 15919 16808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16810">
    <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,8025,a(flip),b,16809,a)].">
      <j1 rule="hyper" parents="58 8025 16809"/>
    </justification>
  </clause>

  <clause id="16811">
    <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(6090(a,1),16810(a,1,2,2,1))].">
      <j1 rule="para" parents="6090 16810"/>
    </justification>
  </clause>

  <clause id="16812">
    <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,15418,a(flip),b,16181,a)].">
      <j1 rule="hyper" parents="58 15418 16181"/>
    </justification>
  </clause>

  <clause id="16813">
    <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,16180,a(flip),b,16812,a),flip(a)].">
      <j1 rule="hyper" parents="58 16180 16812"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16814">
    <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,15076,a(flip),b,16244,a)].">
      <j1 rule="hyper" parents="58 15076 16244"/>
    </justification>
  </clause>

  <clause id="16815">
    <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),16315(a,1,2,1,2))].">
      <j1 rule="para" parents="18 16315"/>
    </justification>
  </clause>

  <clause id="16816">
    <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(16368(a,1),16369(a,1,1))].">
      <j1 rule="para" parents="16368 16369"/>
    </justification>
  </clause>

  <clause id="16817">
    <literal><![CDATA[
      K(x,(y * z) * R(u,z,y)) = K(x,y * (z * u))
    ]]></literal>
    <justification jstring="[hyper(8077,a,16816,a),flip(a)].">
      <j1 rule="hyper" parents="8077 16816"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16818">
    <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(745(a,1),16817(a,2,2))].">
      <j1 rule="para" parents="745 16817"/>
    </justification>
  </clause>

  <clause id="16819">
    <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(11205(a,1),16817(a,2,2))].">
      <j1 rule="para" parents="11205 16817"/>
    </justification>
  </clause>

  <clause id="16820">
    <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),16818(a,1,2,1))].">
      <j1 rule="para" parents="5 16818"/>
    </justification>
  </clause>

  <clause id="16822">
    <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),16820(a,1,2))].">
      <j1 rule="para" parents="238 16820"/>
    </justification>
  </clause>

  <clause id="16823">
    <literal><![CDATA[
      K(x,L(y,z \ u,z) * u) = K(x,(y * (u / z)) * z)
    ]]></literal>
    <justification jstring="[para(10399(a,1),16822(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10399 16822"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16824">
    <literal><![CDATA[
      K(x,y * ((y \ T(z,u)) * u)) = K(x,(u * (z / y)) * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,14191,a(flip),b,16823,a)].">
      <j1 rule="hyper" parents="58 14191 16823"/>
    </justification>
  </clause>

  <clause id="16825">
    <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),16819(a,1,2,1))].">
      <j1 rule="para" parents="7 16819"/>
    </justification>
  </clause>

  <clause id="16827">
    <literal><![CDATA[
      K(x,y * R(T(z,y),u,u \ y)) = K(x,L(z,u,u \ y) * y)
    ]]></literal>
    <justification jstring="[para(10388(a,1),16825(a,1,2,2))].">
      <j1 rule="para" parents="10388 16825"/>
    </justification>
  </clause>

  <clause id="16828">
    <literal><![CDATA[
      K(x,L(y,z,z \ u) * u) = K(x,(y * z) * (z \ u))
    ]]></literal>
    <justification jstring="[para(727(a,1),16827(a,1,2)),flip(a)].">
      <j1 rule="para" parents="727 16827"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16829">
    <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,14291,a,b,16526,a),flip(a)].">
      <j1 rule="hyper" parents="320 14291 16526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16830">
    <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,15359,a(flip),b,16804,a)].">
      <j1 rule="hyper" parents="58 15359 16804"/>
    </justification>
  </clause>

  <clause id="16831">
    <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(5175(a,1),16814(a,1,1,2))].">
      <j1 rule="para" parents="5175 16814"/>
    </justification>
  </clause>

  <clause id="16832">
    <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(16246(a,1),16831(a,1,1,2))].">
      <j1 rule="para" parents="16246 16831"/>
    </justification>
  </clause>

  <clause id="16833">
    <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(7832(a,1),16815(a,1,2))].">
      <j1 rule="para" parents="7832 16815"/>
    </justification>
  </clause>

  <clause id="16834">
    <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(15613(a,1),16829(a,2,3))].">
      <j1 rule="para" parents="15613 16829"/>
    </justification>
  </clause>

  <clause id="16835">
    <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(16204(a,1),16833(a,1,2))].">
      <j1 rule="para" parents="16204 16833"/>
    </justification>
  </clause>

  <clause id="16836">
    <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,9828,a(flip),b,16835,a)].">
      <j1 rule="hyper" parents="58 9828 16835"/>
    </justification>
  </clause>

  <clause id="16837">
    <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(16540(a,2),16836(a,1,2))].">
      <j1 rule="para" parents="16540 16836"/>
    </justification>
  </clause>

  <clause id="16838">
    <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(12229(a,1),16837(a,1,2,1))].">
      <j1 rule="para" parents="12229 16837"/>
    </justification>
  </clause>

  <clause id="16839">
    <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(13870(a,1),16838(a,1,2))].">
      <j1 rule="para" parents="13870 16838"/>
    </justification>
  </clause>

  <clause id="16840">
    <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(5130(a,1),16839(a,1,2))].">
      <j1 rule="para" parents="5130 16839"/>
    </justification>
  </clause>

  <clause id="16841">
    <literal><![CDATA[
      K(x,T(y,z)) * T(u * K(y,x),z) = T(u,z * K(y,x))
    ]]></literal>
    <justification jstring="[hyper(8474,a,16840,a)].">
      <j1 rule="hyper" parents="8474 16840"/>
    </justification>
  </clause>

  <clause id="16842">
    <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,16641,a(flip),b,16841,a)].">
      <j1 rule="hyper" parents="58 16641 16841"/>
    </justification>
  </clause>

  <clause id="16843">
    <literal><![CDATA[
      T(x * K(y,T(z,u)),u) = K(y,z) * T(x,u * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(5147,a,16842,a),flip(a)].">
      <j1 rule="hyper" parents="5147 16842"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16844">
    <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(16843(a,2),14222(a,2,2)),flip(a)].">
      <j1 rule="para" parents="16843 14222"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16845">
    <literal><![CDATA[
      L(x,K(y,T(z,x)),u) = R(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(14161,a,16844,a)].">
      <j1 rule="hyper" parents="14161 16844"/>
    </justification>
  </clause>

  <clause id="16846">
    <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,16476,a(flip),b,16834,a)].">
      <j1 rule="hyper" parents="58 16476 16834"/>
    </justification>
  </clause>

  <clause id="16848">
    <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),15630(a,1,1))].">
      <j1 rule="para" parents="20 15630"/>
    </justification>
  </clause>

  <clause id="16849">
    <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(7440(a,1),16282(a,1,1,2,1))].">
      <j1 rule="para" parents="7440 16282"/>
    </justification>
  </clause>

  <clause id="16850">
    <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(4818(a,1),16849(a,1,1))].">
      <j1 rule="para" parents="4818 16849"/>
    </justification>
  </clause>

  <clause id="16851">
    <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),16564(a,1,2,2,1,1)),flip(a)].">
      <j1 rule="para" parents="4 16564"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16852">
    <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(15622,a,16851,a)].">
      <j1 rule="hyper" parents="15622 16851"/>
    </justification>
  </clause>

  <clause id="16854">
    <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),16852(a,1,2,2,2))].">
      <j1 rule="para" parents="24 16852"/>
    </justification>
  </clause>

  <clause id="16855">
    <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(14942(a,1),16848(a,1,1))].">
      <j1 rule="para" parents="14942 16848"/>
    </justification>
  </clause>

  <clause id="16857">
    <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,8642,a(flip),b,16120,a),flip(a)].">
      <j1 rule="hyper" parents="58 8642 16120"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16859">
    <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,8123,a(flip),b,16857,a),flip(a)].">
      <j1 rule="hyper" parents="320 8123 16857"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16860">
    <literal><![CDATA[
      K(x,T(y * ((z / x) / T(z,x)),z)) = K(x,((z / x) / z) * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(7917,a,16859,a)].">
      <j1 rule="hyper" parents="7917 16859"/>
    </justification>
  </clause>

  <clause id="16861">
    <literal><![CDATA[
      K(x,T(y * ((z / x) / z),z)) = K(x,((z / x) / z) * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,8680,a(flip),b,16860,a)].">
      <j1 rule="hyper" parents="58 8680 16860"/>
    </justification>
  </clause>

  <clause id="16862">
    <literal><![CDATA[
      K(x,T(((y / x) / y) * z,y)) = K(x,((y / x) / y) * T(z,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,16389,a,b,16861,a)].">
      <j1 rule="hyper" parents="58 16389 16861"/>
    </justification>
  </clause>

  <clause id="16863">
    <literal><![CDATA[
      K(x,((y / x) / y) * T(T(z,y),y)) = K(x,z * ((y / x) / y))
    ]]></literal>
    <justification jstring="[hyper(13514,a,16862,a),flip(a)].">
      <j1 rule="hyper" parents="13514 16862"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16864">
    <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(4092(a,1),16863(a,2,2))].">
      <j1 rule="para" parents="4092 16863"/>
    </justification>
  </clause>

  <clause id="16865">
    <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),16864(a,1,2))].">
      <j1 rule="para" parents="452 16864"/>
    </justification>
  </clause>

  <clause id="16866">
    <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,12277,a(flip),b,16865,a)].">
      <j1 rule="hyper" parents="320 12277 16865"/>
    </justification>
  </clause>

  <clause id="16867">
    <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(16866(a,1),12301(a,1))].">
      <j1 rule="para" parents="16866 12301"/>
    </justification>
  </clause>

  <clause id="16868">
    <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(13806(a,1),16275(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="13806 16275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16869">
    <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(10944(a,1),16868(a,2,1))].">
      <j1 rule="para" parents="10944 16868"/>
    </justification>
  </clause>

  <clause id="16870">
    <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,7816,a(flip),b,16869,a),flip(a)].">
      <j1 rule="hyper" parents="320 7816 16869"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16871">
    <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(710(a,1),16870(a,1,2))].">
      <j1 rule="para" parents="710 16870"/>
    </justification>
  </clause>

  <clause id="16872">
    <literal><![CDATA[
      K(x,T(L(y,z,u),y * w)) = K(x,T(L(y,z,u),w))
    ]]></literal>
    <justification jstring="[para(974(a,1),16871(a,1,2))].">
      <j1 rule="para" parents="974 16871"/>
    </justification>
  </clause>

  <clause id="16873">
    <literal><![CDATA[
      K(x,T(L(y,z,u),w / y)) = K(x,T(L(y,z,u),w))
    ]]></literal>
    <justification jstring="[hyper(15946,a,16872,a)].">
      <j1 rule="hyper" parents="15946 16872"/>
    </justification>
  </clause>

  <clause id="16874">
    <literal><![CDATA[
      K(x,L(y / (y / z),u,w)) = K(x,T(L(z,u,w),y))
    ]]></literal>
    <justification jstring="[hyper(58,a,8012,a(flip),b,16873,a)].">
      <j1 rule="hyper" parents="58 8012 16873"/>
    </justification>
  </clause>

  <clause id="16875">
    <literal><![CDATA[
      K(x,T(L(y,z / y,u),z)) = K(x,(z * u) / ((z / y) * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,14780,a(flip),b,16874,a),flip(a)].">
      <j1 rule="hyper" parents="58 14780 16874"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16876">
    <literal><![CDATA[
      K(x,(y * z) / ((y / u) * z)) = T(L(K(x,u),y,z),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,7196,a(flip),b,16875,a),flip(a)].">
      <j1 rule="hyper" parents="58 7196 16875"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16877">
    <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),16876(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7 16876"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16878">
    <literal><![CDATA[
      K(x,y / (((y / z) / u) * z)) = y \ (z * (K(x,u) * (z \ y)))
    ]]></literal>
    <justification jstring="[hyper(58,a,16337,a(flip),b,16877,a),flip(a)].">
      <j1 rule="hyper" parents="58 16337 16877"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16879">
    <literal><![CDATA[
      K(x,(y / x) / ((((y / x) / y) / z) * y)) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,10221,a(flip),b,16878,a),flip(a)].">
      <j1 rule="hyper" parents="320 10221 16878"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16880">
    <literal><![CDATA[
      K(x,y / (((((y / x) / y) / z) * y) * x)) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,7100,a(flip),b,16879,a)].">
      <j1 rule="hyper" parents="58 7100 16879"/>
    </justification>
  </clause>

  <clause id="16881">
    <literal><![CDATA[
      K(x,1 / ((((y / x) / y) / z) * x)) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(11096,a,16880,a)].">
      <j1 rule="hyper" parents="11096 16880"/>
    </justification>
  </clause>

  <clause id="16883">
    <literal><![CDATA[
      K(x,y / (((z / x) / z) * x)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,11097,a(flip),b,16881,a)].">
      <j1 rule="hyper" parents="58 11097 16881"/>
    </justification>
  </clause>

  <clause id="16884">
    <literal><![CDATA[
      K(x,y / (x * ((z / x) / z))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(10650,a,16883,a)].">
      <j1 rule="hyper" parents="10650 16883"/>
    </justification>
  </clause>

  <clause id="16885">
    <literal><![CDATA[
      L(K(x,y / x),y,(z / x) / z) = K(x,y * ((z / x) / z))
    ]]></literal>
    <justification jstring="[hyper(14820,a,16884,a)].">
      <j1 rule="hyper" parents="14820 16884"/>
    </justification>
  </clause>

  <clause id="16886">
    <literal><![CDATA[
      L(K(x,y / x),y,z / (z * x)) = K(x,y * ((z / x) / z))
    ]]></literal>
    <justification jstring="[hyper(14593,a,16885,a)].">
      <j1 rule="hyper" parents="14593 16885"/>
    </justification>
  </clause>

  <clause id="16887">
    <literal><![CDATA[
      K(x,y * ((z / x) / z)) = K(x,y / x)
    ]]></literal>
    <justification jstring="[hyper(16344,a,16886,a),flip(a)].">
      <j1 rule="hyper" parents="16344 16886"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16888">
    <literal><![CDATA[
      K(x,T(T(y,z),z) / x) = K(x,((z / x) / z) * y)
    ]]></literal>
    <justification jstring="[hyper(16867,a,16887,a),flip(a)].">
      <j1 rule="hyper" parents="16867 16887"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16889">
    <literal><![CDATA[
      K(x,((y / x) / y) * z) = K(x,z / x)
    ]]></literal>
    <justification jstring="[hyper(58,a,15166,a(flip),b,16888,a),flip(a)].">
      <j1 rule="hyper" parents="58 15166 16888"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16891">
    <literal><![CDATA[
      K(x / y,z / (x / y)) = K(x / y,(y / x) * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,8279,a(flip),b,16889,a),flip(a)].">
      <j1 rule="hyper" parents="58 8279 16889"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16892">
    <literal><![CDATA[
      K(x,K(y,z)) * K(z / x,(x / z) * y) = K(x \ z,y / (z / x))
    ]]></literal>
    <justification jstring="[para(16891(a,1),16733(a,1,2))].">
      <j1 rule="para" parents="16891 16733"/>
    </justification>
  </clause>

  <clause id="16893">
    <literal><![CDATA[
      K(x \ y,z / (y / x)) = K(x \ y,z * (x / y))
    ]]></literal>
    <justification jstring="[hyper(58,a,16735,a(flip),b,16892,a),flip(a)].">
      <j1 rule="hyper" parents="58 16735 16892"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16894">
    <literal><![CDATA[
      x * K(y \ z,x * (y / z)) = (y \ z) * (x / (y \ z))
    ]]></literal>
    <justification jstring="[para(16893(a,1),8526(a,1,2))].">
      <j1 rule="para" parents="16893 8526"/>
    </justification>
  </clause>

  <clause id="16895">
    <literal><![CDATA[
      (1 / (x \ y)) * (z / (1 / (x \ y))) = (y \ x) * (z / (y \ x))
    ]]></literal>
    <justification jstring="[hyper(58,a,9440,a,b,16894,a)].">
      <j1 rule="hyper" parents="58 9440 16894"/>
    </justification>
  </clause>

  <clause id="16896">
    <literal><![CDATA[
      x * K(y \ z,x * (z \ y)) = (y \ z) * (x / (y \ z))
    ]]></literal>
    <justification jstring="[para(9427(a,1),16894(a,1,2))].">
      <j1 rule="para" parents="9427 16894"/>
    </justification>
  </clause>

  <clause id="16897">
    <literal><![CDATA[
      x * K(y \ z,(z \ y) * x) = (y \ z) * (x / (y \ z))
    ]]></literal>
    <justification jstring="[para(9426(a,2),16896(a,1,2))].">
      <j1 rule="para" parents="9426 16896"/>
    </justification>
  </clause>

  <clause id="16898">
    <literal><![CDATA[
      (((x \ y) * z) \ z) * ((x \ y) * z) = (y \ x) * (z / (y \ x))
    ]]></literal>
    <justification jstring="[hyper(58,a,6280,a,b,16897,a)].">
      <j1 rule="hyper" parents="58 6280 16897"/>
    </justification>
  </clause>

  <clause id="16899">
    <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(7326(a,1),16297(a,1,2,2,1))].">
      <j1 rule="para" parents="7326 16297"/>
    </justification>
  </clause>

  <clause id="16900">
    <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(10846(a,1),16563(a,1,1))].">
      <j1 rule="para" parents="10846 16563"/>
    </justification>
  </clause>

  <clause id="16901">
    <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(6335(a,1),15970(a,1,2,1))].">
      <j1 rule="para" parents="6335 15970"/>
    </justification>
  </clause>

  <clause id="16902">
    <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(12363(a,1),15984(a,1,1))].">
      <j1 rule="para" parents="12363 15984"/>
    </justification>
  </clause>

  <clause id="16903">
    <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(6259(a,1),16902(a,1,2))].">
      <j1 rule="para" parents="6259 16902"/>
    </justification>
  </clause>

  <clause id="16904">
    <literal><![CDATA[
      K((x \ y) \ z,x / y) * K(x / y,z) = a((x \ y) \ 1,z,(x \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(15644(a,1),16903(a,1,2))].">
      <j1 rule="para" parents="15644 16903"/>
    </justification>
  </clause>

  <clause id="16905">
    <literal><![CDATA[
      a((x \ y) \ 1,z,(x \ y) \ 1) = a(y \ x,z,y \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,12849,a(flip),b,16904,a),flip(a)].">
      <j1 rule="hyper" parents="58 12849 16904"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16906">
    <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(16905(a,1),13546(a,1,1))].">
      <j1 rule="para" parents="16905 13546"/>
    </justification>
  </clause>

  <clause id="16907">
    <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(13186(a,1),16587(a,1,2))].">
      <j1 rule="para" parents="13186 16587"/>
    </justification>
  </clause>

  <clause id="16908">
    <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(14554,a,16907,a),flip(a)].">
      <j1 rule="hyper" parents="14554 16907"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16909">
    <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,16395,a(flip),b,16908,a)].">
      <j1 rule="hyper" parents="58 16395 16908"/>
    </justification>
  </clause>

  <clause id="16910">
    <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),16909(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6 16909"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16912">
    <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,16127,a),flip(a)].">
      <j1 rule="hyper" parents="320 20 16127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16913">
    <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(7230(a,1),16444(a,1,2))].">
      <j1 rule="para" parents="7230 16444"/>
    </justification>
  </clause>

  <clause id="16915">
    <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(14478(a,1),16912(a,1,1,2,1))].">
      <j1 rule="para" parents="14478 16912"/>
    </justification>
  </clause>

  <clause id="16916">
    <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(14485(a,1),16915(a,1,1))].">
      <j1 rule="para" parents="14485 16915"/>
    </justification>
  </clause>

  <clause id="16917">
    <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),16916(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6 16916"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16918">
    <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(16102,a,16913,a)].">
      <j1 rule="hyper" parents="16102 16913"/>
    </justification>
  </clause>

  <clause id="16919">
    <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(15886,a,16918,a),flip(a)].">
      <j1 rule="hyper" parents="15886 16918"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16921">
    <literal><![CDATA[
      (x / K(y,T(z,u))) \ (K(z,y) * u) = (x * K(z,y)) \ (u * K(z,y))
    ]]></literal>
    <justification jstring="[para(16419(a,1),16919(a,1,1,2))].">
      <j1 rule="para" parents="16419 16919"/>
    </justification>
  </clause>

  <clause id="16922">
    <literal><![CDATA[
      (x * K(y,T(z,u))) \ (K(y,z) * u) = (x * K(y,z)) \ (u * K(y,z))
    ]]></literal>
    <justification jstring="[para(7230(a,1),16921(a,1,1))].">
      <j1 rule="para" parents="7230 16921"/>
    </justification>
  </clause>

  <clause id="16924">
    <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,16917,a,b,16922,a)].">
      <j1 rule="hyper" parents="58 16917 16922"/>
    </justification>
  </clause>

  <clause id="16925">
    <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(16142,a,16285,a)].">
      <j1 rule="hyper" parents="16142 16285"/>
    </justification>
  </clause>

  <clause id="16927">
    <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(16011(a,1),16925(a,1,1,2))].">
      <j1 rule="para" parents="16011 16925"/>
    </justification>
  </clause>

  <clause id="16929">
    <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),16906(a,1,1,1))].">
      <j1 rule="para" parents="4 16906"/>
    </justification>
  </clause>

  <clause id="16930">
    <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),16929(a,1,1,3)),flip(a)].">
      <j1 rule="para" parents="4 16929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16931">
    <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(6123(a,1),16930(a,2,2))].">
      <j1 rule="para" parents="6123 16930"/>
    </justification>
  </clause>

  <clause id="16932">
    <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),16931(a,2,2,2))].">
      <j1 rule="para" parents="4 16931"/>
    </justification>
  </clause>

  <clause id="16933">
    <literal><![CDATA[
      K(x * (1 / ((y * z) \ y)),1 / ((y * z) \ y)) = a(z,x,z) * K(x,z)
    ]]></literal>
    <justification jstring="[para(4958(a,1),16932(a,2,2))].">
      <j1 rule="para" parents="4958 16932"/>
    </justification>
  </clause>

  <clause id="16934">
    <literal><![CDATA[
      K(x * (1 / ((y * z) \ y)),1 / ((y * z) \ y)) = K(z * x,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,8966,a(flip),b,16933,a),flip(a)].">
      <j1 rule="hyper" parents="320 8966 16933"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16935">
    <literal><![CDATA[
      K(x * (1 / ((y * z) \ y)),y \ (y * z)) = K(z * x,z)
    ]]></literal>
    <justification jstring="[hyper(6483,a,16934,a)].">
      <j1 rule="hyper" parents="6483 16934"/>
    </justification>
  </clause>

  <clause id="16936">
    <literal><![CDATA[
      K(x * (1 / ((y * z) \ y)),z) = K(z * x,z)
    ]]></literal>
    <justification jstring="[para(4(a,1),16935(a,1,2))].">
      <j1 rule="para" parents="4 16935"/>
    </justification>
  </clause>

  <clause id="16937">
    <literal><![CDATA[
      K(x * (((y * z) \ y) \ 1),z) = K(z * x,z)
    ]]></literal>
    <justification jstring="[hyper(14084,a,16936,a)].">
      <j1 rule="hyper" parents="14084 16936"/>
    </justification>
  </clause>

  <clause id="16938">
    <literal><![CDATA[
      K(((x * y) \ x) \ z,y) = K(y * z,y)
    ]]></literal>
    <justification jstring="[hyper(9688,a,16937,a)].">
      <j1 rule="hyper" parents="9688 16937"/>
    </justification>
  </clause>

  <clause id="16939">
    <literal><![CDATA[
      K(((x * y) \ x) \ (y \ z),y) = K(z,y)
    ]]></literal>
    <justification jstring="[para(5(a,1),16938(a,2,1))].">
      <j1 rule="para" parents="5 16938"/>
    </justification>
  </clause>

  <clause id="16940">
    <literal><![CDATA[
      K(((x * y) \ x) * z,y) = K(y \ z,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,10350,a(flip),b,16939,a),flip(a)].">
      <j1 rule="hyper" parents="58 10350 16939"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16941">
    <literal><![CDATA[
      K(x * ((y * z) \ y),z) = K(z \ x,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,9424,a(flip),b,16940,a)].">
      <j1 rule="hyper" parents="58 9424 16940"/>
    </justification>
  </clause>

  <clause id="16942">
    <literal><![CDATA[
      K((x \ y) \ z,x \ y) = K((y \ x) * z,x \ y)
    ]]></literal>
    <justification jstring="[para(5(a,1),16940(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5 16940"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16944">
    <literal><![CDATA[
      K((x \ y) \ z,x \ y) = K(z * (y \ x),x \ y)
    ]]></literal>
    <justification jstring="[para(5(a,1),16941(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 16941"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16945">
    <literal><![CDATA[
      x * K((y \ z) * x,z \ y) = ((z \ y) \ x) * (z \ y)
    ]]></literal>
    <justification jstring="[hyper(119,a,16942,a(flip),b,85,a)].">
      <j1 rule="hyper" parents="119 16942 85"/>
    </justification>
  </clause>

  <clause id="16946">
    <literal><![CDATA[
      K((x \ y) \ z,x \ y) = K(z * (x / y),x \ y)
    ]]></literal>
    <justification jstring="[hyper(320,a,9429,a,b,16944,a),flip(a)].">
      <j1 rule="hyper" parents="320 9429 16944"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16947">
    <literal><![CDATA[
      x * K(x * (y / z),y \ z) = ((y \ z) \ x) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(119,a,16946,a(flip),b,85,a)].">
      <j1 rule="hyper" parents="119 16946 85"/>
    </justification>
  </clause>

  <clause id="16948">
    <literal><![CDATA[
      (((x \ y) \ 1) \ z) * ((x \ y) \ 1) = ((y \ x) \ z) * (y \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,6137,a,b,16945,a)].">
      <j1 rule="hyper" parents="58 6137 16945"/>
    </justification>
  </clause>

  <clause id="16949">
    <literal><![CDATA[
      ((1 / (x \ y)) \ z) * (1 / (x \ y)) = ((y \ x) \ z) * (y \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,9441,a,b,16947,a)].">
      <j1 rule="hyper" parents="58 9441 16947"/>
    </justification>
  </clause>

  <clause id="16950">
    <literal><![CDATA[
      ((x \ y) * z) * (z / ((x \ y) * z)) = ((y \ x) \ z) * (y \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,3928,a(flip),b,16948,a)].">
      <j1 rule="hyper" parents="58 3928 16948"/>
    </justification>
  </clause>

  <clause id="16951">
    <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(16949(a,1),16776(a,1,1,1,2,1,2))].">
      <j1 rule="para" parents="16949 16776"/>
    </justification>
  </clause>

  <clause id="16952">
    <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(16895(a,1),16951(a,1,1,1))].">
      <j1 rule="para" parents="16895 16951"/>
    </justification>
  </clause>

  <clause id="16953">
    <literal><![CDATA[
      K(1 / x,T(y,z / (1 / (u \ w)))) = K(1 / x,T(y,z / (w \ u)))
    ]]></literal>
    <justification jstring="[hyper(16778,a,16952,a),flip(a)].">
      <j1 rule="hyper" parents="16778 16952"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16954">
    <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,16423,a,b,16953,a),flip(a)].">
      <j1 rule="hyper" parents="320 16423 16953"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16955">
    <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,16628,a,b,16954,a)].">
      <j1 rule="hyper" parents="58 16628 16954"/>
    </justification>
  </clause>

  <clause id="16956">
    <literal><![CDATA[
      K(1 / x,T(y,z / (u / w))) = K(1 / x,T(y,(w / u) * z))
    ]]></literal>
    <justification jstring="[hyper(15948,a,16955,a),flip(a)].">
      <j1 rule="hyper" parents="15948 16955"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16957">
    <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(16956(a,1),16629(a,2,1))].">
      <j1 rule="para" parents="16956 16629"/>
    </justification>
  </clause>

  <clause id="16958">
    <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,4904,a(flip),b,16957,a),flip(a)].">
      <j1 rule="hyper" parents="320 4904 16957"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16959">
    <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(16958(a,1),3322(a,1,1))].">
      <j1 rule="para" parents="16958 3322"/>
    </justification>
  </clause>

  <clause id="16960">
    <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,3322,a(flip),b,16959,a),flip(a)].">
      <j1 rule="hyper" parents="58 3322 16959"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16961">
    <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(16960(a,1),13610(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="16960 13610"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16962">
    <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,13610,a(flip),b,16961,a),flip(a)].">
      <j1 rule="hyper" parents="320 13610 16961"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16963">
    <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,7160,a(flip),b,16962,a),flip(a)].">
      <j1 rule="hyper" parents="320 7160 16962"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16964">
    <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(7704,a,16963,a)].">
      <j1 rule="hyper" parents="7704 16963"/>
    </justification>
  </clause>

  <clause id="16965">
    <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,16626,a(flip),b,16964,a)].">
      <j1 rule="hyper" parents="58 16626 16964"/>
    </justification>
  </clause>

  <clause id="16966">
    <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,16627,a(flip),b,16965,a),flip(a)].">
      <j1 rule="hyper" parents="58 16627 16965"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16967">
    <literal><![CDATA[
      K(x,T(y,(T(z,u) / w) * v5)) = K(x,T(y,v5 / (w / z)))
    ]]></literal>
    <justification jstring="[hyper(58,a,8480,a(flip),b,16966,a)].">
      <j1 rule="hyper" parents="58 8480 16966"/>
    </justification>
  </clause>

  <clause id="16968">
    <literal><![CDATA[
      K(x,T(y,z / (u / w))) = K(x,T(y,(w / u) * z))
    ]]></literal>
    <justification jstring="[para(104(a,1),16967(a,1,2,2,1,1)),flip(a)].">
      <j1 rule="para" parents="104 16967"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16969">
    <literal><![CDATA[
      K(x,T(y,z / (u \ w))) = K(x,T(y,(u / w) * z))
    ]]></literal>
    <justification jstring="[hyper(16464,a,16968,a)].">
      <j1 rule="hyper" parents="16464 16968"/>
    </justification>
  </clause>

  <clause id="16971">
    <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,7766,a,b,16969,a)].">
      <j1 rule="hyper" parents="320 7766 16969"/>
    </justification>
  </clause>

  <clause id="16972">
    <literal><![CDATA[
      K(x,K(y,z / (u / w))) = K(x,K(y,(w / u) * z))
    ]]></literal>
    <justification jstring="[hyper(29,a,16465,a,b,16971,a)].">
      <j1 rule="hyper" parents="29 16465 16971"/>
    </justification>
  </clause>

  <clause id="16973">
    <literal><![CDATA[
      K(x,K(y,(z / u) / w)) = K(x,K(y,(u / z) * w))
    ]]></literal>
    <justification jstring="[hyper(8268,a,16972,a)].">
      <j1 rule="hyper" parents="8268 16972"/>
    </justification>
  </clause>

  <clause id="16974">
    <literal><![CDATA[
      K(x,K(y,((z / u) / z) * w)) = K(x,K(y,w / u))
    ]]></literal>
    <justification jstring="[hyper(58,a,16489,a(flip),b,16972,a),flip(a)].">
      <j1 rule="hyper" parents="58 16489 16972"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16975">
    <literal><![CDATA[
      K(x,K(y,(z / (z * u)) * w)) = K(x,K(y,w / u))
    ]]></literal>
    <justification jstring="[hyper(58,a,16487,a(flip),b,16972,a),flip(a)].">
      <j1 rule="hyper" parents="58 16487 16972"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16976">
    <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(16972(a,1),16520(a,1,1))].">
      <j1 rule="para" parents="16972 16520"/>
    </justification>
  </clause>

  <clause id="16977">
    <literal><![CDATA[
      K(x,K(y,z * (u / (u * w)))) = K(x,K(y,z / w))
    ]]></literal>
    <justification jstring="[hyper(15609,a,16975,a)].">
      <j1 rule="hyper" parents="15609 16975"/>
    </justification>
  </clause>

  <clause id="16978">
    <literal><![CDATA[
      K(x,K(y,z / (u \ w))) = K(x,K(y,z * (u / w)))
    ]]></literal>
    <justification jstring="[para(5(a,1),16977(a,1,2,2,2,2)),flip(a)].">
      <j1 rule="para" parents="5 16977"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16979">
    <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(10847,a,16976,a),flip(a)].">
      <j1 rule="hyper" parents="10847 16976"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16980">
    <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,16554,a(flip),b,16979,a),flip(a)].">
      <j1 rule="hyper" parents="58 16554 16979"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16981">
    <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),16979(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="75 16979"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16982">
    <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(15900,a,16981,a)].">
      <j1 rule="hyper" parents="15900 16981"/>
    </justification>
  </clause>

  <clause id="16983">
    <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),16980(a,2,2,2,2))].">
      <j1 rule="para" parents="5 16980"/>
    </justification>
  </clause>

  <clause id="16984">
    <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,16497,a,b,16983,a),flip(a)].">
      <j1 rule="hyper" parents="320 16497 16983"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16985">
    <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(16983(a,2),16535(a,1))].">
      <j1 rule="para" parents="16983 16535"/>
    </justification>
  </clause>

  <clause id="16986">
    <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,16982,a(flip),b,16984,a)].">
      <j1 rule="hyper" parents="58 16982 16984"/>
    </justification>
  </clause>

  <clause id="16987">
    <literal><![CDATA[
      K(x,K((y / z) / u,L(w,z,y))) = K(x,K(w,(y * (1 / u)) / z))
    ]]></literal>
    <justification jstring="[para(13842(a,1),16984(a,1,2))].">
      <j1 rule="para" parents="13842 16984"/>
    </justification>
  </clause>

  <clause id="16988">
    <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(16984(a,2),16535(a,1))].">
      <j1 rule="para" parents="16984 16535"/>
    </justification>
  </clause>

  <clause id="16989">
    <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,16987,a(flip),b,16986,a),flip(a)].">
      <j1 rule="hyper" parents="58 16987 16986"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16990">
    <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(3917(a,2),16986(a,2,2,2,1))].">
      <j1 rule="para" parents="3917 16986"/>
    </justification>
  </clause>

  <clause id="16991">
    <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(13844(a,1),16990(a,1,2))].">
      <j1 rule="para" parents="13844 16990"/>
    </justification>
  </clause>

  <clause id="16992">
    <literal><![CDATA[
      K(x,K(y,(T(z,u) / (1 / u)) / w)) = K(x,K(y,(z * u) / w))
    ]]></literal>
    <justification jstring="[hyper(16985,a,16991,a),flip(a)].">
      <j1 rule="hyper" parents="16985 16991"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16993">
    <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,16973,a(flip),b,16992,a)].">
      <j1 rule="hyper" parents="58 16973 16992"/>
    </justification>
  </clause>

  <clause id="16994">
    <literal><![CDATA[
      K(x,K(y,z * ((1 / u) / w))) = K(x,K(y,(w * u) / z))
    ]]></literal>
    <justification jstring="[hyper(16557,a,16993,a)].">
      <j1 rule="hyper" parents="16557 16993"/>
    </justification>
  </clause>

  <clause id="16995">
    <literal><![CDATA[
      K(x,K(y,((z \ 1) / u) * w)) = K(x,K(y,(u * z) / w))
    ]]></literal>
    <justification jstring="[hyper(58,a,16568,a,b,16994,a)].">
      <j1 rule="hyper" parents="58 16568 16994"/>
    </justification>
  </clause>

  <clause id="16996">
    <literal><![CDATA[
      K(x,K(y,(z * (1 / u)) / w)) = K(x,K(y,(u / z) * w))
    ]]></literal>
    <justification jstring="[hyper(58,a,16566,a(flip),b,16994,a),flip(a)].">
      <j1 rule="hyper" parents="58 16566 16994"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16997">
    <literal><![CDATA[
      K(x,K(y,((z / (z / (u \ 1))) / w) * v5)) = K(x,K(y,(w * u) / v5))
    ]]></literal>
    <justification jstring="[hyper(16569,a,16995,a)].">
      <j1 rule="hyper" parents="16569 16995"/>
    </justification>
  </clause>

  <clause id="16998">
    <literal><![CDATA[
      K(x,K(y,z / ((1 / u) * w))) = K(x,K(y,(u / w) * z))
    ]]></literal>
    <justification jstring="[hyper(16527,a,16996,a)].">
      <j1 rule="hyper" parents="16527 16996"/>
    </justification>
  </clause>

  <clause id="16999">
    <literal><![CDATA[
      K(x,K(y,(z * ((u / w) / u)) / v5)) = K(x,K(y,(w / z) * v5))
    ]]></literal>
    <justification jstring="[hyper(58,a,16989,a,b,16996,a)].">
      <j1 rule="hyper" parents="58 16989 16996"/>
    </justification>
  </clause>

  <clause id="17000">
    <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,15616,a(flip),b,16996,a),flip(a)].">
      <j1 rule="hyper" parents="58 15616 16996"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17001">
    <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,14874,a,b,16998,a)].">
      <j1 rule="hyper" parents="58 14874 16998"/>
    </justification>
  </clause>

  <clause id="17002">
    <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(8213(a,1),16998(a,1,2))].">
      <j1 rule="para" parents="8213 16998"/>
    </justification>
  </clause>

  <clause id="17003">
    <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(14733(a,1),16998(a,1,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="14733 16998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17004">
    <literal><![CDATA[
      K(x,K(y,z / (((u / w) / u) * v5))) = K(x,K(y,(w / v5) * z))
    ]]></literal>
    <justification jstring="[hyper(16527,a,16999,a)].">
      <j1 rule="hyper" parents="16527 16999"/>
    </justification>
  </clause>

  <clause id="17005">
    <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,14706,a(flip),b,17001,a)].">
      <j1 rule="hyper" parents="58 14706 17001"/>
    </justification>
  </clause>

  <clause id="17006">
    <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(16202(a,1),17002(a,1,2)),flip(a)].">
      <j1 rule="para" parents="16202 17002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17007">
    <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,17004,a(flip),b,17003,a),flip(a)].">
      <j1 rule="hyper" parents="320 17004 17003"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17009">
    <literal><![CDATA[
      K(x,K(y,(z * (u / w)) / v5)) = K(x,K(y,((w / u) / z) * v5))
    ]]></literal>
    <justification jstring="[hyper(58,a,16997,a(flip),b,17007,a)].">
      <j1 rule="hyper" parents="58 16997 17007"/>
    </justification>
  </clause>

  <clause id="17010">
    <literal><![CDATA[
      K(x,K(y,((z / u) * w) / v5)) = K(x,K(y,((u / z) / w) * v5))
    ]]></literal>
    <justification jstring="[hyper(16535,a,17009,a)].">
      <j1 rule="hyper" parents="16535 17009"/>
    </justification>
  </clause>

  <clause id="17012">
    <literal><![CDATA[
      K(x,K(y,z / ((u \ w) * v5))) = K(x,K(y,((u / w) / v5) * z))
    ]]></literal>
    <justification jstring="[hyper(58,a,16551,a(flip),b,17009,a)].">
      <j1 rule="hyper" parents="58 16551 17009"/>
    </justification>
  </clause>

  <clause id="17013">
    <literal><![CDATA[
      K(x,K(y,((z \ u) * w) / v5)) = K(x,K(y,((z / u) / w) * v5))
    ]]></literal>
    <justification jstring="[hyper(8268,a,17012,a)].">
      <j1 rule="hyper" parents="8268 17012"/>
    </justification>
  </clause>

  <clause id="17014">
    <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),17012(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="105 17012"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17015">
    <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,16846,a(flip),b,17013,a),flip(a)].">
      <j1 rule="hyper" parents="58 16846 17013"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17016">
    <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(15605,a,17015,a)].">
      <j1 rule="hyper" parents="15605 17015"/>
    </justification>
  </clause>

  <clause id="17017">
    <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,14489,a,b,17015,a),flip(a)].">
      <j1 rule="hyper" parents="320 14489 17015"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17018">
    <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(17015(a,1),7781(a,1))].">
      <j1 rule="para" parents="17015 7781"/>
    </justification>
  </clause>

  <clause id="17019">
    <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),17016(a,1,2,2,2,2))].">
      <j1 rule="para" parents="7 17016"/>
    </justification>
  </clause>

  <clause id="17020">
    <literal><![CDATA[
      K(x,K(y,z / (u * (w \ v5)))) = K(x,K(y,z * ((w / v5) / u)))
    ]]></literal>
    <justification jstring="[hyper(16557,a,17014,a),flip(a)].">
      <j1 rule="hyper" parents="16557 17014"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17021">
    <literal><![CDATA[
      K(x,K(y,z / (u * (w / v5)))) = K(x,K(y,z * ((v5 / w) / u)))
    ]]></literal>
    <justification jstring="[hyper(16603,a,17020,a)].">
      <j1 rule="hyper" parents="16603 17020"/>
    </justification>
  </clause>

  <clause id="17022">
    <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(17021(a,1),16647(a,1))].">
      <j1 rule="para" parents="17021 16647"/>
    </justification>
  </clause>

  <clause id="17023">
    <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),17017(a,2,2))].">
      <j1 rule="para" parents="7 17017"/>
    </justification>
  </clause>

  <clause id="17024">
    <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,8187,a(flip),b,17006,a),flip(a)].">
      <j1 rule="hyper" parents="320 8187 17006"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17025">
    <literal><![CDATA[
      K(x,K(y,z * ((1 / u) * w))) = K(x,K(y,(u / w) / z))
    ]]></literal>
    <justification jstring="[hyper(58,a,16977,a(flip),b,17024,a),flip(a)].">
      <j1 rule="hyper" parents="58 16977 17024"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17027">
    <literal><![CDATA[
      K(x,K(y,z * ((1 / u) * w))) = K(x,K(y,(w / u) * z))
    ]]></literal>
    <justification jstring="[hyper(320,a,16973,a(flip),b,17025,a),flip(a)].">
      <j1 rule="hyper" parents="320 16973 17025"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17028">
    <literal><![CDATA[
      K(x,K(y,z * (u * (1 / w)))) = K(x,K(y,(u / w) * z))
    ]]></literal>
    <justification jstring="[hyper(16559,a,17027,a)].">
      <j1 rule="hyper" parents="16559 17027"/>
    </justification>
  </clause>

  <clause id="17029">
    <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),17027(a,1,2,2,2))].">
      <j1 rule="para" parents="259 17027"/>
    </justification>
  </clause>

  <clause id="17030">
    <literal><![CDATA[
      K(x,K(y,z * L(u,w,1 / w))) = K(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(320,a,16494,a(flip),b,17029,a),flip(a)].">
      <j1 rule="hyper" parents="320 16494 17029"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17032">
    <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,16854,a(flip),b,17030,a),flip(a)].">
      <j1 rule="hyper" parents="58 16854 17030"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17034">
    <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),17032(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="101 17032"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17035">
    <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,16480,a,b,17034,a)].">
      <j1 rule="hyper" parents="58 16480 17034"/>
    </justification>
  </clause>

  <clause id="17036">
    <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(16556,a,17035,a),flip(a)].">
      <j1 rule="hyper" parents="16556 17035"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17037">
    <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,11833,a(flip),b,17035,a)].">
      <j1 rule="hyper" parents="58 11833 17035"/>
    </justification>
  </clause>

  <clause id="17038">
    <literal><![CDATA[
      K(x,K(y,z * (u * ((1 / w) * v5)))) = K(x,K(y,z * ((v5 / w) * u)))
    ]]></literal>
    <justification jstring="[hyper(16556,a,17036,a),flip(a)].">
      <j1 rule="hyper" parents="16556 17036"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17039">
    <literal><![CDATA[
      K(x,K(y,z * (((u / (1 / w)) / w) * v5))) = K(x,K(y,z * (v5 * u)))
    ]]></literal>
    <justification jstring="[hyper(16560,a,17038,a),flip(a)].">
      <j1 rule="hyper" parents="16560 17038"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17040">
    <literal><![CDATA[
      K(x,K(y,z * (((1 / u) * w) * v5))) = K(x,K(y,z * ((w / u) * v5)))
    ]]></literal>
    <justification jstring="[hyper(16559,a,17038,a)].">
      <j1 rule="hyper" parents="16559 17038"/>
    </justification>
  </clause>

  <clause id="17041">
    <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,17000,a(flip),b,17038,a),flip(a)].">
      <j1 rule="hyper" parents="58 17000 17038"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17042">
    <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,17028,a(flip),b,17041,a)].">
      <j1 rule="hyper" parents="58 17028 17041"/>
    </justification>
  </clause>

  <clause id="17043">
    <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,16547,a(flip),b,17039,a),flip(a)].">
      <j1 rule="hyper" parents="320 16547 17039"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17044">
    <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,11833,a(flip),b,17037,a),flip(a)].">
      <j1 rule="hyper" parents="320 11833 17037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17045">
    <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,17010,a(flip),b,17044,a),flip(a)].">
      <j1 rule="hyper" parents="320 17010 17044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17046">
    <literal><![CDATA[
      K(x,K(y,z / (u * ((1 / w) * v5)))) = K(x,K(y,((w / v5) / u) * z))
    ]]></literal>
    <justification jstring="[hyper(8268,a,17045,a)].">
      <j1 rule="hyper" parents="8268 17045"/>
    </justification>
  </clause>

  <clause id="17047">
    <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(13653(a,1),17046(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13653 17046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17048">
    <literal><![CDATA[
      K(x,K(y,z * ((u / (1 / w)) * K(w,v5)))) = K(x,K(y,(w * u) * z))
    ]]></literal>
    <justification jstring="[para(6151(a,1),17043(a,1,2,2,2))].">
      <j1 rule="para" parents="6151 17043"/>
    </justification>
  </clause>

  <clause id="17049">
    <literal><![CDATA[
      K(x,K(y,z * (u / (1 / w)))) = K(x,K(y,(w * u) * z))
    ]]></literal>
    <justification jstring="[hyper(16558,a,17048,a)].">
      <j1 rule="hyper" parents="16558 17048"/>
    </justification>
  </clause>

  <clause id="17050">
    <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,17049,a(flip),b,17042,a)].">
      <j1 rule="hyper" parents="58 17049 17042"/>
    </justification>
  </clause>

  <clause id="17051">
    <literal><![CDATA[
      K(x,K(y,L(z,1 / u,1 / w))) = K(x,K(z,L(y,u,w)))
    ]]></literal>
    <justification jstring="[hyper(17022,a,17050,a),flip(a)].">
      <j1 rule="hyper" parents="17022 17050"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17052">
    <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,14612,a(flip),b,17051,a)].">
      <j1 rule="hyper" parents="58 14612 17051"/>
    </justification>
  </clause>

  <clause id="17053">
    <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,14432,a,b,17047,a),flip(a)].">
      <j1 rule="hyper" parents="320 14432 17047"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17054">
    <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,13045,a(flip),b,16319,a),flip(a)].">
      <j1 rule="hyper" parents="58 13045 16319"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17055">
    <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),17054(a,1,2,1))].">
      <j1 rule="para" parents="60 17054"/>
    </justification>
  </clause>

  <clause id="17056">
    <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(15899,a,16555,a),flip(a)].">
      <j1 rule="hyper" parents="15899 16555"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17058">
    <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(14773(a,1),17056(a,2,2))].">
      <j1 rule="para" parents="14773 17056"/>
    </justification>
  </clause>

  <clause id="17059">
    <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,16622,a(flip),b,17058,a),flip(a)].">
      <j1 rule="hyper" parents="320 16622 17058"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17060">
    <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(16570,a,17059,a)].">
      <j1 rule="hyper" parents="16570 17059"/>
    </justification>
  </clause>

  <clause id="17062">
    <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,16525,a(flip),b,17060,a)].">
      <j1 rule="hyper" parents="58 16525 17060"/>
    </justification>
  </clause>

  <clause id="17063">
    <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,16517,a(flip),b,17062,a),flip(a)].">
      <j1 rule="hyper" parents="58 16517 17062"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17064">
    <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(10872,a,17063,a)].">
      <j1 rule="hyper" parents="10872 17063"/>
    </justification>
  </clause>

  <clause id="17066">
    <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(13712(a,1),17063(a,1,2,2,2))].">
      <j1 rule="para" parents="13712 17063"/>
    </justification>
  </clause>

  <clause id="17067">
    <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,14435,a,b,17064,a),flip(a)].">
      <j1 rule="hyper" parents="320 14435 17064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17068">
    <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,17052,a(flip),b,17066,a),flip(a)].">
      <j1 rule="hyper" parents="320 17052 17066"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17069">
    <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(17068(a,1),16900(a,1,1)),flip(a)].">
      <j1 rule="para" parents="17068 16900"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17070">
    <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(14436,a,17067,a)].">
      <j1 rule="hyper" parents="14436 17067"/>
    </justification>
  </clause>

  <clause id="17071">
    <literal><![CDATA[
      a(x,y * (z / y),K(u,K(w,v5))) = a(x,z,K(u,K(w,v5)))
    ]]></literal>
    <justification jstring="[para(4717(a,1),17070(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4717 17070"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17072">
    <literal><![CDATA[
      a(x,y / z,K(u,K(w,v5))) = a(x,z \ y,K(u,K(w,v5)))
    ]]></literal>
    <justification jstring="[para(4859(a,1),17070(a,1,2))].">
      <j1 rule="para" parents="4859 17070"/>
    </justification>
  </clause>

  <clause id="17073">
    <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,11842,a(flip),b,17071,a),flip(a)].">
      <j1 rule="hyper" parents="58 11842 17071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17074">
    <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(7784(a,2),17073(a,2,3))].">
      <j1 rule="para" parents="7784 17073"/>
    </justification>
  </clause>

  <clause id="17075">
    <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(11837(a,1),17074(a,2,3))].">
      <j1 rule="para" parents="11837 17074"/>
    </justification>
  </clause>

  <clause id="17076">
    <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),17075(a,1,3,2,2))].">
      <j1 rule="para" parents="5 17075"/>
    </justification>
  </clause>

  <clause id="17077">
    <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(7784(a,1),17076(a,1,3))].">
      <j1 rule="para" parents="7784 17076"/>
    </justification>
  </clause>

  <clause id="17078">
    <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),17077(a,2,3,2,2))].">
      <j1 rule="para" parents="5 17077"/>
    </justification>
  </clause>

  <clause id="17079">
    <literal><![CDATA[
      a(x,1 / (y \ z),K(z,K(u,w))) = a(x,y,K(z,K(u,w)))
    ]]></literal>
    <justification jstring="[para(7784(a,1),17078(a,2,3))].">
      <j1 rule="para" parents="7784 17078"/>
    </justification>
  </clause>

  <clause id="17080">
    <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),17079(a,1,2,2))].">
      <j1 rule="para" parents="75 17079"/>
    </justification>
  </clause>

  <clause id="17081">
    <literal><![CDATA[
      a(x,1 / y,K(z,K(u,w))) = a(x,w / y,K(w,K(z,u)))
    ]]></literal>
    <justification jstring="[para(7784(a,2),17080(a,1,3))].">
      <j1 rule="para" parents="7784 17080"/>
    </justification>
  </clause>

  <clause id="17082">
    <literal><![CDATA[
      a(x,1 / y,K(z,K(u,w))) = a(x,w / y,K(z,K(u,w)))
    ]]></literal>
    <justification jstring="[para(7784(a,2),17081(a,2,3))].">
      <j1 rule="para" parents="7784 17081"/>
    </justification>
  </clause>

  <clause id="17083">
    <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,14404,a,b,17082,a)].">
      <j1 rule="hyper" parents="58 14404 17082"/>
    </justification>
  </clause>

  <clause id="17084">
    <literal><![CDATA[
      a(x,1 / y,K(z,K(u,w))) = a(w,u / y,K(z,K(u,x)))
    ]]></literal>
    <justification jstring="[para(7797(a,1),17083(a,2,3))].">
      <j1 rule="para" parents="7797 17083"/>
    </justification>
  </clause>

  <clause id="17085">
    <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(7796(a,1),17069(a,2,2))].">
      <j1 rule="para" parents="7796 17069"/>
    </justification>
  </clause>

  <clause id="17087">
    <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,11529,a(flip),b,17085,a),flip(a)].">
      <j1 rule="hyper" parents="320 11529 17085"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17088">
    <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(6610(a,1),17087(a,2,1))].">
      <j1 rule="para" parents="6610 17087"/>
    </justification>
  </clause>

  <clause id="17089">
    <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,14543,a(flip),b,17088,a),flip(a)].">
      <j1 rule="hyper" parents="320 14543 17088"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17090">
    <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(16562(a,1),17089(a,1,2))].">
      <j1 rule="para" parents="16562 17089"/>
    </justification>
  </clause>

  <clause id="17091">
    <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(7796(a,1),17090(a,1,3))].">
      <j1 rule="para" parents="7796 17090"/>
    </justification>
  </clause>

  <clause id="17092">
    <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(10935,a,17091,a)].">
      <j1 rule="hyper" parents="10935 17091"/>
    </justification>
  </clause>

  <clause id="17093">
    <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),17092(a,1,2,1))].">
      <j1 rule="para" parents="166 17092"/>
    </justification>
  </clause>

  <clause id="17094">
    <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,17053,a,b,17093,a)].">
      <j1 rule="hyper" parents="58 17053 17093"/>
    </justification>
  </clause>

  <clause id="17095">
    <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,17084,a(flip),b,17093,a)].">
      <j1 rule="hyper" parents="58 17084 17093"/>
    </justification>
  </clause>

  <clause id="17096">
    <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,14405,a,b,17095,a),flip(a)].">
      <j1 rule="hyper" parents="320 14405 17095"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17097">
    <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(7784(a,1),17094(a,2,3))].">
      <j1 rule="para" parents="7784 17094"/>
    </justification>
  </clause>

  <clause id="17098">
    <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(5520(a,1),17097(a,1,2,2,2,1))].">
      <j1 rule="para" parents="5520 17097"/>
    </justification>
  </clause>

  <clause id="17099">
    <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(13928(a,1),16645(a,1,2,2,1,2))].">
      <j1 rule="para" parents="13928 16645"/>
    </justification>
  </clause>

  <clause id="17100">
    <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(14205(a,1),17099(a,1,2,2,1))].">
      <j1 rule="para" parents="14205 17099"/>
    </justification>
  </clause>

  <clause id="17101">
    <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(9924(a,1),17098(a,1,2))].">
      <j1 rule="para" parents="9924 17098"/>
    </justification>
  </clause>

  <clause id="17102">
    <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(13935(a,1),17101(a,1,2))].">
      <j1 rule="para" parents="13935 17101"/>
    </justification>
  </clause>

  <clause id="17103">
    <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(6441(a,1),17102(a,1,2,2,1))].">
      <j1 rule="para" parents="6441 17102"/>
    </justification>
  </clause>

  <clause id="17104">
    <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,17040,a(flip),b,17103,a)].">
      <j1 rule="hyper" parents="58 17040 17103"/>
    </justification>
  </clause>

  <clause id="17105">
    <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(16523,a,17104,a)].">
      <j1 rule="hyper" parents="16523 17104"/>
    </justification>
  </clause>

  <clause id="17106">
    <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(6359(a,1),17105(a,2,3,2))].">
      <j1 rule="para" parents="6359 17105"/>
    </justification>
  </clause>

  <clause id="17107">
    <literal><![CDATA[
      K(x,K(y,((z / u) * w) * ((u / w) / z))) = a(w,u,K(x,K(y,z)))
    ]]></literal>
    <justification jstring="[para(16475(a,1),17106(a,2,3))].">
      <j1 rule="para" parents="16475 17106"/>
    </justification>
  </clause>

  <clause id="17108">
    <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,17019,a(flip),b,17107,a)].">
      <j1 rule="hyper" parents="58 17019 17107"/>
    </justification>
  </clause>

  <clause id="17110">
    <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),17108(a,1,3,2,1))].">
      <j1 rule="para" parents="72 17108"/>
    </justification>
  </clause>

  <clause id="17111">
    <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(16978(a,1),17110(a,1,3))].">
      <j1 rule="para" parents="16978 17110"/>
    </justification>
  </clause>

  <clause id="17112">
    <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(7779(a,1),17111(a,1,3))].">
      <j1 rule="para" parents="7779 17111"/>
    </justification>
  </clause>

  <clause id="17113">
    <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(16730(a,1),17112(a,1,3))].">
      <j1 rule="para" parents="16730 17112"/>
    </justification>
  </clause>

  <clause id="17114">
    <literal><![CDATA[
      a(x,y \ z,K(u,K(w,z))) = a(u,z,K(y,K(w,x / z)))
    ]]></literal>
    <justification jstring="[hyper(14453,a,17113,a),flip(a)].">
      <j1 rule="hyper" parents="14453 17113"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17115">
    <literal><![CDATA[
      a(x,y \ z,K(u,K(z,w))) = a(u,z,K(y,K(w,x / z)))
    ]]></literal>
    <justification jstring="[para(7797(a,1),17114(a,1,3))].">
      <j1 rule="para" parents="7797 17114"/>
    </justification>
  </clause>

  <clause id="17116">
    <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,17072,a,b,17115,a)].">
      <j1 rule="hyper" parents="58 17072 17115"/>
    </justification>
  </clause>

  <clause id="17117">
    <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,17096,a(flip),b,17116,a),flip(a)].">
      <j1 rule="hyper" parents="58 17096 17116"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17118">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w / y))) = a(y,z,K(w,K(x,u)))
    ]]></literal>
    <justification jstring="[para(7779(a,1),17117(a,2,3))].">
      <j1 rule="para" parents="7779 17117"/>
    </justification>
  </clause>

  <clause id="17119">
    <literal><![CDATA[
      K(x,K(y,((z / u) / (w * z)) * (w * u))) = a(z,y,K(u,K(x,w)))
    ]]></literal>
    <justification jstring="[hyper(17018,a,17118,a)].">
      <j1 rule="hyper" parents="17018 17118"/>
    </justification>
  </clause>

  <clause id="17120">
    <literal><![CDATA[
      K(x,K(y,((z / u) / (w * z)) * (w * u))) = a(z,y,K(x,K(w,u)))
    ]]></literal>
    <justification jstring="[para(7784(a,2),17119(a,2,3))].">
      <j1 rule="para" parents="7784 17119"/>
    </justification>
  </clause>

  <clause id="17121">
    <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,17023,a(flip),b,17120,a)].">
      <j1 rule="hyper" parents="58 17023 17120"/>
    </justification>
  </clause>

  <clause id="17122">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w / y))) = a(w,x,K(z,K(u,y)))
    ]]></literal>
    <justification jstring="[para(8189(a,1),17121(a,1,3))].">
      <j1 rule="para" parents="8189 17121"/>
    </justification>
  </clause>

  <clause id="17123">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w / y))) = a(w,x,K(z,K(y,u)))
    ]]></literal>
    <justification jstring="[para(7797(a,1),17122(a,2,3))].">
      <j1 rule="para" parents="7797 17122"/>
    </justification>
  </clause>

  <clause id="17124">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) = a(u,z,K(x,K(y,w)))
    ]]></literal>
    <justification jstring="[hyper(58,a,17118,a(flip),b,17123,a),flip(a)].">
      <j1 rule="hyper" parents="58 17118 17123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17125">
    <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(17124(a,1),14403(a,1,1))].">
      <j1 rule="para" parents="17124 14403"/>
    </justification>
  </clause>

  <clause id="17126">
    <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(7779(a,1),17125(a,1,2))].">
      <j1 rule="para" parents="7779 17125"/>
    </justification>
  </clause>

  <clause id="17127">
    <literal><![CDATA[
      L(K(x,K(y,z)),u,w) = K(x,K(z,L(y,w,u)))
    ]]></literal>
    <justification jstring="[hyper(14623,a,17126,a),flip(a)].">
      <j1 rule="hyper" parents="14623 17126"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17128">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w))) = K(x,K(y,L(z,w,u)))
    ]]></literal>
    <justification jstring="[hyper(10936,a,17127,a)].">
      <j1 rule="hyper" parents="10936 17127"/>
    </justification>
  </clause>

  <clause id="17129">
    <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,17005,a(flip),b,17128,a),flip(a)].">
      <j1 rule="hyper" parents="320 17005 17128"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17130">
    <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(698(a,1),17128(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="698 17128"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17131">
    <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(6698(a,1),17128(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6698 17128"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17132">
    <literal><![CDATA[
      K(x,K(y,(z * u) / w)) = K(x,K(y,(z / w) * u))
    ]]></literal>
    <justification jstring="[hyper(16988,a,17129,a)].">
      <j1 rule="hyper" parents="16988 17129"/>
    </justification>
  </clause>

  <clause id="17133">
    <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(17131(a,2),8212(a,1))].">
      <j1 rule="para" parents="17131 8212"/>
    </justification>
  </clause>

  <clause id="17134">
    <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,15610,a,b,17130,a),flip(a)].">
      <j1 rule="hyper" parents="320 15610 17130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17135">
    <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,17132,a(flip),b,17134,a),flip(a)].">
      <j1 rule="hyper" parents="320 17132 17134"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17136">
    <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,16974,a(flip),b,17135,a),flip(a)].">
      <j1 rule="hyper" parents="320 16974 17135"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17139">
    <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(8009(a,1),17136(a,2,2))].">
      <j1 rule="para" parents="8009 17136"/>
    </justification>
  </clause>

  <clause id="17140">
    <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,15742,a(flip),b,17139,a),flip(a)].">
      <j1 rule="hyper" parents="320 15742 17139"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17143">
    <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,14706,a(flip),b,17140,a)].">
      <j1 rule="hyper" parents="58 14706 17140"/>
    </justification>
  </clause>

  <clause id="17144">
    <literal><![CDATA[
      K(x,K(y,L(1 / z,z,u))) = K(x,K(y,L(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(17133,a,17143,a),flip(a)].">
      <j1 rule="hyper" parents="17133 17143"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17147">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w))) = K(x,K(y,1 / z))
    ]]></literal>
    <justification jstring="[para(6500(a,1),17144(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6500 17144"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17149">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w))) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(320,a,8200,a(flip),b,17147,a),flip(a)].">
      <j1 rule="hyper" parents="320 8200 17147"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17150">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,8187,a(flip),b,17147,a),flip(a)].">
      <j1 rule="hyper" parents="320 8187 17147"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17152">
    <literal><![CDATA[
      L(K(x,K(y,z)),u,w) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(10872,a,17149,a)].">
      <j1 rule="hyper" parents="10872 17149"/>
    </justification>
  </clause>

  <clause id="17154">
    <literal><![CDATA[
      K(L(x,y,z),K(u,w)) = K(x,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(7799,a,17149,a)].">
      <j1 rule="hyper" parents="7799 17149"/>
    </justification>
  </clause>

  <clause id="17157">
    <literal><![CDATA[
      T(x,K(y,L(z,u,w))) = x * K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(17149(a,1),10861(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17149 10861"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17158">
    <literal><![CDATA[
      (x * y) * K(z,K(u,w)) = x * (y * K(z,K(u,w)))
    ]]></literal>
    <justification jstring="[para(17149(a,1),10883(a,1,2))].">
      <j1 rule="para" parents="17149 10883"/>
    </justification>
  </clause>

  <clause id="17167">
    <literal><![CDATA[
      T(x,K(y,L(z,u,w))) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(118,a,17150,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 17150 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17168">
    <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(17150(a,1),8390(a,1,1))].">
      <j1 rule="para" parents="17150 8390"/>
    </justification>
  </clause>

  <clause id="17171">
    <literal><![CDATA[
      K(x,K(y,R(z,u,w))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(14776(a,2),17150(a,1,2))].">
      <j1 rule="para" parents="14776 17150"/>
    </justification>
  </clause>

  <clause id="17174">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,17152,a,b,1934,a),flip(a)].">
      <j1 rule="hyper" parents="115 17152 1934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17176">
    <literal><![CDATA[
      a(K(x,y),z,K(u,w)) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,17152,a(flip),b,14311,a),flip(a)].">
      <j1 rule="hyper" parents="115 17152 14311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17177">
    <literal><![CDATA[
      x \ (y * K(z,K(u,w))) = (x \ y) * K(z,K(u,w))
    ]]></literal>
    <justification jstring="[para(17152(a,1),474(a,1,2,2))].">
      <j1 rule="para" parents="17152 474"/>
    </justification>
  </clause>

  <clause id="17178">
    <literal><![CDATA[
      L(K(x,y),z,K(u,w)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(13666,a,17174,a)].">
      <j1 rule="hyper" parents="13666 17174"/>
    </justification>
  </clause>

  <clause id="17179">
    <literal><![CDATA[
      T(x,a(y,z,K(u,w))) = x
    ]]></literal>
    <justification jstring="[hyper(13406,a,17174,a)].">
      <j1 rule="hyper" parents="13406 17174"/>
    </justification>
  </clause>

  <clause id="17182">
    <literal><![CDATA[
      a(K(x,K(y,z)),u,w) = 1
    ]]></literal>
    <justification jstring="[hyper(58,a,14258,a,b,17174,a)].">
      <j1 rule="hyper" parents="58 14258 17174"/>
    </justification>
  </clause>

  <clause id="17183">
    <literal><![CDATA[
      K(x,K(y,a(z,u,w))) = 1
    ]]></literal>
    <justification jstring="[hyper(58,a,14439,a(flip),b,17174,a)].">
      <j1 rule="hyper" parents="58 14439 17174"/>
    </justification>
  </clause>

  <clause id="17185">
    <literal><![CDATA[
      L(x,y,K(z,K(u,w))) = x
    ]]></literal>
    <justification jstring="[hyper(167,a,14929,a,b,17174,a(flip))].">
      <j1 rule="hyper" parents="167 14929 17174"/>
    </justification>
  </clause>

  <clause id="17186">
    <literal><![CDATA[
      L(K(x,y),z,K(u,w)) = K(x,y) * 1
    ]]></literal>
    <justification jstring="[para(17174(a,1),14311(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17174 14311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17188">
    <literal><![CDATA[
      (K(x,y) * z) * K(u,w) = K(x,y) * (z * K(u,w))
    ]]></literal>
    <justification jstring="[hyper(977,a,17176,a)].">
      <j1 rule="hyper" parents="977 17176"/>
    </justification>
  </clause>

  <clause id="17190">
    <literal><![CDATA[
      K(L(x,y,K(z,u)),w) = K(x,w)
    ]]></literal>
    <justification jstring="[hyper(167,a,16212,a,b,17176,a(flip))].">
      <j1 rule="hyper" parents="167 16212 17176"/>
    </justification>
  </clause>

  <clause id="17191">
    <literal><![CDATA[
      L(x,y,T(z,K(u,w))) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(167,a,14998,a,b,17176,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="167 14998 17176"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17192">
    <literal><![CDATA[
      T(x,L(y,z,K(u,w))) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(167,a,10887,a,b,17176,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="167 10887 17176"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17193">
    <literal><![CDATA[
      a(x,y,K(z,u)) * w = w * a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(2342,a,17179,a),flip(a)].">
      <j1 rule="hyper" parents="2342 17179"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17195">
    <literal><![CDATA[
      T(a(x,y,K(z,u)),w) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(49,a,17179,a)].">
      <j1 rule="hyper" parents="49 17179"/>
    </justification>
  </clause>

  <clause id="17196">
    <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(17179(a,1),284(a,1,2))].">
      <j1 rule="para" parents="17179 284"/>
    </justification>
  </clause>

  <clause id="17197">
    <literal><![CDATA[
      T(x,K(y,a(z,u,w))) = x
    ]]></literal>
    <justification jstring="[para(13400(a,1),17179(a,1,2))].">
      <j1 rule="para" parents="13400 17179"/>
    </justification>
  </clause>

  <clause id="17198">
    <literal><![CDATA[
      T(x,K(a(y,z,u),w)) = x
    ]]></literal>
    <justification jstring="[para(13427(a,1),17179(a,1,2))].">
      <j1 rule="para" parents="13427 17179"/>
    </justification>
  </clause>

  <clause id="17199">
    <literal><![CDATA[
      T(x,K(y,L(z,u,w) \ z)) = x
    ]]></literal>
    <justification jstring="[para(14281(a,2),17179(a,1,2))].">
      <j1 rule="para" parents="14281 17179"/>
    </justification>
  </clause>

  <clause id="17201">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) * w = K(x,K(y,z)) * (u * w)
    ]]></literal>
    <justification jstring="[hyper(14747,a,17182,a)].">
      <j1 rule="hyper" parents="14747 17182"/>
    </justification>
  </clause>

  <clause id="17207">
    <literal><![CDATA[
      K(x,T(y,a(z,u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(8070,a,17183,a)].">
      <j1 rule="hyper" parents="8070 17183"/>
    </justification>
  </clause>

  <clause id="17214">
    <literal><![CDATA[
      (K(x,K(y,z)) \ u) \ w = u \ (K(x,K(y,z)) * w)
    ]]></literal>
    <justification jstring="[hyper(760,a,17185,a)].">
      <j1 rule="hyper" parents="760 17185"/>
    </justification>
  </clause>

  <clause id="17216">
    <literal><![CDATA[
      L(x,y,K(z,u) / w) = L(x,y,w \ K(z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,14976,a(flip),b,17185,a)].">
      <j1 rule="hyper" parents="58 14976 17185"/>
    </justification>
  </clause>

  <clause id="17217">
    <literal><![CDATA[
      L(x,y,K(z,K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      v5 = x
    ]]></literal>
    <justification jstring="[para(17185(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="17185 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17218">
    <literal><![CDATA[
      L(x,y,K(z,K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      x = v5
    ]]></literal>
    <justification jstring="[para(17185(a,1),45(a,2))].">
      <j1 rule="para" parents="17185 45"/>
    </justification>
  </clause>

  <clause id="17219">
    <literal><![CDATA[
      K(x,K(y,z)) \ (u * w) = (K(x,K(y,z)) \ u) * w
    ]]></literal>
    <justification jstring="[para(17185(a,1),474(a,1,2,2))].">
      <j1 rule="para" parents="17185 474"/>
    </justification>
  </clause>

  <clause id="17220">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) / w = K(x,K(y,z)) * (u / w)
    ]]></literal>
    <justification jstring="[para(17185(a,1),544(a,1,2))].">
      <j1 rule="para" parents="17185 544"/>
    </justification>
  </clause>

  <clause id="17221">
    <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(17185(a,1),477(a,2,1))].">
      <j1 rule="para" parents="17185 477"/>
    </justification>
  </clause>

  <clause id="17222">
    <literal><![CDATA[
      L(x,y,K(z,u) * w) = L(x,y,w * K(z,u))
    ]]></literal>
    <justification jstring="[para(17185(a,1),15006(a,1,1))].">
      <j1 rule="para" parents="17185 15006"/>
    </justification>
  </clause>

  <clause id="17223">
    <literal><![CDATA[
      T(x,a(y,z,u) * w) = T(x,w * a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(12295,a,17197,a)].">
      <j1 rule="hyper" parents="12295 17197"/>
    </justification>
  </clause>

  <clause id="17224">
    <literal><![CDATA[
      T(a(x,y,z) \ u,K(w,u)) = a(x,y,z) \ u
    ]]></literal>
    <justification jstring="[hyper(8261,a,17197,a)].">
      <j1 rule="hyper" parents="8261 17197"/>
    </justification>
  </clause>

  <clause id="17226">
    <literal><![CDATA[
      T(x,K(y,a(z,u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      x = v5
    ]]></literal>
    <justification jstring="[para(17197(a,1),44(a,2))].">
      <j1 rule="para" parents="17197 44"/>
    </justification>
  </clause>

  <clause id="17227">
    <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(17197(a,1),15105(a,1,2,1,2))].">
      <j1 rule="para" parents="17197 15105"/>
    </justification>
  </clause>

  <clause id="17229">
    <literal><![CDATA[
      T(K(x,y),a(z,u,w)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(14933,a,17178,a)].">
      <j1 rule="hyper" parents="14933 17178"/>
    </justification>
  </clause>

  <clause id="17230">
    <literal><![CDATA[
      K(x,L(y,z,K(u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(10837,a,17178,a)].">
      <j1 rule="hyper" parents="10837 17178"/>
    </justification>
  </clause>

  <clause id="17232">
    <literal><![CDATA[
      K((K(x,y) * z) \ u,w) = K(z \ (K(y,x) * u),w)
    ]]></literal>
    <justification jstring="[hyper(58,a,6629,a(flip),b,17178,a),flip(a)].">
      <j1 rule="hyper" parents="58 6629 17178"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17233">
    <literal><![CDATA[
      L(x * K(y,z),u,K(w,x)) = x * K(y,z)
    ]]></literal>
    <justification jstring="[para(17178(a,1),14977(a,2,2))].">
      <j1 rule="para" parents="17178 14977"/>
    </justification>
  </clause>

  <clause id="17236">
    <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(16430,a,17190,a)].">
      <j1 rule="hyper" parents="16430 17190"/>
    </justification>
  </clause>

  <clause id="17239">
    <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),17192(a,1,2))].">
      <j1 rule="para" parents="564 17192"/>
    </justification>
  </clause>

  <clause id="17240">
    <literal><![CDATA[
      T(x,(K(y,z) * u) \ w) = T(x,u \ (K(z,y) * w))
    ]]></literal>
    <justification jstring="[para(5153(a,1),17192(a,1,2))].">
      <j1 rule="para" parents="5153 17192"/>
    </justification>
  </clause>

  <clause id="17241">
    <literal><![CDATA[
      T(x,L(y,z,T(u,w))) = T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(6872(a,1),17192(a,1,2))].">
      <j1 rule="para" parents="6872 17192"/>
    </justification>
  </clause>

  <clause id="17242">
    <literal><![CDATA[
      ((x * y) * ((K(y,x) * z) * u)) / T((y * x) * z,u) = L(u,z,x * y)
    ]]></literal>
    <justification jstring="[para(17192(a,1),15039(a,1,2))].">
      <j1 rule="para" parents="17192 15039"/>
    </justification>
  </clause>

  <clause id="17243">
    <literal><![CDATA[
      K(x,T(y,L(z,u,w) \ z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(8350,a,17199,a)].">
      <j1 rule="hyper" parents="8350 17199"/>
    </justification>
  </clause>

  <clause id="17244">
    <literal><![CDATA[
      T(x,K(y,z \ L(z,u,w))) = x
    ]]></literal>
    <justification jstring="[hyper(8219,a,17199,a)].">
      <j1 rule="hyper" parents="8219 17199"/>
    </justification>
  </clause>

  <clause id="17245">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      T(y,K(z,L(u,w,v5) \ u)) = x
    ]]></literal>
    <justification jstring="[para(17199(a,1),7851(a,1))].">
      <j1 rule="para" parents="17199 7851"/>
    </justification>
  </clause>

  <clause id="17248">
    <literal><![CDATA[
      K(x,(L(y,z,u) \ w) * y) = K(x,y * (w / L(y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,15252,a(flip),b,17207,a),flip(a)].">
      <j1 rule="hyper" parents="58 15252 17207"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17249">
    <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(17207(a,1),7184(a,1,2))].">
      <j1 rule="para" parents="17207 7184"/>
    </justification>
  </clause>

  <clause id="17250">
    <literal><![CDATA[
      T(K(x,y),a(z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(17207(a,1),7982(a,1,1))].">
      <j1 rule="para" parents="17207 7982"/>
    </justification>
  </clause>

  <clause id="17251">
    <literal><![CDATA[
      K(x,T(y,a(z,u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(17207(a,1),8007(a,1))].">
      <j1 rule="para" parents="17207 8007"/>
    </justification>
  </clause>

  <clause id="17252">
    <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(17207(a,1),12239(a,1))].">
      <j1 rule="para" parents="17207 12239"/>
    </justification>
  </clause>

  <clause id="17253">
    <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(17207(a,1),12302(a,1))].">
      <j1 rule="para" parents="17207 12302"/>
    </justification>
  </clause>

  <clause id="17254">
    <literal><![CDATA[
      K(x,T(y,L(z,u,w))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(14367(a,1),17207(a,1,2))].">
      <j1 rule="para" parents="14367 17207"/>
    </justification>
  </clause>

  <clause id="17256">
    <literal><![CDATA[
      T(a(x,y,z),K(u,w)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(49,a,17229,a)].">
      <j1 rule="hyper" parents="49 17229"/>
    </justification>
  </clause>

  <clause id="17257">
    <literal><![CDATA[
      T(K(x,y) * z,a(z,u,w)) = K(x,y) * z
    ]]></literal>
    <justification jstring="[para(17229(a,1),14525(a,2,1))].">
      <j1 rule="para" parents="17229 14525"/>
    </justification>
  </clause>

  <clause id="17259">
    <literal><![CDATA[
      K(x,L(y,z,T(u,w))) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(6872(a,1),17230(a,1,2))].">
      <j1 rule="para" parents="6872 17230"/>
    </justification>
  </clause>

  <clause id="17260">
    <literal><![CDATA[
      K(x,L(y,z,u / w)) = K(x,L(y,z,w \ u))
    ]]></literal>
    <justification jstring="[para(12750(a,1),17230(a,1,2))].">
      <j1 rule="para" parents="12750 17230"/>
    </justification>
  </clause>

  <clause id="17261">
    <literal><![CDATA[
      K(x,(y * K(z,u)) / w) = K(x,y / (w * K(u,z)))
    ]]></literal>
    <justification jstring="[para(14926(a,1),17230(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14926 17230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17262">
    <literal><![CDATA[
      K(x,T(y,z \ L(z,u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(8350,a,17244,a)].">
      <j1 rule="hyper" parents="8350 17244"/>
    </justification>
  </clause>

  <clause id="17263">
    <literal><![CDATA[
      L(x,y,(y * x) \ z) = L(x,y,(x * y) \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,11228,a(flip),b,17191,a),flip(a)].">
      <j1 rule="hyper" parents="58 11228 17191"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17264">
    <literal><![CDATA[
      L(x,y,T(z,K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = v5
    ]]></literal>
    <justification jstring="[para(6872(a,1),17217(a,1)),flip(b)].">
      <j1 rule="para" parents="6872 17217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17265">
    <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(12750(a,1),17217(a,1)),flip(b)].">
      <j1 rule="para" parents="12750 17217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17266">
    <literal><![CDATA[
      T(x,T(y,a(z,u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = v5
    ]]></literal>
    <justification jstring="[para(7438(a,1),17226(a,1))].">
      <j1 rule="para" parents="7438 17226"/>
    </justification>
  </clause>

  <clause id="17267">
    <literal><![CDATA[
      K(x,K(y,z)) * L(x,u,w) = L(T(x,K(y,z)),u,w)
    ]]></literal>
    <justification jstring="[para(17154(a,1),4844(a,1,1))].">
      <j1 rule="para" parents="17154 4844"/>
    </justification>
  </clause>

  <clause id="17269">
    <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(17167(a,1),284(a,1,2))].">
      <j1 rule="para" parents="17167 284"/>
    </justification>
  </clause>

  <clause id="17270">
    <literal><![CDATA[
      T(x,K(y,(z \ u) \ w)) = T(x,K(y,u \ (z * w)))
    ]]></literal>
    <justification jstring="[para(490(a,1),17167(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="490 17167"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17272">
    <literal><![CDATA[
      K(x,K(y,z \ (u * (w \ z)))) = K(x,K(y,u / w))
    ]]></literal>
    <justification jstring="[hyper(15623,a,17171,a)].">
      <j1 rule="hyper" parents="15623 17171"/>
    </justification>
  </clause>

  <clause id="17279">
    <literal><![CDATA[
      L(K(x,y),z,K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(17186(a,2),127(a,1)),flip(b)].">
      <j1 rule="para" parents="17186 127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17280">
    <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,14116,a(flip),b,17243,a)].">
      <j1 rule="hyper" parents="58 14116 17243"/>
    </justification>
  </clause>

  <clause id="17281">
    <literal><![CDATA[
      K(x,T(y \ R(z,u,w),z)) = K(x,R(z,u,w) / y)
    ]]></literal>
    <justification jstring="[hyper(14770,a,17254,a),flip(a)].">
      <j1 rule="hyper" parents="14770 17254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17282">
    <literal><![CDATA[
      K(x,T(y * (L(y,z,u) \ w),y)) = K(x,(y * w) / L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(8266,a,17254,a),flip(a)].">
      <j1 rule="hyper" parents="8266 17254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17284">
    <literal><![CDATA[
      K(x,T(y,(z * u) \ w)) = K(x,T(y,u \ (z \ w)))
    ]]></literal>
    <justification jstring="[para(298(a,1),17254(a,1,2,2))].">
      <j1 rule="para" parents="298 17254"/>
    </justification>
  </clause>

  <clause id="17286">
    <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(17254(a,1),12304(a,1))].">
      <j1 rule="para" parents="17254 12304"/>
    </justification>
  </clause>

  <clause id="17287">
    <literal><![CDATA[
      K(x,T(y,(z / u) / w)) = K(x,T(y,z / (w * u)))
    ]]></literal>
    <justification jstring="[para(14768(a,1),17254(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14768 17254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17288">
    <literal><![CDATA[
      K(x,(y \ L(y,z,u)) * w) = K(x,w * (y \ L(y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(12302,a,17262,a)].">
      <j1 rule="hyper" parents="12302 17262"/>
    </justification>
  </clause>

  <clause id="17289">
    <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(17262(a,1),12301(a,1))].">
      <j1 rule="para" parents="17262 12301"/>
    </justification>
  </clause>

  <clause id="17290">
    <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,15068,a(flip),b,17241,a),flip(a)].">
      <j1 rule="hyper" parents="58 15068 17241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17291">
    <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,14477,a(flip),b,17241,a),flip(a)].">
      <j1 rule="hyper" parents="58 14477 17241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17292">
    <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(7899(a,1),17250(a,1))].">
      <j1 rule="para" parents="7899 17250"/>
    </justification>
  </clause>

  <clause id="17293">
    <literal><![CDATA[
      K(x,T(y,L(z,u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = v5
    ]]></literal>
    <justification jstring="[para(14367(a,1),17251(a,1,2))].">
      <j1 rule="para" parents="14367 17251"/>
    </justification>
  </clause>

  <clause id="17294">
    <literal><![CDATA[
      K(x,L(y,z,K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(14925(a,2),17251(a,1,2))].">
      <j1 rule="para" parents="14925 17251"/>
    </justification>
  </clause>

  <clause id="17295">
    <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,13490,a(flip),b,17259,a),flip(a)].">
      <j1 rule="hyper" parents="58 13490 17259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17296">
    <literal><![CDATA[
      K(x,L(y,z,u * w)) = K(x,L(y,z,w * u))
    ]]></literal>
    <justification jstring="[para(12572(a,1),17259(a,1,2))].">
      <j1 rule="para" parents="12572 17259"/>
    </justification>
  </clause>

  <clause id="17298">
    <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(14955(a,1),17266(a,1,2))].">
      <j1 rule="para" parents="14955 17266"/>
    </justification>
  </clause>

  <clause id="17299">
    <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(6144(a,2),17279(a,1))].">
      <j1 rule="para" parents="6144 17279"/>
    </justification>
  </clause>

  <clause id="17300">
    <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(6832(a,1),17294(a,1,2))].">
      <j1 rule="para" parents="6832 17294"/>
    </justification>
  </clause>

  <clause id="17301">
    <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(6872(a,1),17294(a,1,2))].">
      <j1 rule="para" parents="6872 17294"/>
    </justification>
  </clause>

  <clause id="17302">
    <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(12750(a,1),17294(a,1,2))].">
      <j1 rule="para" parents="12750 17294"/>
    </justification>
  </clause>

  <clause id="17303">
    <literal><![CDATA[
      T(x,K(y,L(z,u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,z)) = v5
    ]]></literal>
    <justification jstring="[para(17157(a,2),4766(a,1))].">
      <j1 rule="para" parents="17157 4766"/>
    </justification>
  </clause>

  <clause id="17305">
    <literal><![CDATA[
      T(x * K(y,z),a(u,w,x)) = x * K(y,z)
    ]]></literal>
    <justification jstring="[para(17233(a,1),14947(a,1,1))].">
      <j1 rule="para" parents="17233 14947"/>
    </justification>
  </clause>

  <clause id="17306">
    <literal><![CDATA[
      L(K(x,y) * z,u,K(w,z)) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(14982,a,17257,a)].">
      <j1 rule="hyper" parents="14982 17257"/>
    </justification>
  </clause>

  <clause id="17307">
    <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(8091(a,1),17264(a,1,3))].">
      <j1 rule="para" parents="8091 17264"/>
    </justification>
  </clause>

  <clause id="17308">
    <literal><![CDATA[
      L(x,y,T(z,u * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,T(z,w * u)) = v5
    ]]></literal>
    <justification jstring="[para(12286(a,1),17264(a,1,3))].">
      <j1 rule="para" parents="12286 17264"/>
    </justification>
  </clause>

  <clause id="17309">
    <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(17305(a,1),13936(a,2,2))].">
      <j1 rule="para" parents="17305 13936"/>
    </justification>
  </clause>

  <clause id="17310">
    <literal><![CDATA[
      (K(x,y) * z) / a(u,w,z) = a(u,w,z) \ (K(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(116,a,17306,a(flip),b,14959,a),flip(a)].">
      <j1 rule="hyper" parents="116 17306 14959"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17311">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (w * a(u,y,K(z,x))) = w
    ]]></literal>
    <justification jstring="[hyper(14324,a,17193,a)].">
      <j1 rule="hyper" parents="14324 17193"/>
    </justification>
  </clause>

  <clause id="17312">
    <literal><![CDATA[
      (x \ y) * a(z,u,K(w,x)) = T(x,a(z,u,w)) \ y
    ]]></literal>
    <justification jstring="[hyper(13433,a,17193,a),flip(a)].">
      <j1 rule="hyper" parents="13433 17193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17313">
    <literal><![CDATA[
      a(x,y,K(z,u)) * w = w * a(z,y,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(320,a,14265,a,b,17193,a),flip(a)].">
      <j1 rule="hyper" parents="320 14265 17193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17314">
    <literal><![CDATA[
      x \ (y * a(z,u,K(w,v5))) = a(z,u,K(w,v5)) * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(320,a,756,a,b,17193,a)].">
      <j1 rule="hyper" parents="320 756 17193"/>
    </justification>
  </clause>

  <clause id="17315">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (w * x) = w * T(x,a(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,14282,a(flip),b,17193,a),flip(a)].">
      <j1 rule="hyper" parents="320 14282 17193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17316">
    <literal><![CDATA[
      a(x,y,K(z,u)) * w = w * a(u,y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,14265,a(flip),b,17193,a),flip(a)].">
      <j1 rule="hyper" parents="320 14265 17193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17317">
    <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,17193,a),flip(a)].">
      <j1 rule="hyper" parents="320 347 17193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17319">
    <literal><![CDATA[
      K(x,a(y,z,u)) * w = w * a(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[para(14259(a,1),17193(a,1,1))].">
      <j1 rule="para" parents="14259 17193"/>
    </justification>
  </clause>

  <clause id="17320">
    <literal><![CDATA[
      (x * a(y,z,K(u,w))) * v5 = a(y,z,K(u,w)) * (x * v5)
    ]]></literal>
    <justification jstring="[para(17193(a,1),14274(a,1,1))].">
      <j1 rule="para" parents="17193 14274"/>
    </justification>
  </clause>

  <clause id="17321">
    <literal><![CDATA[
      L(x,y,z * a(u,w,K(v5,v6))) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(17193(a,1),15549(a,1,3))].">
      <j1 rule="para" parents="17193 15549"/>
    </justification>
  </clause>

  <clause id="17322">
    <literal><![CDATA[
      L(x,y,z \ L(u,w,K(v5,v6))) = L(x,y,z \ u)
    ]]></literal>
    <justification jstring="[para(14951(a,1),17321(a,1,3))].">
      <j1 rule="para" parents="14951 17321"/>
    </justification>
  </clause>

  <clause id="17323">
    <literal><![CDATA[
      L(x,y,z \ K(z,z \ u)) = L(x,y,K(u,z \ 1) / z)
    ]]></literal>
    <justification jstring="[hyper(58,a,13471,a,b,17216,a),flip(a)].">
      <j1 rule="hyper" parents="58 13471 17216"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17324">
    <literal><![CDATA[
      L(x,y,z * K(u,u \ w)) = L(x,y,K(u,w) * z)
    ]]></literal>
    <justification jstring="[hyper(320,a,12700,a,b,17222,a)].">
      <j1 rule="hyper" parents="320 12700 17222"/>
    </justification>
  </clause>

  <clause id="17325">
    <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(17223(a,1),16361(a,1,2,1,2))].">
      <j1 rule="para" parents="17223 16361"/>
    </justification>
  </clause>

  <clause id="17326">
    <literal><![CDATA[
      K(x,y) * ((a(z,u,w) \ y) * x) = (a(z,u,w) \ y) * T(x,y)
    ]]></literal>
    <justification jstring="[para(17224(a,1),8328(a,1,1)),flip(a)].">
      <j1 rule="para" parents="17224 8328"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17327">
    <literal><![CDATA[
      K(x,L(y,z,(u \ 1) \ w)) = K(x,L(y,z,w * u))
    ]]></literal>
    <justification jstring="[hyper(14531,a,17260,a),flip(a)].">
      <j1 rule="hyper" parents="14531 17260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17328">
    <literal><![CDATA[
      K(x,L(y,z,u \ (w \ u))) = K(x,L(y,z,w \ 1))
    ]]></literal>
    <justification jstring="[hyper(14530,a,17260,a),flip(a)].">
      <j1 rule="hyper" parents="14530 17260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17329">
    <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(17260(a,1),14530(a,1))].">
      <j1 rule="para" parents="17260 14530"/>
    </justification>
  </clause>

  <clause id="17331">
    <literal><![CDATA[
      x / L(y,z,(y * z) \ x) = (x / (z * y)) * z
    ]]></literal>
    <justification jstring="[para(17263(a,1),14136(a,1,2))].">
      <j1 rule="para" parents="17263 14136"/>
    </justification>
  </clause>

  <clause id="17332">
    <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),17293(a,1,2,2))].">
      <j1 rule="para" parents="298 17293"/>
    </justification>
  </clause>

  <clause id="17333">
    <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(14605(a,1),17303(a,1,2))].">
      <j1 rule="para" parents="14605 17303"/>
    </justification>
  </clause>

  <clause id="17334">
    <literal><![CDATA[
      K(x,L(L(y,z,u),w,v5)) * a(y,w,K(v5,x)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(29,a,14380,a,b,17311,a),flip(a)].">
      <j1 rule="hyper" parents="29 14380 17311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17335">
    <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,14515,a(flip),b,17313,a),flip(a)].">
      <j1 rule="hyper" parents="58 14515 17313"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17336">
    <literal><![CDATA[
      (x * y) * a(z,u,K(x,w)) = T(x,a(z,u,w)) * y
    ]]></literal>
    <justification jstring="[hyper(58,a,14363,a(flip),b,17313,a),flip(a)].">
      <j1 rule="hyper" parents="58 14363 17313"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17337">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (w \ z) = w \ L(z,y,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(320,a,14951,a(flip),b,17316,a),flip(a)].">
      <j1 rule="hyper" parents="320 14951 17316"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17338">
    <literal><![CDATA[
      (x / y) * a(x,z,K(u,w)) = T(x,a(w,z,u)) / y
    ]]></literal>
    <justification jstring="[hyper(13833,a,17319,a),flip(a)].">
      <j1 rule="hyper" parents="13833 17319"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17339">
    <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(10797(a,2),17300(a,1))].">
      <j1 rule="para" parents="10797 17300"/>
    </justification>
  </clause>

  <clause id="17340">
    <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(4569(a,1),17301(a,1,2))].">
      <j1 rule="para" parents="4569 17301"/>
    </justification>
  </clause>

  <clause id="17341">
    <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(12572(a,1),17301(a,1,2))].">
      <j1 rule="para" parents="12572 17301"/>
    </justification>
  </clause>

  <clause id="17342">
    <literal><![CDATA[
      L(x,y,z \ (u / a(w,v5,v6))) = L(x,y,z \ (a(w,v5,v6) \ u))
    ]]></literal>
    <justification jstring="[para(14944(a,1),17322(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="14944 17322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17343">
    <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(14713(a,2),17331(a,1,2,3,1))].">
      <j1 rule="para" parents="14713 17331"/>
    </justification>
  </clause>

  <clause id="17344">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * w) = u * (w * K(y,K(x,z)))
    ]]></literal>
    <justification jstring="[hyper(15944,a,17158,a)].">
      <j1 rule="hyper" parents="15944 17158"/>
    </justification>
  </clause>

  <clause id="17345">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * w) = u * (w * K(x,K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(15732,a,17158,a)].">
      <j1 rule="hyper" parents="15732 17158"/>
    </justification>
  </clause>

  <clause id="17348">
    <literal><![CDATA[
      x \ (y * K(z,K(u,w))) = K(z,K(u,w)) * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(320,a,15684,a,b,17177,a),flip(a)].">
      <j1 rule="hyper" parents="320 15684 17177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17349">
    <literal><![CDATA[
      (x \ (y * z)) * K(z,K(u,w)) = x \ (y * T(z,K(u,w)))
    ]]></literal>
    <justification jstring="[para(6116(a,1),17177(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6116 17177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17350">
    <literal><![CDATA[
      (x \ (y * z)) * K(y,K(u,w)) = x \ (T(y,K(u,w)) * z)
    ]]></literal>
    <justification jstring="[para(15694(a,1),17177(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15694 17177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17351">
    <literal><![CDATA[
      x \ T(K(y,K(z,u)) * w,v5) = (x \ T(w,v5)) * K(y,K(z,u))
    ]]></literal>
    <justification jstring="[para(15747(a,2),17177(a,1,2))].">
      <j1 rule="para" parents="15747 17177"/>
    </justification>
  </clause>

  <clause id="17352">
    <literal><![CDATA[
      x \ (y * (z * K(u,K(w,v5)))) = (x \ (y * z)) * K(u,K(w,v5))
    ]]></literal>
    <justification jstring="[para(17158(a,1),17177(a,1,2))].">
      <j1 rule="para" parents="17158 17177"/>
    </justification>
  </clause>

  <clause id="17353">
    <literal><![CDATA[
      (K(x,y) * z) * K(u,T(w,z)) = K(x,y) * (K(u,w) * z)
    ]]></literal>
    <justification jstring="[hyper(320,a,7301,a(flip),b,17188,a),flip(a)].">
      <j1 rule="hyper" parents="320 7301 17188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17354">
    <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(17188(a,1),15(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="17188 15"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17359">
    <literal><![CDATA[
      K(x,K(y,z)) * (T(z,y) * u) = T(z,T(y,x)) * u
    ]]></literal>
    <justification jstring="[para(7538(a,1),17201(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7538 17201"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17360">
    <literal><![CDATA[
      (x * K(y,K(z,u))) * w = K(y,K(z,u)) * (x * w)
    ]]></literal>
    <justification jstring="[para(15684(a,1),17201(a,1,1))].">
      <j1 rule="para" parents="15684 17201"/>
    </justification>
  </clause>

  <clause id="17361">
    <literal><![CDATA[
      (K(x,K(y,z)) \ u) \ (K(x,K(y,z)) \ w) = u \ w
    ]]></literal>
    <justification jstring="[para(5(a,1),17214(a,2,2))].">
      <j1 rule="para" parents="5 17214"/>
    </justification>
  </clause>

  <clause id="17362">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) \ w = u \ (K(x,K(y,z)) * w)
    ]]></literal>
    <justification jstring="[para(7824(a,1),17214(a,1,1))].">
      <j1 rule="para" parents="7824 17214"/>
    </justification>
  </clause>

  <clause id="17363">
    <literal><![CDATA[
      (K(x,K(y,z)) \ u) / w = K(x,K(y,z)) * (u / w)
    ]]></literal>
    <justification jstring="[para(7824(a,2),17220(a,1,1))].">
      <j1 rule="para" parents="7824 17220"/>
    </justification>
  </clause>

  <clause id="17364">
    <literal><![CDATA[
      K((x * K(y,z)) \ u,w) = K(x \ (K(z,y) * u),w)
    ]]></literal>
    <justification jstring="[hyper(16091,a,17232,a)].">
      <j1 rule="hyper" parents="16091 17232"/>
    </justification>
  </clause>

  <clause id="17366">
    <literal><![CDATA[
      K(x,(K(y,z) * u) / w) = K(x,u / (w * K(z,y)))
    ]]></literal>
    <justification jstring="[hyper(16083,a,17261,a)].">
      <j1 rule="hyper" parents="16083 17261"/>
    </justification>
  </clause>

  <clause id="17367">
    <literal><![CDATA[
      K(x,(y * K(z,u)) / w) = K(x,y * (w \ K(z,u)))
    ]]></literal>
    <justification jstring="[hyper(320,a,16153,a(flip),b,17261,a),flip(a)].">
      <j1 rule="hyper" parents="320 16153 17261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17368">
    <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,17267,a(flip),b,7825,a),flip(a)].">
      <j1 rule="hyper" parents="116 17267 7825"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17369">
    <literal><![CDATA[
      T(T(x,(y \ z) \ u),K(w,z \ (y * u))) = T(x,T((y \ z) \ u,w))
    ]]></literal>
    <justification jstring="[hyper(7858,a,17270,a),flip(a)].">
      <j1 rule="hyper" parents="7858 17270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17370">
    <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(17270(a,1),8219(a,1))].">
      <j1 rule="para" parents="17270 8219"/>
    </justification>
  </clause>

  <clause id="17371">
    <literal><![CDATA[
      K(x,K(y,z \ (u * (w \ z)))) = K(x,K(y,w \ u))
    ]]></literal>
    <justification jstring="[hyper(320,a,15610,a(flip),b,17272,a),flip(a)].">
      <j1 rule="hyper" parents="320 15610 17272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17372">
    <literal><![CDATA[
      K(x,T(y,z / (u * w))) = K(x,T(y,u \ (z / w)))
    ]]></literal>
    <justification jstring="[hyper(15795,a,17287,a),flip(a)].">
      <j1 rule="hyper" parents="15795 17287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17373">
    <literal><![CDATA[
      T(x \ 1,a(y,z,u)) = T(x,a(y,z,u)) \ 1
    ]]></literal>
    <justification jstring="[hyper(13434,a,17312,a)].">
      <j1 rule="hyper" parents="13434 17312"/>
    </justification>
  </clause>

  <clause id="17374">
    <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(17373(a,2),13750(a,1,2))].">
      <j1 rule="para" parents="17373 13750"/>
    </justification>
  </clause>

  <clause id="17375">
    <literal><![CDATA[
      L(x,y,K(z,u) * (w * (z \ u))) = L(x,y,w * (u / z))
    ]]></literal>
    <justification jstring="[para(6101(a,1),17324(a,1,3)),flip(a)].">
      <j1 rule="para" parents="6101 17324"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17376">
    <literal><![CDATA[
      L(x,y,K(z,u) * (w / (u / z))) = L(x,y,w / (z \ u))
    ]]></literal>
    <justification jstring="[para(6398(a,1),17324(a,1,3)),flip(a)].">
      <j1 rule="para" parents="6398 17324"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17377">
    <literal><![CDATA[
      K(x,L((y \ 1) \ z,u,u * y)) = K(x,u \ ((u / (y \ 1)) * z))
    ]]></literal>
    <justification jstring="[hyper(58,a,14474,a(flip),b,17327,a),flip(a)].">
      <j1 rule="hyper" parents="58 14474 17327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17378">
    <literal><![CDATA[
      K(x,L(y,z,(u * w) \ w)) = K(x,L(y,z,u \ 1))
    ]]></literal>
    <justification jstring="[hyper(58,a,14502,a,b,17328,a)].">
      <j1 rule="hyper" parents="58 14502 17328"/>
    </justification>
  </clause>

  <clause id="17379">
    <literal><![CDATA[
      (x \ y) * K(z,L(u,y,x \ 1)) = ((x \ y) / y) * (y * K(z,u))
    ]]></literal>
    <justification jstring="[para(17328(a,1),11216(a,1,2))].">
      <j1 rule="para" parents="17328 11216"/>
    </justification>
  </clause>

  <clause id="17380">
    <literal><![CDATA[
      (x / y) * a(x,z,K(u,w)) = L(x,z,K(u,w)) / y
    ]]></literal>
    <justification jstring="[para(14925(a,2),17338(a,2,1))].">
      <j1 rule="para" parents="14925 17338"/>
    </justification>
  </clause>

  <clause id="17381">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * w) = u * (K(x,K(y,z)) * w)
    ]]></literal>
    <justification jstring="[para(15780(a,2),17344(a,2,2))].">
      <j1 rule="para" parents="15780 17344"/>
    </justification>
  </clause>

  <clause id="17382">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) * w = u * (w * K(x,K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(58,a,17201,a,b,17345,a)].">
      <j1 rule="hyper" parents="58 17201 17345"/>
    </justification>
  </clause>

  <clause id="17383">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * (w \ x)) = u * (w \ T(x,K(y,z)))
    ]]></literal>
    <justification jstring="[para(12358(a,1),17345(a,2,2))].">
      <j1 rule="para" parents="12358 17345"/>
    </justification>
  </clause>

  <clause id="17384">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * (w * v5)) = u * (w * (v5 * K(x,K(y,z))))
    ]]></literal>
    <justification jstring="[para(17158(a,1),17345(a,2,2))].">
      <j1 rule="para" parents="17158 17345"/>
    </justification>
  </clause>

  <clause id="17385">
    <literal><![CDATA[
      x \ (K(y,K(z,u)) * w) = K(y,K(z,u)) * (x \ w)
    ]]></literal>
    <justification jstring="[para(15684(a,2),17348(a,1,2))].">
      <j1 rule="para" parents="15684 17348"/>
    </justification>
  </clause>

  <clause id="17386">
    <literal><![CDATA[
      K(x,K(y,z)) * (u \ (K(x,K(y,z)) * w)) = u \ w
    ]]></literal>
    <justification jstring="[para(15848(a,1),17348(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15848 17348"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17387">
    <literal><![CDATA[
      K(x,K(y,z)) * (u \ (T(x,K(y,z)) \ w)) = u \ (x \ w)
    ]]></literal>
    <justification jstring="[para(15748(a,1),17348(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15748 17348"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17388">
    <literal><![CDATA[
      x \ T(K(y,K(z,u)) * w,v5) = K(y,K(z,u)) * (x \ T(w,v5))
    ]]></literal>
    <justification jstring="[para(15747(a,2),17348(a,1,2))].">
      <j1 rule="para" parents="15747 17348"/>
    </justification>
  </clause>

  <clause id="17389">
    <literal><![CDATA[
      x \ T(y * K(z,K(u,w)),v5) = K(z,K(u,w)) * (x \ T(y,v5))
    ]]></literal>
    <justification jstring="[para(15959(a,2),17348(a,1,2))].">
      <j1 rule="para" parents="15959 17348"/>
    </justification>
  </clause>

  <clause id="17390">
    <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(17359(a,1),16194(a,1,2,2))].">
      <j1 rule="para" parents="17359 16194"/>
    </justification>
  </clause>

  <clause id="17391">
    <literal><![CDATA[
      (x * K(y,K(z,u))) * w = x * (w * K(y,K(z,u)))
    ]]></literal>
    <justification jstring="[hyper(320,a,17345,a(flip),b,17360,a),flip(a)].">
      <j1 rule="hyper" parents="320 17345 17360"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17392">
    <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(17363(a,2),7830(a,1))].">
      <j1 rule="para" parents="17363 7830"/>
    </justification>
  </clause>

  <clause id="17393">
    <literal><![CDATA[
      K((x * K(y,z)) \ u,w) = K(x \ (u * K(z,y)),w)
    ]]></literal>
    <justification jstring="[hyper(320,a,16056,a(flip),b,17364,a),flip(a)].">
      <j1 rule="hyper" parents="320 16056 17364"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17394">
    <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,15722,a,b,17364,a)].">
      <j1 rule="hyper" parents="58 15722 17364"/>
    </justification>
  </clause>

  <clause id="17395">
    <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(17364(a,2),16141(a,1))].">
      <j1 rule="para" parents="17364 16141"/>
    </justification>
  </clause>

  <clause id="17396">
    <literal><![CDATA[
      K(x,(K(y,z) * u) / w) = K(x,u * (w \ K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(320,a,16153,a(flip),b,17366,a),flip(a)].">
      <j1 rule="hyper" parents="320 16153 17366"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17397">
    <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(17366(a,2),16251(a,1))].">
      <j1 rule="para" parents="17366 16251"/>
    </justification>
  </clause>

  <clause id="17398">
    <literal><![CDATA[
      T(x,(y * K(z,u)) / w) = T(x,y * (w \ K(z,u)))
    ]]></literal>
    <justification jstring="[hyper(118,a,17367,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 17367 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17399">
    <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,10908,a(flip),b,17367,a),flip(a)].">
      <j1 rule="hyper" parents="58 10908 17367"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17400">
    <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,8859,a(flip),b,17367,a),flip(a)].">
      <j1 rule="hyper" parents="58 8859 17367"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17401">
    <literal><![CDATA[
      K(x,(y / z) * (u \ K(w,z))) = K(x,(y / T(z,w)) / u)
    ]]></literal>
    <justification jstring="[para(6322(a,1),17367(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6322 17367"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17402">
    <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(17367(a,1),16083(a,1))].">
      <j1 rule="para" parents="17367 16083"/>
    </justification>
  </clause>

  <clause id="17403">
    <literal><![CDATA[
      K(x,K(y,(z * u) \ (w * u))) = K(x,K(y,z \ w))
    ]]></literal>
    <justification jstring="[para(4(a,1),17371(a,1,2,2,2,2))].">
      <j1 rule="para" parents="4 17371"/>
    </justification>
  </clause>

  <clause id="17404">
    <literal><![CDATA[
      K(x,T(y,(z * u) \ w)) = K(x,T(y,z \ (w / u)))
    ]]></literal>
    <justification jstring="[hyper(15795,a,17372,a)].">
      <j1 rule="hyper" parents="15795 17372"/>
    </justification>
  </clause>

  <clause id="17406">
    <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,13291,a(flip),b,17378,a),flip(a)].">
      <j1 rule="hyper" parents="58 13291 17378"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17407">
    <literal><![CDATA[
      K(x,L(y \ (z * u),y,z \ 1)) = K(x,((u / (z * u)) * y) \ u)
    ]]></literal>
    <justification jstring="[para(14133(a,1),17378(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14133 17378"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17408">
    <literal><![CDATA[
      ((x * y) \ y) * ((((x * y) \ y) \ z) * K(u,w)) = z * K(u,L(w,z,x \ 1))
    ]]></literal>
    <justification jstring="[para(17378(a,1),14475(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17378 14475"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17410">
    <literal><![CDATA[
      K(x,K(y,z)) \ (u * w) = u * (K(x,K(y,z)) * w)
    ]]></literal>
    <justification jstring="[hyper(7830,a,17381,a)].">
      <j1 rule="hyper" parents="7830 17381"/>
    </justification>
  </clause>

  <clause id="17412">
    <literal><![CDATA[
      (x * K(y,K(z,u))) * w = x * (K(y,K(z,u)) * w)
    ]]></literal>
    <justification jstring="[hyper(58,a,17360,a,b,17381,a)].">
      <j1 rule="hyper" parents="58 17360 17381"/>
    </justification>
  </clause>

  <clause id="17414">
    <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(17381(a,1),16194(a,1,2,2))].">
      <j1 rule="para" parents="17381 16194"/>
    </justification>
  </clause>

  <clause id="17415">
    <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(17382(a,1),13(a,2,1)),flip(a)].">
      <j1 rule="para" parents="17382 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17416">
    <literal><![CDATA[
      (K(x,y) * z) * (u * K(x,K(y,w))) = (K(x,T(y,w)) * z) * u
    ]]></literal>
    <justification jstring="[para(8520(a,1),17382(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8520 17382"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17417">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) \ w = K(x,K(y,z)) * (u \ w)
    ]]></literal>
    <justification jstring="[hyper(58,a,17362,a,b,17385,a)].">
      <j1 rule="hyper" parents="58 17362 17385"/>
    </justification>
  </clause>

  <clause id="17418">
    <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(17391(a,1),9(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="17391 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17419">
    <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(17391(a,1),9(a,2,1)),flip(a)].">
      <j1 rule="para" parents="17391 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17420">
    <literal><![CDATA[
      K((x \ 1) \ (y * K(z,u)),w) = K((x \ K(u,z)) \ y,w)
    ]]></literal>
    <justification jstring="[para(13812(a,1),17393(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="13812 17393"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17421">
    <literal><![CDATA[
      T(x,(K(y,z) * u) / w) = T(x,u * (w \ K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(118,a,17396,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 17396 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17422">
    <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,16614,a(flip),b,17396,a),flip(a)].">
      <j1 rule="hyper" parents="58 16614 17396"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17423">
    <literal><![CDATA[
      K(x,(y * z) * (u \ K(y,w))) = K(x,(T(y,w) * z) / u)
    ]]></literal>
    <justification jstring="[para(4781(a,1),17396(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4781 17396"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17424">
    <literal><![CDATA[
      K(x,(y \ z) * (u \ K(w,y))) = K(x,(T(y,w) \ z) / u)
    ]]></literal>
    <justification jstring="[para(5131(a,1),17396(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5131 17396"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17425">
    <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,16711,a(flip),b,17398,a),flip(a)].">
      <j1 rule="hyper" parents="58 16711 17398"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17426">
    <literal><![CDATA[
      K(x,K(y,(z * u) \ w)) = K(x,K(y,z \ (w / u)))
    ]]></literal>
    <justification jstring="[para(7(a,1),17403(a,1,2,2,2))].">
      <j1 rule="para" parents="7 17403"/>
    </justification>
  </clause>

  <clause id="17427">
    <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(15864,a,17404,a),flip(a)].">
      <j1 rule="hyper" parents="15864 17404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17428">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ w))) = K(x,T(y,u \ (w / z)))
    ]]></literal>
    <justification jstring="[hyper(58,a,17284,a(flip),b,17404,a)].">
      <j1 rule="hyper" parents="58 17284 17404"/>
    </justification>
  </clause>

  <clause id="17429">
    <literal><![CDATA[
      R(x,K(y,K(z,u)),w) = x
    ]]></literal>
    <justification jstring="[hyper(3476,a,17412,a)].">
      <j1 rule="hyper" parents="3476 17412"/>
    </justification>
  </clause>

  <clause id="17430">
    <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,17412,a),flip(a)].">
      <j1 rule="hyper" parents="117 7 17412"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17431">
    <literal><![CDATA[
      (x * (y * K(z,K(u,w)))) * v5 = (x * y) * (K(z,K(u,w)) * v5)
    ]]></literal>
    <justification jstring="[para(17158(a,1),17412(a,1,1))].">
      <j1 rule="para" parents="17158 17412"/>
    </justification>
  </clause>

  <clause id="17432">
    <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(17429(a,1),511(a,1,1,1,2))].">
      <j1 rule="para" parents="17429 511"/>
    </justification>
  </clause>

  <clause id="17433">
    <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,17417,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="116 155 17417"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17434">
    <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(17417(a,2),15697(a,1))].">
      <j1 rule="para" parents="17417 15697"/>
    </justification>
  </clause>

  <clause id="17435">
    <literal><![CDATA[
      (x * (K(y,K(z,u)) * w)) \ v5 = K(y,K(z,u)) * ((x * w) \ v5)
    ]]></literal>
    <justification jstring="[para(17381(a,1),17417(a,1,1))].">
      <j1 rule="para" parents="17381 17417"/>
    </justification>
  </clause>

  <clause id="17436">
    <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,16653,a(flip),b,17421,a)].">
      <j1 rule="hyper" parents="58 16653 17421"/>
    </justification>
  </clause>

  <clause id="17437">
    <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(17421(a,1),15484(a,1,2,1,2))].">
      <j1 rule="para" parents="17421 15484"/>
    </justification>
  </clause>

  <clause id="17438">
    <literal><![CDATA[
      K(x,K(y,(z * u) \ w)) = K(x,K(y,z \ (u \ w)))
    ]]></literal>
    <justification jstring="[hyper(320,a,16492,a(flip),b,17426,a),flip(a)].">
      <j1 rule="hyper" parents="320 16492 17426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17439">
    <literal><![CDATA[
      K(x,T(y,(z / u) \ w)) = K(x,T(y,u \ (w \ z)))
    ]]></literal>
    <justification jstring="[hyper(320,a,8238,a,b,17428,a)].">
      <j1 rule="hyper" parents="320 8238 17428"/>
    </justification>
  </clause>

  <clause id="17440">
    <literal><![CDATA[
      K(x,T(y,(z / u) \ (w \ z))) = K(x,T(y,w \ u))
    ]]></literal>
    <justification jstring="[hyper(320,a,16456,a(flip),b,17428,a),flip(a)].">
      <j1 rule="hyper" parents="320 16456 17428"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17441">
    <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),17428(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="17 17428"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17442">
    <literal><![CDATA[
      x / (K(y,K(z,u)) * w) = K(y,K(z,u)) * (x / w)
    ]]></literal>
    <justification jstring="[hyper(15852,a,17430,a),flip(a)].">
      <j1 rule="hyper" parents="15852 17430"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17443">
    <literal><![CDATA[
      x / (K(y,K(z,u)) * w) = K(y,K(z,u)) \ (x / w)
    ]]></literal>
    <justification jstring="[hyper(116,a,17430,a(flip),b,15684,a),flip(a)].">
      <j1 rule="hyper" parents="116 17430 15684"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17444">
    <literal><![CDATA[
      K(x,(K(y,K(z,u)) \ w) \ v5) = K(x,w \ v5)
    ]]></literal>
    <justification jstring="[para(17433(a,2),16030(a,1,2))].">
      <j1 rule="para" parents="17433 16030"/>
    </justification>
  </clause>

  <clause id="17445">
    <literal><![CDATA[
      K(x,y \ (K(z,K(u,w)) \ v5)) = K(x,y \ v5)
    ]]></literal>
    <justification jstring="[para(17361(a,1),17444(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17361 17444"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17446">
    <literal><![CDATA[
      K(x,y \ (T(z,K(u,w)) * v5)) = K(x,y \ (z * v5))
    ]]></literal>
    <justification jstring="[para(4782(a,1),17445(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4782 17445"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17447">
    <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(15967(a,1),17445(a,1,2,2))].">
      <j1 rule="para" parents="15967 17445"/>
    </justification>
  </clause>

  <clause id="17448">
    <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(17438(a,1),8385(a,1,1))].">
      <j1 rule="para" parents="17438 8385"/>
    </justification>
  </clause>

  <clause id="17449">
    <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(17438(a,1),13106(a,1,1))].">
      <j1 rule="para" parents="17438 13106"/>
    </justification>
  </clause>

  <clause id="17450">
    <literal><![CDATA[
      K(x,T(y,z \ ((u \ w) \ w))) = K(x,T(y,u \ z))
    ]]></literal>
    <justification jstring="[hyper(58,a,17439,a(flip),b,17440,a)].">
      <j1 rule="hyper" parents="58 17439 17440"/>
    </justification>
  </clause>

  <clause id="17451">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ (z * w)))) = K(x,T(y,u \ w))
    ]]></literal>
    <justification jstring="[para(6(a,1),17440(a,1,2,2,1))].">
      <j1 rule="para" parents="6 17440"/>
    </justification>
  </clause>

  <clause id="17452">
    <literal><![CDATA[
      K(x,K(y,z)) * (u / (w \ x)) = u / (w \ T(x,K(y,z)))
    ]]></literal>
    <justification jstring="[para(15750(a,1),17442(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15750 17442"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17453">
    <literal><![CDATA[
      x / T(y * K(z,K(u,w)),v5) = K(z,K(u,w)) * (x / T(y,v5))
    ]]></literal>
    <justification jstring="[para(15975(a,2),17442(a,1,2))].">
      <j1 rule="para" parents="15975 17442"/>
    </justification>
  </clause>

  <clause id="17454">
    <literal><![CDATA[
      K(x,K(y,z)) \ (u / (K(x,K(y,z)) \ w)) = u / w
    ]]></literal>
    <justification jstring="[para(5(a,1),17443(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5 17443"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17455">
    <literal><![CDATA[
      K(x,y \ (T(z,T(u,w)) * v5)) = K(x,y \ (T(z,u) * v5))
    ]]></literal>
    <justification jstring="[para(7438(a,1),17446(a,1,2,2,1))].">
      <j1 rule="para" parents="7438 17446"/>
    </justification>
  </clause>

  <clause id="17456">
    <literal><![CDATA[
      K(x,T(y,z \ (K(u,w) * v5))) = K(x,T(y,z \ v5))
    ]]></literal>
    <justification jstring="[hyper(16431,a,17451,a)].">
      <j1 rule="hyper" parents="16431 17451"/>
    </justification>
  </clause>

  <clause id="17457">
    <literal><![CDATA[
      K(x,T(y,z \ (T(u,w) \ v5))) = K(x,T(y,z \ (u \ v5)))
    ]]></literal>
    <justification jstring="[para(5081(a,1),17456(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="5081 17456"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17458">
    <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(14263(a,2),17196(a,1,1))].">
      <j1 rule="para" parents="14263 17196"/>
    </justification>
  </clause>

  <clause id="17459">
    <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(17316(a,1),17196(a,1))].">
      <j1 rule="para" parents="17316 17196"/>
    </justification>
  </clause>

  <clause id="17460">
    <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(14838(a,1),17292(a,1))].">
      <j1 rule="para" parents="14838 17292"/>
    </justification>
  </clause>

  <clause id="17462">
    <literal><![CDATA[
      K(x,L(y,z,u) * T(w,y)) = K(x,w * L(y,z,u))
    ]]></literal>
    <justification jstring="[para(13347(a,1),17280(a,1,2))].">
      <j1 rule="para" parents="13347 17280"/>
    </justification>
  </clause>

  <clause id="17463">
    <literal><![CDATA[
      K(x,L(y \ z,u,w) * T(y,z)) = K(x,y * L(y \ z,u,w))
    ]]></literal>
    <justification jstring="[hyper(13208,a,17462,a)].">
      <j1 rule="hyper" parents="13208 17462"/>
    </justification>
  </clause>

  <clause id="17465">
    <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(17288(a,2),15525(a,1))].">
      <j1 rule="para" parents="17288 15525"/>
    </justification>
  </clause>

  <clause id="17466">
    <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(14815(a,1),17299(a,1))].">
      <j1 rule="para" parents="14815 17299"/>
    </justification>
  </clause>

  <clause id="17467">
    <literal><![CDATA[
      a(x,y,z) \ (K(u,w) * z) = K(u,w) * (z / a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,14043,a(flip),b,17310,a),flip(a)].">
      <j1 rule="hyper" parents="58 14043 17310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17468">
    <literal><![CDATA[
      x \ (a(y,z,K(u,w)) * v5) = a(y,z,K(u,w)) * (x \ v5)
    ]]></literal>
    <justification jstring="[para(17193(a,2),17314(a,1,2))].">
      <j1 rule="para" parents="17193 17314"/>
    </justification>
  </clause>

  <clause id="17469">
    <literal><![CDATA[
      x * (y * a(z,u,K(x,w))) = L(x,u,K(w,z)) * y
    ]]></literal>
    <justification jstring="[hyper(58,a,14960,a(flip),b,17317,a),flip(a)].">
      <j1 rule="hyper" parents="58 14960 17317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17470">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (w * v5) = w * (a(x,y,K(z,u)) * v5)
    ]]></literal>
    <justification jstring="[para(17193(a,2),17317(a,2,2))].">
      <j1 rule="para" parents="17193 17317"/>
    </justification>
  </clause>

  <clause id="17471">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (w * v5) = w * (a(u,y,K(x,z)) * v5)
    ]]></literal>
    <justification jstring="[para(17313(a,2),17317(a,2,2))].">
      <j1 rule="para" parents="17313 17317"/>
    </justification>
  </clause>

  <clause id="17472">
    <literal><![CDATA[
      L(x,y,K(z,u \ 1) / u) = L(x,y,u \ K(u,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,13190,a(flip),b,17323,a),flip(a)].">
      <j1 rule="hyper" parents="58 13190 17323"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17473">
    <literal><![CDATA[
      L(x,y,z \ K(u,z \ 1)) = L(x,y,z \ K(z,u))
    ]]></literal>
    <justification jstring="[hyper(17265,a,17472,a)].">
      <j1 rule="hyper" parents="17265 17472"/>
    </justification>
  </clause>

  <clause id="17474">
    <literal><![CDATA[
      L(x,y,z \ K(z,y)) = L(x,y,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,11198,a(flip),b,17473,a),flip(a)].">
      <j1 rule="hyper" parents="58 11198 17473"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17475">
    <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(14243(a,1),17474(a,1,3))].">
      <j1 rule="para" parents="14243 17474"/>
    </justification>
  </clause>

  <clause id="17476">
    <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(14310(a,1),17335(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14310 17335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17477">
    <literal><![CDATA[
      T(x,K(y,z)) \ (u \ (w * x)) = x \ (u \ (w * T(x,K(y,z))))
    ]]></literal>
    <justification jstring="[para(17349(a,1),15851(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17349 15851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17478">
    <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(17349(a,1),16081(a,1,2))].">
      <j1 rule="para" parents="17349 16081"/>
    </justification>
  </clause>

  <clause id="17479">
    <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(17350(a,1),16096(a,1,2,2))].">
      <j1 rule="para" parents="17350 16096"/>
    </justification>
  </clause>

  <clause id="17480">
    <literal><![CDATA[
      K(x,y) * (K(z,u) * w) = K(z,u) * (K(x,y) * w)
    ]]></literal>
    <justification jstring="[hyper(16413,a,17353,a)].">
      <j1 rule="hyper" parents="16413 17353"/>
    </justification>
  </clause>

  <clause id="17485">
    <literal><![CDATA[
      (K(x,y) * z) / (K(x,y) * (K(u,w) * z)) = K(w,u)
    ]]></literal>
    <justification jstring="[para(17480(a,1),5142(a,1,2))].">
      <j1 rule="para" parents="17480 5142"/>
    </justification>
  </clause>

  <clause id="17487">
    <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(17383(a,1),16059(a,1,1))].">
      <j1 rule="para" parents="17383 16059"/>
    </justification>
  </clause>

  <clause id="17488">
    <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(17420(a,1),14072(a,1))].">
      <j1 rule="para" parents="17420 14072"/>
    </justification>
  </clause>

  <clause id="17489">
    <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(17441(a,2),16460(a,1))].">
      <j1 rule="para" parents="17441 16460"/>
    </justification>
  </clause>

  <clause id="17490">
    <literal><![CDATA[
      K(x,y / (z \ T(u,K(w,v5)))) = K(x,y / (z \ u))
    ]]></literal>
    <justification jstring="[para(17452(a,1),16027(a,1,2))].">
      <j1 rule="para" parents="17452 16027"/>
    </justification>
  </clause>

  <clause id="17491">
    <literal><![CDATA[
      K(x,y / (z \ (K(u,w) * v5))) = K(x,y / (z \ (v5 * K(u,w))))
    ]]></literal>
    <justification jstring="[para(6337(a,1),17490(a,1,2,2,2))].">
      <j1 rule="para" parents="6337 17490"/>
    </justification>
  </clause>

  <clause id="17492">
    <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(14912(a,1),17490(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="14912 17490"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17493">
    <literal><![CDATA[
      K(x,(y * T(z,u)) \ (T(y,z) * w)) = K(x,(T(z,u) * y) \ (y * w))
    ]]></literal>
    <justification jstring="[para(11207(a,1),17455(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11207 17455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17494">
    <literal><![CDATA[
      a(x,y,z) \ (K(u,w) * z) = K(u,w) * (a(x,y,z) \ z)
    ]]></literal>
    <justification jstring="[para(14985(a,1),17467(a,2,2))].">
      <j1 rule="para" parents="14985 17467"/>
    </justification>
  </clause>

  <clause id="17495">
    <literal><![CDATA[
      (a(x,y,K(z,u)) * w) \ v5 = a(u,y,K(z,x)) * (w \ v5)
    ]]></literal>
    <justification jstring="[hyper(58,a,14512,a,b,17468,a)].">
      <j1 rule="hyper" parents="58 14512 17468"/>
    </justification>
  </clause>

  <clause id="17496">
    <literal><![CDATA[
      (x * a(y,z,K(u,w))) * v5 = x * (a(y,z,K(u,w)) * v5)
    ]]></literal>
    <justification jstring="[hyper(58,a,17320,a,b,17470,a)].">
      <j1 rule="hyper" parents="58 17320 17470"/>
    </justification>
  </clause>

  <clause id="17497">
    <literal><![CDATA[
      a(x,y,K(z,u)) * a(z,y,u) = T(a(z,y,u),x)
    ]]></literal>
    <justification jstring="[hyper(13446,a,17471,a),flip(a)].">
      <j1 rule="hyper" parents="13446 17471"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17498">
    <literal><![CDATA[
      L(x,y,T(a(z,u,w),v5)) = L(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(17497(a,1),15549(a,1,3))].">
      <j1 rule="para" parents="17497 15549"/>
    </justification>
  </clause>

  <clause id="17499">
    <literal><![CDATA[
      T(L(x,y,a(z,u,w)) \ x,v5) = L(x,y,a(z,u,w)) \ x
    ]]></literal>
    <justification jstring="[para(17498(a,1),15101(a,2,1))].">
      <j1 rule="para" parents="17498 15101"/>
    </justification>
  </clause>

  <clause id="17500">
    <literal><![CDATA[
      (x * a(y,z,K(u,w))) \ v5 = a(w,z,K(u,y)) * (x \ v5)
    ]]></literal>
    <justification jstring="[para(17193(a,1),17495(a,1,1))].">
      <j1 rule="para" parents="17193 17495"/>
    </justification>
  </clause>

  <clause id="17501">
    <literal><![CDATA[
      (x * (y * a(z,u,K(w,v5)))) \ v6 = a(v5,u,K(w,z)) * ((x * y) \ v6)
    ]]></literal>
    <justification jstring="[para(17317(a,1),17495(a,1,1))].">
      <j1 rule="para" parents="17317 17495"/>
    </justification>
  </clause>

  <clause id="17502">
    <literal><![CDATA[
      R(x,a(y,z,K(u,w)),v5) = x
    ]]></literal>
    <justification jstring="[hyper(3476,a,17496,a)].">
      <j1 rule="hyper" parents="3476 17496"/>
    </justification>
  </clause>

  <clause id="17503">
    <literal><![CDATA[
      L(x,a(y,z,K(u,w)),v5) = x
    ]]></literal>
    <justification jstring="[hyper(479,a,17496,a)].">
      <j1 rule="hyper" parents="479 17496"/>
    </justification>
  </clause>

  <clause id="17504">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (((x * y) * K(z,u)) \ w) = (x * (y * K(z,u))) \ w
    ]]></literal>
    <justification jstring="[para(17502(a,1),762(a,1,1)),flip(a)].">
      <j1 rule="para" parents="17502 762"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17507">
    <literal><![CDATA[
      x / (a(y,z,K(u,w)) \ v5) = (x / v5) * a(y,z,K(u,w))
    ]]></literal>
    <justification jstring="[para(17503(a,1),498(a,1,2))].">
      <j1 rule="para" parents="17503 498"/>
    </justification>
  </clause>

  <clause id="17508">
    <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(17503(a,1),476(a,1,2,2,1))].">
      <j1 rule="para" parents="17503 476"/>
    </justification>
  </clause>

  <clause id="17509">
    <literal><![CDATA[
      ((L(x,y,a(z,u,w)) \ x) \ v5) \ v5 = L(x,y,a(z,u,w)) \ x
    ]]></literal>
    <justification jstring="[hyper(4291,a,17499,a)].">
      <j1 rule="hyper" parents="4291 17499"/>
    </justification>
  </clause>

  <clause id="17510">
    <literal><![CDATA[
      x / (a(y,z,K(u,w)) * v5) = (x / v5) * a(w,z,K(u,y))
    ]]></literal>
    <justification jstring="[para(14323(a,1),17507(a,1,2))].">
      <j1 rule="para" parents="14323 17507"/>
    </justification>
  </clause>

  <clause id="17511">
    <literal><![CDATA[
      (x / y) * a(z,u,K(y,w)) = x / L(y,u,K(z,w))
    ]]></literal>
    <justification jstring="[para(14938(a,1),17510(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14938 17510"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17512">
    <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(16510(a,2),17333(a,1))].">
      <j1 rule="para" parents="16510 17333"/>
    </justification>
  </clause>

  <clause id="17513">
    <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(17487,a,16075,a),flip(a)].">
      <j1 rule="hyper" parents="17487 16075"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17514">
    <literal><![CDATA[
      K(((x \ K(y,z)) \ 1) * u,w) = K(x * (u * K(z,y)),w)
    ]]></literal>
    <justification jstring="[hyper(17488,a,13860,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="17488 13860"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17515">
    <literal><![CDATA[
      K((K(x,y) * z) * u,w) = K(z * (u * K(x,y)),w)
    ]]></literal>
    <justification jstring="[hyper(58,a,13903,a(flip),b,17514,a)].">
      <j1 rule="hyper" parents="58 13903 17514"/>
    </justification>
  </clause>

  <clause id="17516">
    <literal><![CDATA[
      K((x \ y) * (z * K(u,x)),w) = K((T(x,u) \ y) * z,w)
    ]]></literal>
    <justification jstring="[para(5131(a,1),17515(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5131 17515"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17517">
    <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(16429(a,1),17489(a,1))].">
      <j1 rule="para" parents="16429 17489"/>
    </justification>
  </clause>

  <clause id="17518">
    <literal><![CDATA[
      T(x,K(y,a(z,u,w)) * v5) = v5 \ (x * v5)
    ]]></literal>
    <justification jstring="[para(17198(a,1),17227(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17198 17227"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17519">
    <literal><![CDATA[
      T(x,K(y,a(z,u,w)) * v5) = T(x,v5)
    ]]></literal>
    <justification jstring="[hyper(320,a,17,a,b,17518,a),flip(a)].">
      <j1 rule="hyper" parents="320 17 17518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17520">
    <literal><![CDATA[
      T(x,K(y,a(z,u,w)) * v5) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x,v5) = v6
    ]]></literal>
    <justification jstring="[para(17518(a,2),288(a,1))].">
      <j1 rule="para" parents="17518 288"/>
    </justification>
  </clause>

  <clause id="17522">
    <literal><![CDATA[
      T(x,T(a(y,z,u),w) * v5) = T(x,a(y,z,u) * v5)
    ]]></literal>
    <justification jstring="[hyper(58,a,15120,a(flip),b,17519,a)].">
      <j1 rule="hyper" parents="58 15120 17519"/>
    </justification>
  </clause>

  <clause id="17523">
    <literal><![CDATA[
      T(x,a(y,z,K(u,w)) * v5) = T(x,v5)
    ]]></literal>
    <justification jstring="[para(13400(a,2),17519(a,1,2,1))].">
      <j1 rule="para" parents="13400 17519"/>
    </justification>
  </clause>

  <clause id="17524">
    <literal><![CDATA[
      K(a(x,y,K(z,u)) * w,v5) = v5 / T(v5,w)
    ]]></literal>
    <justification jstring="[para(17523(a,1),4794(a,2,2))].">
      <j1 rule="para" parents="17523 4794"/>
    </justification>
  </clause>

  <clause id="17525">
    <literal><![CDATA[
      T(x,L(K(y,z),u,w) * v5) = T(x,K(y,z) * v5)
    ]]></literal>
    <justification jstring="[para(9909(a,1),17523(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9909 17523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17526">
    <literal><![CDATA[
      T(x,(y * z) * K(u,w)) = T(x,y * (z * K(u,w)))
    ]]></literal>
    <justification jstring="[para(14443(a,1),17523(a,1,2))].">
      <j1 rule="para" parents="14443 17523"/>
    </justification>
  </clause>

  <clause id="17527">
    <literal><![CDATA[
      T(x,K(y,L(z,u,w)) * v5) = T(x,K(y,z) * v5)
    ]]></literal>
    <justification jstring="[para(14511(a,1),17523(a,1,2))].">
      <j1 rule="para" parents="14511 17523"/>
    </justification>
  </clause>

  <clause id="17528">
    <literal><![CDATA[
      K(a(x,y,K(z,u)) * w,v5) = K(w,v5)
    ]]></literal>
    <justification jstring="[hyper(320,a,4794,a,b,17524,a),flip(a)].">
      <j1 rule="hyper" parents="320 4794 17524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17529">
    <literal><![CDATA[
      K(a(x,y,K(z,u)) * w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K(w,v5) = v6
    ]]></literal>
    <justification jstring="[para(17524(a,2),4862(a,1))].">
      <j1 rule="para" parents="17524 4862"/>
    </justification>
  </clause>

  <clause id="17530">
    <literal><![CDATA[
      K(x * a(y,z,K(u,w)),v5) = K(x,v5)
    ]]></literal>
    <justification jstring="[hyper(17252,a,17528,a)].">
      <j1 rule="hyper" parents="17252 17528"/>
    </justification>
  </clause>

  <clause id="17531">
    <literal><![CDATA[
      K((x * y) * K(z,u),w) = K(x * (y * K(z,u)),w)
    ]]></literal>
    <justification jstring="[para(14443(a,1),17528(a,1,1))].">
      <j1 rule="para" parents="14443 17528"/>
    </justification>
  </clause>

  <clause id="17532">
    <literal><![CDATA[
      K(x * T(y,a(z,u,w)),v5) = K(x * y,v5)
    ]]></literal>
    <justification jstring="[para(17315(a,1),17528(a,1,1))].">
      <j1 rule="para" parents="17315 17528"/>
    </justification>
  </clause>

  <clause id="17533">
    <literal><![CDATA[
      K(x \ (y * a(z,u,K(w,v5))),v6) = K(x \ y,v6)
    ]]></literal>
    <justification jstring="[para(17314(a,2),17528(a,1,1))].">
      <j1 rule="para" parents="17314 17528"/>
    </justification>
  </clause>

  <clause id="17534">
    <literal><![CDATA[
      K(x * a(y,z,K(u,w)),v5) = (v6 * K(v5,x)) \ v6
    ]]></literal>
    <justification jstring="[hyper(320,a,6338,a,b,17530,a),flip(a)].">
      <j1 rule="hyper" parents="320 6338 17530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17535">
    <literal><![CDATA[
      K(T(x,y) * L(y,z,u),w) = K(L(y,z,u) * x,w)
    ]]></literal>
    <justification jstring="[hyper(58,a,14462,a(flip),b,17532,a)].">
      <j1 rule="hyper" parents="58 14462 17532"/>
    </justification>
  </clause>

  <clause id="17536">
    <literal><![CDATA[
      T(x,a(y,z,K(u,w)) * v5) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x,v5) = v6
    ]]></literal>
    <justification jstring="[para(13400(a,2),17520(a,1,2,1))].">
      <j1 rule="para" parents="13400 17520"/>
    </justification>
  </clause>

  <clause id="17537">
    <literal><![CDATA[
      K(K(x,a(y,z,u)) * w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K(w,v5) = v6
    ]]></literal>
    <justification jstring="[para(13400(a,1),17529(a,1,1,1))].">
      <j1 rule="para" parents="13400 17529"/>
    </justification>
  </clause>

  <clause id="17538">
    <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(14443(a,1),17536(a,1,2))].">
      <j1 rule="para" parents="14443 17536"/>
    </justification>
  </clause>

  <clause id="17539">
    <literal><![CDATA[
      T(x,L(K(y,z),u,w) \ v5) = T(x,K(z,y) * v5)
    ]]></literal>
    <justification jstring="[para(5889(a,2),17525(a,1,2))].">
      <j1 rule="para" parents="5889 17525"/>
    </justification>
  </clause>

  <clause id="17540">
    <literal><![CDATA[
      T(x,K(y,L(z,u,w)) * v5) = T(x,K(z,y) * v5)
    ]]></literal>
    <justification jstring="[hyper(320,a,15114,a,b,17527,a),flip(a)].">
      <j1 rule="hyper" parents="320 15114 17527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17541">
    <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),17533(a,1,1,2))].">
      <j1 rule="para" parents="80 17533"/>
    </justification>
  </clause>

  <clause id="17542">
    <literal><![CDATA[
      K(x,y * a(z,u,K(w,v5))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(15833,a,17534,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="15833 17534"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17543">
    <literal><![CDATA[
      K(x,a(y,z,K(u,w)) * v5) = K(x,v5)
    ]]></literal>
    <justification jstring="[hyper(17253,a,17542,a)].">
      <j1 rule="hyper" parents="17253 17542"/>
    </justification>
  </clause>

  <clause id="17544">
    <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,17207,a,b,17542,a)].">
      <j1 rule="hyper" parents="320 17207 17542"/>
    </justification>
  </clause>

  <clause id="17545">
    <literal><![CDATA[
      K(x,(y * z) * K(u,w)) = K(x,y * (z * K(u,w)))
    ]]></literal>
    <justification jstring="[para(80(a,1),17542(a,1,2))].">
      <j1 rule="para" parents="80 17542"/>
    </justification>
  </clause>

  <clause id="17546">
    <literal><![CDATA[
      K(x,y * (z * a(u,w,K(v5,v6)))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(347(a,1),17542(a,1,2))].">
      <j1 rule="para" parents="347 17542"/>
    </justification>
  </clause>

  <clause id="17547">
    <literal><![CDATA[
      K(x,y * T(z,a(u,w,v5))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(13402(a,1),17542(a,1,2))].">
      <j1 rule="para" parents="13402 17542"/>
    </justification>
  </clause>

  <clause id="17548">
    <literal><![CDATA[
      K(x,y / T(z,a(u,w,v5))) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(13428(a,1),17542(a,1,2))].">
      <j1 rule="para" parents="13428 17542"/>
    </justification>
  </clause>

  <clause id="17549">
    <literal><![CDATA[
      K(x,(K(y,z) * u) * w) = K(x,K(y,z) * (u * w))
    ]]></literal>
    <justification jstring="[para(14264(a,1),17542(a,1,2))].">
      <j1 rule="para" parents="14264 17542"/>
    </justification>
  </clause>

  <clause id="17550">
    <literal><![CDATA[
      K(x,y * L(z,u,K(w,v5))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(14950(a,1),17542(a,1,2))].">
      <j1 rule="para" parents="14950 17542"/>
    </justification>
  </clause>

  <clause id="17551">
    <literal><![CDATA[
      K(x,y \ L(z,u,K(w,v5))) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(14951(a,1),17542(a,1,2))].">
      <j1 rule="para" parents="14951 17542"/>
    </justification>
  </clause>

  <clause id="17552">
    <literal><![CDATA[
      K(x,y / L(z,u,K(w,v5))) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(17511(a,1),17542(a,1,2))].">
      <j1 rule="para" parents="17511 17542"/>
    </justification>
  </clause>

  <clause id="17553">
    <literal><![CDATA[
      K(x,(a(y,z,K(u,w)) * v5) * v6) = K(x,v5 * v6)
    ]]></literal>
    <justification jstring="[para(14274(a,2),17543(a,1,2))].">
      <j1 rule="para" parents="14274 17543"/>
    </justification>
  </clause>

  <clause id="17554">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w)) * v5) = K(x,K(y,z) * v5)
    ]]></literal>
    <justification jstring="[para(14511(a,1),17543(a,1,2))].">
      <j1 rule="para" parents="14511 17543"/>
    </justification>
  </clause>

  <clause id="17555">
    <literal><![CDATA[
      K(x,(y * a(z,u,K(w,v5))) * v6) = K(x,y * v6)
    ]]></literal>
    <justification jstring="[para(17320(a,2),17543(a,1,2))].">
      <j1 rule="para" parents="17320 17543"/>
    </justification>
  </clause>

  <clause id="17556">
    <literal><![CDATA[
      K(x,y * (a(z,u,K(w,v5)) * v6)) = K(x,y * v6)
    ]]></literal>
    <justification jstring="[para(17470(a,1),17543(a,1,2))].">
      <j1 rule="para" parents="17470 17543"/>
    </justification>
  </clause>

  <clause id="17557">
    <literal><![CDATA[
      K(x,(a(y,z,K(u,w)) * v5) \ v6) = K(x,v5 \ v6)
    ]]></literal>
    <justification jstring="[para(17495(a,2),17543(a,1,2))].">
      <j1 rule="para" parents="17495 17543"/>
    </justification>
  </clause>

  <clause id="17558">
    <literal><![CDATA[
      K(x,y * T(z,L(u,w,v5))) = K(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[para(14367(a,1),17547(a,1,2,2))].">
      <j1 rule="para" parents="14367 17547"/>
    </justification>
  </clause>

  <clause id="17559">
    <literal><![CDATA[
      K(x,y / (a(z,u,w) / v5)) = K(x,y / (v5 \ a(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(15280,a,17548,a)].">
      <j1 rule="hyper" parents="15280 17548"/>
    </justification>
  </clause>

  <clause id="17560">
    <literal><![CDATA[
      K(x,y / ((K(z,u) * w) \ v5)) = K(x,y / (w \ (K(u,z) * v5)))
    ]]></literal>
    <justification jstring="[para(14955(a,1),17548(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="14955 17548"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17561">
    <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),17550(a,1,2,2))].">
      <j1 rule="para" parents="566 17550"/>
    </justification>
  </clause>

  <clause id="17562">
    <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(13981(a,1),17550(a,1,2,2))].">
      <j1 rule="para" parents="13981 17550"/>
    </justification>
  </clause>

  <clause id="17563">
    <literal><![CDATA[
      K(x,y \ ((z \ u) \ (K(z,w) * v5))) = K(x,y \ ((T(z,w) \ u) \ v5))
    ]]></literal>
    <justification jstring="[para(5225(a,1),17551(a,1,2,2))].">
      <j1 rule="para" parents="5225 17551"/>
    </justification>
  </clause>

  <clause id="17564">
    <literal><![CDATA[
      K(x,y \ T(z,L(u,w,v5))) = K(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[para(14942(a,1),17551(a,1,2,2))].">
      <j1 rule="para" parents="14942 17551"/>
    </justification>
  </clause>

  <clause id="17565">
    <literal><![CDATA[
      K(x,y / ((z * ((K(u,w) * z) \ v5)) / z)) = K(x,y / ((K(u,w) \ v5) / z))
    ]]></literal>
    <justification jstring="[para(862(a,1),17552(a,1,2,2))].">
      <j1 rule="para" parents="862 17552"/>
    </justification>
  </clause>

  <clause id="17566">
    <literal><![CDATA[
      T(x,L(K(y,z),u,w) \ v5) = T(x,K(y,z) \ v5)
    ]]></literal>
    <justification jstring="[para(5130(a,2),17539(a,2,2))].">
      <j1 rule="para" parents="5130 17539"/>
    </justification>
  </clause>

  <clause id="17567">
    <literal><![CDATA[
      T(x,(K(y,z) * u) * w) = T(x,K(z,y) * (u * w))
    ]]></literal>
    <justification jstring="[para(14785(a,1),17540(a,1,2))].">
      <j1 rule="para" parents="14785 17540"/>
    </justification>
  </clause>

  <clause id="17569">
    <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),17546(a,1,2,2))].">
      <j1 rule="para" parents="80 17546"/>
    </justification>
  </clause>

  <clause id="17570">
    <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),17546(a,1,2,2))].">
      <j1 rule="para" parents="347 17546"/>
    </justification>
  </clause>

  <clause id="17571">
    <literal><![CDATA[
      K(x,y * (z / L(u,w,K(v5,v6)))) = K(x,y * (z / u))
    ]]></literal>
    <justification jstring="[para(17511(a,1),17546(a,1,2,2))].">
      <j1 rule="para" parents="17511 17546"/>
    </justification>
  </clause>

  <clause id="17572">
    <literal><![CDATA[
      K(x,(y \ L(z,u,K(w,v5))) * v6) = K(x,(y \ z) * v6)
    ]]></literal>
    <justification jstring="[para(17337(a,1),17553(a,1,2,1))].">
      <j1 rule="para" parents="17337 17553"/>
    </justification>
  </clause>

  <clause id="17573">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w)) * v5) = K(x,K(z,y) * v5)
    ]]></literal>
    <justification jstring="[hyper(320,a,15130,a,b,17554,a),flip(a)].">
      <j1 rule="hyper" parents="320 15130 17554"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17574">
    <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,16789,a(flip),b,17554,a),flip(a)].">
      <j1 rule="hyper" parents="58 16789 17554"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17575">
    <literal><![CDATA[
      K(x,K(y,z) * (u * w)) = K(x,u * (w * K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(58,a,15828,a(flip),b,17554,a),flip(a)].">
      <j1 rule="hyper" parents="58 15828 17554"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17576">
    <literal><![CDATA[
      K(x,K((y \ z) \ u,w) * v5) = K(x,K(z \ (y * u),w) * v5)
    ]]></literal>
    <justification jstring="[para(10810(a,1),17554(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10810 17554"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17577">
    <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(17554(a,2),15131(a,1))].">
      <j1 rule="para" parents="17554 15131"/>
    </justification>
  </clause>

  <clause id="17578">
    <literal><![CDATA[
      K(x,(L(y,z,K(u,w)) / v5) * v6) = K(x,(y / v5) * v6)
    ]]></literal>
    <justification jstring="[para(17380(a,1),17555(a,1,2,1))].">
      <j1 rule="para" parents="17380 17555"/>
    </justification>
  </clause>

  <clause id="17579">
    <literal><![CDATA[
      K(x,y * (z \ (a(u,w,K(v5,v6)) * v7))) = K(x,y * (z \ v7))
    ]]></literal>
    <justification jstring="[para(17468(a,2),17556(a,1,2,2))].">
      <j1 rule="para" parents="17468 17556"/>
    </justification>
  </clause>

  <clause id="17580">
    <literal><![CDATA[
      K(x,L(K(y,z),u,w) \ v5) = K(x,K(y,z) \ v5)
    ]]></literal>
    <justification jstring="[para(5953(a,1),17557(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5953 17557"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17581">
    <literal><![CDATA[
      K(x,L(y,z,K(u,w)) \ v5) = K(x,y \ v5)
    ]]></literal>
    <justification jstring="[para(14937(a,1),17557(a,1,2,1))].">
      <j1 rule="para" parents="14937 17557"/>
    </justification>
  </clause>

  <clause id="17582">
    <literal><![CDATA[
      K(x,T(y,L(z,u,w)) \ v5) = K(x,T(y,z) \ v5)
    ]]></literal>
    <justification jstring="[para(14942(a,1),17581(a,1,2,1))].">
      <j1 rule="para" parents="14942 17581"/>
    </justification>
  </clause>

  <clause id="17583">
    <literal><![CDATA[
      K(x,y \ (z * K(u,w))) = K(x,(y \ z) * K(u,w))
    ]]></literal>
    <justification jstring="[para(14931(a,1),17581(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14931 17581"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17584">
    <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,16065,a(flip),b,17558,a),flip(a)].">
      <j1 rule="hyper" parents="320 16065 17558"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17585">
    <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,16062,a(flip),b,17564,a),flip(a)].">
      <j1 rule="hyper" parents="320 16062 17564"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17586">
    <literal><![CDATA[
      K(x,L(K(y,z),u,w) \ v5) = x \ T(x,K(y,z) \ v5)
    ]]></literal>
    <justification jstring="[hyper(116,a,17566,a(flip),b,4755,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="116 17566 4755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17587">
    <literal><![CDATA[
      K(x,y * K(z,L(u,w,v5))) = K(x,K(u,z) * y)
    ]]></literal>
    <justification jstring="[hyper(15682,a,17573,a)].">
      <j1 rule="hyper" parents="15682 17573"/>
    </justification>
  </clause>

  <clause id="17588">
    <literal><![CDATA[
      K(x,K(y,z) * (u * w)) = K(x,u * (w * K(z,y)))
    ]]></literal>
    <justification jstring="[hyper(58,a,15828,a(flip),b,17573,a),flip(a)].">
      <j1 rule="hyper" parents="58 15828 17573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17589">
    <literal><![CDATA[
      K(x,(K(y,z) * u) * w) = K(x,K(z,y) * (u * w))
    ]]></literal>
    <justification jstring="[para(14785(a,1),17573(a,1,2))].">
      <j1 rule="para" parents="14785 17573"/>
    </justification>
  </clause>

  <clause id="17590">
    <literal><![CDATA[
      K(x,K(y,z) * ((z * u) * w)) = K(x,(T(z,y) * u) * w)
    ]]></literal>
    <justification jstring="[para(14851(a,1),17573(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14851 17573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17591">
    <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(17573(a,2),15131(a,1))].">
      <j1 rule="para" parents="17573 15131"/>
    </justification>
  </clause>

  <clause id="17592">
    <literal><![CDATA[
      K(x,T(y,z) \ L(z,u,w)) = K(x,L(z,u,w) / y)
    ]]></literal>
    <justification jstring="[hyper(13133,a,17582,a),flip(a)].">
      <j1 rule="hyper" parents="13133 17582"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17593">
    <literal><![CDATA[
      K(x,y * K(z,L(u,w,v5))) = K(x,y * K(u,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,15653,a(flip),b,17587,a),flip(a)].">
      <j1 rule="hyper" parents="320 15653 17587"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17594">
    <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(17587(a,2),15682(a,1))].">
      <j1 rule="para" parents="17587 15682"/>
    </justification>
  </clause>

  <clause id="17595">
    <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(17593(a,2),15719(a,1))].">
      <j1 rule="para" parents="17593 15719"/>
    </justification>
  </clause>

  <clause id="17596">
    <literal><![CDATA[
      T(x,T(a(y,z,u),w) * v5) = T(x,v5 * a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,17223,a(flip),b,17522,a),flip(a)].">
      <j1 rule="hyper" parents="320 17223 17522"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17597">
    <literal><![CDATA[
      T(x,(y \ z) * (y * K(u,w))) = T(x,T(K(u,w) * z,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,16332,a(flip),b,17526,a),flip(a)].">
      <j1 rule="hyper" parents="58 16332 17526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17598">
    <literal><![CDATA[
      K(K(x,y) * (z * u),w) = K(z * (u * K(y,x)),w)
    ]]></literal>
    <justification jstring="[hyper(15927,a,17531,a)].">
      <j1 rule="hyper" parents="15927 17531"/>
    </justification>
  </clause>

  <clause id="17599">
    <literal><![CDATA[
      K(K(x,y) * (z * u),w) = K(z * (u * K(x,y)),w)
    ]]></literal>
    <justification jstring="[hyper(15718,a,17531,a)].">
      <j1 rule="hyper" parents="15718 17531"/>
    </justification>
  </clause>

  <clause id="17600">
    <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(17531(a,1),15718(a,1))].">
      <j1 rule="para" parents="17531 15718"/>
    </justification>
  </clause>

  <clause id="17602">
    <literal><![CDATA[
      K(L(x,y,z) * u,x * u) = K(u * L(x,y,z),x * u)
    ]]></literal>
    <justification jstring="[hyper(58,a,8785,a(flip),b,17535,a),flip(a)].">
      <j1 rule="hyper" parents="58 8785 17535"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17603">
    <literal><![CDATA[
      K(x,y * a(z,u,K(w,v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v6
    ]]></literal>
    <justification jstring="[para(17544(a,1),17251(a,1))].">
      <j1 rule="para" parents="17544 17251"/>
    </justification>
  </clause>

  <clause id="17604">
    <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),17603(a,1,2))].">
      <j1 rule="para" parents="80 17603"/>
    </justification>
  </clause>

  <clause id="17605">
    <literal><![CDATA[
      K(x,K(y,z) \ (u * w)) = K(x,u * (w * K(z,y)))
    ]]></literal>
    <justification jstring="[hyper(15793,a,17545,a)].">
      <j1 rule="hyper" parents="15793 17545"/>
    </justification>
  </clause>

  <clause id="17606">
    <literal><![CDATA[
      K(x,y * ((1 / z) * K(u,y / z))) = K(x,T(y / z,u))
    ]]></literal>
    <justification jstring="[hyper(14195,a,17545,a),flip(a)].">
      <j1 rule="hyper" parents="14195 17545"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17607">
    <literal><![CDATA[
      K(x,(y * z) * K(u,w)) = K(x,y * (K(u,w) * z))
    ]]></literal>
    <justification jstring="[hyper(320,a,16043,a,b,17545,a),flip(a)].">
      <j1 rule="hyper" parents="320 16043 17545"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17608">
    <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(16944(a,1),17545(a,1,2,2))].">
      <j1 rule="para" parents="16944 17545"/>
    </justification>
  </clause>

  <clause id="17609">
    <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,17554,a(flip),b,17549,a),flip(a)].">
      <j1 rule="hyper" parents="320 17554 17549"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17610">
    <literal><![CDATA[
      K(x,K(y,z) * ((z \ u) * w)) = K(x,(T(z,y) \ u) * w)
    ]]></literal>
    <justification jstring="[para(5131(a,1),17549(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5131 17549"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17611">
    <literal><![CDATA[
      K(x,K(y,z) * ((y / u) * w)) = K(x,(T(y,z) / u) * w)
    ]]></literal>
    <justification jstring="[para(13708(a,1),17549(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="13708 17549"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17612">
    <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(17549(a,2),15131(a,1))].">
      <j1 rule="para" parents="17549 15131"/>
    </justification>
  </clause>

  <clause id="17613">
    <literal><![CDATA[
      T(x,(y \ K(z,u)) \ w) = T(x,K(z,u) * (y * w))
    ]]></literal>
    <justification jstring="[hyper(58,a,13880,a,b,17567,a)].">
      <j1 rule="hyper" parents="58 13880 17567"/>
    </justification>
  </clause>

  <clause id="17614">
    <literal><![CDATA[
      T(x,(y * K(z,u)) * w) = T(x,K(u,z) * (y * w))
    ]]></literal>
    <justification jstring="[hyper(58,a,16009,a(flip),b,17567,a)].">
      <j1 rule="hyper" parents="58 16009 17567"/>
    </justification>
  </clause>

  <clause id="17615">
    <literal><![CDATA[
      K(x,K(y,z) * (u * w)) = K(x,u * (K(z,y) * w))
    ]]></literal>
    <justification jstring="[hyper(320,a,16150,a,b,17575,a),flip(a)].">
      <j1 rule="hyper" parents="320 16150 17575"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17616">
    <literal><![CDATA[
      K(x,K(y,z) * (u * w)) = K(x,u * (K(y,z) * w))
    ]]></literal>
    <justification jstring="[hyper(320,a,16043,a,b,17575,a),flip(a)].">
      <j1 rule="hyper" parents="320 16043 17575"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17617">
    <literal><![CDATA[
      K(x,K(y,z) * (u * (1 / w))) = K(x,u * (w \ K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(320,a,13891,a(flip),b,17575,a),flip(a)].">
      <j1 rule="hyper" parents="320 13891 17575"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17619">
    <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(17575(a,2),16249(a,1))].">
      <j1 rule="para" parents="17575 16249"/>
    </justification>
  </clause>

  <clause id="17620">
    <literal><![CDATA[
      K(x,y \ (K(z,u) * w)) = K(x,(y \ w) * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(16097,a,17583,a)].">
      <j1 rule="hyper" parents="16097 17583"/>
    </justification>
  </clause>

  <clause id="17621">
    <literal><![CDATA[
      K(x,y \ (z * K(u,w))) = K(x,K(u,w) * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(320,a,15653,a,b,17583,a),flip(a)].">
      <j1 rule="hyper" parents="320 15653 17583"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17622">
    <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(10815(a,1),17583(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10815 17583"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17623">
    <literal><![CDATA[
      K(x,K(y,z * u) * (w * v5)) = K(x,w * (v5 * K(y,u * z)))
    ]]></literal>
    <justification jstring="[hyper(16177,a,17588,a)].">
      <j1 rule="hyper" parents="16177 17588"/>
    </justification>
  </clause>

  <clause id="17624">
    <literal><![CDATA[
      K(x,K(y,z) * (u * (z / w))) = K(x,u * (T(z,y) / w))
    ]]></literal>
    <justification jstring="[hyper(320,a,16067,a(flip),b,17588,a),flip(a)].">
      <j1 rule="hyper" parents="320 16067 17588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17625">
    <literal><![CDATA[
      K(x,K(y,z) * (u * (1 / w))) = K(x,u * (w \ K(z,y)))
    ]]></literal>
    <justification jstring="[hyper(320,a,13891,a(flip),b,17588,a),flip(a)].">
      <j1 rule="hyper" parents="320 13891 17588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17626">
    <literal><![CDATA[
      K(x,(y * K(z,u)) * w) = K(x,K(u,z) * (y * w))
    ]]></literal>
    <justification jstring="[hyper(16094,a,17589,a)].">
      <j1 rule="hyper" parents="16094 17589"/>
    </justification>
  </clause>

  <clause id="17627">
    <literal><![CDATA[
      K(x,(y \ K(z,u)) \ w) = K(x,K(z,u) * (y * w))
    ]]></literal>
    <justification jstring="[hyper(14074,a,17589,a)].">
      <j1 rule="hyper" parents="14074 17589"/>
    </justification>
  </clause>

  <clause id="17628">
    <literal><![CDATA[
      K(x,K(y,z) * ((z / u) * w)) = K(x,(T(z,y) / u) * w)
    ]]></literal>
    <justification jstring="[para(13708(a,1),17589(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="13708 17589"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17629">
    <literal><![CDATA[
      K(x,K(y,z) * (((z * y) / u) * w)) = K(x,((T(z,y) * y) / u) * w)
    ]]></literal>
    <justification jstring="[para(14226(a,1),17589(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="14226 17589"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17630">
    <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(17589(a,1),16496(a,1,2))].">
      <j1 rule="para" parents="17589 16496"/>
    </justification>
  </clause>

  <clause id="17631">
    <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(594(a,1),17592(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="594 17592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17632">
    <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(17596(a,1),15788(a,1,2,1))].">
      <j1 rule="para" parents="17596 15788"/>
    </justification>
  </clause>

  <clause id="17633">
    <literal><![CDATA[
      K((K(x,y) * z) * u,w) = K(K(y,x) * (z * u),w)
    ]]></literal>
    <justification jstring="[hyper(320,a,17515,a,b,17598,a)].">
      <j1 rule="hyper" parents="320 17515 17598"/>
    </justification>
  </clause>

  <clause id="17634">
    <literal><![CDATA[
      K(K(x,y) * ((y \ z) * u),w) = K((T(y,x) \ z) * u,w)
    ]]></literal>
    <justification jstring="[hyper(320,a,17516,a(flip),b,17599,a),flip(a)].">
      <j1 rule="hyper" parents="320 17516 17599"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17635">
    <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(10794(a,2),17605(a,2,2,2,2))].">
      <j1 rule="para" parents="10794 17605"/>
    </justification>
  </clause>

  <clause id="17636">
    <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,17587,a(flip),b,17607,a),flip(a)].">
      <j1 rule="hyper" parents="58 17587 17607"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17637">
    <literal><![CDATA[
      K(x,y * (K(z,x) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * u) = w
    ]]></literal>
    <justification jstring="[para(17607(a,1),8398(a,1))].">
      <j1 rule="para" parents="17607 8398"/>
    </justification>
  </clause>

  <clause id="17638">
    <literal><![CDATA[
      K(x,y * (T(z,x) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z * u)) = w
    ]]></literal>
    <justification jstring="[para(4781(a,1),17637(a,1,2,2))].">
      <j1 rule="para" parents="4781 17637"/>
    </justification>
  </clause>

  <clause id="17639">
    <literal><![CDATA[
      K(x,y * (T(z,x) \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z \ u)) = w
    ]]></literal>
    <justification jstring="[para(15426(a,1),17637(a,1))].">
      <j1 rule="para" parents="15426 17637"/>
    </justification>
  </clause>

  <clause id="17640">
    <literal><![CDATA[
      T(x,(K(y,z) / u) \ w) = T(x,K(y,z) * (u * w))
    ]]></literal>
    <justification jstring="[hyper(14126,a,17614,a)].">
      <j1 rule="hyper" parents="14126 17614"/>
    </justification>
  </clause>

  <clause id="17641">
    <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,16803,a(flip),b,17614,a),flip(a)].">
      <j1 rule="hyper" parents="58 16803 17614"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17642">
    <literal><![CDATA[
      T(x,K(y,z) * (u * w)) = T(x,u * (K(z,y) * w))
    ]]></literal>
    <justification jstring="[hyper(118,a,17615,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 17615 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17643">
    <literal><![CDATA[
      K(x,y \ (K(z,u) * w)) = K(x,K(u,z) * (y \ w))
    ]]></literal>
    <justification jstring="[hyper(320,a,15823,a,b,17620,a),flip(a)].">
      <j1 rule="hyper" parents="320 15823 17620"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17644">
    <literal><![CDATA[
      K(x,y \ (K(z,u) * w)) = K(x,K(z,u) * (y \ w))
    ]]></literal>
    <justification jstring="[hyper(320,a,15653,a,b,17620,a),flip(a)].">
      <j1 rule="hyper" parents="320 15653 17620"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17645">
    <literal><![CDATA[
      T(x,y \ (z * K(u,w))) = T(x,K(u,w) * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(118,a,17621,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 17621 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17646">
    <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,12235,a(flip),b,17621,a)].">
      <j1 rule="hyper" parents="58 12235 17621"/>
    </justification>
  </clause>

  <clause id="17647">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ (w * y))) = K(x,u \ (w * T(y,z)))
    ]]></literal>
    <justification jstring="[para(6116(a,1),17621(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6116 17621"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17648">
    <literal><![CDATA[
      K(x,K(y \ z,y) * (u \ (w / (y \ z)))) = K(x,u \ (w / (z / y)))
    ]]></literal>
    <justification jstring="[para(6470(a,1),17621(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6470 17621"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17649">
    <literal><![CDATA[
      K(x,K(y,y \ z) * (u \ (w * z))) = K(x,u \ (w * (y * (z / y))))
    ]]></literal>
    <justification jstring="[para(10347(a,1),17621(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10347 17621"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17650">
    <literal><![CDATA[
      K(x,K(y \ z,y) * (u \ (w * z))) = K(x,u \ (w * ((y \ z) * y)))
    ]]></literal>
    <justification jstring="[para(10353(a,1),17621(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10353 17621"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17651">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ (w \ y))) = K(x,u \ (w \ T(y,z)))
    ]]></literal>
    <justification jstring="[para(13699(a,1),17621(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="13699 17621"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17652">
    <literal><![CDATA[
      K(x,(K(y,z) / u) \ w) = K(x,K(y,z) * (u * w))
    ]]></literal>
    <justification jstring="[hyper(14081,a,17626,a)].">
      <j1 rule="hyper" parents="14081 17626"/>
    </justification>
  </clause>

  <clause id="17653">
    <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,10907,a(flip),b,17626,a),flip(a)].">
      <j1 rule="hyper" parents="58 10907 17626"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17654">
    <literal><![CDATA[
      K(x,K(y,z) * ((u \ z) * w)) = K(x,(u \ T(z,y)) * w)
    ]]></literal>
    <justification jstring="[para(13699(a,1),17626(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="13699 17626"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17655">
    <literal><![CDATA[
      K(x,K(y \ z,y) * ((u \ z) * w)) = K(x,(u \ (y * (z / y))) * w)
    ]]></literal>
    <justification jstring="[para(15014(a,1),17626(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="15014 17626"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17656">
    <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,14631,a(flip),b,17627,a),flip(a)].">
      <j1 rule="hyper" parents="58 14631 17627"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17657">
    <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(17627(a,1),15237(a,1,1,2))].">
      <j1 rule="para" parents="17627 15237"/>
    </justification>
  </clause>

  <clause id="17658">
    <literal><![CDATA[
      K(x * (K(y,z) * u),T(w,u)) = K(K(z,y) * (u * x),w)
    ]]></literal>
    <justification jstring="[hyper(16463,a,17633,a)].">
      <j1 rule="hyper" parents="16463 17633"/>
    </justification>
  </clause>

  <clause id="17659">
    <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(17640(a,1),14100(a,1,2,1,1))].">
      <j1 rule="para" parents="17640 14100"/>
    </justification>
  </clause>

  <clause id="17660">
    <literal><![CDATA[
      T(x,(y \ K(z,u)) \ w) = T(x,y * (K(u,z) * w))
    ]]></literal>
    <justification jstring="[hyper(58,a,17613,a,b,17642,a)].">
      <j1 rule="hyper" parents="58 17613 17642"/>
    </justification>
  </clause>

  <clause id="17662">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ (z * w))) = K(x,u \ (T(z,y) * w))
    ]]></literal>
    <justification jstring="[para(4781(a,1),17643(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4781 17643"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17663">
    <literal><![CDATA[
      K(x,K(y,y \ z) * (u \ (z * w))) = K(x,u \ (((y \ z) * y) * w))
    ]]></literal>
    <justification jstring="[para(11175(a,1),17643(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11175 17643"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17664">
    <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(15364,a,17644,a),flip(a)].">
      <j1 rule="hyper" parents="15364 17644"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17665">
    <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(15124,a,17644,a),flip(a)].">
      <j1 rule="hyper" parents="15124 17644"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17666">
    <literal><![CDATA[
      T(x,y \ (K(z,u) * w)) = T(x,K(z,u) * (y \ w))
    ]]></literal>
    <justification jstring="[hyper(118,a,17644,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 17644 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17667">
    <literal><![CDATA[
      x * K(x,K(y,z) * (u \ w)) = T(x,u \ (K(y,z) * w))
    ]]></literal>
    <justification jstring="[hyper(119,a,17644,a(flip),b,4729,a(flip))].">
      <j1 rule="hyper" parents="119 17644 4729"/>
    </justification>
  </clause>

  <clause id="17668">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ (y * w))) = K(x,u \ (T(y,z) * w))
    ]]></literal>
    <justification jstring="[para(4781(a,1),17644(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4781 17644"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17669">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ (z \ w))) = K(x,u \ (T(z,y) \ w))
    ]]></literal>
    <justification jstring="[para(5131(a,1),17644(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5131 17644"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17670">
    <literal><![CDATA[
      K(x,y \ (z * (K(u,z) * w))) = K(x,K(u,z) * (y \ (z * w)))
    ]]></literal>
    <justification jstring="[para(5256(a,1),17644(a,1,2,2))].">
      <j1 rule="para" parents="5256 17644"/>
    </justification>
  </clause>

  <clause id="17671">
    <literal><![CDATA[
      K(x,K(y \ z,y) * (u \ ((z / y) * w))) = K(x,u \ ((y \ z) * w))
    ]]></literal>
    <justification jstring="[para(5443(a,1),17644(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5443 17644"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17672">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ ((z * y) * w))) = K(x,u \ ((y * z) * w))
    ]]></literal>
    <justification jstring="[para(11157(a,1),17644(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11157 17644"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17673">
    <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(17645(a,1),16060(a,1,2,2))].">
      <j1 rule="para" parents="17645 16060"/>
    </justification>
  </clause>

  <clause id="17674">
    <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,17100,a(flip),b,17652,a)].">
      <j1 rule="hyper" parents="58 17100 17652"/>
    </justification>
  </clause>

  <clause id="17675">
    <literal><![CDATA[
      T(x,(y \ z) * (K(u,z \ y) * w)) = T(x,T((y \ z) \ 1,u) \ w)
    ]]></literal>
    <justification jstring="[para(6271(a,1),17660(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6271 17660"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17676">
    <literal><![CDATA[
      T(x,(K(y,z) * u) \ w) = T(x,K(z,y) * (u \ w))
    ]]></literal>
    <justification jstring="[hyper(17298,a,17666,a)].">
      <j1 rule="hyper" parents="17298 17666"/>
    </justification>
  </clause>

  <clause id="17677">
    <literal><![CDATA[
      T(x,K(y,z) * ((z / u) \ w)) = T(x,(T(z,y) / u) \ w)
    ]]></literal>
    <justification jstring="[para(13708(a,1),17676(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="13708 17676"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17678">
    <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(17676(a,1),16104(a,2,2,2))].">
      <j1 rule="para" parents="17676 16104"/>
    </justification>
  </clause>

  <clause id="17679">
    <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),17571(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="544 17571"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17680">
    <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(4937(a,1),17572(a,1,2,1,2))].">
      <j1 rule="para" parents="4937 17572"/>
    </justification>
  </clause>

  <clause id="17681">
    <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),17578(a,1,2,1,1))].">
      <j1 rule="para" parents="564 17578"/>
    </justification>
  </clause>

  <clause id="17682">
    <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(17586(a,2),4838(a,1))].">
      <j1 rule="para" parents="17586 4838"/>
    </justification>
  </clause>

  <clause id="17683">
    <literal><![CDATA[
      K(x,(T(y,z) * (u / y)) * w) = K(x,K(z,y) * (T(u,y) * w))
    ]]></literal>
    <justification jstring="[hyper(16597,a,17590,a),flip(a)].">
      <j1 rule="hyper" parents="16597 17590"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17684">
    <literal><![CDATA[
      K(x,y * (K(z,u \ y) / u)) = K(x,T(y / u,z))
    ]]></literal>
    <justification jstring="[para(13990(a,1),17606(a,1,2,2))].">
      <j1 rule="para" parents="13990 17606"/>
    </justification>
  </clause>

  <clause id="17685">
    <literal><![CDATA[
      K(x,y * (z \ K(u,z \ y))) = K(x,T(y / z,u))
    ]]></literal>
    <justification jstring="[hyper(16136,a,17684,a)].">
      <j1 rule="hyper" parents="16136 17684"/>
    </justification>
  </clause>

  <clause id="17686">
    <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(8672(a,1),17685(a,1,2,2,2))].">
      <j1 rule="para" parents="8672 17685"/>
    </justification>
  </clause>

  <clause id="17687">
    <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(11246(a,1),17685(a,1,2,2,2))].">
      <j1 rule="para" parents="11246 17685"/>
    </justification>
  </clause>

  <clause id="17688">
    <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(11259(a,1),17685(a,1,2,2,2))].">
      <j1 rule="para" parents="11259 17685"/>
    </justification>
  </clause>

  <clause id="17689">
    <literal><![CDATA[
      K(x,(y \ z) * (u * K(w,y))) = K(x,(T(y,w) \ z) * u)
    ]]></literal>
    <justification jstring="[hyper(58,a,17575,a(flip),b,17610,a)].">
      <j1 rule="hyper" parents="58 17575 17610"/>
    </justification>
  </clause>

  <clause id="17690">
    <literal><![CDATA[
      K(x,K(y,z) * ((y / u) * w)) = K(x,(T(y,K(v5,v6) * z) / u) * w)
    ]]></literal>
    <justification jstring="[hyper(16691,a,17611,a)].">
      <j1 rule="hyper" parents="16691 17611"/>
    </justification>
  </clause>

  <clause id="17691">
    <literal><![CDATA[
      K(x,(K(y,z) * (z / u)) * w) = K(x,(T(z,y) / u) * w)
    ]]></literal>
    <justification jstring="[hyper(58,a,17589,a,b,17611,a)].">
      <j1 rule="hyper" parents="58 17589 17611"/>
    </justification>
  </clause>

  <clause id="17692">
    <literal><![CDATA[
      K(x,y * (z \ K(u,L(w,v5,v6)))) = K(x,K(w,u) * (y * (1 / z)))
    ]]></literal>
    <justification jstring="[hyper(17577,a,17617,a),flip(a)].">
      <j1 rule="hyper" parents="17577 17617"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17693">
    <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,16830,a(flip),b,17624,a),flip(a)].">
      <j1 rule="hyper" parents="58 16830 17624"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17694">
    <literal><![CDATA[
      K(x,y * (z \ K(u,w))) = K(x,y * (z \ K(w,u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,17617,a(flip),b,17625,a)].">
      <j1 rule="hyper" parents="58 17617 17625"/>
    </justification>
  </clause>

  <clause id="17695">
    <literal><![CDATA[
      K(x,y * (z \ K(z,u))) = K(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[hyper(14075,a,17694,a),flip(a)].">
      <j1 rule="hyper" parents="14075 17694"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17696">
    <literal><![CDATA[
      K(x,y * (z \ K(u \ w,u))) = K(x,y * (z \ K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(320,a,13195,a,b,17694,a)].">
      <j1 rule="hyper" parents="320 13195 17694"/>
    </justification>
  </clause>

  <clause id="17697">
    <literal><![CDATA[
      K(x,(y \ z) * (u \ K(y,w))) = K(x,(T(y,w) \ z) / u)
    ]]></literal>
    <justification jstring="[hyper(320,a,17424,a(flip),b,17694,a),flip(a)].">
      <j1 rule="hyper" parents="320 17424 17694"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17698">
    <literal><![CDATA[
      K(x,(y * z) * (u \ K(w,y))) = K(x,(T(y,w) * z) / u)
    ]]></literal>
    <justification jstring="[hyper(320,a,17423,a(flip),b,17694,a),flip(a)].">
      <j1 rule="hyper" parents="320 17423 17694"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17699">
    <literal><![CDATA[
      K(x,(y / z) * (u \ K(z,w))) = K(x,(y / T(z,w)) / u)
    ]]></literal>
    <justification jstring="[hyper(320,a,17401,a(flip),b,17694,a),flip(a)].">
      <j1 rule="hyper" parents="320 17401 17694"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17700">
    <literal><![CDATA[
      K(x,y * ((z / u) \ K(w,u))) = K(x,y / (z / T(u,w)))
    ]]></literal>
    <justification jstring="[hyper(320,a,16185,a(flip),b,17694,a),flip(a)].">
      <j1 rule="hyper" parents="320 16185 17694"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17701">
    <literal><![CDATA[
      K(x,y * ((z * u) \ K(u,w))) = K(x,y / (z * T(u,w)))
    ]]></literal>
    <justification jstring="[hyper(320,a,16184,a(flip),b,17694,a),flip(a)].">
      <j1 rule="hyper" parents="320 16184 17694"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17702">
    <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(5908(a,2),17695(a,2,2,2))].">
      <j1 rule="para" parents="5908 17695"/>
    </justification>
  </clause>

  <clause id="17703">
    <literal><![CDATA[
      K(x,(T(y,x) / z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(y / z) * u) = w
    ]]></literal>
    <justification jstring="[para(17628(a,1),7360(a,1))].">
      <j1 rule="para" parents="17628 7360"/>
    </justification>
  </clause>

  <clause id="17704">
    <literal><![CDATA[
      K(x,L(y,z,z \ u) * u) = K(x,(T(u,y) / z) * (z * y))
    ]]></literal>
    <justification jstring="[para(14184(a,1),17628(a,1,2))].">
      <j1 rule="para" parents="14184 17628"/>
    </justification>
  </clause>

  <clause id="17705">
    <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),17703(a,1,2,1,1))].">
      <j1 rule="para" parents="18 17703"/>
    </justification>
  </clause>

  <clause id="17706">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ (w * z))) = K(x,u \ (w * T(z,y)))
    ]]></literal>
    <justification jstring="[hyper(15131,a,17647,a)].">
      <j1 rule="hyper" parents="15131 17647"/>
    </justification>
  </clause>

  <clause id="17707">
    <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(17651(a,1),16028(a,1))].">
      <j1 rule="para" parents="17651 16028"/>
    </justification>
  </clause>

  <clause id="17708">
    <literal><![CDATA[
      K(x,K(y,z) * ((u \ y) * w)) = K(x,(u \ T(y,z)) * w)
    ]]></literal>
    <justification jstring="[hyper(15131,a,17654,a)].">
      <j1 rule="hyper" parents="15131 17654"/>
    </justification>
  </clause>

  <clause id="17709">
    <literal><![CDATA[
      K(x,(y \ T(z,x)) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(y \ z) * u) = w
    ]]></literal>
    <justification jstring="[para(17654(a,1),7360(a,1))].">
      <j1 rule="para" parents="17654 7360"/>
    </justification>
  </clause>

  <clause id="17710">
    <literal><![CDATA[
      K(K(x,y) * (z * u),T(w,z)) = K(u * (K(y,x) * z),w)
    ]]></literal>
    <justification jstring="[hyper(8007,a,17658,a),flip(a)].">
      <j1 rule="hyper" parents="8007 17658"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17711">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ (z * x))) = K(x,u \ (x * T(z,y)))
    ]]></literal>
    <justification jstring="[hyper(320,a,8452,a(flip),b,17662,a),flip(a)].">
      <j1 rule="hyper" parents="320 8452 17662"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17712">
    <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(17667(a,1),4766(a,1))].">
      <j1 rule="para" parents="17667 4766"/>
    </justification>
  </clause>

  <clause id="17713">
    <literal><![CDATA[
      K(x,T(y,z) \ (z \ u)) = K(x,y \ (T(z,y) \ u))
    ]]></literal>
    <justification jstring="[hyper(58,a,15137,a(flip),b,17669,a)].">
      <j1 rule="hyper" parents="58 15137 17669"/>
    </justification>
  </clause>

  <clause id="17714">
    <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(17713(a,2),8145(a,1,2))].">
      <j1 rule="para" parents="17713 8145"/>
    </justification>
  </clause>

  <clause id="17715">
    <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(15142(a,1),17682(a,1))].">
      <j1 rule="para" parents="15142 17682"/>
    </justification>
  </clause>

  <clause id="17716">
    <literal><![CDATA[
      K(x,(T(y,z) \ u) * (w \ (y * z))) = K(x,(y \ u) * (w \ (z * y)))
    ]]></literal>
    <justification jstring="[para(14209(a,1),17689(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="14209 17689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17717">
    <literal><![CDATA[
      K(x,(T(y,z) / (u \ 1)) * w) = K(x,(y / (u \ K(y,z))) * w)
    ]]></literal>
    <justification jstring="[para(14004(a,1),17691(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="14004 17691"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17718">
    <literal><![CDATA[
      K(x,(T(y \ z,y) / u) * w) = K(x,((z / y) / u) * w)
    ]]></literal>
    <justification jstring="[para(14023(a,1),17691(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="14023 17691"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17719">
    <literal><![CDATA[
      K(x,(K(y \ z,y) * u) / w) = K(x,u * (w \ K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(17402,a,17696,a)].">
      <j1 rule="hyper" parents="17402 17696"/>
    </justification>
  </clause>

  <clause id="17720">
    <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,16183,a(flip),b,17696,a),flip(a)].">
      <j1 rule="hyper" parents="58 16183 17696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17721">
    <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,16351,a,b,17698,a)].">
      <j1 rule="hyper" parents="320 16351 17698"/>
    </justification>
  </clause>

  <clause id="17722">
    <literal><![CDATA[
      T(x,y * ((z / u) \ K(w,u))) = T(x,y / (z / T(u,w)))
    ]]></literal>
    <justification jstring="[hyper(118,a,17700,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 17700 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17723">
    <literal><![CDATA[
      K(x,y / (z * ((u * w) / u))) = K(x,y / (z * T(w,u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,16186,a,b,17701,a)].">
      <j1 rule="hyper" parents="58 16186 17701"/>
    </justification>
  </clause>

  <clause id="17724">
    <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,17634,a(flip),b,17710,a)].">
      <j1 rule="hyper" parents="58 17634 17710"/>
    </justification>
  </clause>

  <clause id="17725">
    <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(15114(a,1),17718(a,1,2,1,1))].">
      <j1 rule="para" parents="15114 17718"/>
    </justification>
  </clause>

  <clause id="17726">
    <literal><![CDATA[
      K(x,(y * (1 / z)) * (u \ K(z,y))) = K(x,T(y * (1 / z),z) / u)
    ]]></literal>
    <justification jstring="[para(5863(a,1),17719(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5863 17719"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17727">
    <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,16179,a(flip),b,17722,a),flip(a)].">
      <j1 rule="hyper" parents="58 16179 17722"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17728">
    <literal><![CDATA[
      K(x,y / (z * T(u \ w,u))) = K(x,y / (z * (w / u)))
    ]]></literal>
    <justification jstring="[para(5(a,1),17723(a,1,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5 17723"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17729">
    <literal><![CDATA[
      K(x,y / (z * T(T(u,w),w))) = K(x,y / (z * u))
    ]]></literal>
    <justification jstring="[para(225(a,1),17723(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="225 17723"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17730">
    <literal><![CDATA[
      K(x,y * (z * ((K(u,w) * v5) * v6))) = K(x,y * (z * (K(u,w) * (v5 * v6))))
    ]]></literal>
    <justification jstring="[para(14264(a,1),17570(a,1,2,2,2))].">
      <j1 rule="para" parents="14264 17570"/>
    </justification>
  </clause>

  <clause id="17731">
    <literal><![CDATA[
      K(x,y * (z \ ((u * w) * K(v5,v6)))) = K(x,y * (z \ (u * (w * K(v5,v6)))))
    ]]></literal>
    <justification jstring="[para(14443(a,1),17579(a,1,2,2,2))].">
      <j1 rule="para" parents="14443 17579"/>
    </justification>
  </clause>

  <clause id="17732">
    <literal><![CDATA[
      K(x,y * T(z,u / (w * v5))) = K(x,y * T(z,w \ (u / v5)))
    ]]></literal>
    <justification jstring="[para(14768(a,1),17584(a,1,2,2))].">
      <j1 rule="para" parents="14768 17584"/>
    </justification>
  </clause>

  <clause id="17733">
    <literal><![CDATA[
      K(x,y \ T(z,u / (w * v5))) = K(x,y \ T(z,w \ (u / v5)))
    ]]></literal>
    <justification jstring="[para(14768(a,1),17585(a,1,2,2))].">
      <j1 rule="para" parents="14768 17585"/>
    </justification>
  </clause>

  <clause id="17734">
    <literal><![CDATA[
      K(x,((K(y,z) * u) * w) * v5) = K(x,K(y,z) * ((u * w) * v5))
    ]]></literal>
    <justification jstring="[para(14785(a,1),17609(a,1,2,1))].">
      <j1 rule="para" parents="14785 17609"/>
    </justification>
  </clause>

  <clause id="17735">
    <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(16038(a,1),17612(a,1))].">
      <j1 rule="para" parents="16038 17612"/>
    </justification>
  </clause>

  <clause id="17736">
    <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(16687(a,1),17619(a,1))].">
      <j1 rule="para" parents="16687 17619"/>
    </justification>
  </clause>

  <clause id="17737">
    <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,17616,a(flip),b,17636,a),flip(a)].">
      <j1 rule="hyper" parents="320 17616 17636"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17738">
    <literal><![CDATA[
      K(x,(T(y,z) / u) * (u * z)) = K(x,(z * u) * (u \ y))
    ]]></literal>
    <justification jstring="[hyper(58,a,16828,a(flip),b,17704,a),flip(a)].">
      <j1 rule="hyper" parents="58 16828 17704"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17739">
    <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(10137(a,2),17738(a,1,2,2))].">
      <j1 rule="para" parents="10137 17738"/>
    </justification>
  </clause>

  <clause id="17740">
    <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(17240(a,2),17712(a,1))].">
      <j1 rule="para" parents="17240 17712"/>
    </justification>
  </clause>

  <clause id="17741">
    <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(10896(a,1),17737(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10896 17737"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17742">
    <literal><![CDATA[
      T(x,T((K(y,z) \ u) \ w,v5)) = T(x,T(u \ (K(z,y) \ w),v5))
    ]]></literal>
    <justification jstring="[para(5130(a,2),17239(a,1,2,1,1))].">
      <j1 rule="para" parents="5130 17239"/>
    </justification>
  </clause>

  <clause id="17743">
    <literal><![CDATA[
      K(x,(y * z) / L(y,u,w)) = K(x,(L(y,u,w) \ z) * y)
    ]]></literal>
    <justification jstring="[hyper(12301,a,17282,a),flip(a)].">
      <j1 rule="hyper" parents="12301 17282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17744">
    <literal><![CDATA[
      K(x,(y * z) / L(y,u,w)) = K(x,y * (z / L(y,u,w)))
    ]]></literal>
    <justification jstring="[hyper(320,a,17248,a(flip),b,17743,a),flip(a)].">
      <j1 rule="hyper" parents="320 17248 17743"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17745">
    <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(17351(a,2),15732(a,1))].">
      <j1 rule="para" parents="17351 15732"/>
    </justification>
  </clause>

  <clause id="17746">
    <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,17352,a),flip(a)].">
      <j1 rule="hyper" parents="691 17352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17747">
    <literal><![CDATA[
      x \ (y * (K(z,K(u,w)) * v5)) = (x \ (y * v5)) * K(z,K(u,w))
    ]]></literal>
    <justification jstring="[para(15684(a,2),17352(a,1,2,2))].">
      <j1 rule="para" parents="15684 17352"/>
    </justification>
  </clause>

  <clause id="17748">
    <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(14925(a,2),17374(a,1,2))].">
      <j1 rule="para" parents="14925 17374"/>
    </justification>
  </clause>

  <clause id="17749">
    <literal><![CDATA[
      (x * (y * (z * K(u,K(w,v5))))) \ v6 = K(u,K(w,v5)) * ((x * (y * z)) \ v6)
    ]]></literal>
    <justification jstring="[para(17384(a,1),17417(a,1,1))].">
      <j1 rule="para" parents="17384 17417"/>
    </justification>
  </clause>

  <clause id="17750">
    <literal><![CDATA[
      (K(x,T(y,z)) * u) * z = (K(x,y) * u) * T(z,K(y,x))
    ]]></literal>
    <justification jstring="[para(7757(a,1),17416(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7757 17416"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17751">
    <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),17435(a,2,2,1))].">
      <j1 rule="para" parents="90 17435"/>
    </justification>
  </clause>

  <clause id="17752">
    <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(17453(a,2),16028(a,1,2))].">
      <j1 rule="para" parents="17453 16028"/>
    </justification>
  </clause>

  <clause id="17753">
    <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(10113(a,1),17463(a,1,2,1,1))].">
      <j1 rule="para" parents="10113 17463"/>
    </justification>
  </clause>

  <clause id="17754">
    <literal><![CDATA[
      T(x,a(y \ 1,z,u)) = T(x,a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(36,a,17335,a(flip),b,17476,a),flip(a)].">
      <j1 rule="hyper" parents="36 17335 17476"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17755">
    <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,16899,a(flip),b,17569,a)].">
      <j1 rule="hyper" parents="58 16899 17569"/>
    </justification>
  </clause>

  <clause id="17756">
    <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(17569(a,1),15791(a,1))].">
      <j1 rule="para" parents="17569 15791"/>
    </justification>
  </clause>

  <clause id="17757">
    <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,15366,a(flip),b,17576,a),flip(a)].">
      <j1 rule="hyper" parents="58 15366 17576"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17758">
    <literal><![CDATA[
      K(x,y * (z * K((u * w) \ y,u * w))) = K(x,(((w * u) \ y) * (w * u)) * z)
    ]]></literal>
    <justification jstring="[para(13171(a,1),17623(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13171 17623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17759">
    <literal><![CDATA[
      K(x,K(y,z * K(u,w)) * (v5 \ ((y * z) * v6))) = K(x,v5 \ ((z * y) * v6))
    ]]></literal>
    <justification jstring="[hyper(16685,a,17672,a)].">
      <j1 rule="hyper" parents="16685 17672"/>
    </justification>
  </clause>

  <clause id="17760">
    <literal><![CDATA[
      K(x,((y \ z) * T(y,u)) * w) = K(x,K(u,y) * (T(z,y) * w))
    ]]></literal>
    <justification jstring="[hyper(16248,a,17683,a)].">
      <j1 rule="hyper" parents="16248 17683"/>
    </justification>
  </clause>

  <clause id="17761">
    <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,15401,a,b,17683,a)].">
      <j1 rule="hyper" parents="58 15401 17683"/>
    </justification>
  </clause>

  <clause id="17762">
    <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,15201,a(flip),b,17727,a)].">
      <j1 rule="hyper" parents="58 15201 17727"/>
    </justification>
  </clause>

  <clause id="17763">
    <literal><![CDATA[
      K(x,y * T(z,(u * w) \ v5)) = K(x,y * T(z,u \ (v5 / w)))
    ]]></literal>
    <justification jstring="[hyper(16132,a,17732,a)].">
      <j1 rule="hyper" parents="16132 17732"/>
    </justification>
  </clause>

  <clause id="17764">
    <literal><![CDATA[
      K(x,y \ T(z,(u * w) \ v5)) = K(x,y \ T(z,u \ (v5 / w)))
    ]]></literal>
    <justification jstring="[hyper(16137,a,17733,a)].">
      <j1 rule="hyper" parents="16137 17733"/>
    </justification>
  </clause>

  <clause id="17765">
    <literal><![CDATA[
      K(x,((K(y,z) * u) * w) * v5) = K(x,K(z,y) * ((u * w) * v5))
    ]]></literal>
    <justification jstring="[hyper(320,a,15130,a,b,17734,a),flip(a)].">
      <j1 rule="hyper" parents="320 15130 17734"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17766">
    <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),17741(a,2,2,1))].">
      <j1 rule="para" parents="20 17741"/>
    </justification>
  </clause>

  <clause id="17767">
    <literal><![CDATA[
      T(x,T(y \ (K(z,u) \ w),y)) = T(x,w / (K(u,z) \ y))
    ]]></literal>
    <justification jstring="[hyper(58,a,16449,a(flip),b,17742,a),flip(a)].">
      <j1 rule="hyper" parents="58 16449 17742"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17768">
    <literal><![CDATA[
      T(x,(K(y,z) \ u) / w) = T(x,u / (K(z,y) \ w))
    ]]></literal>
    <justification jstring="[hyper(58,a,7942,a(flip),b,17767,a)].">
      <j1 rule="hyper" parents="58 7942 17767"/>
    </justification>
  </clause>

  <clause id="17769">
    <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(14925(a,2),17748(a,2,2))].">
      <j1 rule="para" parents="14925 17748"/>
    </justification>
  </clause>

  <clause id="17770">
    <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,15419,a(flip),b,17760,a)].">
      <j1 rule="hyper" parents="58 15419 17760"/>
    </justification>
  </clause>

  <clause id="17771">
    <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,16317,a(flip),b,17762,a),flip(a)].">
      <j1 rule="hyper" parents="320 16317 17762"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17772">
    <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(17763(a,2),16574(a,1))].">
      <j1 rule="para" parents="17763 16574"/>
    </justification>
  </clause>

  <clause id="17773">
    <literal><![CDATA[
      K(x,((y * K(z,u)) * w) * v5) = K(x,K(u,z) * ((y * w) * v5))
    ]]></literal>
    <justification jstring="[hyper(16247,a,17765,a)].">
      <j1 rule="hyper" parents="16247 17765"/>
    </justification>
  </clause>

  <clause id="17774">
    <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,13086,a(flip),b,17766,a)].">
      <j1 rule="hyper" parents="58 13086 17766"/>
    </justification>
  </clause>

  <clause id="17775">
    <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,15917,a,b,17771,a)].">
      <j1 rule="hyper" parents="58 15917 17771"/>
    </justification>
  </clause>

  <clause id="17776">
    <literal><![CDATA[
      (x * (y / z)) * K(u,L(z,y,x)) = x * (y / T(z,u))
    ]]></literal>
    <justification jstring="[hyper(17269,a,14629,a)].">
      <j1 rule="hyper" parents="17269 14629"/>
    </justification>
  </clause>

  <clause id="17777">
    <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(17776(a,1),15430(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="17776 15430"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17778">
    <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(17776(a,1),16683(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17776 16683"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17779">
    <literal><![CDATA[
      K(x,L(T(y,z) / u,y,z)) = K(x,(z * y) / (u * z))
    ]]></literal>
    <justification jstring="[hyper(17339,a,16357,a)].">
      <j1 rule="hyper" parents="17339 16357"/>
    </justification>
  </clause>

  <clause id="17780">
    <literal><![CDATA[
      K(x,L(y * z,u,u * y)) = K(x,u \ ((u / (y \ 1)) * z))
    ]]></literal>
    <justification jstring="[hyper(14145,a,17377,a)].">
      <j1 rule="hyper" parents="14145 17377"/>
    </justification>
  </clause>

  <clause id="17781">
    <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(6030(a,1),17377(a,2,2,2,1))].">
      <j1 rule="para" parents="6030 17377"/>
    </justification>
  </clause>

  <clause id="17782">
    <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),17780(a,1,2,3))].">
      <j1 rule="para" parents="105 17780"/>
    </justification>
  </clause>

  <clause id="17783">
    <literal><![CDATA[
      ((x \ y) / y) * (y * K(z,u)) = x \ (y * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,14599,a(flip),b,17379,a),flip(a)].">
      <j1 rule="hyper" parents="58 14599 17379"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17784">
    <literal><![CDATA[
      (x \ (y * K(z,u))) / (y * K(z,u)) = (x \ y) / y
    ]]></literal>
    <justification jstring="[hyper(117,a,14599,a(flip),b,17379,a(flip))].">
      <j1 rule="hyper" parents="117 14599 17379"/>
    </justification>
  </clause>

  <clause id="17785">
    <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(17783(a,1),7557(a,2,2,1))].">
      <j1 rule="para" parents="17783 7557"/>
    </justification>
  </clause>

  <clause id="17786">
    <literal><![CDATA[
      (x \ (K(y,z) * u)) / (K(y,z) * u) = (x \ u) / u
    ]]></literal>
    <justification jstring="[hyper(58,a,14212,a,b,17784,a)].">
      <j1 rule="hyper" parents="58 14212 17784"/>
    </justification>
  </clause>

  <clause id="17787">
    <literal><![CDATA[
      (x \ y) / (K(x,z) * y) = (T(x,z) \ y) / y
    ]]></literal>
    <justification jstring="[para(5080(a,1),17786(a,1,1))].">
      <j1 rule="para" parents="5080 17786"/>
    </justification>
  </clause>

  <clause id="17788">
    <literal><![CDATA[
      ((x \ y) / y) * K(z,x) = (T(x,z) \ y) / y
    ]]></literal>
    <justification jstring="[hyper(58,a,14167,a(flip),b,17787,a)].">
      <j1 rule="hyper" parents="58 14167 17787"/>
    </justification>
  </clause>

  <clause id="17789">
    <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(17788(a,1),5154(a,2,1))].">
      <j1 rule="para" parents="17788 5154"/>
    </justification>
  </clause>

  <clause id="17790">
    <literal><![CDATA[
      K(x,((y / (z * y)) * u) \ y) = K(x,(z \ u) \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,14605,a(flip),b,17407,a),flip(a)].">
      <j1 rule="hyper" parents="58 14605 17407"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17791">
    <literal><![CDATA[
      K(x,((y / z) \ u) \ z) = K(x,((z / y) * u) \ z)
    ]]></literal>
    <justification jstring="[para(7(a,1),17790(a,1,2,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7 17790"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17792">
    <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(17791(a,2),14103(a,1))].">
      <j1 rule="para" parents="17791 14103"/>
    </justification>
  </clause>

  <clause id="17793">
    <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(8388(a,1),17414(a,1,2,2,2))].">
      <j1 rule="para" parents="8388 17414"/>
    </justification>
  </clause>

  <clause id="17794">
    <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(8277(a,1),17705(a,1))].">
      <j1 rule="para" parents="8277 17705"/>
    </justification>
  </clause>

  <clause id="17795">
    <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,7930,a(flip),b,17236,a),flip(a)].">
      <j1 rule="hyper" parents="320 7930 17236"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17796">
    <literal><![CDATA[
      K((x * K(y,z)) \ ((x * u) * K(y,z)),w) = K(u,w)
    ]]></literal>
    <justification jstring="[hyper(320,a,7883,a(flip),b,17795,a),flip(a)].">
      <j1 rule="hyper" parents="320 7883 17795"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17798">
    <literal><![CDATA[
      K((x * K(y,z)) \ (x * (u * K(y,z))),w) = K(u,w)
    ]]></literal>
    <justification jstring="[hyper(58,a,17541,a(flip),b,17796,a)].">
      <j1 rule="hyper" parents="58 17541 17796"/>
    </justification>
  </clause>

  <clause id="17799">
    <literal><![CDATA[
      K(L(T(x,K(y,z)),K(y,z),u),w) = K(x,w)
    ]]></literal>
    <justification jstring="[para(232(a,1),17798(a,1,1))].">
      <j1 rule="para" parents="232 17798"/>
    </justification>
  </clause>

  <clause id="17800">
    <literal><![CDATA[
      K(L(x,K(y,z),u),T(w,K(y,z))) = K(x,w)
    ]]></literal>
    <justification jstring="[hyper(7706,a,17799,a)].">
      <j1 rule="hyper" parents="7706 17799"/>
    </justification>
  </clause>

  <clause id="17801">
    <literal><![CDATA[
      K(L(x,K(y,z),u),w) = K(x,w)
    ]]></literal>
    <justification jstring="[hyper(15680,a,17800,a)].">
      <j1 rule="hyper" parents="15680 17800"/>
    </justification>
  </clause>

  <clause id="17802">
    <literal><![CDATA[
      K((x * K(y,z)) \ u,w) = K((x \ u) * K(z,y),w)
    ]]></literal>
    <justification jstring="[hyper(15802,a,17801,a)].">
      <j1 rule="hyper" parents="15802 17801"/>
    </justification>
  </clause>

  <clause id="17803">
    <literal><![CDATA[
      L(K(x,y),K(z,u),w) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(10871,a,17801,a)].">
      <j1 rule="hyper" parents="10871 17801"/>
    </justification>
  </clause>

  <clause id="17804">
    <literal><![CDATA[
      K(x,L(y,K(z,u),w)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(10870,a,17801,a)].">
      <j1 rule="hyper" parents="10870 17801"/>
    </justification>
  </clause>

  <clause id="17808">
    <literal><![CDATA[
      a(x,K(y,z),K(u,w)) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,17801,a,b,10842,a),flip(a)].">
      <j1 rule="hyper" parents="115 17801 10842"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17810">
    <literal><![CDATA[
      K(x \ (K(y,z) * u),w) = K((x \ u) * K(y,z),w)
    ]]></literal>
    <justification jstring="[hyper(58,a,17394,a(flip),b,17801,a)].">
      <j1 rule="hyper" parents="58 17394 17801"/>
    </justification>
  </clause>

  <clause id="17813">
    <literal><![CDATA[
      L(x,K(y,z),K(u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(13666,a,17808,a)].">
      <j1 rule="hyper" parents="13666 17808"/>
    </justification>
  </clause>

  <clause id="17814">
    <literal><![CDATA[
      (x * K(y,z)) * K(u,w) = x * (K(y,z) * K(u,w))
    ]]></literal>
    <justification jstring="[hyper(977,a,17808,a)].">
      <j1 rule="hyper" parents="977 17808"/>
    </justification>
  </clause>

  <clause id="17816">
    <literal><![CDATA[
      L(x,K(y,z),T(u,w)) = L(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(167,a,14998,a,b,17808,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="167 14998 17808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17817">
    <literal><![CDATA[
      T(x,L(y,K(z,u),w)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(167,a,10887,a,b,17808,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="167 10887 17808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17822">
    <literal><![CDATA[
      R(x,K(y,z),K(u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(58,a,14924,a,b,17813,a)].">
      <j1 rule="hyper" parents="58 14924 17813"/>
    </justification>
  </clause>

  <clause id="17823">
    <literal><![CDATA[
      L(x,K(y,z),u / w) = L(x,K(y,z),w \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,14976,a(flip),b,17813,a)].">
      <j1 rule="hyper" parents="58 14976 17813"/>
    </justification>
  </clause>

  <clause id="17826">
    <literal><![CDATA[
      L(x,K(y,z),K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      v5 = x
    ]]></literal>
    <justification jstring="[para(17813(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="17813 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17831">
    <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,16740,a(flip),b,17822,a)].">
      <j1 rule="hyper" parents="58 16740 17822"/>
    </justification>
  </clause>

  <clause id="17840">
    <literal><![CDATA[
      K(x,(y * K(z,u)) \ w) = K(x,K(z,u) \ (y \ w))
    ]]></literal>
    <justification jstring="[hyper(58,a,10818,a(flip),b,17803,a)].">
      <j1 rule="hyper" parents="58 10818 17803"/>
    </justification>
  </clause>

  <clause id="17841">
    <literal><![CDATA[
      K(x,(y \ z) \ K(u,w)) = K(x,z \ (y * K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(58,a,6584,a(flip),b,17803,a),flip(a)].">
      <j1 rule="hyper" parents="58 6584 17803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17843">
    <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(17803(a,1),286(a,1,2))].">
      <j1 rule="para" parents="17803 286"/>
    </justification>
  </clause>

  <clause id="17845">
    <literal><![CDATA[
      L(K(x,y),L(K(z,u),w,v5),v6) = K(x,y)
    ]]></literal>
    <justification jstring="[para(5677(a,1),17803(a,1,2))].">
      <j1 rule="para" parents="5677 17803"/>
    </justification>
  </clause>

  <clause id="17847">
    <literal><![CDATA[
      K(x,(y / z) / K(u,w)) = K(x,y / (K(u,w) * z))
    ]]></literal>
    <justification jstring="[hyper(58,a,14781,a(flip),b,17804,a),flip(a)].">
      <j1 rule="hyper" parents="58 14781 17804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17848">
    <literal><![CDATA[
      K(x,(y * K(z,u)) \ w) = K(x,K(u,z) * (y \ w))
    ]]></literal>
    <justification jstring="[para(5154(a,1),17804(a,1,2))].">
      <j1 rule="para" parents="5154 17804"/>
    </justification>
  </clause>

  <clause id="17850">
    <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,16901,a(flip),b,17817,a)].">
      <j1 rule="hyper" parents="58 16901 17817"/>
    </justification>
  </clause>

  <clause id="17851">
    <literal><![CDATA[
      T(x,(y * K(z,u)) \ w) = T(x,K(u,z) * (y \ w))
    ]]></literal>
    <justification jstring="[para(5154(a,1),17817(a,1,2))].">
      <j1 rule="para" parents="5154 17817"/>
    </justification>
  </clause>

  <clause id="17852">
    <literal><![CDATA[
      T(x,L(y,K(z,u),w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = v5
    ]]></literal>
    <justification jstring="[para(14942(a,1),17826(a,1)),flip(b)].">
      <j1 rule="para" parents="14942 17826"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17853">
    <literal><![CDATA[
      L(x,K(y,z),(u \ w) \ w) = L(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(2113,a,17816,a)].">
      <j1 rule="hyper" parents="2113 17816"/>
    </justification>
  </clause>

  <clause id="17854">
    <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,10818,a(flip),b,17845,a)].">
      <j1 rule="hyper" parents="58 10818 17845"/>
    </justification>
  </clause>

  <clause id="17856">
    <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(16342(a,1),17852(a,1))].">
      <j1 rule="para" parents="16342 17852"/>
    </justification>
  </clause>

  <clause id="17857">
    <literal><![CDATA[
      K(x \ (y * K(z,u)),w) = K((x \ y) * K(z,u),w)
    ]]></literal>
    <justification jstring="[hyper(17395,a,17802,a)].">
      <j1 rule="hyper" parents="17395 17802"/>
    </justification>
  </clause>

  <clause id="17858">
    <literal><![CDATA[
      K((K(x,y) * z) \ u,w) = K((z \ u) * K(y,x),w)
    ]]></literal>
    <justification jstring="[hyper(16090,a,17802,a)].">
      <j1 rule="hyper" parents="16090 17802"/>
    </justification>
  </clause>

  <clause id="17860">
    <literal><![CDATA[
      K(((x * y) \ z) * K(u,y),w) = K((x * T(y,u)) \ z,w)
    ]]></literal>
    <justification jstring="[para(6116(a,1),17802(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6116 17802"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17861">
    <literal><![CDATA[
      K(((x \ y) \ z) * K(u,y),w) = K((x \ T(y,u)) \ z,w)
    ]]></literal>
    <justification jstring="[para(13699(a,1),17802(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="13699 17802"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17862">
    <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(17802(a,1),14312(a,2,3))].">
      <j1 rule="para" parents="17802 14312"/>
    </justification>
  </clause>

  <clause id="17864">
    <literal><![CDATA[
      K(x \ (K(y,z) * u),w) = K(K(z,y) * (x \ u),w)
    ]]></literal>
    <justification jstring="[hyper(320,a,15862,a,b,17810,a),flip(a)].">
      <j1 rule="hyper" parents="320 15862 17810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17865">
    <literal><![CDATA[
      (x * K(y,z)) * K(u,w) = x * (K(u,w) * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,15711,a,b,17814,a),flip(a)].">
      <j1 rule="hyper" parents="320 15711 17814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17866">
    <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,14952,a,b,17814,a)].">
      <j1 rule="hyper" parents="117 14952 17814"/>
    </justification>
  </clause>

  <clause id="17867">
    <literal><![CDATA[
      K(x,T(y,z)) * (z * K(u,w)) = z * (K(u,w) * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,16425,a,b,17814,a)].">
      <j1 rule="hyper" parents="58 16425 17814"/>
    </justification>
  </clause>

  <clause id="17868">
    <literal><![CDATA[
      (x * (K(y,z) * K(u,w))) / (u * w) = (x * K(y,z)) / (w * u)
    ]]></literal>
    <justification jstring="[hyper(117,a,17814,a(flip),b,10380,a)].">
      <j1 rule="hyper" parents="117 17814 10380"/>
    </justification>
  </clause>

  <clause id="17870">
    <literal><![CDATA[
      T(x * (K(y,z) * K(u,w)),K(w,u)) = K(u,w) * (x * K(y,z))
    ]]></literal>
    <justification jstring="[para(17814(a,1),6337(a,1,1))].">
      <j1 rule="para" parents="17814 6337"/>
    </justification>
  </clause>

  <clause id="17871">
    <literal><![CDATA[
      K(x,K(y,z) \ ((u / z) \ w)) = K(x,(u / T(z,y)) \ w)
    ]]></literal>
    <justification jstring="[para(6322(a,1),17840(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6322 17840"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17872">
    <literal><![CDATA[
      K(x,(y \ z) \ K(u,w)) = K(x,K(u,w) * (z \ y))
    ]]></literal>
    <justification jstring="[hyper(320,a,17621,a(flip),b,17841,a),flip(a)].">
      <j1 rule="hyper" parents="320 17621 17841"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17873">
    <literal><![CDATA[
      K(x,(y / z) / K(u,w)) = K(x,y / (K(w,u) \ z))
    ]]></literal>
    <justification jstring="[para(5130(a,2),17847(a,2,2,2))].">
      <j1 rule="para" parents="5130 17847"/>
    </justification>
  </clause>

  <clause id="17874">
    <literal><![CDATA[
      K(x,y / (K(z,u) * w)) = K(x,(y / w) * K(u,z))
    ]]></literal>
    <justification jstring="[para(6335(a,1),17847(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6335 17847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17875">
    <literal><![CDATA[
      K(x,(K(y,z) * u) \ w) = K(x,K(z,y) * (u \ w))
    ]]></literal>
    <justification jstring="[hyper(16068,a,17848,a)].">
      <j1 rule="hyper" parents="16068 17848"/>
    </justification>
  </clause>

  <clause id="17876">
    <literal><![CDATA[
      K(x,K(y,z) * ((u \ z) \ w)) = K(x,(u \ T(z,y)) \ w)
    ]]></literal>
    <justification jstring="[para(13699(a,1),17848(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="13699 17848"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17877">
    <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,15455,a,b,17851,a)].">
      <j1 rule="hyper" parents="58 15455 17851"/>
    </justification>
  </clause>

  <clause id="17878">
    <literal><![CDATA[
      T(x,K(y,z) * ((u * z) \ w)) = T(x,(u * T(z,y)) \ w)
    ]]></literal>
    <justification jstring="[para(6116(a,1),17851(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6116 17851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17879">
    <literal><![CDATA[
      T(x,K(y,z) * ((u / y) \ w)) = T(x,(u / T(y,z)) \ w)
    ]]></literal>
    <justification jstring="[para(6322(a,1),17851(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6322 17851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17880">
    <literal><![CDATA[
      T(x,K(y \ z,y) * ((u \ (y \ z)) \ w)) = T(x,(u \ (z / y)) \ w)
    ]]></literal>
    <justification jstring="[para(13963(a,1),17851(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="13963 17851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17881">
    <literal><![CDATA[
      K(x \ (y * K(z,u)),w) = K(K(u,z) * (x \ y),w)
    ]]></literal>
    <justification jstring="[hyper(320,a,15862,a,b,17857,a),flip(a)].">
      <j1 rule="hyper" parents="320 15862 17857"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17882">
    <literal><![CDATA[
      K((K(x,y) * z) \ u,w) = K(K(y,x) * (z \ u),w)
    ]]></literal>
    <justification jstring="[hyper(320,a,15704,a,b,17858,a),flip(a)].">
      <j1 rule="hyper" parents="320 15704 17858"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17883">
    <literal><![CDATA[
      K(K(x,y) * (z \ (K(x,y) * u)),w) = K(z \ u,w)
    ]]></literal>
    <justification jstring="[para(5133(a,1),17864(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5133 17864"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17889">
    <literal><![CDATA[
      K(x,(y \ z) \ K(z,u)) = K(x,T(z,u) \ y)
    ]]></literal>
    <justification jstring="[hyper(320,a,15137,a(flip),b,17872,a),flip(a)].">
      <j1 rule="hyper" parents="320 15137 17872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17890">
    <literal><![CDATA[
      T(x,(y \ z) \ K(z,u)) = T(x,T(z,u) \ y)
    ]]></literal>
    <justification jstring="[hyper(118,a,17889,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 17889 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17891">
    <literal><![CDATA[
      T(x,(y \ (z / u)) \ K(u \ z,w)) = T(x,T(z / u,w) \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,16164,a(flip),b,17890,a)].">
      <j1 rule="hyper" parents="58 16164 17890"/>
    </justification>
  </clause>

  <clause id="17892">
    <literal><![CDATA[
      K(x,y / (K(z,u) \ w)) = K(x,K(u,z) \ (y / w))
    ]]></literal>
    <justification jstring="[hyper(15789,a,17873,a),flip(a)].">
      <j1 rule="hyper" parents="15789 17873"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17893">
    <literal><![CDATA[
      K(x,(y / z) * K(u,w)) = K(x,y * (z \ K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(16273,a,17874,a),flip(a)].">
      <j1 rule="hyper" parents="16273 17874"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17894">
    <literal><![CDATA[
      K(x,y / (K(z,u) * w)) = K(x,K(u,z) * (y / w))
    ]]></literal>
    <justification jstring="[hyper(320,a,15653,a,b,17874,a),flip(a)].">
      <j1 rule="hyper" parents="320 15653 17874"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17895">
    <literal><![CDATA[
      K(x,y \ (z * (K(u,z) * x))) = K(x,K(u,z) * ((z \ y) \ x))
    ]]></literal>
    <justification jstring="[hyper(58,a,6713,a(flip),b,17875,a)].">
      <j1 rule="hyper" parents="58 6713 17875"/>
    </justification>
  </clause>

  <clause id="17896">
    <literal><![CDATA[
      K(x,K(y,z) * ((y \ u) \ w)) = K(x,(T(y,z) \ u) \ w)
    ]]></literal>
    <justification jstring="[para(5131(a,1),17875(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5131 17875"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17897">
    <literal><![CDATA[
      K(K(x,y) * (z \ (u * K(x,y))),w) = K(z \ u,w)
    ]]></literal>
    <justification jstring="[para(6329(a,1),17881(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6329 17881"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17898">
    <literal><![CDATA[
      K(K(x,y) * (((x * y) * z) \ u),w) = K(((y * x) * z) \ u,w)
    ]]></literal>
    <justification jstring="[para(11157(a,1),17882(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="11157 17882"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17899">
    <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(17883(a,1),17604(a,1,2,2))].">
      <j1 rule="para" parents="17883 17604"/>
    </justification>
  </clause>

  <clause id="17900">
    <literal><![CDATA[
      T(x,y / (K(z,u) \ w)) = T(x,K(u,z) \ (y / w))
    ]]></literal>
    <justification jstring="[hyper(118,a,17892,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 17892 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17901">
    <literal><![CDATA[
      K(x,y * (z \ K(u,K(w,v5)))) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(16081,a,17893,a),flip(a)].">
      <j1 rule="hyper" parents="16081 17893"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17902">
    <literal><![CDATA[
      K(x,K(y,z) * (u / w)) = K(x,u * (w \ K(z,y)))
    ]]></literal>
    <justification jstring="[hyper(15829,a,17893,a)].">
      <j1 rule="hyper" parents="15829 17893"/>
    </justification>
  </clause>

  <clause id="17903">
    <literal><![CDATA[
      K(x,K(y,z) * (u / w)) = K(x,u * (w \ K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(15719,a,17893,a)].">
      <j1 rule="hyper" parents="15719 17893"/>
    </justification>
  </clause>

  <clause id="17904">
    <literal><![CDATA[
      K(x,y * (z \ K(y,u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u) / z) = w
    ]]></literal>
    <justification jstring="[para(17893(a,1),15801(a,1))].">
      <j1 rule="para" parents="17893 15801"/>
    </justification>
  </clause>

  <clause id="17905">
    <literal><![CDATA[
      K(x,(y / T(z,K(u,w))) / v5) = K(x,(y / z) / v5)
    ]]></literal>
    <justification jstring="[hyper(58,a,17699,a(flip),b,17901,a)].">
      <j1 rule="hyper" parents="58 17699 17901"/>
    </justification>
  </clause>

  <clause id="17906">
    <literal><![CDATA[
      K(x,K(y,z) * (u / (w \ z))) = K(x,u / (w \ T(z,y)))
    ]]></literal>
    <justification jstring="[hyper(16140,a,17894,a),flip(a)].">
      <j1 rule="hyper" parents="16140 17894"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17907">
    <literal><![CDATA[
      K(x,K(y,z) * (u / (y \ w))) = K(x,u / (T(y,z) \ w))
    ]]></literal>
    <justification jstring="[para(5131(a,1),17894(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5131 17894"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17908">
    <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(17894(a,1),16273(a,1))].">
      <j1 rule="para" parents="17894 16273"/>
    </justification>
  </clause>

  <clause id="17909">
    <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(17897(a,2),8398(a,1))].">
      <j1 rule="para" parents="17897 8398"/>
    </justification>
  </clause>

  <clause id="17910">
    <literal><![CDATA[
      T(x,(K(y,z) \ u) / w) = T(x,K(y,z) \ (u / w))
    ]]></literal>
    <justification jstring="[hyper(58,a,17768,a,b,17900,a)].">
      <j1 rule="hyper" parents="58 17768 17900"/>
    </justification>
  </clause>

  <clause id="17911">
    <literal><![CDATA[
      T(x,K(y,z) * (u / w)) = T(x,u * (w \ K(z,y)))
    ]]></literal>
    <justification jstring="[hyper(118,a,17902,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 17902 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17912">
    <literal><![CDATA[
      T(x,K(y,z) * (u / w)) = T(x,u * (w \ K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(118,a,17903,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 17903 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17914">
    <literal><![CDATA[
      K(x,(y / T(z,T(u,w))) / v5) = K(x,(y / T(z,u)) / v5)
    ]]></literal>
    <justification jstring="[para(7438(a,1),17905(a,1,2,1,2))].">
      <j1 rule="para" parents="7438 17905"/>
    </justification>
  </clause>

  <clause id="17915">
    <literal><![CDATA[
      T(x,K(y,z) \ ((T(z,y) \ u) / w)) = T(x,(z \ u) / w)
    ]]></literal>
    <justification jstring="[para(5129(a,1),17910(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5129 17910"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17916">
    <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,14160,a(flip),b,17911,a),flip(a)].">
      <j1 rule="hyper" parents="320 14160 17911"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17917">
    <literal><![CDATA[
      T(x,K(y,z) * (u / (y \ w))) = T(x,u / (T(y,z) \ w))
    ]]></literal>
    <justification jstring="[hyper(320,a,14007,a(flip),b,17912,a),flip(a)].">
      <j1 rule="hyper" parents="320 14007 17912"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17918">
    <literal><![CDATA[
      K(x,y * (z \ K(u,y))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u) / z) = w
    ]]></literal>
    <justification jstring="[para(17694(a,1),17904(a,1))].">
      <j1 rule="para" parents="17694 17904"/>
    </justification>
  </clause>

  <clause id="17919">
    <literal><![CDATA[
      K(K(x,y) * ((z * x) \ u),w) = K((z * T(x,y)) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(15927,a,17860,a)].">
      <j1 rule="hyper" parents="15927 17860"/>
    </justification>
  </clause>

  <clause id="17920">
    <literal><![CDATA[
      K((x \ T(y,x)) \ z,u) = K((y / x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,15926,a(flip),b,17861,a),flip(a)].">
      <j1 rule="hyper" parents="58 15926 17861"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17921">
    <literal><![CDATA[
      K((T(x,y) \ y) \ z,u) = K((y / x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,9053,a,b,17920,a)].">
      <j1 rule="hyper" parents="58 9053 17920"/>
    </justification>
  </clause>

  <clause id="17922">
    <literal><![CDATA[
      x * (y * (K(x,z) * K(x,z))) = T(x,z) * (K(x,z) * y)
    ]]></literal>
    <justification jstring="[para(17867(a,1),7192(a,1,2))].">
      <j1 rule="para" parents="17867 7192"/>
    </justification>
  </clause>

  <clause id="17923">
    <literal><![CDATA[
      K(x,(y / T(z,z \ u)) \ w) = K(x,K(u,z) \ ((y / z) \ w))
    ]]></literal>
    <justification jstring="[hyper(58,a,13144,a(flip),b,17871,a),flip(a)].">
      <j1 rule="hyper" parents="58 13144 17871"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17924">
    <literal><![CDATA[
      K(x,K(y,z) * ((u \ y) \ w)) = K(x,(u \ T(y,z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(15131,a,17876,a)].">
      <j1 rule="hyper" parents="15131 17876"/>
    </justification>
  </clause>

  <clause id="17925">
    <literal><![CDATA[
      T(x,(y * T(z,u)) \ T(z,w)) = T(x,(y * z) \ T(T(z,w),u))
    ]]></literal>
    <justification jstring="[hyper(16100,a,17878,a),flip(a)].">
      <j1 rule="hyper" parents="16100 17878"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17926">
    <literal><![CDATA[
      T(x,K(y,z) * ((u * y) \ w)) = T(x,(u * T(y,z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(15334,a,17878,a)].">
      <j1 rule="hyper" parents="15334 17878"/>
    </justification>
  </clause>

  <clause id="17927">
    <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,16698,a(flip),b,17879,a),flip(a)].">
      <j1 rule="hyper" parents="58 16698 17879"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17928">
    <literal><![CDATA[
      K(x,K(y,z) * ((z \ u) \ w)) = K(x,(T(z,y) \ u) \ w)
    ]]></literal>
    <justification jstring="[hyper(15131,a,17896,a)].">
      <j1 rule="hyper" parents="15131 17896"/>
    </justification>
  </clause>

  <clause id="17929">
    <literal><![CDATA[
      K(x,y / (z \ T(u,z))) = K(x,y / (u / z))
    ]]></literal>
    <justification jstring="[hyper(58,a,15875,a(flip),b,17906,a),flip(a)].">
      <j1 rule="hyper" parents="58 15875 17906"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17930">
    <literal><![CDATA[
      K(x,y / (T(z,u) \ u)) = K(x,y / (u / z))
    ]]></literal>
    <justification jstring="[para(4248(a,2),17929(a,1,2,2))].">
      <j1 rule="para" parents="4248 17929"/>
    </justification>
  </clause>

  <clause id="17931">
    <literal><![CDATA[
      K(x,(y / z) \ T(u,y / z)) = K(x,u / (T(z,y) \ y))
    ]]></literal>
    <justification jstring="[hyper(320,a,13131,a,b,17930,a)].">
      <j1 rule="hyper" parents="320 13131 17930"/>
    </justification>
  </clause>

  <clause id="17932">
    <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(16253,a,17914,a)].">
      <j1 rule="hyper" parents="16253 17914"/>
    </justification>
  </clause>

  <clause id="17933">
    <literal><![CDATA[
      T(x,(((y \ T(z,y)) \ z) \ z) / u) = T(x,(y \ z) / u)
    ]]></literal>
    <justification jstring="[hyper(58,a,16746,a,b,17915,a)].">
      <j1 rule="hyper" parents="58 16746 17915"/>
    </justification>
  </clause>

  <clause id="17934">
    <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,16293,a(flip),b,17917,a)].">
      <j1 rule="hyper" parents="58 16293 17917"/>
    </justification>
  </clause>

  <clause id="17935">
    <literal><![CDATA[
      x * (y * (K(x,z) * K(x,z))) = T(T(x,z),z) * y
    ]]></literal>
    <justification jstring="[hyper(320,a,5097,a(flip),b,17922,a),flip(a)].">
      <j1 rule="hyper" parents="320 5097 17922"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17936">
    <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(17935(a,1),11769(a,2,2,1))].">
      <j1 rule="para" parents="17935 11769"/>
    </justification>
  </clause>

  <clause id="17937">
    <literal><![CDATA[
      T(x,K(y,z) * ((u \ y) \ w)) = T(x,(u \ T(y,z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(118,a,17924,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 17924 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17938">
    <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,16707,a(flip),b,17926,a),flip(a)].">
      <j1 rule="hyper" parents="58 16707 17926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17939">
    <literal><![CDATA[
      K(x,(T(y,z) \ z) \ u) = K(x,(z / y) \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,13145,a(flip),b,17928,a),flip(a)].">
      <j1 rule="hyper" parents="58 13145 17928"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17940">
    <literal><![CDATA[
      T(x,(T(y,z) \ z) \ u) = T(x,(z / y) \ u)
    ]]></literal>
    <justification jstring="[hyper(118,a,17939,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 17939 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17941">
    <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(7942(a,1),17940(a,1,2,1,1))].">
      <j1 rule="para" parents="7942 17940"/>
    </justification>
  </clause>

  <clause id="17942">
    <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(17940(a,1),16157(a,1,2,2))].">
      <j1 rule="para" parents="17940 16157"/>
    </justification>
  </clause>

  <clause id="17943">
    <literal><![CDATA[
      K(x,y / (T(z,u) \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (u / z)) = w
    ]]></literal>
    <justification jstring="[para(17931(a,1),13132(a,1))].">
      <j1 rule="para" parents="17931 13132"/>
    </justification>
  </clause>

  <clause id="17944">
    <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(12738(a,1),17943(a,1,2,2,1))].">
      <j1 rule="para" parents="12738 17943"/>
    </justification>
  </clause>

  <clause id="17945">
    <literal><![CDATA[
      K(x,K(y,z) * (u / (y \ z))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u / (z / y)) = w
    ]]></literal>
    <justification jstring="[para(17907(a,2),17943(a,1))].">
      <j1 rule="para" parents="17907 17943"/>
    </justification>
  </clause>

  <clause id="17947">
    <literal><![CDATA[
      T(x,T(T(y,z) \ z,y) / u) = T(x,(y \ z) / u)
    ]]></literal>
    <justification jstring="[para(7659(a,1),17933(a,1,2,1))].">
      <j1 rule="para" parents="7659 17933"/>
    </justification>
  </clause>

  <clause id="17948">
    <literal><![CDATA[
      T(x,(y / T(z,y)) / u) = T(x,(z \ y) / u)
    ]]></literal>
    <justification jstring="[hyper(58,a,16106,a(flip),b,17947,a)].">
      <j1 rule="hyper" parents="58 16106 17947"/>
    </justification>
  </clause>

  <clause id="17949">
    <literal><![CDATA[
      T(x,(y \ z) / T(u,y \ z)) = T(x,u \ (z / T(y,z)))
    ]]></literal>
    <justification jstring="[hyper(12745,a,17948,a),flip(a)].">
      <j1 rule="hyper" parents="12745 17948"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17950">
    <literal><![CDATA[
      T(x,K(y,z) * ((u \ y) \ w)) = T(x,((u \ T(y,z)) \ 1) * w)
    ]]></literal>
    <justification jstring="[hyper(320,a,13878,a,b,17937,a),flip(a)].">
      <j1 rule="hyper" parents="320 13878 17937"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17951">
    <literal><![CDATA[
      T(x,y \ (z / T(u,z))) = T(x,y \ (u \ z))
    ]]></literal>
    <justification jstring="[hyper(12742,a,17949,a),flip(a)].">
      <j1 rule="hyper" parents="12742 17949"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17952">
    <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(17951(a,1),5043(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="17951 5043"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17953">
    <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(17865(a,1),17843(a,1))].">
      <j1 rule="para" parents="17865 17843"/>
    </justification>
  </clause>

  <clause id="17954">
    <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(13859(a,1),17856(a,1))].">
      <j1 rule="para" parents="13859 17856"/>
    </justification>
  </clause>

  <clause id="17955">
    <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(15263(a,2),17908(a,1))].">
      <j1 rule="para" parents="15263 17908"/>
    </justification>
  </clause>

  <clause id="17956">
    <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(17902(a,1),17908(a,1))].">
      <j1 rule="para" parents="17902 17908"/>
    </justification>
  </clause>

  <clause id="17957">
    <literal><![CDATA[
      K(x,K(y,z) * (u / ((K(w,v5) * y) \ z))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,u / (z / (K(w,v5) * y))) = v6
    ]]></literal>
    <justification jstring="[para(16684(a,1),17945(a,1))].">
      <j1 rule="para" parents="16684 17945"/>
    </justification>
  </clause>

  <clause id="17958">
    <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(13195(a,2),17956(a,1))].">
      <j1 rule="para" parents="13195 17956"/>
    </justification>
  </clause>

  <clause id="17959">
    <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(17617(a,2),17956(a,1))].">
      <j1 rule="para" parents="17617 17956"/>
    </justification>
  </clause>

  <clause id="17960">
    <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(17696(a,2),17956(a,1))].">
      <j1 rule="para" parents="17696 17956"/>
    </justification>
  </clause>

  <clause id="17962">
    <literal><![CDATA[
      (x * K(y,z)) / (z * y) = x / (T(z,y) * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,16592,a(flip),b,17868,a),flip(a)].">
      <j1 rule="hyper" parents="58 16592 17868"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17963">
    <literal><![CDATA[
      (x / (y * z)) * K(z,y) = x / (T(y,z) * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,10643,a(flip),b,17962,a)].">
      <j1 rule="hyper" parents="58 10643 17962"/>
    </justification>
  </clause>

  <clause id="17964">
    <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(439,a,14566,a,b,17963,a),flip(a)].">
      <j1 rule="hyper" parents="439 14566 17963"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17965">
    <literal><![CDATA[
      x / (K(y,z) * K(u,w)) = x * (K(z,y) * K(w,u))
    ]]></literal>
    <justification jstring="[hyper(35,a,17831,a,b,17870,a)].">
      <j1 rule="hyper" parents="35 17831 17870"/>
    </justification>
  </clause>

  <clause id="17968">
    <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(17965(a,2),17953(a,1))].">
      <j1 rule="para" parents="17965 17953"/>
    </justification>
  </clause>

  <clause id="17969">
    <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(15664(a,1),17968(a,1,2))].">
      <j1 rule="para" parents="15664 17968"/>
    </justification>
  </clause>

  <clause id="17970">
    <literal><![CDATA[
      K(x,K(y,z) * ((z \ u) \ x)) = K(x,K(y,z) * (u \ (z * x)))
    ]]></literal>
    <justification jstring="[hyper(58,a,17670,a(flip),b,17895,a),flip(a)].">
      <j1 rule="hyper" parents="58 17670 17895"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17971">
    <literal><![CDATA[
      K(((a(x,y,z) * u) * w) \ v5,v6) = K(((u * a(x,y,z)) * w) \ v5,v6)
    ]]></literal>
    <justification jstring="[hyper(17537,a,17898,a),flip(a)].">
      <j1 rule="hyper" parents="17537 17898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17972">
    <literal><![CDATA[
      K(x,(y / T(z,z \ u)) \ w) = K(x,(y / T(z,u)) \ w)
    ]]></literal>
    <justification jstring="[hyper(320,a,17871,a(flip),b,17923,a),flip(a)].">
      <j1 rule="hyper" parents="320 17871 17923"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17973">
    <literal><![CDATA[
      K(x,(y / T(z,y)) \ u) = K(x,(z \ y) \ u)
    ]]></literal>
    <justification jstring="[para(265(a,1),17972(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="265 17972"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17974">
    <literal><![CDATA[
      T(x,(y / T(z,y)) \ u) = T(x,(z \ y) \ u)
    ]]></literal>
    <justification jstring="[hyper(118,a,17973,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 17973 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17975">
    <literal><![CDATA[
      K(x,(T(y,z) / z) \ u) = K(x,(z \ y) \ u)
    ]]></literal>
    <justification jstring="[para(4246(a,2),17973(a,1,2,1))].">
      <j1 rule="para" parents="4246 17973"/>
    </justification>
  </clause>

  <clause id="17976">
    <literal><![CDATA[
      T(x,(T(y,z) / z) \ u) = T(x,(z \ y) \ u)
    ]]></literal>
    <justification jstring="[para(4246(a,2),17974(a,1,2,1))].">
      <j1 rule="para" parents="4246 17974"/>
    </justification>
  </clause>

  <clause id="17977">
    <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,13119,a(flip),b,17925,a),flip(a)].">
      <j1 rule="hyper" parents="58 13119 17925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17978">
    <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,17640,a(flip),b,17927,a),flip(a)].">
      <j1 rule="hyper" parents="58 17640 17927"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17979">
    <literal><![CDATA[
      T(x,T(y \ K(z,u),w) * v5) = T(x,K(z,u) * (T(y,w) \ v5))
    ]]></literal>
    <justification jstring="[hyper(17740,a,17938,a),flip(a)].">
      <j1 rule="hyper" parents="17740 17938"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17980">
    <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(17950(a,2),14124(a,1))].">
      <j1 rule="para" parents="17950 14124"/>
    </justification>
  </clause>

  <clause id="17981">
    <literal><![CDATA[
      K(x,K(y,z) * ((z \ u) \ x)) = K(x,u \ (x * T(z,y)))
    ]]></literal>
    <justification jstring="[hyper(320,a,17711,a(flip),b,17970,a),flip(a)].">
      <j1 rule="hyper" parents="320 17711 17970"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17982">
    <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,15375,a(flip),b,17978,a)].">
      <j1 rule="hyper" parents="58 15375 17978"/>
    </justification>
  </clause>

  <clause id="17983">
    <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,15376,a(flip),b,17979,a),flip(a)].">
      <j1 rule="hyper" parents="58 15376 17979"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17984">
    <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,16024,a,b,17982,a)].">
      <j1 rule="hyper" parents="58 16024 17982"/>
    </justification>
  </clause>

  <clause id="17985">
    <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,13979,a(flip),b,17984,a),flip(a)].">
      <j1 rule="hyper" parents="58 13979 17984"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17986">
    <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(17692(a,2),17959(a,1))].">
      <j1 rule="para" parents="17692 17959"/>
    </justification>
  </clause>

  <clause id="17987">
    <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(17694(a,1),17960(a,1))].">
      <j1 rule="para" parents="17694 17960"/>
    </justification>
  </clause>

  <clause id="17990">
    <literal><![CDATA[
      T(x,L(y,z \ T(u * z,w),u)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = v5
    ]]></literal>
    <justification jstring="[para(17291(a,2),17852(a,1))].">
      <j1 rule="para" parents="17291 17852"/>
    </justification>
  </clause>

  <clause id="17991">
    <literal><![CDATA[
      T(T(x,y \ (z * z)),K(u,y \ (z * z))) = T(x,T((z \ y) \ z,u))
    ]]></literal>
    <justification jstring="[para(13957(a,1),17369(a,1,1))].">
      <j1 rule="para" parents="13957 17369"/>
    </justification>
  </clause>

  <clause id="17992">
    <literal><![CDATA[
      K(x * K(y,z),T(u,w / x)) = K(K(y,z) * x,T(u,w))
    ]]></literal>
    <justification jstring="[hyper(16431,a,17427,a)].">
      <j1 rule="hyper" parents="16431 17427"/>
    </justification>
  </clause>

  <clause id="17993">
    <literal><![CDATA[
      K(x * K(y,z),T(u,x \ w)) = K(K(y,z) * x,T(u,w))
    ]]></literal>
    <justification jstring="[hyper(15795,a,17992,a)].">
      <j1 rule="hyper" parents="15795 17992"/>
    </justification>
  </clause>

  <clause id="17994">
    <literal><![CDATA[
      L(x,T(y,z),(y / z) \ 1) = L(x,T(y,z),(z \ y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,12607,a(flip),b,17475,a)].">
      <j1 rule="hyper" parents="58 12607 17475"/>
    </justification>
  </clause>

  <clause id="17995">
    <literal><![CDATA[
      L(x,T(y,z),(z \ y) \ 1) = L(x,y,(y / z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(14970,a,17994,a),flip(a)].">
      <j1 rule="hyper" parents="14970 17994"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17996">
    <literal><![CDATA[
      L(x,y,(y / z) \ 1) = L(x,y,(z \ y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(13277,a,17995,a),flip(a)].">
      <j1 rule="hyper" parents="13277 17995"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17997">
    <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(1503(a,1),17996(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="1503 17996"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17998">
    <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(6197(a,2),17492(a,1,2,2))].">
      <j1 rule="para" parents="6197 17492"/>
    </justification>
  </clause>

  <clause id="17999">
    <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(15874,a,17630,a)].">
      <j1 rule="hyper" parents="15874 17630"/>
    </justification>
  </clause>

  <clause id="18000">
    <literal><![CDATA[
      K(x,y * (z * L(K(u,w),v5,v6))) = K(x,K(u,w) \ (y * z))
    ]]></literal>
    <justification jstring="[hyper(17715,a,17635,a),flip(a)].">
      <j1 rule="hyper" parents="17715 17635"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18001">
    <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(18000(a,2),8403(a,1))].">
      <j1 rule="para" parents="18000 8403"/>
    </justification>
  </clause>

  <clause id="18002">
    <literal><![CDATA[
      K(x,y * ((z \ 1) \ K(u,x))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = w
    ]]></literal>
    <justification jstring="[para(11372(a,1),18001(a,1))].">
      <j1 rule="para" parents="11372 18001"/>
    </justification>
  </clause>

  <clause id="18003">
    <literal><![CDATA[
      K(x,y / (z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = u
    ]]></literal>
    <justification jstring="[para(13838(a,1),18002(a,1))].">
      <j1 rule="para" parents="13838 18002"/>
    </justification>
  </clause>

  <clause id="18004">
    <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(4068(a,1),18003(a,1,2,2))].">
      <j1 rule="para" parents="4068 18003"/>
    </justification>
  </clause>

  <clause id="18005">
    <literal><![CDATA[
      K(x,y / (1 / z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = u
    ]]></literal>
    <justification jstring="[para(5316(a,2),18003(a,1))].">
      <j1 rule="para" parents="5316 18003"/>
    </justification>
  </clause>

  <clause id="18006">
    <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(13853(a,1),18003(a,1))].">
      <j1 rule="para" parents="13853 18003"/>
    </justification>
  </clause>

  <clause id="18007">
    <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(13876(a,1),18005(a,1,2,2))].">
      <j1 rule="para" parents="13876 18005"/>
    </justification>
  </clause>

  <clause id="18008">
    <literal><![CDATA[
      K(x,(y / (y / z)) \ (u / (y / z))) = K(x,z \ (u / (z \ y)))
    ]]></literal>
    <justification jstring="[para(5415(a,1),17648(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5415 17648"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18009">
    <literal><![CDATA[
      K(x,y \ (z * (u * (w / u)))) = K(x,K(u,w) * (y \ (z * w)))
    ]]></literal>
    <justification jstring="[hyper(15174,a,17649,a),flip(a)].">
      <j1 rule="hyper" parents="15174 17649"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18010">
    <literal><![CDATA[
      K(x,y \ (z * (u * (w / u)))) = K(x,y \ (z * T(w,u)))
    ]]></literal>
    <justification jstring="[hyper(320,a,17706,a(flip),b,18009,a),flip(a)].">
      <j1 rule="hyper" parents="320 17706 18009"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18011">
    <literal><![CDATA[
      K(x,y \ (z * T(u * w,w))) = K(x,y \ (z * (w * u)))
    ]]></literal>
    <justification jstring="[para(6(a,1),18010(a,1,2,2,2,2)),flip(a)].">
      <j1 rule="para" parents="6 18010"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18012">
    <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,15327,a(flip),b,18011,a),flip(a)].">
      <j1 rule="hyper" parents="58 15327 18011"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18013">
    <literal><![CDATA[
      K(x,y \ (z * ((u \ w) * u))) = K(x,K(w,u) * (y \ (z * w)))
    ]]></literal>
    <justification jstring="[hyper(13183,a,17650,a),flip(a)].">
      <j1 rule="hyper" parents="13183 17650"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18014">
    <literal><![CDATA[
      K(x,y \ (z * ((u \ w) * u))) = K(x,y \ (z * T(w,u)))
    ]]></literal>
    <justification jstring="[hyper(320,a,17647,a(flip),b,18013,a),flip(a)].">
      <j1 rule="hyper" parents="320 17647 18013"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18015">
    <literal><![CDATA[
      K(x,y \ (z * T(u * w,u))) = K(x,y \ (z * (w * u)))
    ]]></literal>
    <justification jstring="[para(4(a,1),18014(a,1,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="4 18014"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18016">
    <literal><![CDATA[
      K(x,K(y,z) * ((u \ y) * w)) = K(x,(u \ (z * (y / z))) * w)
    ]]></literal>
    <justification jstring="[hyper(13183,a,17655,a)].">
      <j1 rule="hyper" parents="13183 17655"/>
    </justification>
  </clause>

  <clause id="18017">
    <literal><![CDATA[
      K(x,(y \ (z * (u / z))) * w) = K(x,(y \ T(u,z)) * w)
    ]]></literal>
    <justification jstring="[hyper(58,a,17708,a(flip),b,18016,a),flip(a)].">
      <j1 rule="hyper" parents="58 17708 18016"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18018">
    <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,15482,a(flip),b,18017,a),flip(a)].">
      <j1 rule="hyper" parents="58 15482 18017"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18019">
    <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,16174,a(flip),b,17657,a),flip(a)].">
      <j1 rule="hyper" parents="58 16174 17657"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18020">
    <literal><![CDATA[
      K(x,y \ (((z \ u) * z) * w)) = K(x,K(z,u) * (y \ (u * w)))
    ]]></literal>
    <justification jstring="[hyper(15174,a,17663,a),flip(a)].">
      <j1 rule="hyper" parents="15174 17663"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18021">
    <literal><![CDATA[
      K(x,y \ (((z \ u) * z) * w)) = K(x,y \ (T(u,z) * w))
    ]]></literal>
    <justification jstring="[hyper(320,a,17662,a(flip),b,18020,a),flip(a)].">
      <j1 rule="hyper" parents="320 17662 18020"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18022">
    <literal><![CDATA[
      K(x,y \ ((z / (T(u,z) \ 1)) * w)) = K(x,y \ (T(z / (u \ 1),z) * w))
    ]]></literal>
    <justification jstring="[para(10108(a,1),18021(a,1,2,2,1))].">
      <j1 rule="para" parents="10108 18021"/>
    </justification>
  </clause>

  <clause id="18023">
    <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,17396,a(flip),b,17665,a),flip(a)].">
      <j1 rule="hyper" parents="320 17396 17665"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18024">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ ((y / z) * w))) = K(x,u \ ((z \ y) * w))
    ]]></literal>
    <justification jstring="[hyper(13183,a,17671,a)].">
      <j1 rule="hyper" parents="13183 17671"/>
    </justification>
  </clause>

  <clause id="18025">
    <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,16008,a(flip),b,17675,a)].">
      <j1 rule="hyper" parents="58 16008 17675"/>
    </justification>
  </clause>

  <clause id="18026">
    <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,17611,a(flip),b,17690,a),flip(a)].">
      <j1 rule="hyper" parents="58 17611 17690"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18027">
    <literal><![CDATA[
      K(x,y * ((z \ (u \ w)) \ K(u,w))) = K(x,y / (z \ (w / u)))
    ]]></literal>
    <justification jstring="[hyper(17639,a,17720,a)].">
      <j1 rule="hyper" parents="17639 17720"/>
    </justification>
  </clause>

  <clause id="18028">
    <literal><![CDATA[
      K(x,y / (z \ (u \ T(w,u)))) = K(x,y / (z \ (w / u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,16187,a(flip),b,18027,a)].">
      <j1 rule="hyper" parents="58 16187 18027"/>
    </justification>
  </clause>

  <clause id="18029">
    <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(17721(a,1),16352(a,1))].">
      <j1 rule="para" parents="17721 16352"/>
    </justification>
  </clause>

  <clause id="18030">
    <literal><![CDATA[
      K(x * (K(y,z) * (y \ u)),w) = K(x * (T(y,z) \ u),w)
    ]]></literal>
    <justification jstring="[hyper(16455,a,17724,a),flip(a)].">
      <j1 rule="hyper" parents="16455 17724"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18031">
    <literal><![CDATA[
      K(x * ((y \ z) * K(y,u)),w) = K(x * (T(y,u) \ z),w)
    ]]></literal>
    <justification jstring="[hyper(16092,a,18030,a)].">
      <j1 rule="hyper" parents="16092 18030"/>
    </justification>
  </clause>

  <clause id="18032">
    <literal><![CDATA[
      K(x * (((y * z) / y) \ u),w) = K(x * (T(z,y) \ u),w)
    ]]></literal>
    <justification jstring="[hyper(58,a,16288,a,b,18030,a)].">
      <j1 rule="hyper" parents="58 16288 18030"/>
    </justification>
  </clause>

  <clause id="18033">
    <literal><![CDATA[
      K(K(x,y) * (z * (x \ u)),w) = K(z * (T(x,y) \ u),w)
    ]]></literal>
    <justification jstring="[hyper(17600,a,18031,a)].">
      <j1 rule="hyper" parents="17600 18031"/>
    </justification>
  </clause>

  <clause id="18034">
    <literal><![CDATA[
      K(x,(y * (1 / z)) * (u \ K(z,y))) = K(x,((z \ 1) * y) / u)
    ]]></literal>
    <justification jstring="[hyper(320,a,13221,a(flip),b,17726,a),flip(a)].">
      <j1 rule="hyper" parents="320 13221 17726"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18035">
    <literal><![CDATA[
      K(x,(T(y,z) * (1 / z)) / u) = K(x,((z \ 1) * y) / u)
    ]]></literal>
    <justification jstring="[hyper(18029,a,18034,a)].">
      <j1 rule="hyper" parents="18029 18034"/>
    </justification>
  </clause>

  <clause id="18036">
    <literal><![CDATA[
      K(x,(y * (1 / T(z,y))) / u) = K(x,((z \ 1) * y) / u)
    ]]></literal>
    <justification jstring="[para(5264(a,1),18035(a,1,2,1))].">
      <j1 rule="para" parents="5264 18035"/>
    </justification>
  </clause>

  <clause id="18037">
    <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,14919,a(flip),b,18036,a)].">
      <j1 rule="hyper" parents="58 14919 18036"/>
    </justification>
  </clause>

  <clause id="18038">
    <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,17757,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 17757 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18039">
    <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,16047,a(flip),b,17775,a),flip(a)].">
      <j1 rule="hyper" parents="320 16047 17775"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18040">
    <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,17580,a(flip),b,17854,a),flip(a)].">
      <j1 rule="hyper" parents="320 17580 17854"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18042">
    <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),18040(a,1,2,1))].">
      <j1 rule="para" parents="90 18040"/>
    </justification>
  </clause>

  <clause id="18043">
    <literal><![CDATA[
      K(x,(y * (z * K(u,w))) \ v5) = K(x,((y * z) \ v5) * K(w,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,15708,a(flip),b,18042,a),flip(a)].">
      <j1 rule="hyper" parents="320 15708 18042"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18044">
    <literal><![CDATA[
      K(x,(y * (z * K(u,w))) \ v5) = K(x,K(w,u) * ((y * z) \ v5))
    ]]></literal>
    <justification jstring="[para(5130(a,1),18042(a,2,2))].">
      <j1 rule="para" parents="5130 18042"/>
    </justification>
  </clause>

  <clause id="18045">
    <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(18043(a,2),15719(a,1))].">
      <j1 rule="para" parents="18043 15719"/>
    </justification>
  </clause>

  <clause id="18046">
    <literal><![CDATA[
      T(x,(y \ T(z \ u,z)) \ w) = T(x,(y \ (u / z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(17980,a,17880,a)].">
      <j1 rule="hyper" parents="17980 17880"/>
    </justification>
  </clause>

  <clause id="18047">
    <literal><![CDATA[
      T(x,K(y * z,u) * (w / T(z,y))) = T(x,w / (T(z \ y,u) \ y))
    ]]></literal>
    <justification jstring="[hyper(16713,a,17934,a)].">
      <j1 rule="hyper" parents="16713 17934"/>
    </justification>
  </clause>

  <clause id="18048">
    <literal><![CDATA[
      K((x / (x / (y * a(z,u,w)))) \ v5,v6) = K(((a(z,u,w) * y) * K((y * a(z,u,w)) \ x,y * a(z,u,w))) \ v5,v6)
    ]]></literal>
    <justification jstring="[para(4710(a,2),17971(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="4710 17971"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18049">
    <literal><![CDATA[
      T(x,T((y \ z) \ y,u)) = T(x,T(z \ (y * y),u))
    ]]></literal>
    <justification jstring="[hyper(7858,a,17991,a),flip(a)].">
      <j1 rule="hyper" parents="7858 17991"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18050">
    <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(13726(a,1),18049(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="13726 18049"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18051">
    <literal><![CDATA[
      K(x,y / T(z,K(u,w) * v5)) = K(x,y / T(z,v5))
    ]]></literal>
    <justification jstring="[hyper(17752,a,17998,a),flip(a)].">
      <j1 rule="hyper" parents="17752 17998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18053">
    <literal><![CDATA[
      T(x,y / T(z,K(u,w) * v5)) = T(x,y / T(z,v5))
    ]]></literal>
    <justification jstring="[hyper(118,a,18051,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 18051 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18054">
    <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,15316,a(flip),b,18051,a),flip(a)].">
      <j1 rule="hyper" parents="58 15316 18051"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18055">
    <literal><![CDATA[
      T(x,y \ K(K(z,u) * w,v5)) = T(x,(y \ v5) / T(v5,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,14144,a(flip),b,18053,a)].">
      <j1 rule="hyper" parents="58 14144 18053"/>
    </justification>
  </clause>

  <clause id="18056">
    <literal><![CDATA[
      T(x,y / T(z,u * T(w,v5))) = T(x,y / T(z,u * w))
    ]]></literal>
    <justification jstring="[para(5555(a,1),18053(a,1,2,2,2))].">
      <j1 rule="para" parents="5555 18053"/>
    </justification>
  </clause>

  <clause id="18057">
    <literal><![CDATA[
      T(x,y \ K(K(z,u) * w,v5)) = T(x,y \ K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(320,a,14144,a(flip),b,18055,a),flip(a)].">
      <j1 rule="hyper" parents="320 14144 18055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18058">
    <literal><![CDATA[
      T(x,y \ K(T(z,u) \ w,v5)) = T(x,y \ K(z \ w,v5))
    ]]></literal>
    <justification jstring="[para(5081(a,1),18057(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5081 18057"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18059">
    <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(16198,a,18056,a),flip(a)].">
      <j1 rule="hyper" parents="16198 18056"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18060">
    <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(18056(a,1),16105(a,1))].">
      <j1 rule="para" parents="18056 16105"/>
    </justification>
  </clause>

  <clause id="18061">
    <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,17891,a(flip),b,18058,a),flip(a)].">
      <j1 rule="hyper" parents="58 17891 18058"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18062">
    <literal><![CDATA[
      K(x,y \ (T(z * u,u) * w)) = K(x,y \ ((u * z) * w))
    ]]></literal>
    <justification jstring="[hyper(58,a,15326,a(flip),b,18012,a),flip(a)].">
      <j1 rule="hyper" parents="58 15326 18012"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18063">
    <literal><![CDATA[
      K(x,((y * (z / y)) / u) * w) = K(x,(T(z,y) / u) * w)
    ]]></literal>
    <justification jstring="[hyper(58,a,15480,a(flip),b,18018,a),flip(a)].">
      <j1 rule="hyper" parents="58 15480 18018"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18064">
    <literal><![CDATA[
      K(x,(T(y * z,y) / u) * w) = K(x,((T(y,z) * z) / u) * w)
    ]]></literal>
    <justification jstring="[para(4092(a,2),18063(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="4092 18063"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18065">
    <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(15131,a,18023,a)].">
      <j1 rule="hyper" parents="15131 18023"/>
    </justification>
  </clause>

  <clause id="18066">
    <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,17597,a(flip),b,18025,a)].">
      <j1 rule="hyper" parents="58 17597 18025"/>
    </justification>
  </clause>

  <clause id="18067">
    <literal><![CDATA[
      T(x,T(y * K(z,y \ u),u)) = T(x,T((u \ y) \ 1,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(15806,a,18066,a)].">
      <j1 rule="hyper" parents="15806 18066"/>
    </justification>
  </clause>

  <clause id="18068">
    <literal><![CDATA[
      T(x,T((y \ z) \ 1,u) \ y) = T(x,T(z \ y,u) \ y)
    ]]></literal>
    <justification jstring="[hyper(7716,a,18067,a),flip(a)].">
      <j1 rule="hyper" parents="7716 18067"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18069">
    <literal><![CDATA[
      T(x,T(y \ z,u) \ z) = T(x,T(z \ y,u) * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,15370,a(flip),b,18068,a),flip(a)].">
      <j1 rule="hyper" parents="58 15370 18068"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18070">
    <literal><![CDATA[
      T(x,T(y \ z,u) \ z) = T(x,z * T(y / z,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,12293,a(flip),b,18069,a),flip(a)].">
      <j1 rule="hyper" parents="320 12293 18069"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18071">
    <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,16383,a(flip),b,18070,a),flip(a)].">
      <j1 rule="hyper" parents="58 16383 18070"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18072">
    <literal><![CDATA[
      T(x,T(y / z,u) \ y) = T(x,y * T(y \ z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,16385,a(flip),b,18071,a),flip(a)].">
      <j1 rule="hyper" parents="58 16385 18071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18073">
    <literal><![CDATA[
      T(x,y * K(z,u \ (w * (v5 \ 1)))) = T(x,K(z,v5 * (w \ u)) * y)
    ]]></literal>
    <justification jstring="[hyper(15940,a,18038,a)].">
      <j1 rule="hyper" parents="15940 18038"/>
    </justification>
  </clause>

  <clause id="18074">
    <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,16743,a,b,18039,a)].">
      <j1 rule="hyper" parents="58 16743 18039"/>
    </justification>
  </clause>

  <clause id="18075">
    <literal><![CDATA[
      T(x,y / (T(z \ u,w) \ u)) = T(x,y / (u \ T(z * u,w)))
    ]]></literal>
    <justification jstring="[hyper(58,a,17916,a(flip),b,18047,a),flip(a)].">
      <j1 rule="hyper" parents="58 17916 18047"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18076">
    <literal><![CDATA[
      T(x,y / ((z \ T(u,w)) \ u)) = T(x,y * T(z \ K(w,u),u))
    ]]></literal>
    <justification jstring="[para(16221(a,1),18074(a,1,2,2))].">
      <j1 rule="para" parents="16221 18074"/>
    </justification>
  </clause>

  <clause id="18077">
    <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,16762,a(flip),b,18076,a),flip(a)].">
      <j1 rule="hyper" parents="58 16762 18076"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18078">
    <literal><![CDATA[
      L(x,K(y,z) * u,z * y) = L(x,u,z * y)
    ]]></literal>
    <justification jstring="[hyper(14162,a,17242,a)].">
      <j1 rule="hyper" parents="14162 17242"/>
    </justification>
  </clause>

  <clause id="18080">
    <literal><![CDATA[
      L(x,K(y,z / y) * u,z) = L(x,u,(z / y) * y)
    ]]></literal>
    <justification jstring="[para(7(a,1),18078(a,1,3))].">
      <j1 rule="para" parents="7 18078"/>
    </justification>
  </clause>

  <clause id="18081">
    <literal><![CDATA[
      L(x,K(y,y \ z) * u,z) = L(x,u,(z / y) * y)
    ]]></literal>
    <justification jstring="[para(4912(a,1),18080(a,1,2,1))].">
      <j1 rule="para" parents="4912 18080"/>
    </justification>
  </clause>

  <clause id="18082">
    <literal><![CDATA[
      L(x,K(y,z) * u,z) = L(x,u,(z / y) * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,13261,a(flip),b,18081,a)].">
      <j1 rule="hyper" parents="58 13261 18081"/>
    </justification>
  </clause>

  <clause id="18083">
    <literal><![CDATA[
      L(x,K(y,z) * u,z) = L(x,u,z)
    ]]></literal>
    <justification jstring="[para(7(a,1),18082(a,2,3))].">
      <j1 rule="para" parents="7 18082"/>
    </justification>
  </clause>

  <clause id="18084">
    <literal><![CDATA[
      L(x,K(y,z) * u,y) = L(x,u,y)
    ]]></literal>
    <justification jstring="[para(5133(a,1),18083(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5133 18083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18089">
    <literal><![CDATA[
      L(x,y \ K(z,u),z) = L(x,y \ 1,z)
    ]]></literal>
    <justification jstring="[para(13881(a,1),18084(a,1,2))].">
      <j1 rule="para" parents="13881 18084"/>
    </justification>
  </clause>

  <clause id="18090">
    <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(6116(a,1),17504(a,2,1,2))].">
      <j1 rule="para" parents="6116 17504"/>
    </justification>
  </clause>

  <clause id="18091">
    <literal><![CDATA[
      K(x,y \ (z * (u * K(w,v5)))) = K(x,K(v5,w) * (y \ (z * u)))
    ]]></literal>
    <justification jstring="[hyper(17595,a,17622,a),flip(a)].">
      <j1 rule="hyper" parents="17595 17622"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18092">
    <literal><![CDATA[
      K(x,y \ (z * (u * K(w,v5)))) = K(x,(y \ (z * u)) * K(v5,w))
    ]]></literal>
    <justification jstring="[hyper(17594,a,17622,a),flip(a)].">
      <j1 rule="hyper" parents="17594 17622"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18094">
    <literal><![CDATA[
      K(x,y \ (z * (u * K(w,v5)))) = K(x,K(w,v5) * (y \ (z * u)))
    ]]></literal>
    <justification jstring="[hyper(320,a,15130,a,b,18091,a),flip(a)].">
      <j1 rule="hyper" parents="320 15130 18091"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18095">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ (w * (v5 \ z)))) = K(x,u \ (w * (v5 \ T(z,y))))
    ]]></literal>
    <justification jstring="[para(13699(a,1),18091(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="13699 18091"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18096">
    <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,16595,a(flip),b,18092,a),flip(a)].">
      <j1 rule="hyper" parents="58 16595 18092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18097">
    <literal><![CDATA[
      K(x,K(y,T(z,u)) * (w \ (v5 * u))) = K(x,w \ (v5 * (K(y,z) * u)))
    ]]></literal>
    <justification jstring="[para(7179(a,1),18094(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="7179 18094"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18098">
    <literal><![CDATA[
      K(x,T(y,z) \ (u * (w \ y))) = K(x,y \ (u * (w \ T(y,z))))
    ]]></literal>
    <justification jstring="[para(5131(a,1),18095(a,1,2))].">
      <j1 rule="para" parents="5131 18095"/>
    </justification>
  </clause>

  <clause id="18099">
    <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),18096(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="105 18096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18100">
    <literal><![CDATA[
      K(x,y \ ((K(z,u) * w) * v5)) = K(x,K(z,u) * (y \ (w * v5)))
    ]]></literal>
    <justification jstring="[hyper(320,a,15823,a,b,18099,a),flip(a)].">
      <j1 rule="hyper" parents="320 15823 18099"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18101">
    <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),18099(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13 18099"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18102">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ ((y * w) * v5))) = K(x,u \ ((T(y,z) * w) * v5))
    ]]></literal>
    <justification jstring="[para(4781(a,1),18100(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="4781 18100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18103">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ ((y / z) * w))) = K(x,u \ ((T(y,z) / z) * w))
    ]]></literal>
    <justification jstring="[para(5249(a,1),18100(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5249 18100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18105">
    <literal><![CDATA[
      K(x,y \ (z * (K(u,w) * v5))) = K(x,K(w,u) * (y \ (z * v5)))
    ]]></literal>
    <justification jstring="[hyper(16129,a,18097,a),flip(a)].">
      <j1 rule="hyper" parents="16129 18097"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18106">
    <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(18097(a,1),16129(a,1))].">
      <j1 rule="para" parents="18097 16129"/>
    </justification>
  </clause>

  <clause id="18108">
    <literal><![CDATA[
      K(x,y \ ((T(z,u) / u) * w)) = K(x,y \ ((u \ z) * w))
    ]]></literal>
    <justification jstring="[hyper(58,a,18024,a(flip),b,18103,a),flip(a)].">
      <j1 rule="hyper" parents="58 18024 18103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18109">
    <literal><![CDATA[
      K(x,T(y / (z \ u),x) * (w \ K(z,u))) = K(x,(y / (u / z)) / w)
    ]]></literal>
    <justification jstring="[hyper(17958,a,17400,a)].">
      <j1 rule="hyper" parents="17958 17400"/>
    </justification>
  </clause>

  <clause id="18110">
    <literal><![CDATA[
      K(x,(y / (z \ u)) * (w \ K(z,u))) = K(x,(y / (u / z)) / w)
    ]]></literal>
    <justification jstring="[hyper(8401,a,18109,a)].">
      <j1 rule="hyper" parents="8401 18109"/>
    </justification>
  </clause>

  <clause id="18111">
    <literal><![CDATA[
      K(x,(y / (T(z,u) \ u)) / w) = K(x,(y / (u / z)) / w)
    ]]></literal>
    <justification jstring="[hyper(58,a,17422,a(flip),b,18110,a)].">
      <j1 rule="hyper" parents="58 17422 18110"/>
    </justification>
  </clause>

  <clause id="18112">
    <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,17425,a(flip),b,17436,a),flip(a)].">
      <j1 rule="hyper" parents="320 17425 17436"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18113">
    <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(17712,a,18112,a)].">
      <j1 rule="hyper" parents="17712 18112"/>
    </justification>
  </clause>

  <clause id="18114">
    <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,17983,a(flip),b,18113,a),flip(a)].">
      <j1 rule="hyper" parents="58 17983 18113"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18115">
    <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,18070,a(flip),b,18114,a),flip(a)].">
      <j1 rule="hyper" parents="320 18070 18114"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18116">
    <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(17513(a,2),14061(a,1))].">
      <j1 rule="para" parents="17513 14061"/>
    </justification>
  </clause>

  <clause id="18117">
    <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(18116,a,16927,a)].">
      <j1 rule="hyper" parents="18116 16927"/>
    </justification>
  </clause>

  <clause id="18118">
    <literal><![CDATA[
      K(x,y / T((K(z,u) * w) \ v5,w)) = K(x,y / ((K(z,u) \ v5) / w))
    ]]></literal>
    <justification jstring="[hyper(15997,a,17565,a)].">
      <j1 rule="hyper" parents="15997 17565"/>
    </justification>
  </clause>

  <clause id="18119">
    <literal><![CDATA[
      K(x,y / ((K(z,u) \ w) / v5)) = K(x,y / (w / (K(z,u) * v5)))
    ]]></literal>
    <justification jstring="[hyper(58,a,18054,a(flip),b,18118,a),flip(a)].">
      <j1 rule="hyper" parents="58 18054 18118"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18120">
    <literal><![CDATA[
      K(x,y / ((K(z,u) * w) / v5)) = K(x,y / (w / (K(u,z) * v5)))
    ]]></literal>
    <justification jstring="[para(5130(a,1),18119(a,1,2,2,1))].">
      <j1 rule="para" parents="5130 18119"/>
    </justification>
  </clause>

  <clause id="18121">
    <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(15174,a,17574,a)].">
      <j1 rule="hyper" parents="15174 17574"/>
    </justification>
  </clause>

  <clause id="18123">
    <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,17610,a(flip),b,18121,a)].">
      <j1 rule="hyper" parents="58 17610 18121"/>
    </justification>
  </clause>

  <clause id="18124">
    <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(6469(a,1),18121(a,1,2,2,2,1))].">
      <j1 rule="para" parents="6469 18121"/>
    </justification>
  </clause>

  <clause id="18125">
    <literal><![CDATA[
      K(x,K(y,z) * (((z * y) / u) * w)) = K(x,(((y * z) / u) \ 1) \ w)
    ]]></literal>
    <justification jstring="[hyper(16129,a,17656,a)].">
      <j1 rule="hyper" parents="16129 17656"/>
    </justification>
  </clause>

  <clause id="18126">
    <literal><![CDATA[
      K(x,(((y * z) / u) \ 1) \ w) = K(x,((T(z,y) * y) / u) * w)
    ]]></literal>
    <justification jstring="[hyper(58,a,17629,a(flip),b,18125,a),flip(a)].">
      <j1 rule="hyper" parents="58 17629 18125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18127">
    <literal><![CDATA[
      K(x,((T(y,z) * z) / u) * w) = K(x,((z * y) / u) * w)
    ]]></literal>
    <justification jstring="[hyper(14008,a,18126,a),flip(a)].">
      <j1 rule="hyper" parents="14008 18126"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18128">
    <literal><![CDATA[
      K(x,(T(y * z,y) / u) * w) = K(x,((z * y) / u) * w)
    ]]></literal>
    <justification jstring="[hyper(58,a,18064,a,b,18127,a)].">
      <j1 rule="hyper" parents="58 18064 18127"/>
    </justification>
  </clause>

  <clause id="18129">
    <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(17693(a,2),16079(a,1))].">
      <j1 rule="para" parents="17693 16079"/>
    </justification>
  </clause>

  <clause id="18131">
    <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,18102,a(flip),b,17759,a)].">
      <j1 rule="hyper" parents="58 18102 17759"/>
    </justification>
  </clause>

  <clause id="18132">
    <literal><![CDATA[
      K(x,y \ ((T(z,u) * u) * w)) = K(x,y \ ((u * z) * w))
    ]]></literal>
    <justification jstring="[para(178(a,1),18131(a,1,2,2,1,1,2))].">
      <j1 rule="para" parents="178 18131"/>
    </justification>
  </clause>

  <clause id="18133">
    <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(16194,a,17774,a),flip(a)].">
      <j1 rule="hyper" parents="16194 17774"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18135">
    <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(16579(a,2),17850(a,1,2,2))].">
      <j1 rule="para" parents="16579 17850"/>
    </justification>
  </clause>

  <clause id="18136">
    <literal><![CDATA[
      K(x,y \ (z / T(u,T(w,v5)))) = K(x,y \ (z / T(u,w)))
    ]]></literal>
    <justification jstring="[hyper(320,a,16156,a(flip),b,17932,a),flip(a)].">
      <j1 rule="hyper" parents="320 16156 17932"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18137">
    <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,18046,a(flip),b,17941,a)].">
      <j1 rule="hyper" parents="58 18046 17941"/>
    </justification>
  </clause>

  <clause id="18138">
    <literal><![CDATA[
      T(x,(T(y \ z,y) / u) \ w) = T(x,((z / y) / u) \ w)
    ]]></literal>
    <justification jstring="[hyper(58,a,17940,a(flip),b,18137,a),flip(a)].">
      <j1 rule="hyper" parents="58 17940 18137"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18139">
    <literal><![CDATA[
      T(x,((((y \ z) \ z) \ z) / u) \ w) = T(x,((z / y) / u) \ w)
    ]]></literal>
    <justification jstring="[para(4239(a,1),18138(a,1,2,1,1))].">
      <j1 rule="para" parents="4239 18138"/>
    </justification>
  </clause>

  <clause id="18140">
    <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,15270,a(flip),b,17985,a)].">
      <j1 rule="hyper" parents="58 15270 17985"/>
    </justification>
  </clause>

  <clause id="18141">
    <literal><![CDATA[
      K(x,y \ ((z / (T(u,z) \ 1)) * w)) = K(x,y \ (((u \ 1) \ z) * w))
    ]]></literal>
    <justification jstring="[hyper(320,a,13166,a(flip),b,18022,a),flip(a)].">
      <j1 rule="hyper" parents="320 13166 18022"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18142">
    <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,17782,a,b,18141,a)].">
      <j1 rule="hyper" parents="58 17782 18141"/>
    </justification>
  </clause>

  <clause id="18143">
    <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(13822(a,1),18050(a,2,2,1))].">
      <j1 rule="para" parents="13822 18050"/>
    </justification>
  </clause>

  <clause id="18144">
    <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(4307(a,1),18143(a,2,2,1,2))].">
      <j1 rule="para" parents="4307 18143"/>
    </justification>
  </clause>

  <clause id="18145">
    <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,13237,a(flip),b,18144,a),flip(a)].">
      <j1 rule="hyper" parents="320 13237 18144"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18146">
    <literal><![CDATA[
      T(x,T(T(y * z,y) \ (y * y),u)) = T(x,T(y / z,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,12747,a(flip),b,18145,a),flip(a)].">
      <j1 rule="hyper" parents="320 12747 18145"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18147">
    <literal><![CDATA[
      T(x,T((y * z) \ (z * z),u)) = T(x,T(z / y,u))
    ]]></literal>
    <justification jstring="[hyper(13236,a,18146,a)].">
      <j1 rule="hyper" parents="13236 18146"/>
    </justification>
  </clause>

  <clause id="18148">
    <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(439,a,18147,a,b,13907,a)].">
      <j1 rule="hyper" parents="439 18147 13907"/>
    </justification>
  </clause>

  <clause id="18149">
    <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,15480,a(flip),b,18123,a)].">
      <j1 rule="hyper" parents="58 15480 18123"/>
    </justification>
  </clause>

  <clause id="18150">
    <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,15162,a(flip),b,18133,a)].">
      <j1 rule="hyper" parents="58 15162 18133"/>
    </justification>
  </clause>

  <clause id="18151">
    <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,16330,a(flip),b,18135,a)].">
      <j1 rule="hyper" parents="58 16330 18135"/>
    </justification>
  </clause>

  <clause id="18152">
    <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,17641,a(flip),b,18140,a),flip(a)].">
      <j1 rule="hyper" parents="58 17641 18140"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18153">
    <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,18115,a,b,18152,a)].">
      <j1 rule="hyper" parents="58 18115 18152"/>
    </justification>
  </clause>

  <clause id="18154">
    <literal><![CDATA[
      T(x,T(T(y \ z,u) \ z,w)) = T(x,T(z * T(y / z,u),w))
    ]]></literal>
    <justification jstring="[hyper(15804,a,18153,a)].">
      <j1 rule="hyper" parents="15804 18153"/>
    </justification>
  </clause>

  <clause id="18156">
    <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,18115,a(flip),b,18154,a),flip(a)].">
      <j1 rule="hyper" parents="58 18115 18154"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18158">
    <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(18156(a,1),15804(a,1))].">
      <j1 rule="para" parents="18156 15804"/>
    </justification>
  </clause>

  <clause id="18159">
    <literal><![CDATA[
      K(x,T(y * z,x) * (u \ K(w,v5))) = K(x,(y * (z * K(w,v5))) / u)
    ]]></literal>
    <justification jstring="[hyper(17986,a,17399,a)].">
      <j1 rule="hyper" parents="17986 17399"/>
    </justification>
  </clause>

  <clause id="18160">
    <literal><![CDATA[
      K(x,(y * (z * K(u,w))) / v5) = K(x,(y * z) * (v5 \ K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(8401,a,18159,a),flip(a)].">
      <j1 rule="hyper" parents="8401 18159"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18161">
    <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,16594,a(flip),b,18160,a),flip(a)].">
      <j1 rule="hyper" parents="58 16594 18160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18162">
    <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),18161(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="105 18161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18163">
    <literal><![CDATA[
      (x / (y * x)) * ((y * x) * K(z,u)) = x * K(z,L(u,x,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(5802,a,17408,a)].">
      <j1 rule="hyper" parents="5802 17408"/>
    </justification>
  </clause>

  <clause id="18164">
    <literal><![CDATA[
      K(x,y / (z \ a(u \ 1,u,z))) = K(x,a(u \ 1,u,z) \ (y * z))
    ]]></literal>
    <justification jstring="[hyper(17460,a,17559,a),flip(a)].">
      <j1 rule="hyper" parents="17460 17559"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18165">
    <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(18164(a,1),18004(a,1))].">
      <j1 rule="para" parents="18164 18004"/>
    </justification>
  </clause>

  <clause id="18166">
    <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,17981,a(flip),b,17646,a)].">
      <j1 rule="hyper" parents="320 17981 17646"/>
    </justification>
  </clause>

  <clause id="18167">
    <literal><![CDATA[
      K(x,R(y,y \ (x * z),y) / z) = K(x,z \ T(y,z * x))
    ]]></literal>
    <justification jstring="[hyper(7391,a,18166,a),flip(a)].">
      <j1 rule="hyper" parents="7391 18166"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18168">
    <literal><![CDATA[
      K(x,y \ T(z,y * x)) = K(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(13062,a,18167,a),flip(a)].">
      <j1 rule="hyper" parents="13062 18167"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18170">
    <literal><![CDATA[
      K(x,(1 / y) \ T(T(z,y),(1 / y) * x)) = K(x,z / (K(y,z) / y))
    ]]></literal>
    <justification jstring="[para(13828(a,1),18168(a,2,2))].">
      <j1 rule="para" parents="13828 18168"/>
    </justification>
  </clause>

  <clause id="18171">
    <literal><![CDATA[
      K(x,(1 / y) \ T(T(z,y),y \ x)) = K(x,z / (K(y,z) / y))
    ]]></literal>
    <justification jstring="[para(13801(a,1),18170(a,1,2,2))].">
      <j1 rule="para" parents="13801 18170"/>
    </justification>
  </clause>

  <clause id="18172">
    <literal><![CDATA[
      K(x,y / (K(z,y) / z)) = K(x,z * T(T(y,z),z \ x))
    ]]></literal>
    <justification jstring="[hyper(14070,a,18171,a),flip(a)].">
      <j1 rule="hyper" parents="14070 18171"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18173">
    <literal><![CDATA[
      K(x,y / (K(z,y) / z)) = K(x,T(y,z \ x) * z)
    ]]></literal>
    <justification jstring="[para(236(a,1),18172(a,2,2))].">
      <j1 rule="para" parents="236 18172"/>
    </justification>
  </clause>

  <clause id="18174">
    <literal><![CDATA[
      K(x,T(y,z \ x) * z) = K(x,y * (z * K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(18007,a,18173,a),flip(a)].">
      <j1 rule="hyper" parents="18007 18173"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18175">
    <literal><![CDATA[
      K(x,T(y,z \ x) * z) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(320,a,12292,a(flip),b,18174,a),flip(a)].">
      <j1 rule="hyper" parents="320 12292 18174"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18176">
    <literal><![CDATA[
      K(x,T(y,(x * z) \ x) * (x * z)) = K(x,(z * x) * y)
    ]]></literal>
    <justification jstring="[hyper(320,a,7556,a,b,18175,a),flip(a)].">
      <j1 rule="hyper" parents="320 7556 18175"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18177">
    <literal><![CDATA[
      K(x,T(y,z \ 1) * (x * z)) = K(x,(z * x) * y)
    ]]></literal>
    <justification jstring="[para(6174(a,1),18176(a,1,2,1))].">
      <j1 rule="para" parents="6174 18176"/>
    </justification>
  </clause>

  <clause id="18178">
    <literal><![CDATA[
      K(x,T(y,z) * (x * z)) = K(x,(z * x) * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,15391,a(flip),b,18177,a)].">
      <j1 rule="hyper" parents="58 15391 18177"/>
    </justification>
  </clause>

  <clause id="18180">
    <literal><![CDATA[
      K(x,y * (T(z,y) * x)) = K(x,(z * x) * y)
    ]]></literal>
    <justification jstring="[hyper(15973,a,18178,a)].">
      <j1 rule="hyper" parents="15973 18178"/>
    </justification>
  </clause>

  <clause id="18181">
    <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(18180(a,1),7916(a,1,2,2))].">
      <j1 rule="para" parents="18180 7916"/>
    </justification>
  </clause>

  <clause id="18182">
    <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(10840(a,1),17653(a,1,2,1))].">
      <j1 rule="para" parents="10840 17653"/>
    </justification>
  </clause>

  <clause id="18183">
    <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(10840(a,1),17777(a,1,2,2,2))].">
      <j1 rule="para" parents="10840 17777"/>
    </justification>
  </clause>

  <clause id="18184">
    <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(11009(a,1),17778(a,1,2))].">
      <j1 rule="para" parents="11009 17778"/>
    </justification>
  </clause>

  <clause id="18185">
    <literal><![CDATA[
      K(x,y * (z / T(u,K(w,v5) * v6))) = K(x,y * (z / T(u,v6)))
    ]]></literal>
    <justification jstring="[hyper(16257,a,18184,a),flip(a)].">
      <j1 rule="hyper" parents="16257 18184"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18186">
    <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,13142,a(flip),b,18185,a),flip(a)].">
      <j1 rule="hyper" parents="58 13142 18185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18187">
    <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,17679,a(flip),b,18186,a)].">
      <j1 rule="hyper" parents="58 17679 18186"/>
    </justification>
  </clause>

  <clause id="18188">
    <literal><![CDATA[
      K(x,y * (z \ (K(u,w) * v5))) = K(x,y * (K(u,w) * (z \ v5)))
    ]]></literal>
    <justification jstring="[hyper(58,a,13215,a(flip),b,18187,a),flip(a)].">
      <j1 rule="hyper" parents="58 13215 18187"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18189">
    <literal><![CDATA[
      K(x,y * (K(z,u) * (w \ (v5 \ 1)))) = K(x,y * (w \ (v5 \ K(z,u))))
    ]]></literal>
    <justification jstring="[hyper(16256,a,18188,a),flip(a)].">
      <j1 rule="hyper" parents="16256 18188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18190">
    <literal><![CDATA[
      K(x,y * (z \ (u * K(w,v5)))) = K(x,y * (K(w,v5) * (z \ u)))
    ]]></literal>
    <justification jstring="[hyper(16254,a,18188,a)].">
      <j1 rule="hyper" parents="16254 18188"/>
    </justification>
  </clause>

  <clause id="18191">
    <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,17731,a(flip),b,18190,a)].">
      <j1 rule="hyper" parents="58 17731 18190"/>
    </justification>
  </clause>

  <clause id="18192">
    <literal><![CDATA[
      K(x,y * ((T(z,u) \ u) \ (w \ K(u,z)))) = K(x,y * ((z \ u) \ (w \ 1)))
    ]]></literal>
    <justification jstring="[para(13288(a,1),18189(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="13288 18189"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18193">
    <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),17909(a,1,2))].">
      <j1 rule="para" parents="178 17909"/>
    </justification>
  </clause>

  <clause id="18194">
    <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),18158(a,1,2,2,1,1,2))].">
      <j1 rule="para" parents="104 18158"/>
    </justification>
  </clause>

  <clause id="18195">
    <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(18140(a,2),18158(a,1))].">
      <j1 rule="para" parents="18140 18158"/>
    </justification>
  </clause>

  <clause id="18196">
    <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(17638,a,18182,a)].">
      <j1 rule="hyper" parents="17638 18182"/>
    </justification>
  </clause>

  <clause id="18197">
    <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(18196(a,1),17591(a,1))].">
      <j1 rule="para" parents="18196 17591"/>
    </justification>
  </clause>

  <clause id="18198">
    <literal><![CDATA[
      K(x,y * (z * ((u / w) * K(w,v5)))) = K(x,y * (z * (u / T(w,v5))))
    ]]></literal>
    <justification jstring="[para(10910(a,1),18183(a,1,2,2))].">
      <j1 rule="para" parents="10910 18183"/>
    </justification>
  </clause>

  <clause id="18199">
    <literal><![CDATA[
      K(x,T(y,z) * (u * (w / y))) = K(x,y * (u * (w / T(y,z))))
    ]]></literal>
    <justification jstring="[hyper(17756,a,18198,a)].">
      <j1 rule="hyper" parents="17756 18198"/>
    </justification>
  </clause>

  <clause id="18200">
    <literal><![CDATA[
      K(x,y * (z * (u / T(y,u * z)))) = K(x,(z * (u / y)) * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,16605,a(flip),b,18199,a),flip(a)].">
      <j1 rule="hyper" parents="58 16605 18199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18201">
    <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(17614(a,2),18195(a,1))].">
      <j1 rule="para" parents="17614 18195"/>
    </justification>
  </clause>

  <clause id="18202">
    <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(16802(a,2),18201(a,1))].">
      <j1 rule="para" parents="16802 18201"/>
    </justification>
  </clause>

  <clause id="18203">
    <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(16211(a,1),18202(a,1))].">
      <j1 rule="para" parents="16211 18202"/>
    </justification>
  </clause>

  <clause id="18204">
    <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(12311(a,2),18203(a,1))].">
      <j1 rule="para" parents="12311 18203"/>
    </justification>
  </clause>

  <clause id="18205">
    <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(16770(a,1),18204(a,1))].">
      <j1 rule="para" parents="16770 18204"/>
    </justification>
  </clause>

  <clause id="18206">
    <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(6335(a,1),17447(a,1,2,2,1))].">
      <j1 rule="para" parents="6335 17447"/>
    </justification>
  </clause>

  <clause id="18207">
    <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(17620(a,1),17466(a,1))].">
      <j1 rule="para" parents="17620 17466"/>
    </justification>
  </clause>

  <clause id="18208">
    <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(5130(a,1),17561(a,2,2,2,1,2))].">
      <j1 rule="para" parents="5130 17561"/>
    </justification>
  </clause>

  <clause id="18209">
    <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,13854,a(flip),b,17631,a),flip(a)].">
      <j1 rule="hyper" parents="320 13854 17631"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18210">
    <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(18209(a,1),18005(a,1))].">
      <j1 rule="para" parents="18209 18005"/>
    </justification>
  </clause>

  <clause id="18211">
    <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(18149(a,1),18210(a,1))].">
      <j1 rule="para" parents="18149 18210"/>
    </justification>
  </clause>

  <clause id="18212">
    <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(15360,a,17664,a)].">
      <j1 rule="hyper" parents="15360 17664"/>
    </justification>
  </clause>

  <clause id="18213">
    <literal><![CDATA[
      K(x,(K(y \ z,z) * u) / w) = K(x,u * (w \ K(z,y)))
    ]]></literal>
    <justification jstring="[hyper(58,a,18065,a(flip),b,18212,a),flip(a)].">
      <j1 rule="hyper" parents="58 18065 18212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18214">
    <literal><![CDATA[
      K(x,y * (z \ K(u \ w,w))) = K(x,y * (z \ K(w,u)))
    ]]></literal>
    <justification jstring="[hyper(17397,a,18213,a)].">
      <j1 rule="hyper" parents="17397 18213"/>
    </justification>
  </clause>

  <clause id="18215">
    <literal><![CDATA[
      K(x,y * (z \ K(u,w \ u))) = K(x,y * (z \ K(w,u)))
    ]]></literal>
    <justification jstring="[para(6293(a,1),18214(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="6293 18214"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18216">
    <literal><![CDATA[
      K(x,(y \ (z * u)) * (u \ K(z,y \ z))) = K(x,T((y \ (z * u)) / u,z))
    ]]></literal>
    <justification jstring="[hyper(16196,a,17686,a)].">
      <j1 rule="hyper" parents="16196 17686"/>
    </justification>
  </clause>

  <clause id="18217">
    <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,18215,a(flip),b,18216,a)].">
      <j1 rule="hyper" parents="58 18215 18216"/>
    </justification>
  </clause>

  <clause id="18218">
    <literal><![CDATA[
      K(x,(T(y,z) \ (z * u)) / u) = K(x,T((y \ (z * u)) / u,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,17697,a(flip),b,18217,a)].">
      <j1 rule="hyper" parents="58 17697 18217"/>
    </justification>
  </clause>

  <clause id="18219">
    <literal><![CDATA[
      K(x,(y \ (z * u)) * (u \ K(y,y \ z))) = K(x,T((y \ (z * u)) / u,y))
    ]]></literal>
    <justification jstring="[hyper(16196,a,17687,a)].">
      <j1 rule="hyper" parents="16196 17687"/>
    </justification>
  </clause>

  <clause id="18220">
    <literal><![CDATA[
      K(x,(y \ (z * u)) * (u \ K(z,y))) = K(x,T((y \ (z * u)) / u,y))
    ]]></literal>
    <justification jstring="[hyper(17987,a,18219,a)].">
      <j1 rule="hyper" parents="17987 18219"/>
    </justification>
  </clause>

  <clause id="18221">
    <literal><![CDATA[
      K(x,T((y \ (z * u)) / u,y)) = K(x,(T(y,z) \ (z * u)) / u)
    ]]></literal>
    <justification jstring="[hyper(58,a,17424,a(flip),b,18220,a),flip(a)].">
      <j1 rule="hyper" parents="58 17424 18220"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18222">
    <literal><![CDATA[
      K(x,T((y \ (z * u)) / u,z)) = K(x,T((y \ (z * u)) / u,y))
    ]]></literal>
    <justification jstring="[hyper(320,a,18218,a(flip),b,18221,a)].">
      <j1 rule="hyper" parents="320 18218 18221"/>
    </justification>
  </clause>

  <clause id="18223">
    <literal><![CDATA[
      K(x,y * ((z \ (u * y)) \ K(u,u \ z))) = K(x,T(y / (z \ (u * y)),u))
    ]]></literal>
    <justification jstring="[hyper(16196,a,17688,a)].">
      <j1 rule="hyper" parents="16196 17688"/>
    </justification>
  </clause>

  <clause id="18224">
    <literal><![CDATA[
      K(x,y * ((z \ (u * y)) \ K(z,u))) = K(x,T(y / (z \ (u * y)),u))
    ]]></literal>
    <justification jstring="[hyper(17987,a,18223,a)].">
      <j1 rule="hyper" parents="17987 18223"/>
    </justification>
  </clause>

  <clause id="18225">
    <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(18224(a,1),14077(a,1))].">
      <j1 rule="para" parents="18224 14077"/>
    </justification>
  </clause>

  <clause id="18226">
    <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,13214,a(flip),b,17758,a),flip(a)].">
      <j1 rule="hyper" parents="320 13214 17758"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18227">
    <literal><![CDATA[
      K(x,y * (z * K(u \ (w \ y),w * u))) = K(x,T(y,u * w) * z)
    ]]></literal>
    <justification jstring="[para(13965(a,1),18226(a,1,2,2,2))].">
      <j1 rule="para" parents="13965 18226"/>
    </justification>
  </clause>

  <clause id="18228">
    <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(18197,a,17785,a)].">
      <j1 rule="hyper" parents="18197 17785"/>
    </justification>
  </clause>

  <clause id="18229">
    <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(4777(a,1),18117(a,1,1,2,1))].">
      <j1 rule="para" parents="4777 18117"/>
    </justification>
  </clause>

  <clause id="18230">
    <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(17388(a,1),18229(a,1,1))].">
      <j1 rule="para" parents="17388 18229"/>
    </justification>
  </clause>

  <clause id="18231">
    <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,13170,a(flip),b,18230,a)].">
      <j1 rule="hyper" parents="58 13170 18230"/>
    </justification>
  </clause>

  <clause id="18232">
    <literal><![CDATA[
      K(x \ T(y,K(z,u) * w),v5) = K(x \ T(y,w),v5)
    ]]></literal>
    <justification jstring="[hyper(16059,a,18231,a),flip(a)].">
      <j1 rule="hyper" parents="16059 18231"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18233">
    <literal><![CDATA[
      K((x * y) \ T(x,z),u) = K(y \ K(x,z * K(w,v5)),u)
    ]]></literal>
    <justification jstring="[hyper(16161,a,18232,a),flip(a)].">
      <j1 rule="hyper" parents="16161 18232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18235">
    <literal><![CDATA[
      K(x \ K(y,z * K(u,w)),v5) = K(x \ K(y,z),v5)
    ]]></literal>
    <justification jstring="[hyper(6712,a,18233,a),flip(a)].">
      <j1 rule="hyper" parents="6712 18233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18236">
    <literal><![CDATA[
      K(x \ K(y \ K(z,u),w),v5) = K(x \ K(w,y),v5)
    ]]></literal>
    <justification jstring="[hyper(58,a,18019,a,b,18235,a)].">
      <j1 rule="hyper" parents="58 18019 18235"/>
    </justification>
  </clause>

  <clause id="18237">
    <literal><![CDATA[
      K((x / y) \ K(y,z),u) = K(T(y,z \ K(w,v5)) / x,u)
    ]]></literal>
    <justification jstring="[hyper(16381,a,18236,a),flip(a)].">
      <j1 rule="hyper" parents="16381 18236"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18239">
    <literal><![CDATA[
      K(T(x,y \ K(z,u)) / w,v5) = K(T(x,y) / w,v5)
    ]]></literal>
    <justification jstring="[hyper(16380,a,18237,a),flip(a)].">
      <j1 rule="hyper" parents="16380 18237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18240">
    <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,16739,a(flip),b,18239,a),flip(a)].">
      <j1 rule="hyper" parents="58 16739 18239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18241">
    <literal><![CDATA[
      K(T(x,y \ T(z,u)) / w,v5) = K(T(x,z \ y) / w,v5)
    ]]></literal>
    <justification jstring="[para(6558(a,1),18239(a,1,1,1))].">
      <j1 rule="para" parents="6558 18239"/>
    </justification>
  </clause>

  <clause id="18242">
    <literal><![CDATA[
      K(x,T(y,z \ T(u,w)) / v5) = (v6 * K(T(y,u \ z) / v5,x)) \ v6
    ]]></literal>
    <justification jstring="[para(18241(a,1),6338(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="18241 6338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18244">
    <literal><![CDATA[
      K(((x * y) * (1 / y)) / z,u) = K(L(x,y,y \ 1) / z,u)
    ]]></literal>
    <justification jstring="[para(2340(a,1),18240(a,1,1,1))].">
      <j1 rule="para" parents="2340 18240"/>
    </justification>
  </clause>

  <clause id="18245">
    <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(18244(a,1),13598(a,1,2,2))].">
      <j1 rule="para" parents="18244 13598"/>
    </justification>
  </clause>

  <clause id="18246">
    <literal><![CDATA[
      K(x,T(y,z \ T(u,w)) / v5) = K(x,T(y,u \ z) / v5)
    ]]></literal>
    <justification jstring="[hyper(320,a,15662,a(flip),b,18242,a),flip(a)].">
      <j1 rule="hyper" parents="320 15662 18242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18247">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ z)) / w) = K(x,T(y,u) / w)
    ]]></literal>
    <justification jstring="[para(7107(a,1),18246(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7107 18246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18248">
    <literal><![CDATA[
      K(x,T(T(y,z) \ u,z * y)) = K(x,T(u,z) / y)
    ]]></literal>
    <justification jstring="[hyper(58,a,16616,a,b,18247,a)].">
      <j1 rule="hyper" parents="58 16616 18247"/>
    </justification>
  </clause>

  <clause id="18250">
    <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(5592(a,1),18248(a,1,2,1))].">
      <j1 rule="para" parents="5592 18248"/>
    </justification>
  </clause>

  <clause id="18251">
    <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(15996,a,18181,a)].">
      <j1 rule="hyper" parents="15996 18181"/>
    </justification>
  </clause>

  <clause id="18252">
    <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(17604,a,18251,a)].">
      <j1 rule="hyper" parents="17604 18251"/>
    </justification>
  </clause>

  <clause id="18253">
    <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,17569,a(flip),b,18252,a)].">
      <j1 rule="hyper" parents="58 17569 18252"/>
    </justification>
  </clause>

  <clause id="18254">
    <literal><![CDATA[
      K(x,y * ((y \ T(z * y,u)) * u)) = K(x,T(y * (T(z,y) * u),u))
    ]]></literal>
    <justification jstring="[para(14085(a,1),18253(a,1,2,2))].">
      <j1 rule="para" parents="14085 18253"/>
    </justification>
  </clause>

  <clause id="18255">
    <literal><![CDATA[
      K(x,T(y * (T(z,y) * u),u)) = K(x,(u * ((z * y) / y)) * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,16824,a(flip),b,18254,a),flip(a)].">
      <j1 rule="hyper" parents="58 16824 18254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18256">
    <literal><![CDATA[
      K(x,T(y * (T(z,y) * u),u)) = K(x,(u * z) * y)
    ]]></literal>
    <justification jstring="[para(6(a,1),18255(a,2,2,1,2))].">
      <j1 rule="para" parents="6 18255"/>
    </justification>
  </clause>

  <clause id="18257">
    <literal><![CDATA[
      K(x,L(y,z,u) * (z * u)) = K(x,(y * z) * u)
    ]]></literal>
    <justification jstring="[hyper(17286,a,18256,a)].">
      <j1 rule="hyper" parents="17286 18256"/>
    </justification>
  </clause>

  <clause id="18258">
    <literal><![CDATA[
      T(x,L(y,z,u) * (z * u)) = T(x,(y * z) * u)
    ]]></literal>
    <justification jstring="[hyper(118,a,18257,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 18257 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18259">
    <literal><![CDATA[
      K(x,((y * z) \ (z * u)) * (y * z)) = K(x,((T(y,z) \ u) * y) * z)
    ]]></literal>
    <justification jstring="[para(11188(a,1),18257(a,1,2,1))].">
      <j1 rule="para" parents="11188 18257"/>
    </justification>
  </clause>

  <clause id="18260">
    <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(4948(a,1),18258(a,1,2,2))].">
      <j1 rule="para" parents="4948 18258"/>
    </justification>
  </clause>

  <clause id="18261">
    <literal><![CDATA[
      K(x,((T(y,z) \ u) * y) * z) = K(x,T(z * u,y * z))
    ]]></literal>
    <justification jstring="[hyper(12294,a,18259,a),flip(a)].">
      <j1 rule="hyper" parents="12294 18259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18262">
    <literal><![CDATA[
      K(x,K(y,z) * (T(u,z) * y)) = K(x,T(y * u,z * y))
    ]]></literal>
    <justification jstring="[hyper(58,a,17761,a(flip),b,18261,a)].">
      <j1 rule="hyper" parents="58 17761 18261"/>
    </justification>
  </clause>

  <clause id="18263">
    <literal><![CDATA[
      K(x,T(y * z,u * y)) = K(x,T(z,u) * T(y,u))
    ]]></literal>
    <justification jstring="[hyper(15796,a,18262,a),flip(a)].">
      <j1 rule="hyper" parents="15796 18262"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18264">
    <literal><![CDATA[
      K(x,T(y * (z \ u),z * y)) = K(x,(u / z) * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,15149,a(flip),b,18263,a),flip(a)].">
      <j1 rule="hyper" parents="320 15149 18263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18265">
    <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(16766(a,1),18206(a,1,2,2))].">
      <j1 rule="para" parents="16766 18206"/>
    </justification>
  </clause>

  <clause id="18266">
    <literal><![CDATA[
      K(x,y \ T(z,u / K(w,v5))) = K(x,y \ (u \ (z * u)))
    ]]></literal>
    <justification jstring="[hyper(17707,a,18265,a),flip(a)].">
      <j1 rule="hyper" parents="17707 18265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18267">
    <literal><![CDATA[
      K(x,y \ T(z,u / K(w,v5))) = K(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[para(17(a,2),18266(a,2,2,2))].">
      <j1 rule="para" parents="17 18266"/>
    </justification>
  </clause>

  <clause id="18268">
    <literal><![CDATA[
      K(x,y \ T(z,u * T(w,v5))) = K(x,y \ T(z,u * w))
    ]]></literal>
    <justification jstring="[para(6349(a,1),18267(a,1,2,2,2))].">
      <j1 rule="para" parents="6349 18267"/>
    </justification>
  </clause>

  <clause id="18269">
    <literal><![CDATA[
      K(x,y \ T(z,u * (w / v5))) = K(x,y \ T(z,u * (v5 \ w)))
    ]]></literal>
    <justification jstring="[para(6510(a,1),18267(a,1,2,2,2))].">
      <j1 rule="para" parents="6510 18267"/>
    </justification>
  </clause>

  <clause id="18270">
    <literal><![CDATA[
      K(x,y \ T(z,K(u,w) * v5)) = K(x,y \ T(z,v5))
    ]]></literal>
    <justification jstring="[para(7285(a,1),18267(a,1,2,2,2))].">
      <j1 rule="para" parents="7285 18267"/>
    </justification>
  </clause>

  <clause id="18271">
    <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),18270(a,1,2)),flip(a)].">
      <j1 rule="para" parents="504 18270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18272">
    <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(18268(a,2),16138(a,1))].">
      <j1 rule="para" parents="18268 16138"/>
    </justification>
  </clause>

  <clause id="18273">
    <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(17593(a,1),18207(a,1))].">
      <j1 rule="para" parents="17593 18207"/>
    </justification>
  </clause>

  <clause id="18275">
    <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),18228(a,1,2,2,1))].">
      <j1 rule="para" parents="453 18228"/>
    </justification>
  </clause>

  <clause id="18276">
    <literal><![CDATA[
      K(x,T((y \ z) \ u,y \ z) / y) = K(x,T(y \ ((z / y) \ u),z))
    ]]></literal>
    <justification jstring="[hyper(15898,a,18250,a),flip(a)].">
      <j1 rule="hyper" parents="15898 18250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18277">
    <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(18276(a,2),14901(a,1))].">
      <j1 rule="para" parents="18276 14901"/>
    </justification>
  </clause>

  <clause id="18278">
    <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,17749,a,b,17751,a),flip(a)].">
      <j1 rule="hyper" parents="34 17749 17751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18279">
    <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,18278,a)].">
      <j1 rule="hyper" parents="479 18278"/>
    </justification>
  </clause>

  <clause id="18280">
    <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,15698,a,b,18279,a),flip(a)].">
      <j1 rule="hyper" parents="320 15698 18279"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18281">
    <literal><![CDATA[
      L(x * K(y,K(z,u)),w,v5) * K(y,K(z,u)) = L(x,w,v5)
    ]]></literal>
    <justification jstring="[hyper(15882,a,18279,a(flip))].">
      <j1 rule="hyper" parents="15882 18279"/>
    </justification>
  </clause>

  <clause id="18282">
    <literal><![CDATA[
      K(x,L(y * K(z,K(u,w)),v5,v6)) = K(x,L(y,v5,v6))
    ]]></literal>
    <justification jstring="[para(18279(a,2),16027(a,1,2))].">
      <j1 rule="para" parents="18279 16027"/>
    </justification>
  </clause>

  <clause id="18283">
    <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(18279(a,2),16194(a,1,2,2))].">
      <j1 rule="para" parents="18279 16194"/>
    </justification>
  </clause>

  <clause id="18284">
    <literal><![CDATA[
      K(x,L(T(y,K(z,u)) \ w,v5,v6)) = K(x,L(y \ w,v5,v6))
    ]]></literal>
    <justification jstring="[para(15748(a,1),18282(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="15748 18282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18285">
    <literal><![CDATA[
      L(K(x,K(y,z)) * u,w,v5) = L(u,w,v5) * K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(15684(a,2),18280(a,1,1))].">
      <j1 rule="para" parents="15684 18280"/>
    </justification>
  </clause>

  <clause id="18286">
    <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),18281(a,1,1))].">
      <j1 rule="para" parents="13 18281"/>
    </justification>
  </clause>

  <clause id="18287">
    <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(7438(a,1),18284(a,1,2,1,1))].">
      <j1 rule="para" parents="7438 18284"/>
    </justification>
  </clause>

  <clause id="18288">
    <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(18285(a,2),16045(a,1,2,2))].">
      <j1 rule="para" parents="18285 16045"/>
    </justification>
  </clause>

  <clause id="18289">
    <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(5399(a,1),18288(a,1,2,2,1))].">
      <j1 rule="para" parents="5399 18288"/>
    </justification>
  </clause>

  <clause id="18290">
    <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(6335(a,1),18289(a,1,2,2,1,1)),flip(a)].">
      <j1 rule="para" parents="6335 18289"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18291">
    <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,13189,a(flip),b,17789,a)].">
      <j1 rule="hyper" parents="58 13189 17789"/>
    </justification>
  </clause>

  <clause id="18292">
    <literal><![CDATA[
      K(x,y / (T(z,u / w) \ (u / w))) = K(x,y / ((w \ T(u,w)) / z))
    ]]></literal>
    <justification jstring="[hyper(17944,a,18028,a),flip(a)].">
      <j1 rule="hyper" parents="17944 18028"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18293">
    <literal><![CDATA[
      K(x,y / ((z \ T(u,z)) / w)) = K(x,y / ((u / z) / w))
    ]]></literal>
    <justification jstring="[hyper(17943,a,18292,a),flip(a)].">
      <j1 rule="hyper" parents="17943 18292"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18294">
    <literal><![CDATA[
      K(x,y / ((T(z,u) \ u) / w)) = K(x,y / ((u / z) / w))
    ]]></literal>
    <justification jstring="[hyper(58,a,9680,a,b,18293,a)].">
      <j1 rule="hyper" parents="58 9680 18293"/>
    </justification>
  </clause>

  <clause id="18295">
    <literal><![CDATA[
      K(x,y / ((K(z,u) * w) \ T(v5,w))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (v5 / (K(z,u) * w))) = v6
    ]]></literal>
    <justification jstring="[para(17906(a,1),17957(a,1))].">
      <j1 rule="para" parents="17906 17957"/>
    </justification>
  </clause>

  <clause id="18296">
    <literal><![CDATA[
      K(x,y / (z \ (K(u,w) * T(v5,z)))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (v5 / (K(w,u) * z))) = v6
    ]]></literal>
    <justification jstring="[para(17560(a,1),18295(a,1))].">
      <j1 rule="para" parents="17560 18295"/>
    </justification>
  </clause>

  <clause id="18297">
    <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,18090,a),flip(a)].">
      <j1 rule="hyper" parents="320 9 18090"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18298">
    <literal><![CDATA[
      K(x,L(y,z,K(u,w) * v5)) = K(x,(v5 * z) \ (v5 * (z * y)))
    ]]></literal>
    <justification jstring="[hyper(18273,a,18101,a),flip(a)].">
      <j1 rule="hyper" parents="18273 18101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18299">
    <literal><![CDATA[
      K(x,L(y,z,K(u,w) * v5)) = K(x,L(y,z,v5))
    ]]></literal>
    <justification jstring="[para(13(a,2),18298(a,2,2))].">
      <j1 rule="para" parents="13 18298"/>
    </justification>
  </clause>

  <clause id="18300">
    <literal><![CDATA[
      K(x,L(y,z,u * K(w,v5))) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(17341,a,18299,a)].">
      <j1 rule="hyper" parents="17341 18299"/>
    </justification>
  </clause>

  <clause id="18301">
    <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(14482,a,18299,a)].">
      <j1 rule="hyper" parents="14482 18299"/>
    </justification>
  </clause>

  <clause id="18302">
    <literal><![CDATA[
      K(x,L(y,z,K(u,w) * v5)) = K(x,(z * v5) / ((y \ z) * v5))
    ]]></literal>
    <justification jstring="[hyper(320,a,14787,a,b,18299,a),flip(a)].">
      <j1 rule="hyper" parents="320 14787 18299"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18304">
    <literal><![CDATA[
      K(x,L(y,z,T(u,w) \ v5)) = K(x,L(y,z,u \ v5))
    ]]></literal>
    <justification jstring="[para(5081(a,1),18299(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="5081 18299"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18306">
    <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(18299(a,1),14785(a,1,1))].">
      <j1 rule="para" parents="18299 14785"/>
    </justification>
  </clause>

  <clause id="18307">
    <literal><![CDATA[
      K(x,L(y,z,u * (w / v5))) = K(x,L(y,z,u * (v5 \ w)))
    ]]></literal>
    <justification jstring="[para(17375(a,1),18299(a,1,2))].">
      <j1 rule="para" parents="17375 18299"/>
    </justification>
  </clause>

  <clause id="18308">
    <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,14735,a(flip),b,18300,a),flip(a)].">
      <j1 rule="hyper" parents="58 14735 18300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18309">
    <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(13728(a,1),18300(a,1,2,3))].">
      <j1 rule="para" parents="13728 18300"/>
    </justification>
  </clause>

  <clause id="18310">
    <literal><![CDATA[
      a(x,y,K(z * K(u,w),v5)) = K(v5,x) * K(x,L(v5,y,z))
    ]]></literal>
    <justification jstring="[para(18300(a,1),14302(a,1,2)),flip(a)].">
      <j1 rule="para" parents="18300 14302"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18311">
    <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(18300(a,1),14785(a,1,1))].">
      <j1 rule="para" parents="18300 14785"/>
    </justification>
  </clause>

  <clause id="18312">
    <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(18300(a,1),15957(a,1,1,1))].">
      <j1 rule="para" parents="18300 15957"/>
    </justification>
  </clause>

  <clause id="18313">
    <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,14876,a(flip),b,18304,a),flip(a)].">
      <j1 rule="hyper" parents="58 14876 18304"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18314">
    <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,10652,a(flip),b,18304,a),flip(a)].">
      <j1 rule="hyper" parents="58 10652 18304"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18315">
    <literal><![CDATA[
      a(x,y,K(z * K(u,w),v5)) = a(x,y,K(z,v5))
    ]]></literal>
    <justification jstring="[hyper(320,a,14302,a(flip),b,18310,a),flip(a)].">
      <j1 rule="hyper" parents="320 14302 18310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18316">
    <literal><![CDATA[
      a(x * K(y,z),u,K(w,v5)) = a(v5,u,K(x,w))
    ]]></literal>
    <justification jstring="[hyper(14349,a,18315,a)].">
      <j1 rule="hyper" parents="14349 18315"/>
    </justification>
  </clause>

  <clause id="18317">
    <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,17862,a,b,18315,a)].">
      <j1 rule="hyper" parents="58 17862 18315"/>
    </justification>
  </clause>

  <clause id="18318">
    <literal><![CDATA[
      a(x,y,K(z * u,w)) = a(x,y,K(u * z,w))
    ]]></literal>
    <justification jstring="[para(84(a,1),18315(a,1,3,1))].">
      <j1 rule="para" parents="84 18315"/>
    </justification>
  </clause>

  <clause id="18319">
    <literal><![CDATA[
      a(x,y,K(z / u,w)) = a(x,y,K(u \ z,w))
    ]]></literal>
    <justification jstring="[para(4776(a,1),18315(a,1,3,1))].">
      <j1 rule="para" parents="4776 18315"/>
    </justification>
  </clause>

  <clause id="18320">
    <literal><![CDATA[
      a(x,y,K(z,T(u,w))) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[para(7930(a,1),18315(a,1,3))].">
      <j1 rule="para" parents="7930 18315"/>
    </justification>
  </clause>

  <clause id="18321">
    <literal><![CDATA[
      a(x,y,K(z \ (u / w),v5)) = a(x,y,K(z \ (w \ u),v5))
    ]]></literal>
    <justification jstring="[para(13963(a,1),18315(a,1,3,1))].">
      <j1 rule="para" parents="13963 18315"/>
    </justification>
  </clause>

  <clause id="18322">
    <literal><![CDATA[
      a(x,y,K((z / u) \ w,v5)) = a(x,y,K((u \ z) \ w,v5))
    ]]></literal>
    <justification jstring="[para(15926(a,1),18315(a,1,3))].">
      <j1 rule="para" parents="15926 18315"/>
    </justification>
  </clause>

  <clause id="18323">
    <literal><![CDATA[
      a(x,y,K(z,T(u,w))) = a(z,y,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(320,a,14263,a,b,18320,a),flip(a)].">
      <j1 rule="hyper" parents="320 14263 18320"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18324">
    <literal><![CDATA[
      a(x,y,K(z,T(u,w))) = a(u,y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,14263,a(flip),b,18320,a),flip(a)].">
      <j1 rule="hyper" parents="320 14263 18320"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18325">
    <literal><![CDATA[
      a(x,y,K(z,u / w)) = a(x,y,K(z,w \ u))
    ]]></literal>
    <justification jstring="[para(107(a,1),18320(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="107 18320"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18326">
    <literal><![CDATA[
      a(x,y,K(z,u * w)) = a(x,y,K(z,w * u))
    ]]></literal>
    <justification jstring="[para(12262(a,1),18320(a,1,3))].">
      <j1 rule="para" parents="12262 18320"/>
    </justification>
  </clause>

  <clause id="18327">
    <literal><![CDATA[
      T(x,a(y,z,T(u,w))) = x * a(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(119,a,18323,a(flip),b,13399,a),flip(a)].">
      <j1 rule="hyper" parents="119 18323 13399"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18330">
    <literal><![CDATA[
      a(x * y,z,K(u,w)) = a(w,z,K(y * x,u))
    ]]></literal>
    <justification jstring="[para(12230(a,1),18323(a,1,3)),flip(a)].">
      <j1 rule="para" parents="12230 18323"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18332">
    <literal><![CDATA[
      a(T(x,y),z,K(u,w)) = a(x,z,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(14387,a,18324,a)].">
      <j1 rule="hyper" parents="14387 18324"/>
    </justification>
  </clause>

  <clause id="18334">
    <literal><![CDATA[
      a(x * y,z,K(u,w)) = a(u,z,K(w,y * x))
    ]]></literal>
    <justification jstring="[para(12262(a,1),18324(a,1,3)),flip(a)].">
      <j1 rule="para" parents="12262 18324"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18335">
    <literal><![CDATA[
      K(L(x,y,z) * u,x * u) = a(x,y,K(z,x * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,14540,a(flip),b,18332,a)].">
      <j1 rule="hyper" parents="58 14540 18332"/>
    </justification>
  </clause>

  <clause id="18336">
    <literal><![CDATA[
      a(x * y,z,K(u,w)) = a(y * x,z,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,12798,a(flip),b,18332,a)].">
      <j1 rule="hyper" parents="58 12798 18332"/>
    </justification>
  </clause>

  <clause id="18337">
    <literal><![CDATA[
      a(x / y,z,K(u,w)) = a(y \ x,z,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,12783,a(flip),b,18332,a),flip(a)].">
      <j1 rule="hyper" parents="58 12783 18332"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18338">
    <literal><![CDATA[
      a(x * K(y,z),u,K(w,v5)) = a(w,u,K(v5,x))
    ]]></literal>
    <justification jstring="[hyper(320,a,14263,a(flip),b,18316,a),flip(a)].">
      <j1 rule="hyper" parents="320 14263 18316"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18339">
    <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(18316(a,1),14940(a,2,1))].">
      <j1 rule="para" parents="18316 14940"/>
    </justification>
  </clause>

  <clause id="18340">
    <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(18318(a,1),14349(a,1))].">
      <j1 rule="para" parents="18318 14349"/>
    </justification>
  </clause>

  <clause id="18341">
    <literal><![CDATA[
      a(x,y,K(z,x \ (u * (x / w)))) = a(z,y,K(w \ u,x))
    ]]></literal>
    <justification jstring="[hyper(14395,a,18319,a)].">
      <j1 rule="hyper" parents="14395 18319"/>
    </justification>
  </clause>

  <clause id="18342">
    <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(18319(a,1),14353(a,1,2))].">
      <j1 rule="para" parents="18319 14353"/>
    </justification>
  </clause>

  <clause id="18343">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(u \ w,y)) = K(x,L(y,z,w / (y * u)))
    ]]></literal>
    <justification jstring="[para(18319(a,1),14594(a,1,2))].">
      <j1 rule="para" parents="18319 14594"/>
    </justification>
  </clause>

  <clause id="18344">
    <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(18325(a,1),14414(a,1,2))].">
      <j1 rule="para" parents="18325 14414"/>
    </justification>
  </clause>

  <clause id="18345">
    <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(18325(a,1),14849(a,1,1))].">
      <j1 rule="para" parents="18325 14849"/>
    </justification>
  </clause>

  <clause id="18346">
    <literal><![CDATA[
      a(x,y,K(z,y \ u)) \ K(z,(y * x) / u) = K(z,y / (u / x))
    ]]></literal>
    <justification jstring="[para(18325(a,1),14883(a,1,1))].">
      <j1 rule="para" parents="18325 14883"/>
    </justification>
  </clause>

  <clause id="18347">
    <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(18326(a,1),14387(a,1))].">
      <j1 rule="para" parents="18326 14387"/>
    </justification>
  </clause>

  <clause id="18348">
    <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(17626(a,1),18326(a,1,3))].">
      <j1 rule="para" parents="17626 18326"/>
    </justification>
  </clause>

  <clause id="18349">
    <literal><![CDATA[
      T(x,a(y,z,T(u,w))) = T(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,14283,a(flip),b,18327,a),flip(a)].">
      <j1 rule="hyper" parents="320 14283 18327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18350">
    <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(18327(a,2),14287(a,1))].">
      <j1 rule="para" parents="18327 14287"/>
    </justification>
  </clause>

  <clause id="18351">
    <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,17305,a(flip),b,18349,a),flip(a)].">
      <j1 rule="hyper" parents="58 17305 18349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18352">
    <literal><![CDATA[
      T(x,a(y,T(z,u),u)) = T(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(6649(a,1),18349(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6649 18349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18353">
    <literal><![CDATA[
      T(x,a(y,z * u,u)) = T(x,a(y,u * z,u))
    ]]></literal>
    <justification jstring="[para(13330(a,1),18352(a,1,2))].">
      <j1 rule="para" parents="13330 18352"/>
    </justification>
  </clause>

  <clause id="18354">
    <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(18330(a,2),14349(a,1))].">
      <j1 rule="para" parents="18330 14349"/>
    </justification>
  </clause>

  <clause id="18355">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w) * v5)) = a(z,y,K(v5,x))
    ]]></literal>
    <justification jstring="[hyper(58,a,18316,a(flip),b,18334,a),flip(a)].">
      <j1 rule="hyper" parents="58 18316 18334"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18356">
    <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(18334(a,1),14349(a,1))].">
      <j1 rule="para" parents="18334 14349"/>
    </justification>
  </clause>

  <clause id="18357">
    <literal><![CDATA[
      a(K(x,y),z,u \ w) = a(w / u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(320,a,14293,a,b,18337,a)].">
      <j1 rule="hyper" parents="320 14293 18337"/>
    </justification>
  </clause>

  <clause id="18358">
    <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(18337(a,1),14726(a,1,2))].">
      <j1 rule="para" parents="18337 14726"/>
    </justification>
  </clause>

  <clause id="18359">
    <literal><![CDATA[
      a(x,y,K(z,u * K(w,v5))) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(14349,a,18338,a)].">
      <j1 rule="hyper" parents="14349 18338"/>
    </justification>
  </clause>

  <clause id="18360">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w) * v5)) = a(x,y,K(z,v5))
    ]]></literal>
    <justification jstring="[hyper(58,a,18334,a(flip),b,18338,a)].">
      <j1 rule="hyper" parents="58 18334 18338"/>
    </justification>
  </clause>

  <clause id="18361">
    <literal><![CDATA[
      T(x,a(y * K(z,u),w,v5)) = x * a(x,w,K(v5,y))
    ]]></literal>
    <justification jstring="[hyper(119,a,18338,a(flip),b,13399,a),flip(a)].">
      <j1 rule="hyper" parents="119 18338 13399"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18362">
    <literal><![CDATA[
      a(x,y,K(z,u * K(w,v5))) = a(u,y,K(x,z))
    ]]></literal>
    <justification jstring="[para(6329(a,1),18338(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6329 18338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18363">
    <literal><![CDATA[
      T(x,a(y,z * u,u)) = T(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,14430,a(flip),b,18353,a),flip(a)].">
      <j1 rule="hyper" parents="320 14430 18353"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18364">
    <literal><![CDATA[
      L(x,y * z,K(z,u)) = T(x,a(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(14980,a,18363,a)].">
      <j1 rule="hyper" parents="14980 18363"/>
    </justification>
  </clause>

  <clause id="18365">
    <literal><![CDATA[
      L(x,y * z,K(z,u)) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,14925,a,b,18364,a),flip(a)].">
      <j1 rule="hyper" parents="320 14925 18364"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18367">
    <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,7691,a(flip),b,18365,a)].">
      <j1 rule="hyper" parents="58 7691 18365"/>
    </justification>
  </clause>

  <clause id="18368">
    <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(18365(a,1),14932(a,1))].">
      <j1 rule="para" parents="18365 14932"/>
    </justification>
  </clause>

  <clause id="18369">
    <literal><![CDATA[
      T(x,a(K(y,z) * u,w,v5)) = x * a(v5,w,K(u,x))
    ]]></literal>
    <justification jstring="[para(18355(a,1),14283(a,1,2)),flip(a)].">
      <j1 rule="para" parents="18355 14283"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18370">
    <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(18355(a,1),16786(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="18355 16786"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18372">
    <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(18357(a,1),14386(a,1))].">
      <j1 rule="para" parents="18357 14386"/>
    </justification>
  </clause>

  <clause id="18373">
    <literal><![CDATA[
      a(x,y,K(z,(u / w) * v5)) = a(x,y,K(z,(w \ u) * v5))
    ]]></literal>
    <justification jstring="[para(6524(a,1),18359(a,1,3,2))].">
      <j1 rule="para" parents="6524 18359"/>
    </justification>
  </clause>

  <clause id="18374">
    <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(18360(a,2),14349(a,1))].">
      <j1 rule="para" parents="18360 14349"/>
    </justification>
  </clause>

  <clause id="18375">
    <literal><![CDATA[
      a(K(x,y) * z,u,K(w,v5)) = a(z,u,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(58,a,18334,a,b,18362,a)].">
      <j1 rule="hyper" parents="58 18334 18362"/>
    </justification>
  </clause>

  <clause id="18376">
    <literal><![CDATA[
      a(T(x,y) \ z,u,K(w,v5)) = a(x \ z,u,K(w,v5))
    ]]></literal>
    <justification jstring="[para(5081(a,1),18375(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5081 18375"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18377">
    <literal><![CDATA[
      a(x \ T(y,z),u,K(w,v5)) = a(x \ y,u,K(w,v5))
    ]]></literal>
    <justification jstring="[para(5408(a,1),18375(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5408 18375"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18378">
    <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(18375(a,2),14387(a,1))].">
      <j1 rule="para" parents="18375 14387"/>
    </justification>
  </clause>

  <clause id="18380">
    <literal><![CDATA[
      K(L(x,y,z) * u,x * u) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,14355,a(flip),b,18335,a),flip(a)].">
      <j1 rule="hyper" parents="320 14355 18335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18381">
    <literal><![CDATA[
      K(x * L(y,z,u),y * x) = a(y,z,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(58,a,17602,a(flip),b,18380,a)].">
      <j1 rule="hyper" parents="58 17602 18380"/>
    </justification>
  </clause>

  <clause id="18382">
    <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(2406(a,1),18381(a,1,1,2))].">
      <j1 rule="para" parents="2406 18381"/>
    </justification>
  </clause>

  <clause id="18383">
    <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(18361(a,2),14287(a,1))].">
      <j1 rule="para" parents="18361 14287"/>
    </justification>
  </clause>

  <clause id="18387">
    <literal><![CDATA[
      T(x * y,a(K(z,u) * y,w,v5)) = (x * y) * a(v5,w,K(y,x))
    ]]></literal>
    <justification jstring="[para(11032(a,1),18369(a,2,2))].">
      <j1 rule="para" parents="11032 18369"/>
    </justification>
  </clause>

  <clause id="18388">
    <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),18376(a,1,1,1))].">
      <j1 rule="para" parents="20 18376"/>
    </justification>
  </clause>

  <clause id="18389">
    <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),18377(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="107 18377"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18390">
    <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(18032(a,1),18340(a,1,3))].">
      <j1 rule="para" parents="18032 18340"/>
    </justification>
  </clause>

  <clause id="18391">
    <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(14365(a,1),18372(a,1))].">
      <j1 rule="para" parents="14365 18372"/>
    </justification>
  </clause>

  <clause id="18392">
    <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(13963(a,1),18383(a,1,2,1))].">
      <j1 rule="para" parents="13963 18383"/>
    </justification>
  </clause>

  <clause id="18394">
    <literal><![CDATA[
      x * a(y,z,K(u \ (w \ v5),x)) = T(x,a(u \ (v5 / w),z,y))
    ]]></literal>
    <justification jstring="[para(18321(a,1),14319(a,1,2))].">
      <j1 rule="para" parents="18321 14319"/>
    </justification>
  </clause>

  <clause id="18395">
    <literal><![CDATA[
      a(x,y,K(z * (u / w),u)) = a(x,y,K(w \ z,u))
    ]]></literal>
    <justification jstring="[hyper(14452,a,18341,a)].">
      <j1 rule="hyper" parents="14452 18341"/>
    </justification>
  </clause>

  <clause id="18396">
    <literal><![CDATA[
      a(x,y,K(z * (u \ w),w)) = a(x,y,K(u \ z,w))
    ]]></literal>
    <justification jstring="[para(15868(a,1),18395(a,1,3))].">
      <j1 rule="para" parents="15868 18395"/>
    </justification>
  </clause>

  <clause id="18397">
    <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(18396(a,1),14412(a,2,2))].">
      <j1 rule="para" parents="18396 14412"/>
    </justification>
  </clause>

  <clause id="18398">
    <literal><![CDATA[
      a((x * y) \ (z \ u),w,K(v5,v6)) = a(y \ (x \ (u / z)),w,K(v5,v6))
    ]]></literal>
    <justification jstring="[hyper(14514,a,18389,a),flip(a)].">
      <j1 rule="hyper" parents="14514 18389"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18399">
    <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(18302(a,2),14804(a,1))].">
      <j1 rule="para" parents="18302 14804"/>
    </justification>
  </clause>

  <clause id="18400">
    <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(5131(a,1),18399(a,1,2,3))].">
      <j1 rule="para" parents="5131 18399"/>
    </justification>
  </clause>

  <clause id="18401">
    <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(7288(a,1),18399(a,1,2,3))].">
      <j1 rule="para" parents="7288 18399"/>
    </justification>
  </clause>

  <clause id="18402">
    <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(11156(a,1),18399(a,1,2,3))].">
      <j1 rule="para" parents="11156 18399"/>
    </justification>
  </clause>

  <clause id="18403">
    <literal><![CDATA[
      K(x,L(y,(K(z,u) * w) \ v5,w)) = K(x,L(y,v5,w))
    ]]></literal>
    <justification jstring="[hyper(18399,a,18301,a)].">
      <j1 rule="hyper" parents="18399 18301"/>
    </justification>
  </clause>

  <clause id="18405">
    <literal><![CDATA[
      K(x,L(y,z \ (u \ w),z)) = K(x,L(y,w / u,z * K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(17340,a,18308,a)].">
      <j1 rule="hyper" parents="17340 18308"/>
    </justification>
  </clause>

  <clause id="18407">
    <literal><![CDATA[
      K(x,L(y,z,u / (y * w))) = K(x,L(y,z,w \ u))
    ]]></literal>
    <justification jstring="[hyper(14329,a,18343,a),flip(a)].">
      <j1 rule="hyper" parents="14329 18343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18408">
    <literal><![CDATA[
      K(x,L(y,z,(y * u) \ w)) = K(x,L(y,z,u \ w))
    ]]></literal>
    <justification jstring="[hyper(17302,a,18407,a)].">
      <j1 rule="hyper" parents="17302 18407"/>
    </justification>
  </clause>

  <clause id="18409">
    <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,13402,a(flip),b,18387,a),flip(a)].">
      <j1 rule="hyper" parents="320 13402 18387"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18410">
    <literal><![CDATA[
      T(x,a(x \ ((y * x) / z),u,w)) = x * a(w,u,K(z \ y,x))
    ]]></literal>
    <justification jstring="[para(10376(a,1),18394(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="10376 18394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18411">
    <literal><![CDATA[
      K(x,L(y,z / u,w * K(u,z))) = K(x,L(y,u \ z,w))
    ]]></literal>
    <justification jstring="[hyper(14466,a,18405,a),flip(a)].">
      <j1 rule="hyper" parents="14466 18405"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18412">
    <literal><![CDATA[
      K(x,L(y,z / u,w)) = K(x,L(y,u \ z,w))
    ]]></literal>
    <justification jstring="[hyper(18401,a,18411,a)].">
      <j1 rule="hyper" parents="18401 18411"/>
    </justification>
  </clause>

  <clause id="18414">
    <literal><![CDATA[
      K(x,L(y,(z * u) / z,w)) = K(x,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(4(a,1),18412(a,2,2,2))].">
      <j1 rule="para" parents="4 18412"/>
    </justification>
  </clause>

  <clause id="18415">
    <literal><![CDATA[
      K(x,L(y,T(z,u),w)) = K(x,L(y,z,w))
    ]]></literal>
    <justification jstring="[para(225(a,1),18414(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="225 18414"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18419">
    <literal><![CDATA[
      K(x,L(y,z * u,w)) = K(x,L(y,u * z,w))
    ]]></literal>
    <justification jstring="[para(13256(a,1),18415(a,1,2))].">
      <j1 rule="para" parents="13256 18415"/>
    </justification>
  </clause>

  <clause id="18420">
    <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(14955(a,1),18415(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="14955 18415"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18421">
    <literal><![CDATA[
      T(x,a(x \ ((y * x) / z),u,w)) = T(x,a(z \ y,u,w))
    ]]></literal>
    <justification jstring="[hyper(320,a,14319,a(flip),b,18410,a),flip(a)].">
      <j1 rule="hyper" parents="320 14319 18410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18422">
    <literal><![CDATA[
      a(x \ y,x,K(z,u)) * K(z,(x * u) / y) = K(z,x / (y / u))
    ]]></literal>
    <justification jstring="[hyper(14399,a,18346,a)].">
      <j1 rule="hyper" parents="14399 18346"/>
    </justification>
  </clause>

  <clause id="18423">
    <literal><![CDATA[
      a(x \ K(y,z),u,K(w,v5)) = a(w,u,K(x,v5))
    ]]></literal>
    <justification jstring="[hyper(18391,a,18316,a)].">
      <j1 rule="hyper" parents="18391 18316"/>
    </justification>
  </clause>

  <clause id="18424">
    <literal><![CDATA[
      T(x,a(x \ (y \ (z * x)),u,w)) = T(x,a(y \ z,u,w))
    ]]></literal>
    <justification jstring="[hyper(18392,a,18421,a)].">
      <j1 rule="hyper" parents="18392 18421"/>
    </justification>
  </clause>

  <clause id="18425">
    <literal><![CDATA[
      T(x,a(y \ (z * x),u,w)) = T(x,a(y \ z,u,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,14426,a(flip),b,18424,a)].">
      <j1 rule="hyper" parents="58 14426 18424"/>
    </justification>
  </clause>

  <clause id="18426">
    <literal><![CDATA[
      T(x,a(y \ 1,z,u)) = T(x,a(y \ x,z,u))
    ]]></literal>
    <justification jstring="[para(2(a,1),18425(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="2 18425"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18427">
    <literal><![CDATA[
      T(x,a(y \ x,z,u)) = T(x,a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,17754,a(flip),b,18426,a),flip(a)].">
      <j1 rule="hyper" parents="58 17754 18426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18428">
    <literal><![CDATA[
      L(x,y,K(z,u \ x)) = T(x,a(z,y,u))
    ]]></literal>
    <justification jstring="[hyper(14980,a,18427,a)].">
      <j1 rule="hyper" parents="14980 18427"/>
    </justification>
  </clause>

  <clause id="18429">
    <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(5175(a,1),18427(a,1,2,1))].">
      <j1 rule="para" parents="5175 18427"/>
    </justification>
  </clause>

  <clause id="18430">
    <literal><![CDATA[
      L(x,y,K(z,u \ x)) = L(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,14925,a,b,18428,a),flip(a)].">
      <j1 rule="hyper" parents="320 14925 18428"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18431">
    <literal><![CDATA[
      L(x,y,K(x \ z,u)) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,12716,a,b,18430,a)].">
      <j1 rule="hyper" parents="58 12716 18430"/>
    </justification>
  </clause>

  <clause id="18432">
    <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(18429(a,2),18350(a,1))].">
      <j1 rule="para" parents="18429 18350"/>
    </justification>
  </clause>

  <clause id="18433">
    <literal><![CDATA[
      K(x,L(y,z,(u * w) \ v5)) = K(x,L(y,z,u \ (w \ v5)))
    ]]></literal>
    <justification jstring="[hyper(18402,a,14502,a)].">
      <j1 rule="hyper" parents="18402 14502"/>
    </justification>
  </clause>

  <clause id="18434">
    <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,14637,a(flip),b,18433,a),flip(a)].">
      <j1 rule="hyper" parents="320 14637 18433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18435">
    <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,14806,a(flip),b,18434,a),flip(a)].">
      <j1 rule="hyper" parents="58 14806 18434"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18436">
    <literal><![CDATA[
      a(x,y,K(z \ y,u)) * K(x,(y * u) / z) = K(x,y / (z / u))
    ]]></literal>
    <justification jstring="[para(14312(a,1),18422(a,1,1))].">
      <j1 rule="para" parents="14312 18422"/>
    </justification>
  </clause>

  <clause id="18437">
    <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(18323(a,1),18422(a,1,1))].">
      <j1 rule="para" parents="18323 18422"/>
    </justification>
  </clause>

  <clause id="18438">
    <literal><![CDATA[
      T(x * y,a(z,u,x)) = x * T(y,a(z,u,x))
    ]]></literal>
    <justification jstring="[hyper(18432,a,18409,a)].">
      <j1 rule="hyper" parents="18432 18409"/>
    </justification>
  </clause>

  <clause id="18439">
    <literal><![CDATA[
      T(x * y,a(z,u,x)) = x * L(y,u,K(x,z))
    ]]></literal>
    <justification jstring="[para(14925(a,2),18438(a,2,2))].">
      <j1 rule="para" parents="14925 18438"/>
    </justification>
  </clause>

  <clause id="18440">
    <literal><![CDATA[
      L(x * y,z,K(x,u)) = x * L(y,z,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(14980,a,18439,a)].">
      <j1 rule="hyper" parents="14980 18439"/>
    </justification>
  </clause>

  <clause id="18441">
    <literal><![CDATA[
      K(x \ (y * (((z / y) * y) \ x)),u) = K((z * (y \ x)) \ x,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,14881,a(flip),b,18435,a),flip(a)].">
      <j1 rule="hyper" parents="58 14881 18435"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18442">
    <literal><![CDATA[
      K((x * (y \ z)) \ z,u) = K(z \ (y * (x \ z)),u)
    ]]></literal>
    <justification jstring="[para(7(a,1),18441(a,1,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="7 18441"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18444">
    <literal><![CDATA[
      x / (K(y \ (z * (u \ y)),w) * x) = K(w,(u * (z \ y)) \ y)
    ]]></literal>
    <justification jstring="[para(18442(a,1),5142(a,1,2,1))].">
      <j1 rule="para" parents="18442 5142"/>
    </justification>
  </clause>

  <clause id="18445">
    <literal><![CDATA[
      K(x,(y * (z \ u)) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u \ (z * (y \ u))) = w
    ]]></literal>
    <justification jstring="[para(18444(a,1),5150(a,1))].">
      <j1 rule="para" parents="18444 5150"/>
    </justification>
  </clause>

  <clause id="18446">
    <literal><![CDATA[
      K(x,(y * z) / u) * a(z,y,K(x,u \ y)) = K(x,y / (u / z))
    ]]></literal>
    <justification jstring="[hyper(17458,a,18436,a)].">
      <j1 rule="hyper" parents="17458 18436"/>
    </justification>
  </clause>

  <clause id="18447">
    <literal><![CDATA[
      K(x,(y * z) / u) * a(x,y,K(u \ y,z)) = K(x,y / (u / z))
    ]]></literal>
    <justification jstring="[hyper(17249,a,18436,a)].">
      <j1 rule="hyper" parents="17249 18436"/>
    </justification>
  </clause>

  <clause id="18448">
    <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(12642(a,1),18436(a,1,1,3,1))].">
      <j1 rule="para" parents="12642 18436"/>
    </justification>
  </clause>

  <clause id="18449">
    <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,14875,a(flip),b,18309,a),flip(a)].">
      <j1 rule="hyper" parents="58 14875 18309"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18450">
    <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(13876(a,1),18339(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13876 18339"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18451">
    <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(11023(a,1),18342(a,1,2))].">
      <j1 rule="para" parents="11023 18342"/>
    </justification>
  </clause>

  <clause id="18452">
    <literal><![CDATA[
      a(x,y,K(z,u * (w * K(v5,v6)))) = a(z,y,K(w * u,x))
    ]]></literal>
    <justification jstring="[hyper(18374,a,18348,a),flip(a)].">
      <j1 rule="hyper" parents="18374 18348"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18454">
    <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(18452(a,1),14417(a,1,2)),flip(a)].">
      <j1 rule="para" parents="18452 14417"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18455">
    <literal><![CDATA[
      R(x,y,K(K(z,u) * w,v5)) = x * a(x,y,K(w,v5))
    ]]></literal>
    <justification jstring="[para(17195(a,1),18370(a,2,2))].">
      <j1 rule="para" parents="17195 18370"/>
    </justification>
  </clause>

  <clause id="18457">
    <literal><![CDATA[
      R(x,y,K(K(z,u) * w,v5)) = L(x,y,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(320,a,14928,a(flip),b,18455,a),flip(a)].">
      <j1 rule="hyper" parents="320 14928 18455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18459">
    <literal><![CDATA[
      L(x,y,K(K(z,u) * w,v5)) = L(x,y,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(14981,a,18457,a)].">
      <j1 rule="hyper" parents="14981 18457"/>
    </justification>
  </clause>

  <clause id="18460">
    <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(14983,a,18459,a)].">
      <j1 rule="hyper" parents="14983 18459"/>
    </justification>
  </clause>

  <clause id="18461">
    <literal><![CDATA[
      L(x,y,K(z / u,w)) = L(x,y,K(u \ z,w))
    ]]></literal>
    <justification jstring="[para(4859(a,1),18459(a,1,3,1))].">
      <j1 rule="para" parents="4859 18459"/>
    </justification>
  </clause>

  <clause id="18462">
    <literal><![CDATA[
      L(x,y,K(z / x,u)) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,18431,a(flip),b,18461,a),flip(a)].">
      <j1 rule="hyper" parents="320 18431 18461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18463">
    <literal><![CDATA[
      L(x,y,K(z * x,u)) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[para(6(a,1),18462(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="6 18462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18464">
    <literal><![CDATA[
      L(x,(K(y,z) * u) \ w,K(u,v5)) = L(x,w,K(u,v5))
    ]]></literal>
    <justification jstring="[hyper(58,a,18459,a(flip),b,18460,a)].">
      <j1 rule="hyper" parents="58 18459 18460"/>
    </justification>
  </clause>

  <clause id="18466">
    <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),18388(a,1,1,1,1))].">
      <j1 rule="para" parents="319 18388"/>
    </justification>
  </clause>

  <clause id="18467">
    <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,14325,a(flip),b,18397,a),flip(a)].">
      <j1 rule="hyper" parents="320 14325 18397"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18468">
    <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(18398(a,1),14514(a,1))].">
      <j1 rule="para" parents="18398 14514"/>
    </justification>
  </clause>

  <clause id="18469">
    <literal><![CDATA[
      K(x,L(y,z \ (K(u,w) * v5),z)) = K(x,L(y,v5,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,18403,a(flip),b,18420,a),flip(a)].">
      <j1 rule="hyper" parents="58 18403 18420"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18470">
    <literal><![CDATA[
      K(x,L(y,K(z,u) * w,v5)) = K(x,L(y,w,v5))
    ]]></literal>
    <justification jstring="[hyper(14466,a,18469,a)].">
      <j1 rule="hyper" parents="14466 18469"/>
    </justification>
  </clause>

  <clause id="18471">
    <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,18469,a(flip),b,14374,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 18469 14374"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18477">
    <literal><![CDATA[
      K(x,L(y,z * (K(u,w) * v5),v6)) = K(x,L(y,z * v5,v6))
    ]]></literal>
    <justification jstring="[para(6038(a,1),18470(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6038 18470"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18478">
    <literal><![CDATA[
      a(x,K(y,z) * u,K(w,v5)) = a(v5,u,K(x,w))
    ]]></literal>
    <justification jstring="[hyper(320,a,14302,a(flip),b,18471,a),flip(a)].">
      <j1 rule="hyper" parents="320 14302 18471"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18479">
    <literal><![CDATA[
      a(x,K(y,z) * u,K(w,v5)) = a(x,u,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(320,a,10824,a(flip),b,18471,a),flip(a)].">
      <j1 rule="hyper" parents="320 10824 18471"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18480">
    <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,18478,a)].">
      <j1 rule="hyper" parents="52 18478"/>
    </justification>
  </clause>

  <clause id="18482">
    <literal><![CDATA[
      a(x,y * z,K(u,w)) = a(x,z * y,K(u,w))
    ]]></literal>
    <justification jstring="[para(4813(a,1),18479(a,1,2))].">
      <j1 rule="para" parents="4813 18479"/>
    </justification>
  </clause>

  <clause id="18486">
    <literal><![CDATA[
      x * a(x,y * z,K(u,w)) = L(x,z * y,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(119,a,18482,a,b,14929,a)].">
      <j1 rule="hyper" parents="119 18482 14929"/>
    </justification>
  </clause>

  <clause id="18487">
    <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(18486(a,1),14957(a,1))].">
      <j1 rule="para" parents="18486 14957"/>
    </justification>
  </clause>

  <clause id="18488">
    <literal><![CDATA[
      L(x,y * (y \ z),K(u,w)) = L(x,T(z,y),K(u,w))
    ]]></literal>
    <justification jstring="[hyper(18487,a,13270,a)].">
      <j1 rule="hyper" parents="18487 13270"/>
    </justification>
  </clause>

  <clause id="18489">
    <literal><![CDATA[
      L(x,T(y,z),K(u,w)) = L(x,y,K(u,w))
    ]]></literal>
    <justification jstring="[para(5(a,1),18488(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5 18488"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18490">
    <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(14955(a,1),18489(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14955 18489"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18491">
    <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,18419,a,b,18477,a),flip(a)].">
      <j1 rule="hyper" parents="320 18419 18477"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18492">
    <literal><![CDATA[
      K(x,L(y,z * (u * K(w,v5)),v6)) = K(x,L(y,u * z,v6))
    ]]></literal>
    <justification jstring="[para(7288(a,1),18491(a,1,2,2,2))].">
      <j1 rule="para" parents="7288 18491"/>
    </justification>
  </clause>

  <clause id="18493">
    <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(18492(a,1),14844(a,1,1,1))].">
      <j1 rule="para" parents="18492 14844"/>
    </justification>
  </clause>

  <clause id="18494">
    <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,14325,a(flip),b,18454,a),flip(a)].">
      <j1 rule="hyper" parents="320 14325 18454"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18496">
    <literal><![CDATA[
      L(x,y \ (K(z,u) * w),K(y,v5)) = L(x,w,K(y,v5))
    ]]></literal>
    <justification jstring="[hyper(58,a,18464,a(flip),b,18490,a),flip(a)].">
      <j1 rule="hyper" parents="58 18464 18490"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18497">
    <literal><![CDATA[
      L(x,K(y,z) * u,K(w,v5)) = L(x,u,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(58,a,14958,a(flip),b,18496,a)].">
      <j1 rule="hyper" parents="58 14958 18496"/>
    </justification>
  </clause>

  <clause id="18498">
    <literal><![CDATA[
      L(x,y * K(z,u),K(w,v5)) = L(x,y,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(18487,a,18497,a)].">
      <j1 rule="hyper" parents="18487 18497"/>
    </justification>
  </clause>

  <clause id="18500">
    <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,11237,a(flip),b,18498,a),flip(a)].">
      <j1 rule="hyper" parents="58 11237 18498"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18501">
    <literal><![CDATA[
      L(x,y \ (z * K(u,w)),K(v5,v6)) = L(x,y \ z,K(v5,v6))
    ]]></literal>
    <justification jstring="[para(14599(a,1),18498(a,1,2))].">
      <j1 rule="para" parents="14599 18498"/>
    </justification>
  </clause>

  <clause id="18502">
    <literal><![CDATA[
      L(x,y \ (K(z,u) * w),K(v5,v6)) = L(x,y \ w,K(v5,v6))
    ]]></literal>
    <justification jstring="[para(7148(a,1),18501(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7148 18501"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18503">
    <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,10406,a(flip),b,18502,a),flip(a)].">
      <j1 rule="hyper" parents="58 10406 18502"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18505">
    <literal><![CDATA[
      K(x,L(y,z,u / (T(w,x) * v5))) = K(x,L(y,z,(w * v5) \ u))
    ]]></literal>
    <justification jstring="[hyper(14330,a,18344,a),flip(a)].">
      <j1 rule="hyper" parents="14330 18344"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18506">
    <literal><![CDATA[
      K(x,L(y,z,(T(u,x) * w) \ v5)) = K(x,L(y,z,(u * w) \ v5))
    ]]></literal>
    <justification jstring="[hyper(17302,a,18505,a)].">
      <j1 rule="hyper" parents="17302 18505"/>
    </justification>
  </clause>

  <clause id="18507">
    <literal><![CDATA[
      K(x,L(y,z,(y * z) \ u)) * u = (y * z) * ((T(y,x) * z) \ u)
    ]]></literal>
    <justification jstring="[para(18506(a,1),14834(a,1,1))].">
      <j1 rule="para" parents="18506 14834"/>
    </justification>
  </clause>

  <clause id="18508">
    <literal><![CDATA[
      K(x,L(y,z,z \ u)) * u = (y * z) * ((T(y,x) * z) \ u)
    ]]></literal>
    <justification jstring="[para(18408(a,1),18507(a,1,1))].">
      <j1 rule="para" parents="18408 18507"/>
    </justification>
  </clause>

  <clause id="18509">
    <literal><![CDATA[
      (x * y) * ((T(x,z) * y) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      (K(z,x) * y) * (y \ u) = w
    ]]></literal>
    <justification jstring="[para(18508(a,1),14793(a,1))].">
      <j1 rule="para" parents="18508 14793"/>
    </justification>
  </clause>

  <clause id="18510">
    <literal><![CDATA[
      K(x,L((y * z) / u,y,z \ 1)) = K(x,y / (u / z))
    ]]></literal>
    <justification jstring="[hyper(58,a,18447,a(flip),b,18451,a),flip(a)].">
      <j1 rule="hyper" parents="58 18447 18451"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18511">
    <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(14190,a,18510,a)].">
      <j1 rule="hyper" parents="14190 18510"/>
    </justification>
  </clause>

  <clause id="18512">
    <literal><![CDATA[
      K(x,L((y * z) * u,y,z \ 1)) = K(x,y / ((u \ 1) / z))
    ]]></literal>
    <justification jstring="[hyper(14151,a,18510,a)].">
      <j1 rule="hyper" parents="14151 18510"/>
    </justification>
  </clause>

  <clause id="18513">
    <literal><![CDATA[
      K(x,y / (z * (y / (u * y)))) = K(x,y / (z / u))
    ]]></literal>
    <justification jstring="[hyper(58,a,16910,a(flip),b,18510,a)].">
      <j1 rule="hyper" parents="58 16910 18510"/>
    </justification>
  </clause>

  <clause id="18514">
    <literal><![CDATA[
      K(x,(y \ z) / (u * ((y \ z) / z))) = K(x,(y \ z) / (u / y))
    ]]></literal>
    <justification jstring="[para(5(a,1),18513(a,1,2,2,2,2))].">
      <j1 rule="para" parents="5 18513"/>
    </justification>
  </clause>

  <clause id="18515">
    <literal><![CDATA[
      K(x,y) * (((x \ z) / z) \ u) = ((T(x,y) \ z) / z) \ u
    ]]></literal>
    <justification jstring="[hyper(12658,a,18291,a)].">
      <j1 rule="hyper" parents="12658 18291"/>
    </justification>
  </clause>

  <clause id="18517">
    <literal><![CDATA[
      T(x,((T(y,z) \ u) / u) \ w) = T(x,T((y \ u) / u,z) \ w)
    ]]></literal>
    <justification jstring="[para(18515(a,1),15412(a,1,2))].">
      <j1 rule="para" parents="18515 15412"/>
    </justification>
  </clause>

  <clause id="18518">
    <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(10867,a,18314,a),flip(a)].">
      <j1 rule="hyper" parents="10867 18314"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18520">
    <literal><![CDATA[
      K(x,((T(y,z) \ 1) * u) \ ((y \ 1) * (z * y))) = K(x,(y \ u) \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,14605,a(flip),b,18314,a),flip(a)].">
      <j1 rule="hyper" parents="58 14605 18314"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18521">
    <literal><![CDATA[
      K(x * (1 / (1 / (y \ z))),(z \ y) \ x) = a(1 / (z \ y),z \ y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(14055,a,18382,a)].">
      <j1 rule="hyper" parents="14055 18382"/>
    </justification>
  </clause>

  <clause id="18522">
    <literal><![CDATA[
      K(x * (y \ z),(z \ y) \ x) = a(1 / (z \ y),z \ y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(14083,a,18521,a)].">
      <j1 rule="hyper" parents="14083 18521"/>
    </justification>
  </clause>

  <clause id="18523">
    <literal><![CDATA[
      K(x * (y \ z),(z \ y) \ x) = 1
    ]]></literal>
    <justification jstring="[hyper(320,a,13780,a(flip),b,18522,a),flip(a)].">
      <j1 rule="hyper" parents="320 13780 18522"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18524">
    <literal><![CDATA[
      K(x * (y \ z),x / (z \ y)) = 1
    ]]></literal>
    <justification jstring="[hyper(16608,a,18523,a)].">
      <j1 rule="hyper" parents="16608 18523"/>
    </justification>
  </clause>

  <clause id="18527">
    <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,14987,a(flip),b,18503,a)].">
      <j1 rule="hyper" parents="58 14987 18503"/>
    </justification>
  </clause>

  <clause id="18528">
    <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,16924,a(flip),b,18527,a),flip(a)].">
      <j1 rule="hyper" parents="58 16924 18527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18529">
    <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(18528(a,1),14956(a,1,1))].">
      <j1 rule="para" parents="18528 14956"/>
    </justification>
  </clause>

  <clause id="18530">
    <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,18190,a(flip),b,17562,a)].">
      <j1 rule="hyper" parents="58 18190 17562"/>
    </justification>
  </clause>

  <clause id="18531">
    <literal><![CDATA[
      K(x,y * (z * K((u \ w) \ v5,u \ w))) = K(x,(y * z) * K(w \ u,v5))
    ]]></literal>
    <justification jstring="[hyper(15995,a,17608,a),flip(a)].">
      <j1 rule="hyper" parents="15995 17608"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18532">
    <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,15826,a(flip),b,18531,a),flip(a)].">
      <j1 rule="hyper" parents="320 15826 18531"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18533">
    <literal><![CDATA[
      K(x,y * (z * K(u * (w \ y),u \ w))) = K(x,T(y,w \ u) * z)
    ]]></literal>
    <justification jstring="[para(12470(a,1),18532(a,1,2,2,2))].">
      <j1 rule="para" parents="12470 18532"/>
    </justification>
  </clause>

  <clause id="18534">
    <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,18053,a(flip),b,17678,a),flip(a)].">
      <j1 rule="hyper" parents="320 18053 17678"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18536">
    <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,16320,a(flip),b,18534,a),flip(a)].">
      <j1 rule="hyper" parents="320 16320 18534"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18537">
    <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,16020,a(flip),b,18536,a),flip(a)].">
      <j1 rule="hyper" parents="58 16020 18536"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18538">
    <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,16320,a(flip),b,18537,a),flip(a)].">
      <j1 rule="hyper" parents="320 16320 18537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18539">
    <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,18077,a(flip),b,18538,a),flip(a)].">
      <j1 rule="hyper" parents="58 18077 18538"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18540">
    <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,18151,a(flip),b,18539,a),flip(a)].">
      <j1 rule="hyper" parents="58 18151 18539"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18541">
    <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,18075,a(flip),b,18540,a)].">
      <j1 rule="hyper" parents="58 18075 18540"/>
    </justification>
  </clause>

  <clause id="18542">
    <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(5130(a,1),17681(a,2,2,1,1,1,2))].">
      <j1 rule="para" parents="5130 17681"/>
    </justification>
  </clause>

  <clause id="18543">
    <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(5365(a,1),17702(a,1,2,2,2))].">
      <j1 rule="para" parents="5365 17702"/>
    </justification>
  </clause>

  <clause id="18544">
    <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,18214,a(flip),b,18543,a),flip(a)].">
      <j1 rule="hyper" parents="58 18214 18543"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18545">
    <literal><![CDATA[
      K(x,y * (((z \ 1) * u) \ K(u,z))) = K(x,y / T((z \ 1) * u,u))
    ]]></literal>
    <justification jstring="[para(5908(a,1),18544(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5908 18544"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18546">
    <literal><![CDATA[
      K(x,y * (((z \ 1) * u) \ K(u,z))) = K(x,y / (u * (z \ 1)))
    ]]></literal>
    <justification jstring="[hyper(320,a,16209,a(flip),b,18545,a),flip(a)].">
      <j1 rule="hyper" parents="320 16209 18545"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18547">
    <literal><![CDATA[
      K(x,y / ((z \ 1) * T(u,z))) = K(x,y / (u * (z \ 1)))
    ]]></literal>
    <justification jstring="[hyper(58,a,17701,a(flip),b,18546,a)].">
      <j1 rule="hyper" parents="58 17701 18546"/>
    </justification>
  </clause>

  <clause id="18548">
    <literal><![CDATA[
      K(x,y / (T(z,u) * (u \ 1))) = K(x,y / ((u \ 1) * z))
    ]]></literal>
    <justification jstring="[hyper(58,a,17729,a(flip),b,18547,a),flip(a)].">
      <j1 rule="hyper" parents="58 17729 18547"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18549">
    <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,13064,a(flip),b,17877,a),flip(a)].">
      <j1 rule="hyper" parents="320 13064 17877"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18550">
    <literal><![CDATA[
      T(x,(((y \ z) \ z) / u) \ w) = T(x,K(z,y) * ((y / u) \ w))
    ]]></literal>
    <justification jstring="[hyper(58,a,16007,a(flip),b,18549,a)].">
      <j1 rule="hyper" parents="58 16007 18549"/>
    </justification>
  </clause>

  <clause id="18551">
    <literal><![CDATA[
      T(x,(((y \ z) \ z) / u) \ w) = T(x,(T(y,z) / u) \ w)
    ]]></literal>
    <justification jstring="[hyper(320,a,17677,a(flip),b,18550,a),flip(a)].">
      <j1 rule="hyper" parents="320 17677 18550"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18553">
    <literal><![CDATA[
      T(x,(T(y \ z,z) / u) \ w) = T(x,((z / y) / u) \ w)
    ]]></literal>
    <justification jstring="[hyper(58,a,18139,a(flip),b,18551,a),flip(a)].">
      <j1 rule="hyper" parents="58 18139 18551"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18554">
    <literal><![CDATA[
      T(x,((y / z) / y) \ u) = T(x,(y \ (z \ y)) \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,17976,a(flip),b,18553,a),flip(a)].">
      <j1 rule="hyper" parents="58 17976 18553"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18555">
    <literal><![CDATA[
      T(x,(y \ ((z \ K(z,y)) \ y)) \ u) = T(x,(y \ (y / (z \ 1))) \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,15413,a(flip),b,18554,a),flip(a)].">
      <j1 rule="hyper" parents="58 15413 18554"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18556">
    <literal><![CDATA[
      T(x,(((y \ 1) \ z) / z) \ u) = T(x,(z \ (z / (y \ 1))) \ u)
    ]]></literal>
    <justification jstring="[para(10138(a,1),18555(a,1,2,1))].">
      <j1 rule="para" parents="10138 18555"/>
    </justification>
  </clause>

  <clause id="18557">
    <literal><![CDATA[
      T(x,(y \ (y / ((z \ 1) \ 1))) \ u) = T(x,((z \ y) / y) \ u)
    ]]></literal>
    <justification jstring="[hyper(14130,a,18556,a),flip(a)].">
      <j1 rule="hyper" parents="14130 18556"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18558">
    <literal><![CDATA[
      T(x,((y \ z) / z) \ u) = T(x,(z \ (z / y)) \ u)
    ]]></literal>
    <justification jstring="[hyper(14129,a,18557,a),flip(a)].">
      <j1 rule="hyper" parents="14129 18557"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18559">
    <literal><![CDATA[
      T(x,T((y \ z) / z,u) \ w) = T(x,(z \ (z / T(y,u))) \ w)
    ]]></literal>
    <justification jstring="[hyper(58,a,18517,a(flip),b,18558,a)].">
      <j1 rule="hyper" parents="58 18517 18558"/>
    </justification>
  </clause>

  <clause id="18560">
    <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,18061,a(flip),b,18559,a),flip(a)].">
      <j1 rule="hyper" parents="320 18061 18559"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18561">
    <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(16785,a,18560,a)].">
      <j1 rule="hyper" parents="16785 18560"/>
    </justification>
  </clause>

  <clause id="18562">
    <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,15454,a(flip),b,18561,a)].">
      <j1 rule="hyper" parents="58 15454 18561"/>
    </justification>
  </clause>

  <clause id="18563">
    <literal><![CDATA[
      T(x,T(T(y / z,u) \ y,w)) = T(x,T(y / T(z,w),u) \ y)
    ]]></literal>
    <justification jstring="[para(7628(a,1),18562(a,1,2,1))].">
      <j1 rule="para" parents="7628 18562"/>
    </justification>
  </clause>

  <clause id="18564">
    <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,18072,a(flip),b,18563,a),flip(a)].">
      <j1 rule="hyper" parents="320 18072 18563"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18565">
    <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,12382,a,b,18564,a)].">
      <j1 rule="hyper" parents="320 12382 18564"/>
    </justification>
  </clause>

  <clause id="18566">
    <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(18194,a,18565,a)].">
      <j1 rule="hyper" parents="18194 18565"/>
    </justification>
  </clause>

  <clause id="18567">
    <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,12369,a(flip),b,18566,a),flip(a)].">
      <j1 rule="hyper" parents="58 12369 18566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18568">
    <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),18567(a,2,2,1))].">
      <j1 rule="para" parents="453 18567"/>
    </justification>
  </clause>

  <clause id="18569">
    <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,18564,a(flip),b,18568,a),flip(a)].">
      <j1 rule="hyper" parents="58 18564 18568"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18570">
    <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,13286,a(flip),b,17997,a),flip(a)].">
      <j1 rule="hyper" parents="320 13286 17997"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18571">
    <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,16813,a(flip),b,18059,a)].">
      <j1 rule="hyper" parents="58 16813 18059"/>
    </justification>
  </clause>

  <clause id="18572">
    <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(18571(a,1),18060(a,1))].">
      <j1 rule="para" parents="18571 18060"/>
    </justification>
  </clause>

  <clause id="18573">
    <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(16811(a,1),18572(a,1))].">
      <j1 rule="para" parents="16811 18572"/>
    </justification>
  </clause>

  <clause id="18574">
    <literal><![CDATA[
      L(x,(y * z) / y,(y \ z) \ 1) = L(x,y * (z / y),(z / y) \ 1)
    ]]></literal>
    <justification jstring="[para(4120(a,1),18570(a,1,3,1))].">
      <j1 rule="para" parents="4120 18570"/>
    </justification>
  </clause>

  <clause id="18575">
    <literal><![CDATA[
      L(x,y * (z / y),(z / y) \ 1) = L(x,y * (z / y),(y \ z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,13286,a(flip),b,18574,a),flip(a)].">
      <j1 rule="hyper" parents="58 13286 18574"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18576">
    <literal><![CDATA[
      L(x,y * (z / y),(z / y) \ 1) = L(x,z,(y \ z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(320,a,13300,a(flip),b,18575,a),flip(a)].">
      <j1 rule="hyper" parents="320 13300 18575"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18577">
    <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(18576(a,1),10152(a,1,2))].">
      <j1 rule="para" parents="18576 10152"/>
    </justification>
  </clause>

  <clause id="18578">
    <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(17410(a,2),17221(a,1,1))].">
      <j1 rule="para" parents="17410 17221"/>
    </justification>
  </clause>

  <clause id="18579">
    <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(13427(a,2),17309(a,1,2,1,2))].">
      <j1 rule="para" parents="13427 17309"/>
    </justification>
  </clause>

  <clause id="18580">
    <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(14552,a,17406,a)].">
      <j1 rule="hyper" parents="14552 17406"/>
    </justification>
  </clause>

  <clause id="18582">
    <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(15528,a,18580,a)].">
      <j1 rule="hyper" parents="15528 18580"/>
    </justification>
  </clause>

  <clause id="18583">
    <literal><![CDATA[
      K(x,(((y * z) \ z) * u) \ T(z,y)) = K(x,L(u \ (y * z),z,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(15490,a,18582,a),flip(a)].">
      <j1 rule="hyper" parents="15490 18582"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18584">
    <literal><![CDATA[
      K(x,L(y \ (z * u),u,z \ 1)) = K(x,(((u * z) \ u) * y) \ u)
    ]]></literal>
    <justification jstring="[para(13821(a,1),18583(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13821 18583"/>
      <j2 rule="flip"/>
    </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(17382(a,1),17415(a,1,2))].">
      <j1 rule="para" parents="17382 17415"/>
    </justification>
  </clause>

  <clause id="18586">
    <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(17794,a,17770,a),flip(a)].">
      <j1 rule="hyper" parents="17794 17770"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18587">
    <literal><![CDATA[
      K(x,T(T(y,x) / (z \ 1),y) * u) = K(x,(T(y,z) / (z \ 1)) * u)
    ]]></literal>
    <justification jstring="[hyper(7360,a,18586,a)].">
      <j1 rule="hyper" parents="7360 18586"/>
    </justification>
  </clause>

  <clause id="18589">
    <literal><![CDATA[
      K(x,((y \ 1) \ T(z,x)) * u) = K(x,(T(z,y) / (y \ 1)) * u)
    ]]></literal>
    <justification jstring="[hyper(58,a,16122,a(flip),b,18587,a)].">
      <j1 rule="hyper" parents="58 16122 18587"/>
    </justification>
  </clause>

  <clause id="18590">
    <literal><![CDATA[
      K(x,(T(y,z) / (z \ 1)) * u) = K(x,((z \ 1) \ y) * u)
    ]]></literal>
    <justification jstring="[hyper(17709,a,18589,a),flip(a)].">
      <j1 rule="hyper" parents="17709 18589"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18591">
    <literal><![CDATA[
      K(x,(y / (z \ K(y,z))) * u) = K(x,((z \ 1) \ y) * u)
    ]]></literal>
    <justification jstring="[hyper(58,a,17717,a(flip),b,18590,a)].">
      <j1 rule="hyper" parents="58 17717 18590"/>
    </justification>
  </clause>

  <clause id="18592">
    <literal><![CDATA[
      K(x,(y / (z / u)) / T(w,(z / u) \ y)) = K(x,w \ (y / (T(u,z) \ z)))
    ]]></literal>
    <justification jstring="[hyper(17942,a,18111,a),flip(a)].">
      <j1 rule="hyper" parents="17942 18111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18593">
    <literal><![CDATA[
      K(x,y \ (z / (T(u,w) \ w))) = K(x,y \ (z / (w / u)))
    ]]></literal>
    <justification jstring="[hyper(16157,a,18592,a),flip(a)].">
      <j1 rule="hyper" parents="16157 18592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18594">
    <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(18592(a,1),16157(a,1))].">
      <j1 rule="para" parents="18592 16157"/>
    </justification>
  </clause>

  <clause id="18595">
    <literal><![CDATA[
      K(x,y \ (z / (z / u))) = K(x,y \ T(u,z))
    ]]></literal>
    <justification jstring="[para(72(a,1),18593(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="72 18593"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18596">
    <literal><![CDATA[
      K(x,y \ T(z \ u,u)) = K(x,y \ (u / z))
    ]]></literal>
    <justification jstring="[para(72(a,1),18595(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="72 18595"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18597">
    <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(10116(a,1),18595(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="10116 18595"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18598">
    <literal><![CDATA[
      K(x,y \ (z \ T(u,z \ 1))) = K(x,y \ (u / z))
    ]]></literal>
    <justification jstring="[hyper(58,a,15324,a(flip),b,18596,a)].">
      <j1 rule="hyper" parents="58 15324 18596"/>
    </justification>
  </clause>

  <clause id="18599">
    <literal><![CDATA[
      K(x,(y / (y / z)) \ (u / (y / z))) = K(x,z \ ((z \ y) \ T(u,(y / z) \ 1)))
    ]]></literal>
    <justification jstring="[para(5602(a,1),18598(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5602 18598"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18600">
    <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,16660,a(flip),b,18597,a),flip(a)].">
      <j1 rule="hyper" parents="320 16660 18597"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18601">
    <literal><![CDATA[
      K(x,(y / (y / z)) \ (u / (y / z))) = K(x,z \ ((z \ y) \ T(u,z / y)))
    ]]></literal>
    <justification jstring="[para(4456(a,1),18599(a,2,2,2,2))].">
      <j1 rule="para" parents="4456 18599"/>
    </justification>
  </clause>

  <clause id="18602">
    <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,13076,a(flip),b,18600,a),flip(a)].">
      <j1 rule="hyper" parents="58 13076 18600"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18603">
    <literal><![CDATA[
      K(x,y \ (T((z * u) \ z,w) \ z)) = K(x,y \ (u * (K(w,u \ 1) * z)))
    ]]></literal>
    <justification jstring="[para(12648(a,1),18602(a,2,2,2))].">
      <j1 rule="para" parents="12648 18602"/>
    </justification>
  </clause>

  <clause id="18604">
    <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,18105,a(flip),b,18603,a),flip(a)].">
      <j1 rule="hyper" parents="320 18105 18603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18605">
    <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,15343,a(flip),b,18604,a),flip(a)].">
      <j1 rule="hyper" parents="320 15343 18604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18606">
    <literal><![CDATA[
      K(x,y \ (T((z * u) \ z,w) \ z)) = K(x,y \ (T(u,w) * z))
    ]]></literal>
    <justification jstring="[hyper(320,a,17668,a(flip),b,18605,a),flip(a)].">
      <j1 rule="hyper" parents="320 17668 18605"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18607">
    <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,15036,a(flip),b,18606,a)].">
      <j1 rule="hyper" parents="58 15036 18606"/>
    </justification>
  </clause>

  <clause id="18608">
    <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,5741,a(flip),b,18607,a),flip(a)].">
      <j1 rule="hyper" parents="320 5741 18607"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18609">
    <literal><![CDATA[
      K(x,y \ ((1 / T(z,u)) * w)) = K(x,y \ (T(z \ 1,u) * w))
    ]]></literal>
    <justification jstring="[hyper(58,a,13076,a(flip),b,18608,a)].">
      <j1 rule="hyper" parents="58 13076 18608"/>
    </justification>
  </clause>

  <clause id="18610">
    <literal><![CDATA[
      K(x,y \ (T(z \ 1,u) * w)) = K(x,y \ ((T(z,u) \ 1) * w))
    ]]></literal>
    <justification jstring="[hyper(58,a,5338,a(flip),b,18609,a),flip(a)].">
      <j1 rule="hyper" parents="58 5338 18609"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18611">
    <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,10930,a(flip),b,18610,a),flip(a)].">
      <j1 rule="hyper" parents="320 10930 18610"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18612">
    <literal><![CDATA[
      K(x,y \ (z / T(u,z))) = K(x,y \ (u \ z))
    ]]></literal>
    <justification jstring="[hyper(320,a,5043,a(flip),b,17952,a),flip(a)].">
      <j1 rule="hyper" parents="320 5043 17952"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18613">
    <literal><![CDATA[
      K(x,y \ (T(z,u) / u)) = K(x,y \ (u \ z))
    ]]></literal>
    <justification jstring="[para(4246(a,2),18612(a,1,2,2))].">
      <j1 rule="para" parents="4246 18612"/>
    </justification>
  </clause>

  <clause id="18614">
    <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(12737(a,1),18613(a,1,2,2,1))].">
      <j1 rule="para" parents="12737 18613"/>
    </justification>
  </clause>

  <clause id="18615">
    <literal><![CDATA[
      K(x,y \ (T(z,u / w) / (u / w))) = K(x,y \ ((T(w,u) \ u) \ z))
    ]]></literal>
    <justification jstring="[hyper(18594,a,18614,a)].">
      <j1 rule="hyper" parents="18594 18614"/>
    </justification>
  </clause>

  <clause id="18616">
    <literal><![CDATA[
      K(x,y \ ((T(z,u) \ u) \ w)) = K(x,y \ ((u / z) \ w))
    ]]></literal>
    <justification jstring="[hyper(58,a,18613,a(flip),b,18615,a),flip(a)].">
      <j1 rule="hyper" parents="58 18613 18615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18617">
    <literal><![CDATA[
      K(x,(y \ 1) \ ((z / u) \ w)) = K(x,y * ((u \ T(z,u)) \ w))
    ]]></literal>
    <justification jstring="[hyper(14069,a,18616,a),flip(a)].">
      <j1 rule="hyper" parents="14069 18616"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18618">
    <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(18617(a,1),14008(a,1))].">
      <j1 rule="para" parents="18617 14008"/>
    </justification>
  </clause>

  <clause id="18619">
    <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(4248(a,2),18618(a,1,2,2,1))].">
      <j1 rule="para" parents="4248 18618"/>
    </justification>
  </clause>

  <clause id="18620">
    <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(18192(a,1),18619(a,1))].">
      <j1 rule="para" parents="18192 18619"/>
    </justification>
  </clause>

  <clause id="18621">
    <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(18089(a,1),18260(a,1,2,1))].">
      <j1 rule="para" parents="18089 18260"/>
    </justification>
  </clause>

  <clause id="18622">
    <literal><![CDATA[
      T(x,(y * (z \ K(u,z \ 1))) * u) = T(x,u * ((z \ 1) * T(y,u / z)))
    ]]></literal>
    <justification jstring="[para(13858(a,1),18621(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13858 18621"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18624">
    <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,16144,a(flip),b,18622,a),flip(a)].">
      <j1 rule="hyper" parents="320 16144 18622"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18625">
    <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,16799,a(flip),b,18624,a),flip(a)].">
      <j1 rule="hyper" parents="58 16799 18624"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18626">
    <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(17230(a,1),18312(a,1,1,1))].">
      <j1 rule="para" parents="17230 18312"/>
    </justification>
  </clause>

  <clause id="18628">
    <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(17969,a,18626,a)].">
      <j1 rule="hyper" parents="17969 18626"/>
    </justification>
  </clause>

  <clause id="18630">
    <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(17965(a,1),18628(a,2,2))].">
      <j1 rule="para" parents="17965 18628"/>
    </justification>
  </clause>

  <clause id="18631">
    <literal><![CDATA[
      L(K(x,y) * K(z,u),w,K(v5,v6)) = K(z,u) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(4028,a,18630,a)].">
      <j1 rule="hyper" parents="4028 18630"/>
    </justification>
  </clause>

  <clause id="18632">
    <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(18631(a,1),17866(a,1,1,1))].">
      <j1 rule="para" parents="18631 17866"/>
    </justification>
  </clause>

  <clause id="18633">
    <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(14041(a,1),18632(a,1,1))].">
      <j1 rule="para" parents="14041 18632"/>
    </justification>
  </clause>

  <clause id="18635">
    <literal><![CDATA[
      T(K(x,y) * a(z,u,w),K(v5,v6)) = a(z,u,w) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(7864,a,18633,a)].">
      <j1 rule="hyper" parents="7864 18633"/>
    </justification>
  </clause>

  <clause id="18636">
    <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(12472(a,1),18345(a,1,1))].">
      <j1 rule="para" parents="12472 18345"/>
    </justification>
  </clause>

  <clause id="18637">
    <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(4065(a,1),18358(a,1,2))].">
      <j1 rule="para" parents="4065 18358"/>
    </justification>
  </clause>

  <clause id="18638">
    <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(14470(a,1),18493(a,1,1,1))].">
      <j1 rule="para" parents="14470 18493"/>
    </justification>
  </clause>

  <clause id="18640">
    <literal><![CDATA[
      ((K(x,y) * z) * (u * K(w,v5))) / u = K(x,y) * ((z * u) / (u * K(v5,w)))
    ]]></literal>
    <justification jstring="[para(18311(a,1),18638(a,1,1))].">
      <j1 rule="para" parents="18311 18638"/>
    </justification>
  </clause>

  <clause id="18641">
    <literal><![CDATA[
      ((K(x,y) * z) * u) / (u * K(w,v5)) = K(x,y) * ((z * u) / (u * K(w,v5)))
    ]]></literal>
    <justification jstring="[hyper(14567,a,18640,a)].">
      <j1 rule="hyper" parents="14567 18640"/>
    </justification>
  </clause>

  <clause id="18642">
    <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(16618,a,18511,a)].">
      <j1 rule="hyper" parents="16618 18511"/>
    </justification>
  </clause>

  <clause id="18643">
    <literal><![CDATA[
      K(x,y / (T((z \ u) \ 1,u) / w)) = K(x,y / (((u / z) \ 1) / w))
    ]]></literal>
    <justification jstring="[hyper(58,a,18512,a(flip),b,18642,a),flip(a)].">
      <j1 rule="hyper" parents="58 18512 18642"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18644">
    <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(443,a,18446,a,b,18643,a)].">
      <j1 rule="hyper" parents="443 18446 18643"/>
    </justification>
  </clause>

  <clause id="18645">
    <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,14557,a(flip),b,18518,a),flip(a)].">
      <j1 rule="hyper" parents="320 14557 18518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18646">
    <literal><![CDATA[
      K(x,L(y \ (z * u),u,z \ 1)) = K(x,(z \ y) \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,18520,a(flip),b,18645,a),flip(a)].">
      <j1 rule="hyper" parents="58 18520 18645"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18647">
    <literal><![CDATA[
      K(x,(((y * z) \ y) * u) \ y) = K(x,(z \ u) \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,18584,a(flip),b,18646,a)].">
      <j1 rule="hyper" parents="58 18584 18646"/>
    </justification>
  </clause>

  <clause id="18648">
    <literal><![CDATA[
      K(x,y \ (z * (((y * u) \ y) \ y))) = K(x,(u \ (z \ y)) \ y)
    ]]></literal>
    <justification jstring="[hyper(18445,a,18647,a)].">
      <j1 rule="hyper" parents="18445 18647"/>
    </justification>
  </clause>

  <clause id="18649">
    <literal><![CDATA[
      K(x,(((y * z) \ y) * T(u,z \ 1)) \ y) = K(x,(u / z) \ y)
    ]]></literal>
    <justification jstring="[hyper(320,a,15277,a(flip),b,18647,a),flip(a)].">
      <j1 rule="hyper" parents="320 15277 18647"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18650">
    <literal><![CDATA[
      K(x,((y \ z) \ u) \ y) = K(x,((z \ y) * u) \ y)
    ]]></literal>
    <justification jstring="[para(5(a,1),18647(a,1,2,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5 18647"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18651">
    <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(14486(a,1),18647(a,2,2,1))].">
      <j1 rule="para" parents="14486 18647"/>
    </justification>
  </clause>

  <clause id="18652">
    <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(18647(a,2),16077(a,1))].">
      <j1 rule="para" parents="18647 16077"/>
    </justification>
  </clause>

  <clause id="18653">
    <literal><![CDATA[
      K(x,((y \ z) * u) \ z) * K(x,K(z,y \ u)) = K(x,z / ((z \ y) \ u))
    ]]></literal>
    <justification jstring="[para(18650(a,1),9934(a,1,1))].">
      <j1 rule="para" parents="18650 9934"/>
    </justification>
  </clause>

  <clause id="18654">
    <literal><![CDATA[
      K(x,y \ (z * T(y * u,y))) = K(x,(u \ (z \ y)) \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,13165,a(flip),b,18648,a)].">
      <j1 rule="hyper" parents="58 13165 18648"/>
    </justification>
  </clause>

  <clause id="18655">
    <literal><![CDATA[
      K(x,(y \ (z \ u)) \ u) = K(x,u \ (z * (y * u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,18015,a(flip),b,18654,a),flip(a)].">
      <j1 rule="hyper" parents="58 18015 18654"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18656">
    <literal><![CDATA[
      K(x,y \ ((y / z) * (u * y))) = K(x,(u \ z) \ y)
    ]]></literal>
    <justification jstring="[para(75(a,1),18655(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="75 18655"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18657">
    <literal><![CDATA[
      K(x,(y \ (z * u)) \ u) = K(x,u \ (z \ (y * u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,14898,a(flip),b,18656,a),flip(a)].">
      <j1 rule="hyper" parents="58 14898 18656"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18659">
    <literal><![CDATA[
      K(x,((y / z) \ u) \ z) = K(x,z \ ((z / u) * y))
    ]]></literal>
    <justification jstring="[para(7(a,1),18656(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="7 18656"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18660">
    <literal><![CDATA[
      T(K(x,y \ (z \ (u * y))),y) = K(x,y / (u \ (z * y)))
    ]]></literal>
    <justification jstring="[para(18657(a,1),7881(a,1,1))].">
      <j1 rule="para" parents="18657 7881"/>
    </justification>
  </clause>

  <clause id="18661">
    <literal><![CDATA[
      K(x * (y * (x \ 1)),z \ ((z / u) * w)) = K(y,T(((z / w) * u) \ z,x))
    ]]></literal>
    <justification jstring="[hyper(17792,a,18659,a),flip(a)].">
      <j1 rule="hyper" parents="17792 18659"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18662">
    <literal><![CDATA[
      K(x,(y \ (z * u)) / u) = K(x,u / (z \ (y * u)))
    ]]></literal>
    <justification jstring="[hyper(8052,a,18660,a)].">
      <j1 rule="hyper" parents="8052 18660"/>
    </justification>
  </clause>

  <clause id="18663">
    <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,14628,a,b,18660,a)].">
      <j1 rule="hyper" parents="58 14628 18660"/>
    </justification>
  </clause>

  <clause id="18664">
    <literal><![CDATA[
      K(x * (y * (x \ 1)),z / (u \ (w * z))) = K(y,T((w \ (u * z)) / z,x))
    ]]></literal>
    <justification jstring="[hyper(14103,a,18662,a),flip(a)].">
      <j1 rule="hyper" parents="14103 18662"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18665">
    <literal><![CDATA[
      K(x,y / (z \ (T(u,z) * y))) = K(x,T((u \ (z * y)) / y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,18218,a(flip),b,18662,a),flip(a)].">
      <j1 rule="hyper" parents="58 18218 18662"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18666">
    <literal><![CDATA[
      K(x,(y * ((z * u) \ z)) \ z) = K(x,(y / u) \ z)
    ]]></literal>
    <justification jstring="[para(6207(a,1),18649(a,1,2,1))].">
      <j1 rule="para" parents="6207 18649"/>
    </justification>
  </clause>

  <clause id="18667">
    <literal><![CDATA[
      K(x,y \ ((y * z) * (u \ y))) = K(x,(u / z) \ y)
    ]]></literal>
    <justification jstring="[hyper(18445,a,18666,a)].">
      <j1 rule="hyper" parents="18445 18666"/>
    </justification>
  </clause>

  <clause id="18668">
    <literal><![CDATA[
      K(x,((y / z) / u) \ y) = K(x,y \ ((y * u) * z))
    ]]></literal>
    <justification jstring="[para(75(a,1),18667(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="75 18667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18669">
    <literal><![CDATA[
      K(x,y \ ((z * y) * (u \ y))) = K(x,(u / T(z,y)) \ y)
    ]]></literal>
    <justification jstring="[para(105(a,1),18667(a,1,2,2,1))].">
      <j1 rule="para" parents="105 18667"/>
    </justification>
  </clause>

  <clause id="18670">
    <literal><![CDATA[
      K(x,((y * ((y * z) / y)) / u) \ z) = K(x,z \ ((z * u) * ((y * z) \ T(z,y))))
    ]]></literal>
    <justification jstring="[para(13975(a,1),18667(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="13975 18667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18671">
    <literal><![CDATA[
      K(x,T(y,z * u) / ((y / z) / u)) = K(x,y \ ((y * u) * z))
    ]]></literal>
    <justification jstring="[hyper(58,a,16268,a,b,18668,a)].">
      <j1 rule="hyper" parents="58 16268 18668"/>
    </justification>
  </clause>

  <clause id="18672">
    <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(5955(a,1),18669(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5955 18669"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18673">
    <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(18652,a,18044,a)].">
      <j1 rule="hyper" parents="18652 18044"/>
    </justification>
  </clause>

  <clause id="18674">
    <literal><![CDATA[
      K(x,y / ((y \ z) \ u)) = K(x,y / ((z \ y) * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,14106,a(flip),b,18653,a),flip(a)].">
      <j1 rule="hyper" parents="58 14106 18653"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18675">
    <literal><![CDATA[
      K(x,T(((y / z) * u) \ y,w)) = K(x,T(y \ ((y / u) * z),w))
    ]]></literal>
    <justification jstring="[hyper(14103,a,18661,a),flip(a)].">
      <j1 rule="hyper" parents="14103 18661"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18676">
    <literal><![CDATA[
      K(x,T(y \ ((y / z) * u),z)) = K(x,y / (z * (u \ y)))
    ]]></literal>
    <justification jstring="[hyper(58,a,16358,a(flip),b,18675,a),flip(a)].">
      <j1 rule="hyper" parents="58 16358 18675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18677">
    <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(18664(a,1),14103(a,1))].">
      <j1 rule="para" parents="18664 14103"/>
    </justification>
  </clause>

  <clause id="18678">
    <literal><![CDATA[
      K(x,T((y \ (z * u)) / u,y)) = K(x,T(u / (z \ (y * u)),z))
    ]]></literal>
    <justification jstring="[hyper(18677,a,18222,a),flip(a)].">
      <j1 rule="hyper" parents="18677 18222"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18679">
    <literal><![CDATA[
      K(x,y / (z \ (T(u,z) * y))) = K(x,T(y / (z \ (u * y)),z))
    ]]></literal>
    <justification jstring="[hyper(18677,a,18665,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="18677 18665"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18680">
    <literal><![CDATA[
      K(x,T(y / (z \ (u * y)),u)) = K(x,T(y / (z \ (u * y)),z))
    ]]></literal>
    <justification jstring="[hyper(18677,a,18678,a)].">
      <j1 rule="hyper" parents="18677 18678"/>
    </justification>
  </clause>

  <clause id="18681">
    <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(18045,a,18651,a)].">
      <j1 rule="hyper" parents="18045 18651"/>
    </justification>
  </clause>

  <clause id="18682">
    <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(10840(a,1),18681(a,1,2,1))].">
      <j1 rule="para" parents="10840 18681"/>
    </justification>
  </clause>

  <clause id="18683">
    <literal><![CDATA[
      K(x,K(y,z) * ((((u * w) \ u) * v5) \ u)) = K(x,((w \ v5) * K(z,y)) \ u)
    ]]></literal>
    <justification jstring="[hyper(17591,a,18682,a)].">
      <j1 rule="hyper" parents="17591 18682"/>
    </justification>
  </clause>

  <clause id="18684">
    <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,17848,a(flip),b,18683,a),flip(a)].">
      <j1 rule="hyper" parents="320 17848 18683"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18686">
    <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,18684,a(flip),b,18673,a),flip(a)].">
      <j1 rule="hyper" parents="320 18684 18673"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18687">
    <literal><![CDATA[
      K(x,(y \ (z * K(u,w))) \ v5) = K(x,K(w,u) * ((y \ z) \ v5))
    ]]></literal>
    <justification jstring="[hyper(16082,a,18686,a)].">
      <j1 rule="hyper" parents="16082 18686"/>
    </justification>
  </clause>

  <clause id="18688">
    <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(17410(a,2),18578(a,1,2))].">
      <j1 rule="para" parents="17410 18578"/>
    </justification>
  </clause>

  <clause id="18689">
    <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(17336(a,1),18579(a,1,2,1))].">
      <j1 rule="para" parents="17336 18579"/>
    </justification>
  </clause>

  <clause id="18690">
    <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(18351(a,1),18689(a,1,2)),flip(a)].">
      <j1 rule="para" parents="18351 18689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18691">
    <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,13876,a(flip),b,18690,a),flip(a)].">
      <j1 rule="hyper" parents="320 13876 18690"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18693">
    <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(14259(a,2),18691(a,1,1))].">
      <j1 rule="para" parents="14259 18691"/>
    </justification>
  </clause>

  <clause id="18694">
    <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(14925(a,2),18693(a,2,2))].">
      <j1 rule="para" parents="14925 18693"/>
    </justification>
  </clause>

  <clause id="18695">
    <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,18450,a(flip),b,18694,a)].">
      <j1 rule="hyper" parents="58 18450 18694"/>
    </justification>
  </clause>

  <clause id="18696">
    <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,17769,a(flip),b,18695,a),flip(a)].">
      <j1 rule="hyper" parents="320 17769 18695"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18697">
    <literal><![CDATA[
      L(K(x,y) * z,u,K(w,v5)) = K(x,y) * L(z,u,K(w,v5))
    ]]></literal>
    <justification jstring="[para(13750(a,1),18696(a,1,1))].">
      <j1 rule="para" parents="13750 18696"/>
    </justification>
  </clause>

  <clause id="18698">
    <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,15070,a(flip),b,18697,a),flip(a)].">
      <j1 rule="hyper" parents="320 15070 18697"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18699">
    <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(18697(a,2),16855(a,1,2,1))].">
      <j1 rule="para" parents="18697 16855"/>
    </justification>
  </clause>

  <clause id="18700">
    <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(17158(a,1),18585(a,1,2,2))].">
      <j1 rule="para" parents="17158 18585"/>
    </justification>
  </clause>

  <clause id="18701">
    <literal><![CDATA[
      (x / (1 / y)) * (K(z,T(u,y)) / y) = (x / (y \ 1)) * (y \ K(z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,14702,a(flip),b,18637,a),flip(a)].">
      <j1 rule="hyper" parents="58 14702 18637"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18702">
    <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,5814,a(flip),b,18688,a)].">
      <j1 rule="hyper" parents="58 5814 18688"/>
    </justification>
  </clause>

  <clause id="18703">
    <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(7755(a,1),18702(a,1,3))].">
      <j1 rule="para" parents="7755 18702"/>
    </justification>
  </clause>

  <clause id="18704">
    <literal><![CDATA[
      L(x,K(y,K(z,u)) * w,v5) = L(x,w,v5)
    ]]></literal>
    <justification jstring="[hyper(17218,a,18703,a),flip(a)].">
      <j1 rule="hyper" parents="17218 18703"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18705">
    <literal><![CDATA[
      L(x,K(y,K(z,u)) * w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,w,v5) = v6
    ]]></literal>
    <justification jstring="[para(18703(a,1),17217(a,1)),flip(b)].">
      <j1 rule="para" parents="18703 17217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18708">
    <literal><![CDATA[
      L(x,K(y,T(z,u)),w) = L(x,K(y,z),w)
    ]]></literal>
    <justification jstring="[para(7166(a,1),18704(a,1,2))].">
      <j1 rule="para" parents="7166 18704"/>
    </justification>
  </clause>

  <clause id="18709">
    <literal><![CDATA[
      R(x,K(y,z),u) = L(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(58,a,16845,a(flip),b,18708,a)].">
      <j1 rule="hyper" parents="58 16845 18708"/>
    </justification>
  </clause>

  <clause id="18710">
    <literal><![CDATA[
      L((x / y) * K(z,u),K(u,z),y) = x / (K(u,z) * y)
    ]]></literal>
    <justification jstring="[hyper(6356,a,18709,a),flip(a)].">
      <j1 rule="hyper" parents="6356 18709"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18712">
    <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,15771,a,b,18709,a)].">
      <j1 rule="hyper" parents="58 15771 18709"/>
    </justification>
  </clause>

  <clause id="18713">
    <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,9498,a(flip),b,18709,a),flip(a)].">
      <j1 rule="hyper" parents="58 9498 18709"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18714">
    <literal><![CDATA[
      L(x,K(y,z),u * K(z,y)) * u = (x * K(y,z)) * (K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(18709(a,1),9869(a,1,1))].">
      <j1 rule="para" parents="18709 9869"/>
    </justification>
  </clause>

  <clause id="18715">
    <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(7166(a,1),18705(a,1,2))].">
      <j1 rule="para" parents="7166 18705"/>
    </justification>
  </clause>

  <clause id="18716">
    <literal><![CDATA[
      R(x,K(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,K(y,z),u) = w
    ]]></literal>
    <justification jstring="[para(16845(a,1),18715(a,1))].">
      <j1 rule="para" parents="16845 18715"/>
    </justification>
  </clause>

  <clause id="18717">
    <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(17354(a,2),18716(a,1))].">
      <j1 rule="para" parents="17354 18716"/>
    </justification>
  </clause>

  <clause id="18718">
    <literal><![CDATA[
      L(x * K(y,z),K(z,y),u) = (x * u) / (K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(6(a,1),18710(a,1,1,1))].">
      <j1 rule="para" parents="6 18710"/>
    </justification>
  </clause>

  <clause id="18719">
    <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(18718(a,1),6453(a,1,1)),flip(a)].">
      <j1 rule="para" parents="18718 6453"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18720">
    <literal><![CDATA[
      L(x * K(y,T(z,u)),K(z,y),u) = (x * u) / (u * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(18715,a,18713,a)].">
      <j1 rule="hyper" parents="18715 18713"/>
    </justification>
  </clause>

  <clause id="18721">
    <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,14566,a,b,18720,a),flip(a)].">
      <j1 rule="hyper" parents="320 14566 18720"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18723">
    <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(18721(a,2),14567(a,1))].">
      <j1 rule="para" parents="18721 14567"/>
    </justification>
  </clause>

  <clause id="18724">
    <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(15978(a,2),18723(a,1))].">
      <j1 rule="para" parents="15978 18723"/>
    </justification>
  </clause>

  <clause id="18725">
    <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,18708,a(flip),b,18712,a),flip(a)].">
      <j1 rule="hyper" parents="320 18708 18712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18727">
    <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,18641,a(flip),b,18725,a)].">
      <j1 rule="hyper" parents="58 18641 18725"/>
    </justification>
  </clause>

  <clause id="18728">
    <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(9836(a,1),18698(a,1,1))].">
      <j1 rule="para" parents="9836 18698"/>
    </justification>
  </clause>

  <clause id="18729">
    <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(11850(a,1),18728(a,1,1))].">
      <j1 rule="para" parents="11850 18728"/>
    </justification>
  </clause>

  <clause id="18730">
    <literal><![CDATA[
      T(a(x,y,z) \ u,K(w,v5)) = a(x,y,z) \ T(u,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(14949,a,18729,a),flip(a)].">
      <j1 rule="hyper" parents="14949 18729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18731">
    <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,15606,a(flip),b,18730,a),flip(a)].">
      <j1 rule="hyper" parents="320 15606 18730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18732">
    <literal><![CDATA[
      x * K(y,K(z,x * a(u,w,v5))) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(4(a,1),18731(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4 18731"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18733">
    <literal><![CDATA[
      K(x,K(y,z * a(u,w,v5))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(29,a,7794,a,b,18732,a),flip(a)].">
      <j1 rule="hyper" parents="29 7794 18732"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18734">
    <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,18732,a(flip),b,15606,a),flip(a)].">
      <j1 rule="hyper" parents="119 18732 15606"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18735">
    <literal><![CDATA[
      T(x,K(y,z * a(u,w,v5))) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(118,a,18733,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 18733 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18736">
    <literal><![CDATA[
      T(x,K(y,(z * u) * w)) = T(x,K(y,z * (u * w)))
    ]]></literal>
    <justification jstring="[para(80(a,1),18735(a,1,2,2))].">
      <j1 rule="para" parents="80 18735"/>
    </justification>
  </clause>

  <clause id="18737">
    <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(18735(a,1),15103(a,1,2,1,2))].">
      <j1 rule="para" parents="18735 15103"/>
    </justification>
  </clause>

  <clause id="18738">
    <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,18734,a,b,7807,a(flip))].">
      <j1 rule="hyper" parents="116 18734 7807"/>
    </justification>
  </clause>

  <clause id="18739">
    <literal><![CDATA[
      K(x,K(y,a(z,u,w) \ v5)) = v5 \ T(v5,K(x,y))
    ]]></literal>
    <justification jstring="[para(5(a,1),18738(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 18738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18740">
    <literal><![CDATA[
      K(x,K(y,a(z,u,w) \ v5)) = K(v5,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(320,a,4729,a,b,18739,a),flip(a)].">
      <j1 rule="hyper" parents="320 4729 18739"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18741">
    <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(18740(a,1),15964(a,1,1))].">
      <j1 rule="para" parents="18740 15964"/>
    </justification>
  </clause>

  <clause id="18742">
    <literal><![CDATA[
      K(x,T(y,a(z,u,w) \ v5)) = K(x,T(y,v5))
    ]]></literal>
    <justification jstring="[hyper(15983,a,18741,a),flip(a)].">
      <j1 rule="hyper" parents="15983 18741"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18743">
    <literal><![CDATA[
      K(x,T(y,a(z,u,w) * v5)) = K(x,T(y,v5))
    ]]></literal>
    <justification jstring="[hyper(15949,a,18742,a)].">
      <j1 rule="hyper" parents="15949 18742"/>
    </justification>
  </clause>

  <clause id="18744">
    <literal><![CDATA[
      K(x,T(y,(z * u) * w)) = K(x,T(y,z * (u * w)))
    ]]></literal>
    <justification jstring="[para(14443(a,1),18743(a,1,2,2))].">
      <j1 rule="para" parents="14443 18743"/>
    </justification>
  </clause>

  <clause id="18745">
    <literal><![CDATA[
      K(x,T(y,T(z * u,w) * v5)) = K(x,T(y,u * (z * v5)))
    ]]></literal>
    <justification jstring="[hyper(58,a,16552,a,b,18744,a)].">
      <j1 rule="hyper" parents="58 16552 18744"/>
    </justification>
  </clause>

  <clause id="18747">
    <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,18743,a(flip),b,18745,a),flip(a)].">
      <j1 rule="hyper" parents="320 18743 18745"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18748">
    <literal><![CDATA[
      K(x,T(y,(z * a(u,w,v5)) * v6)) = K(x,T(y,z * v6))
    ]]></literal>
    <justification jstring="[hyper(16458,a,18747,a)].">
      <j1 rule="hyper" parents="16458 18747"/>
    </justification>
  </clause>

  <clause id="18749">
    <literal><![CDATA[
      K(x,T(y,z * (a(u,w,v5) * v6))) = K(x,T(y,z * v6))
    ]]></literal>
    <justification jstring="[hyper(58,a,18744,a(flip),b,18748,a)].">
      <j1 rule="hyper" parents="58 18744 18748"/>
    </justification>
  </clause>

  <clause id="18750">
    <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(18735(a,1),18737(a,1,2)),flip(a)].">
      <j1 rule="para" parents="18735 18737"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18751">
    <literal><![CDATA[
      T(x,K(y * a(z,u,w),v5) * v6) = T(x,K(y,v5) * v6)
    ]]></literal>
    <justification jstring="[hyper(320,a,15103,a(flip),b,18750,a),flip(a)].">
      <j1 rule="hyper" parents="320 15103 18750"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18753">
    <literal><![CDATA[
      T(x,K(a(y,z,u) * w,v5) * v6) = T(x,K(w,v5) * v6)
    ]]></literal>
    <justification jstring="[hyper(16176,a,18751,a)].">
      <j1 rule="hyper" parents="16176 18751"/>
    </justification>
  </clause>

  <clause id="18754">
    <literal><![CDATA[
      T(x,T(y,z * a(u,w,v5)) \ v6) = T(x,K(z,y) * (y \ v6))
    ]]></literal>
    <justification jstring="[para(5131(a,1),18751(a,1,2))].">
      <j1 rule="para" parents="5131 18751"/>
    </justification>
  </clause>

  <clause id="18755">
    <literal><![CDATA[
      T(x,y * K(z,a(u,w,v5) * v6)) = T(x,K(v6,z) * y)
    ]]></literal>
    <justification jstring="[hyper(15940,a,18753,a)].">
      <j1 rule="hyper" parents="15940 18753"/>
    </justification>
  </clause>

  <clause id="18756">
    <literal><![CDATA[
      x / T(x,K(y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(u * K(z,a(v5,v6,v7) * y),x) = w
    ]]></literal>
    <justification jstring="[para(18755(a,1),4862(a,1,2))].">
      <j1 rule="para" parents="18755 4862"/>
    </justification>
  </clause>

  <clause id="18757">
    <literal><![CDATA[
      T(x,T(y,z * a(u,w,v5)) \ v6) = T(x,T(y,z) \ v6)
    ]]></literal>
    <justification jstring="[para(5131(a,1),18754(a,2,2))].">
      <j1 rule="para" parents="5131 18754"/>
    </justification>
  </clause>

  <clause id="18758">
    <literal><![CDATA[
      K(x * K(y,a(z,u,w) * v5),v6) = K(K(v5,y) * x,v6)
    ]]></literal>
    <justification jstring="[hyper(18756,a,4794,a(flip))].">
      <j1 rule="hyper" parents="18756 4794"/>
    </justification>
  </clause>

  <clause id="18759">
    <literal><![CDATA[
      K(x * K(y * a(z,u,w),v5),v6) = K(K(y,v5) * x,v6)
    ]]></literal>
    <justification jstring="[hyper(16178,a,18758,a)].">
      <j1 rule="hyper" parents="16178 18758"/>
    </justification>
  </clause>

  <clause id="18760">
    <literal><![CDATA[
      K(K(a(x,y,z) \ u,w) * v5,v6) = K(v5 * K(w,u),v6)
    ]]></literal>
    <justification jstring="[para(5(a,1),18758(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5 18758"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18761">
    <literal><![CDATA[
      K(K(x,a(y,z,u) \ w) * v5,v6) = K(v5 * K(x,w),v6)
    ]]></literal>
    <justification jstring="[hyper(15942,a,18760,a)].">
      <j1 rule="hyper" parents="15942 18760"/>
    </justification>
  </clause>

  <clause id="18762">
    <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),18699(a,1,2))].">
      <j1 rule="para" parents="20 18699"/>
    </justification>
  </clause>

  <clause id="18763">
    <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(17345(a,2),18700(a,1,1))].">
      <j1 rule="para" parents="17345 18700"/>
    </justification>
  </clause>

  <clause id="18764">
    <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(14942(a,1),18762(a,1,2))].">
      <j1 rule="para" parents="14942 18762"/>
    </justification>
  </clause>

  <clause id="18765">
    <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(15629,a,18764,a),flip(a)].">
      <j1 rule="hyper" parents="15629 18764"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18766">
    <literal><![CDATA[
      K(x,T(y,L(z,u,w) * v5)) = K(x,T(y,z * v5))
    ]]></literal>
    <justification jstring="[hyper(17293,a,18765,a),flip(a)].">
      <j1 rule="hyper" parents="17293 18765"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18767">
    <literal><![CDATA[
      K(x,T(y,z * L(u,w,v5))) = K(x,T(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(15799,a,18766,a)].">
      <j1 rule="hyper" parents="15799 18766"/>
    </justification>
  </clause>

  <clause id="18769">
    <literal><![CDATA[
      K(x,T(y,(z \ u) * (z * w))) = K(x,T(y,w * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,16609,a(flip),b,18766,a)].">
      <j1 rule="hyper" parents="58 16609 18766"/>
    </justification>
  </clause>

  <clause id="18770">
    <literal><![CDATA[
      K(x,T(y,z * L(u,w,v5))) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[hyper(320,a,15575,a,b,18767,a),flip(a)].">
      <j1 rule="hyper" parents="320 15575 18767"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18771">
    <literal><![CDATA[
      T(x * K(y,T(x,z * u)),y) = T(x,K(y,z * L(u,w,v5)))
    ]]></literal>
    <justification jstring="[para(18770(a,1),8133(a,1,1,2))].">
      <j1 rule="para" parents="18770 8133"/>
    </justification>
  </clause>

  <clause id="18772">
    <literal><![CDATA[
      K(x,T(y,(z * u) * (z \ w))) = K(x,T(y,u * w))
    ]]></literal>
    <justification jstring="[hyper(15799,a,18769,a)].">
      <j1 rule="hyper" parents="15799 18769"/>
    </justification>
  </clause>

  <clause id="18774">
    <literal><![CDATA[
      K(x,T(y,(z \ u) * w)) = K(x,T(y,u * (z \ w)))
    ]]></literal>
    <justification jstring="[para(5(a,1),18772(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5 18772"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18775">
    <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,16779,a(flip),b,18774,a),flip(a)].">
      <j1 rule="hyper" parents="58 16779 18774"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18776">
    <literal><![CDATA[
      T(x,K(y,z * L(u,w,v5))) = T(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[hyper(8351,a,18771,a),flip(a)].">
      <j1 rule="hyper" parents="8351 18771"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18777">
    <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),18776(a,1,2,2,2))].">
      <j1 rule="para" parents="298 18776"/>
    </justification>
  </clause>

  <clause id="18778">
    <literal><![CDATA[
      T(x,K(y,z * ((u * z) \ w))) = T(x,K(y,u \ w))
    ]]></literal>
    <justification jstring="[para(5(a,1),18777(a,2,2,2))].">
      <j1 rule="para" parents="5 18777"/>
    </justification>
  </clause>

  <clause id="18779">
    <literal><![CDATA[
      T(x,K(y,(z / u) \ w)) = T(x,K(y,u * (z \ w)))
    ]]></literal>
    <justification jstring="[para(7(a,1),18778(a,1,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="7 18778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18780">
    <literal><![CDATA[
      T(x,K(y,z \ (u * w))) = T(x,K(y,u * (z \ w)))
    ]]></literal>
    <justification jstring="[hyper(17512,a,18779,a)].">
      <j1 rule="hyper" parents="17512 18779"/>
    </justification>
  </clause>

  <clause id="18781">
    <literal><![CDATA[
      T(x,K(y,z \ (u \ w))) = T(x,K(y,u * (w \ z)))
    ]]></literal>
    <justification jstring="[hyper(17370,a,18780,a)].">
      <j1 rule="hyper" parents="17370 18780"/>
    </justification>
  </clause>

  <clause id="18782">
    <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,17714,a(flip),b,18781,a),flip(a)].">
      <j1 rule="hyper" parents="58 17714 18781"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18783">
    <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,16530,a(flip),b,18782,a)].">
      <j1 rule="hyper" parents="58 16530 18782"/>
    </justification>
  </clause>

  <clause id="18785">
    <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,8145,a(flip),b,18783,a),flip(a)].">
      <j1 rule="hyper" parents="58 8145 18783"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18786">
    <literal><![CDATA[
      x * K(y,T(x,z \ (u \ w))) = x * K(y,T(x,u * (w \ z)))
    ]]></literal>
    <justification jstring="[para(17457(a,1),18785(a,1,2))].">
      <j1 rule="para" parents="17457 18785"/>
    </justification>
  </clause>

  <clause id="18787">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ w))) = K(x,T(y,u * (w \ z)))
    ]]></literal>
    <justification jstring="[hyper(278,a,18786,a),flip(a)].">
      <j1 rule="hyper" parents="278 18786"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18790">
    <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(18787(a,1),17517(a,1))].">
      <j1 rule="para" parents="18787 17517"/>
    </justification>
  </clause>

  <clause id="18791">
    <literal><![CDATA[
      K(x * K(y \ (z \ x),y),T(u,x \ z)) = K(((z * y) \ x) * (y * z),u)
    ]]></literal>
    <justification jstring="[hyper(18790,a,18775,a)].">
      <j1 rule="hyper" parents="18790 18775"/>
    </justification>
  </clause>

  <clause id="18792">
    <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,17993,a(flip),b,18791,a)].">
      <j1 rule="hyper" parents="58 17993 18791"/>
    </justification>
  </clause>

  <clause id="18793">
    <literal><![CDATA[
      K(x * K(y \ (x / z),y),T(u,z)) = K(((z * y) \ x) * (y * z),u)
    ]]></literal>
    <justification jstring="[para(11129(a,1),18792(a,1,1))].">
      <j1 rule="para" parents="11129 18792"/>
    </justification>
  </clause>

  <clause id="18794">
    <literal><![CDATA[
      K(K(x / y,z) * x,T(u,y)) = K(((y * z) \ x) * (z * y),u)
    ]]></literal>
    <justification jstring="[hyper(15865,a,18793,a)].">
      <j1 rule="hyper" parents="15865 18793"/>
    </justification>
  </clause>

  <clause id="18795">
    <literal><![CDATA[
      K(((x * y) \ z) * (y * x),u) = K(z * K(x \ z,y),T(u,x))
    ]]></literal>
    <justification jstring="[para(6290(a,1),18794(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6290 18794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18796">
    <literal><![CDATA[
      K(((x * y) \ z) * (y * x),u) = K(x * T(z / x,y),u)
    ]]></literal>
    <justification jstring="[hyper(320,a,12247,a(flip),b,18795,a),flip(a)].">
      <j1 rule="hyper" parents="320 12247 18795"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18797">
    <literal><![CDATA[
      K(K(x,y) * z,T(u,x * y)) = K(y * T(z / y,x),u)
    ]]></literal>
    <justification jstring="[hyper(12299,a,18796,a)].">
      <j1 rule="hyper" parents="12299 18796"/>
    </justification>
  </clause>

  <clause id="18798">
    <literal><![CDATA[
      K(x \ T(y * x,z),u) = K(x * T(y / x,z),u)
    ]]></literal>
    <justification jstring="[hyper(58,a,16637,a(flip),b,18797,a)].">
      <j1 rule="hyper" parents="58 16637 18797"/>
    </justification>
  </clause>

  <clause id="18799">
    <literal><![CDATA[
      K(x * K(x * y,z),T(u,y)) = K(y * T(x / y,z),u)
    ]]></literal>
    <justification jstring="[hyper(16226,a,18798,a)].">
      <j1 rule="hyper" parents="16226 18798"/>
    </justification>
  </clause>

  <clause id="18800">
    <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(18799(a,1),16584(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="18799 16584"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18801">
    <literal><![CDATA[
      T(x,T(y * z,u) / T(z,y)) = T(x,z * T(y / z,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,5253,a(flip),b,18800,a),flip(a)].">
      <j1 rule="hyper" parents="320 5253 18800"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18802">
    <literal><![CDATA[
      T(x,T(y * K(y * z,u),z)) = T(x,z * T(y / z,u))
    ]]></literal>
    <justification jstring="[para(16582(a,1),18801(a,1,2))].">
      <j1 rule="para" parents="16582 18801"/>
    </justification>
  </clause>

  <clause id="18803">
    <literal><![CDATA[
      T(x,y \ T(z * y,u)) = T(x,y * T(z / y,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,16103,a(flip),b,18802,a)].">
      <j1 rule="hyper" parents="58 16103 18802"/>
    </justification>
  </clause>

  <clause id="18804">
    <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,16631,a(flip),b,18803,a),flip(a)].">
      <j1 rule="hyper" parents="58 16631 18803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18805">
    <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(18194,a,18804,a)].">
      <j1 rule="hyper" parents="18194 18804"/>
    </justification>
  </clause>

  <clause id="18806">
    <literal><![CDATA[
      T(x,T(y * T(z / y,u),y)) = T(x,T(y,z) \ T(z * y,u))
    ]]></literal>
    <justification jstring="[hyper(18205,a,18805,a)].">
      <j1 rule="hyper" parents="18205 18805"/>
    </justification>
  </clause>

  <clause id="18807">
    <literal><![CDATA[
      T(x,T(y,z) \ T(z * y,u)) = T(x,T(z / y,u) * y)
    ]]></literal>
    <justification jstring="[hyper(12263,a,18806,a),flip(a)].">
      <j1 rule="hyper" parents="12263 18806"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18808">
    <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),18807(a,2,2))].">
      <j1 rule="para" parents="453 18807"/>
    </justification>
  </clause>

  <clause id="18809">
    <literal><![CDATA[
      T(x,y \ T(z * T(y,z),u)) = T(x,y * T(y \ z,u))
    ]]></literal>
    <justification jstring="[hyper(18573,a,18808,a)].">
      <j1 rule="hyper" parents="18573 18808"/>
    </justification>
  </clause>

  <clause id="18810">
    <literal><![CDATA[
      T(x,y \ T(y * z,u)) = T(x,y * T(y \ z,u))
    ]]></literal>
    <justification jstring="[para(105(a,1),18809(a,1,2,2,1))].">
      <j1 rule="para" parents="105 18809"/>
    </justification>
  </clause>

  <clause id="18811">
    <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(17434,a,18763,a)].">
      <j1 rule="hyper" parents="17434 18763"/>
    </justification>
  </clause>

  <clause id="18812">
    <literal><![CDATA[
      L(x,y,K(z,K(u,w)) * v5) = L(x,y,v5)
    ]]></literal>
    <justification jstring="[hyper(58,a,18286,a(flip),b,18811,a),flip(a)].">
      <j1 rule="hyper" parents="58 18286 18811"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18813">
    <literal><![CDATA[
      L(x,y,z * T(u,K(w,v5))) = L(x,y,z * u)
    ]]></literal>
    <justification jstring="[hyper(17307,a,18812,a)].">
      <j1 rule="hyper" parents="17307 18812"/>
    </justification>
  </clause>

  <clause id="18815">
    <literal><![CDATA[
      L(x,y,z / (K(u,w) / v5)) = L(x,y,z / (v5 \ K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(58,a,17376,a(flip),b,18812,a),flip(a)].">
      <j1 rule="hyper" parents="58 17376 18812"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18816">
    <literal><![CDATA[
      L(x,y,T(z,K(u,w)) \ v5) = L(x,y,z \ v5)
    ]]></literal>
    <justification jstring="[para(5081(a,1),18812(a,1,3)),flip(a)].">
      <j1 rule="para" parents="5081 18812"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18818">
    <literal><![CDATA[
      L(x,y,z * (T(u,T(w,v5)) / v5)) = L(x,y,z * (T(u,w) / v5))
    ]]></literal>
    <justification jstring="[para(8147(a,1),18813(a,1,3,2))].">
      <j1 rule="para" parents="8147 18813"/>
    </justification>
  </clause>

  <clause id="18819">
    <literal><![CDATA[
      L(x,y,(K(z,u) / w) \ v5) = L(x,y,(w \ K(z,u)) \ v5)
    ]]></literal>
    <justification jstring="[hyper(58,a,12609,a(flip),b,18816,a),flip(a)].">
      <j1 rule="hyper" parents="58 12609 18816"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18820">
    <literal><![CDATA[
      K(x,L(y,z,u / (w \ K(v5,v6)))) = K(x,L(y,z,w * u))
    ]]></literal>
    <justification jstring="[para(18815(a,1),18494(a,1,2))].">
      <j1 rule="para" parents="18815 18494"/>
    </justification>
  </clause>

  <clause id="18821">
    <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(18819(a,1),14607(a,1,2,2,2))].">
      <j1 rule="para" parents="18819 14607"/>
    </justification>
  </clause>

  <clause id="18822">
    <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(18819(a,1),16787(a,1,2,2))].">
      <j1 rule="para" parents="18819 16787"/>
    </justification>
  </clause>

  <clause id="18823">
    <literal><![CDATA[
      K(x,L(y,z,(u \ K(w,v5)) \ v6)) = K(x,L(y,z,u * v6))
    ]]></literal>
    <justification jstring="[hyper(17302,a,18820,a)].">
      <j1 rule="hyper" parents="17302 18820"/>
    </justification>
  </clause>

  <clause id="18824">
    <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,17296,a,b,18823,a),flip(a)].">
      <j1 rule="hyper" parents="320 17296 18823"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18825">
    <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(18824(a,2),17341(a,1))].">
      <j1 rule="para" parents="18824 17341"/>
    </justification>
  </clause>

  <clause id="18826">
    <literal><![CDATA[
      x * K(y,L(T(z,u \ 1),x,u * x)) = (x / (K(z,y) / u)) * (1 / u)
    ]]></literal>
    <justification jstring="[para(18823(a,1),18822(a,1,2))].">
      <j1 rule="para" parents="18823 18822"/>
    </justification>
  </clause>

  <clause id="18827">
    <literal><![CDATA[
      x * K(y,L(T(z,u),x,u * x)) = (x / (K(z,y) / u)) * (1 / u)
    ]]></literal>
    <justification jstring="[para(8631(a,1),18826(a,1,2))].">
      <j1 rule="para" parents="8631 18826"/>
    </justification>
  </clause>

  <clause id="18829">
    <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,14614,a(flip),b,18827,a),flip(a)].">
      <j1 rule="hyper" parents="320 14614 18827"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18830">
    <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(13082(a,1),17449(a,1,2))].">
      <j1 rule="para" parents="13082 17449"/>
    </justification>
  </clause>

  <clause id="18831">
    <literal><![CDATA[
      K(x,y / (T(z * u,z) \ w)) = K(x,y / ((u * z) \ w))
    ]]></literal>
    <justification jstring="[hyper(58,a,17448,a(flip),b,18830,a),flip(a)].">
      <j1 rule="hyper" parents="58 17448 18830"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18832">
    <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,18542,a(flip),b,17725,a)].">
      <j1 rule="hyper" parents="58 18542 17725"/>
    </justification>
  </clause>

  <clause id="18833">
    <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,13118,a(flip),b,17977,a)].">
      <j1 rule="hyper" parents="58 13118 17977"/>
    </justification>
  </clause>

  <clause id="18834">
    <literal><![CDATA[
      a(x,y * z,K(z,u)) * a(x,y,z) = a(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[para(14616(a,1),18297(a,1,2))].">
      <j1 rule="para" parents="14616 18297"/>
    </justification>
  </clause>

  <clause id="18835">
    <literal><![CDATA[
      a(x,y,K(z,u)) * a(x,y,z) = a(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[para(10875(a,1),18834(a,1,1))].">
      <j1 rule="para" parents="10875 18834"/>
    </justification>
  </clause>

  <clause id="18837">
    <literal><![CDATA[
      a(x,y,T(z,u)) = T(a(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(13431,a,18835,a),flip(a)].">
      <j1 rule="hyper" parents="13431 18835"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18838">
    <literal><![CDATA[
      a(x,y,z) \ a(x,y,T(z,u)) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(116,a,18835,a(flip),b,17193,a(flip))].">
      <j1 rule="hyper" parents="116 18835 17193"/>
    </justification>
  </clause>

  <clause id="18839">
    <literal><![CDATA[
      a(x,y,T(z,K(u,w))) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,17256,a(flip),b,18837,a),flip(a)].">
      <j1 rule="hyper" parents="320 17256 18837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18841">
    <literal><![CDATA[
      T(x,a(y,z,u)) / a(y,z,u) = x / a(y,z,T(u,x))
    ]]></literal>
    <justification jstring="[para(18837(a,2),4246(a,2,2))].">
      <j1 rule="para" parents="18837 4246"/>
    </justification>
  </clause>

  <clause id="18842">
    <literal><![CDATA[
      a(x,y,T(z,T(u,w))) = a(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[para(7438(a,1),18839(a,1,3))].">
      <j1 rule="para" parents="7438 18839"/>
    </justification>
  </clause>

  <clause id="18843">
    <literal><![CDATA[
      a(x,y,T(z,T(x * y,u))) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,14549,a(flip),b,18842,a),flip(a)].">
      <j1 rule="hyper" parents="320 14549 18842"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18844">
    <literal><![CDATA[
      a(x,y,T(z,y * x)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(12254(a,1),18843(a,1,3))].">
      <j1 rule="para" parents="12254 18843"/>
    </justification>
  </clause>

  <clause id="18845">
    <literal><![CDATA[
      a(x,y,z) \ ((y * x) * T(z,x * T(y,x))) = L(z,y,x) * (y * x)
    ]]></literal>
    <justification jstring="[para(18844(a,1),14738(a,1,1))].">
      <j1 rule="para" parents="18844 14738"/>
    </justification>
  </clause>

  <clause id="18846">
    <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),18845(a,1,2,2,2))].">
      <j1 rule="para" parents="105 18845"/>
    </justification>
  </clause>

  <clause id="18847">
    <literal><![CDATA[
      a(x,y,z) \ (z * (y * x)) = L(z,y,x) * (y * x)
    ]]></literal>
    <justification jstring="[para(105(a,1),18846(a,1,2))].">
      <j1 rule="para" parents="105 18846"/>
    </justification>
  </clause>

  <clause id="18848">
    <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,18026,a(flip),b,18832,a)].">
      <j1 rule="hyper" parents="58 18026 18832"/>
    </justification>
  </clause>

  <clause id="18850">
    <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,17718,a(flip),b,18848,a)].">
      <j1 rule="hyper" parents="58 17718 18848"/>
    </justification>
  </clause>

  <clause id="18852">
    <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(17290(a,1),17990(a,1))].">
      <j1 rule="para" parents="17290 17990"/>
    </justification>
  </clause>

  <clause id="18853">
    <literal><![CDATA[
      T(x,y * K(z,u \ w)) = T(x,y * K(z,w * u))
    ]]></literal>
    <justification jstring="[hyper(18852,a,18541,a),flip(a)].">
      <j1 rule="hyper" parents="18852 18541"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18854">
    <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(18853(a,1),14715(a,1,1,2))].">
      <j1 rule="para" parents="18853 14715"/>
    </justification>
  </clause>

  <clause id="18855">
    <literal><![CDATA[
      K(x * y,z * K(u,w \ v5)) = K(x * y,z * K(u,v5 * w))
    ]]></literal>
    <justification jstring="[hyper(14716,a,18854,a),flip(a)].">
      <j1 rule="hyper" parents="14716 18854"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18856">
    <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(18854(a,1),14716(a,1))].">
      <j1 rule="para" parents="18854 14716"/>
    </justification>
  </clause>

  <clause id="18857">
    <literal><![CDATA[
      K(K(x,y) * (z \ (u * K(x,y))),w * K(v5,u * z)) = K(z \ u,w)
    ]]></literal>
    <justification jstring="[hyper(17909,a,18855,a),flip(a)].">
      <j1 rule="hyper" parents="17909 18855"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18858">
    <literal><![CDATA[
      K(x \ y,z * K(u,y * x)) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(18193,a,18857,a)].">
      <j1 rule="hyper" parents="18193 18857"/>
    </justification>
  </clause>

  <clause id="18859">
    <literal><![CDATA[
      K(x * K(y,z * u),u \ z) = w / (K(u \ z,x) * w)
    ]]></literal>
    <justification jstring="[para(18858(a,1),5142(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="18858 5142"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18860">
    <literal><![CDATA[
      K(x * K(y,z * u),u \ z) = K(x,u \ z)
    ]]></literal>
    <justification jstring="[hyper(320,a,17485,a(flip),b,18859,a),flip(a)].">
      <j1 rule="hyper" parents="320 17485 18859"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18861">
    <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(16773,a,18860,a)].">
      <j1 rule="hyper" parents="16773 18860"/>
    </justification>
  </clause>

  <clause id="18862">
    <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(16138,a,18860,a)].">
      <j1 rule="hyper" parents="16138 18860"/>
    </justification>
  </clause>

  <clause id="18863">
    <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(10401(a,1),18860(a,1,1,2,2))].">
      <j1 rule="para" parents="10401 18860"/>
    </justification>
  </clause>

  <clause id="18864">
    <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(16109(a,1),18860(a,1,1,2))].">
      <j1 rule="para" parents="16109 18860"/>
    </justification>
  </clause>

  <clause id="18865">
    <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,16705,a(flip),b,18861,a)].">
      <j1 rule="hyper" parents="58 16705 18861"/>
    </justification>
  </clause>

  <clause id="18868">
    <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,16705,a(flip),b,18862,a)].">
      <j1 rule="hyper" parents="58 16705 18862"/>
    </justification>
  </clause>

  <clause id="18870">
    <literal><![CDATA[
      K(x,y \ T(z,u \ w)) = K(x,y \ T(z,u * w))
    ]]></literal>
    <justification jstring="[hyper(58,a,18865,a(flip),b,18868,a)].">
      <j1 rule="hyper" parents="58 18865 18868"/>
    </justification>
  </clause>

  <clause id="18871">
    <literal><![CDATA[
      K(x,y \ T(z,u \ (w / v5))) = K(x,y \ T(z,(u * v5) * w))
    ]]></literal>
    <justification jstring="[hyper(58,a,17764,a(flip),b,18870,a)].">
      <j1 rule="hyper" parents="58 17764 18870"/>
    </justification>
  </clause>

  <clause id="18872">
    <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(18847(a,1),18870(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="18847 18870"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18873">
    <literal><![CDATA[
      K(x,y \ T(z,(u * w) * v5)) = K(x,y \ T(z,u * (v5 / w)))
    ]]></literal>
    <justification jstring="[hyper(58,a,18870,a(flip),b,18871,a),flip(a)].">
      <j1 rule="hyper" parents="58 18870 18871"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18874">
    <literal><![CDATA[
      K(x,y \ T(z,(u * w) * v5)) = K(x,y \ T(z,u * (w \ v5)))
    ]]></literal>
    <justification jstring="[hyper(320,a,18269,a(flip),b,18873,a),flip(a)].">
      <j1 rule="hyper" parents="320 18269 18873"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18875">
    <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(18258(a,1),18872(a,2,2,2))].">
      <j1 rule="para" parents="18258 18872"/>
    </justification>
  </clause>

  <clause id="18876">
    <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,18874,a(flip),b,18875,a),flip(a)].">
      <j1 rule="hyper" parents="320 18874 18875"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18877">
    <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,18749,a(flip),b,17325,a)].">
      <j1 rule="hyper" parents="58 18749 17325"/>
    </justification>
  </clause>

  <clause id="18879">
    <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(17391(a,2),17418(a,1,2,1))].">
      <j1 rule="para" parents="17391 17418"/>
    </justification>
  </clause>

  <clause id="18880">
    <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(17431(a,1),17418(a,1,2))].">
      <j1 rule="para" parents="17431 17418"/>
    </justification>
  </clause>

  <clause id="18881">
    <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(17158(a,1),17419(a,1,1,2))].">
      <j1 rule="para" parents="17158 17419"/>
    </justification>
  </clause>

  <clause id="18882">
    <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(17632,a,18757,a),flip(a)].">
      <j1 rule="hyper" parents="17632 18757"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18883">
    <literal><![CDATA[
      T(x,y / T(z,T(a(u,w,v5),v6) * v7)) = T(x,y / T(z,v7))
    ]]></literal>
    <justification jstring="[hyper(15788,a,18882,a),flip(a)].">
      <j1 rule="hyper" parents="15788 18882"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18884">
    <literal><![CDATA[
      T(x,y / T(z,u * a(w,v5,v6))) = T(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[para(12291(a,1),18883(a,1,2,2))].">
      <j1 rule="para" parents="12291 18883"/>
    </justification>
  </clause>

  <clause id="18885">
    <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(18884(a,1),7202(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="18884 7202"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18886">
    <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(18885(a,2),7707(a,1))].">
      <j1 rule="para" parents="18885 7707"/>
    </justification>
  </clause>

  <clause id="18887">
    <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(18886,a,18877,a)].">
      <j1 rule="hyper" parents="18886 18877"/>
    </justification>
  </clause>

  <clause id="18888">
    <literal><![CDATA[
      K(x,y \ T(z,a(u,w,v5) * v6)) = K(x,y \ T(z,v6))
    ]]></literal>
    <justification jstring="[hyper(58,a,16361,a(flip),b,18887,a),flip(a)].">
      <j1 rule="hyper" parents="58 16361 18887"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18889">
    <literal><![CDATA[
      K(x,y \ T(z,u * (w \ v5))) = K(x,y \ T(z,u * (w * v5)))
    ]]></literal>
    <justification jstring="[hyper(58,a,18876,a(flip),b,18888,a)].">
      <j1 rule="hyper" parents="58 18876 18888"/>
    </justification>
  </clause>

  <clause id="18891">
    <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,17747,a,b,17746,a)].">
      <j1 rule="hyper" parents="58 17747 17746"/>
    </justification>
  </clause>

  <clause id="18892">
    <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(17749(a,1),17746(a,1,1))].">
      <j1 rule="para" parents="17749 17746"/>
    </justification>
  </clause>

  <clause id="18893">
    <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(17329,a,18313,a)].">
      <j1 rule="hyper" parents="17329 18313"/>
    </justification>
  </clause>

  <clause id="18896">
    <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,14558,a(flip),b,18893,a),flip(a)].">
      <j1 rule="hyper" parents="58 14558 18893"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18897">
    <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,17779,a(flip),b,18896,a),flip(a)].">
      <j1 rule="hyper" parents="320 17779 18896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18898">
    <literal><![CDATA[
      K(x,(y \ z) / (u * ((y \ z) / z))) = K(x,((y \ 1) * z) / (u * (y \ 1)))
    ]]></literal>
    <justification jstring="[hyper(58,a,17728,a(flip),b,18897,a)].">
      <j1 rule="hyper" parents="58 17728 18897"/>
    </justification>
  </clause>

  <clause id="18899">
    <literal><![CDATA[
      K(x,((y \ 1) * z) / (u * (y \ 1))) = K(x,(y \ z) / (u / y))
    ]]></literal>
    <justification jstring="[hyper(58,a,18514,a(flip),b,18898,a),flip(a)].">
      <j1 rule="hyper" parents="58 18514 18898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18900">
    <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,18037,a,b,18899,a)].">
      <j1 rule="hyper" parents="58 18037 18899"/>
    </justification>
  </clause>

  <clause id="18901">
    <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(14539,a,18577,a)].">
      <j1 rule="hyper" parents="14539 18577"/>
    </justification>
  </clause>

  <clause id="18902">
    <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(15319,a,18901,a),flip(a)].">
      <j1 rule="hyper" parents="15319 18901"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18903">
    <literal><![CDATA[
      K(x,(((y \ z) \ 1) * z) \ (((z / y) \ 1) * u)) = K(x,y \ ((T(y,z) / z) * u))
    ]]></literal>
    <justification jstring="[para(13284(a,1),18902(a,2,2))].">
      <j1 rule="para" parents="13284 18902"/>
    </justification>
  </clause>

  <clause id="18904">
    <literal><![CDATA[
      K(x,(((y \ z) \ 1) * z) \ (((z / y) \ 1) * u)) = K(x,y \ ((z \ y) * u))
    ]]></literal>
    <justification jstring="[hyper(320,a,18108,a(flip),b,18903,a),flip(a)].">
      <j1 rule="hyper" parents="320 18108 18903"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18905">
    <literal><![CDATA[
      K(x,(y * ((y / z) \ 1)) \ (((y / z) \ 1) * u)) = K(x,z \ ((y \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(15276,a,18904,a)].">
      <j1 rule="hyper" parents="15276 18904"/>
    </justification>
  </clause>

  <clause id="18906">
    <literal><![CDATA[
      K(x,(y / (y / z)) \ ((y / z) \ u)) = K(x,z \ ((y \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,14720,a(flip),b,18905,a)].">
      <j1 rule="hyper" parents="58 14720 18905"/>
    </justification>
  </clause>

  <clause id="18907">
    <literal><![CDATA[
      K(x,y \ ((y \ z) \ u)) = K(x,y \ ((z \ y) * u))
    ]]></literal>
    <justification jstring="[para(5602(a,1),18906(a,1,2))].">
      <j1 rule="para" parents="5602 18906"/>
    </justification>
  </clause>

  <clause id="18908">
    <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,18601,a,b,18907,a)].">
      <j1 rule="hyper" parents="58 18601 18907"/>
    </justification>
  </clause>

  <clause id="18909">
    <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,17563,a(flip),b,18907,a),flip(a)].">
      <j1 rule="hyper" parents="58 17563 18907"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18910">
    <literal><![CDATA[
      K(x,y \ (((K(z,y) * u) \ y) * w)) = K(x,y \ ((T(y,z) \ u) \ w))
    ]]></literal>
    <justification jstring="[para(5106(a,1),18907(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5106 18907"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18911">
    <literal><![CDATA[
      K(x,K(y,z \ u)) * K(x,y \ ((z \ y) * u)) = K(x,((y \ z) \ u) / y)
    ]]></literal>
    <justification jstring="[para(18907(a,1),9935(a,1,2))].">
      <j1 rule="para" parents="18907 9935"/>
    </justification>
  </clause>

  <clause id="18912">
    <literal><![CDATA[
      K(x,K(y,z) * (z \ ((u \ z) * w))) = K(x,z \ ((T(z,y) \ u) \ w))
    ]]></literal>
    <justification jstring="[hyper(18106,a,18909,a)].">
      <j1 rule="hyper" parents="18106 18909"/>
    </justification>
  </clause>

  <clause id="18913">
    <literal><![CDATA[
      K(x,y \ ((T(y,z) \ u) \ w)) = K(x,y \ ((u \ T(y,z)) * w))
    ]]></literal>
    <justification jstring="[para(13714(a,1),18910(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="13714 18910"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18914">
    <literal><![CDATA[
      K(x,T(y,z) \ ((u \ y) * w)) = K(x,y \ ((T(y,z) \ u) \ w))
    ]]></literal>
    <justification jstring="[para(5131(a,1),18912(a,1,2))].">
      <j1 rule="para" parents="5131 18912"/>
    </justification>
  </clause>

  <clause id="18915">
    <literal><![CDATA[
      K(x,T(y,z) \ ((u \ y) * w)) = K(x,y \ ((u \ T(y,z)) * w))
    ]]></literal>
    <justification jstring="[hyper(320,a,18913,a(flip),b,18914,a),flip(a)].">
      <j1 rule="hyper" parents="320 18913 18914"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18916">
    <literal><![CDATA[
      K(x,(y / (y / z)) \ (u / (y / z))) = K(x,z \ T(u * (y \ z),K(y,z)))
    ]]></literal>
    <justification jstring="[para(9051(a,2),18908(a,2,2,2))].">
      <j1 rule="para" parents="9051 18908"/>
    </justification>
  </clause>

  <clause id="18917">
    <literal><![CDATA[
      K(x,((y \ z) \ u) / y) = K(x,((z \ y) * u) / y)
    ]]></literal>
    <justification jstring="[hyper(58,a,14107,a(flip),b,18911,a),flip(a)].">
      <j1 rule="hyper" parents="58 14107 18911"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18918">
    <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(4195(a,1),18917(a,2,2,1))].">
      <j1 rule="para" parents="4195 18917"/>
    </justification>
  </clause>

  <clause id="18919">
    <literal><![CDATA[
      K(x,(y / (y / z)) \ (u / (y / z))) = K(x,z \ (u * (y \ z)))
    ]]></literal>
    <justification jstring="[hyper(320,a,16031,a(flip),b,18916,a),flip(a)].">
      <j1 rule="hyper" parents="320 16031 18916"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18921">
    <literal><![CDATA[
      K(x,y \ (z / (y \ u))) = K(x,y \ (z * (u \ y)))
    ]]></literal>
    <justification jstring="[hyper(58,a,18008,a(flip),b,18919,a)].">
      <j1 rule="hyper" parents="58 18008 18919"/>
    </justification>
  </clause>

  <clause id="18922">
    <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(8528(a,1),18921(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="8528 18921"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18923">
    <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(14223(a,1),18636(a,1,2,2))].">
      <j1 rule="para" parents="14223 18636"/>
    </justification>
  </clause>

  <clause id="18924">
    <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,18879,a(flip),b,18881,a),flip(a)].">
      <j1 rule="hyper" parents="58 18879 18881"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18925">
    <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,18880,a,b,18924,a)].">
      <j1 rule="hyper" parents="320 18880 18924"/>
    </justification>
  </clause>

  <clause id="18926">
    <literal><![CDATA[
      a(x,y,z * K(u,K(w,v5))) = (x * (y * z)) \ ((x * y) * z)
    ]]></literal>
    <justification jstring="[hyper(15853,a,18892,a),flip(a)].">
      <j1 rule="hyper" parents="15853 18892"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18928">
    <literal><![CDATA[
      a(x,y,z * K(u,K(w,v5))) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(320,a,9,a,b,18926,a),flip(a)].">
      <j1 rule="hyper" parents="320 9 18926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18929">
    <literal><![CDATA[
      a(x,y,z * K(u,K(w,v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = v6
    ]]></literal>
    <justification jstring="[para(18926(a,2),691(a,1))].">
      <j1 rule="para" parents="18926 691"/>
    </justification>
  </clause>

  <clause id="18930">
    <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),18929(a,1,3))].">
      <j1 rule="para" parents="84 18929"/>
    </justification>
  </clause>

  <clause id="18931">
    <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(13339(a,2),18930(a,1))].">
      <j1 rule="para" parents="13339 18930"/>
    </justification>
  </clause>

  <clause id="18932">
    <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,18891,a(flip),b,18925,a),flip(a)].">
      <j1 rule="hyper" parents="58 18891 18925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18933">
    <literal><![CDATA[
      a(x * K(y,K(z,u)),w,v5) = a(x,w,v5)
    ]]></literal>
    <justification jstring="[hyper(320,a,18928,a(flip),b,18932,a),flip(a)].">
      <j1 rule="hyper" parents="320 18928 18932"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18935">
    <literal><![CDATA[
      a(K(x,y) * z,u,w) = a(z * K(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(84(a,1),18933(a,1,1)),flip(a)].">
      <j1 rule="para" parents="84 18933"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18936">
    <literal><![CDATA[
      a(T(x,K(y,z)),u,w) = a(x,u,w)
    ]]></literal>
    <justification jstring="[para(1029(a,2),18933(a,1,1))].">
      <j1 rule="para" parents="1029 18933"/>
    </justification>
  </clause>

  <clause id="18937">
    <literal><![CDATA[
      a(T(x,K(y,z)) \ u,w,v5) = a(x \ u,w,v5)
    ]]></literal>
    <justification jstring="[para(15748(a,1),18933(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15748 18933"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18938">
    <literal><![CDATA[
      a(K(x,y) * (z \ x),u,w) = a(z \ T(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(15966(a,1),18933(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15966 18933"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18939">
    <literal><![CDATA[
      a(T(x,T(y,z)),u,w) = a(T(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(7438(a,1),18936(a,1,1))].">
      <j1 rule="para" parents="7438 18936"/>
    </justification>
  </clause>

  <clause id="18940">
    <literal><![CDATA[
      a(T(x / T(y,z),y),u,w) = a(T(y,z) \ x,u,w)
    ]]></literal>
    <justification jstring="[para(7952(a,1),18936(a,1,1))].">
      <j1 rule="para" parents="7952 18936"/>
    </justification>
  </clause>

  <clause id="18941">
    <literal><![CDATA[
      a(K(x,y) * (z \ 1),u,w) = a(z \ K(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(13895(a,1),18936(a,1,1))].">
      <j1 rule="para" parents="13895 18936"/>
    </justification>
  </clause>

  <clause id="18943">
    <literal><![CDATA[
      a(T(x * ((x / y) / x),x),z,u) = a(x * ((y \ x) / x),z,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,12890,a(flip),b,18939,a),flip(a)].">
      <j1 rule="hyper" parents="58 12890 18939"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18944">
    <literal><![CDATA[
      a(K(x,x \ y) * z,u,w) = a(z * K(x,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(320,a,12973,a(flip),b,18935,a),flip(a)].">
      <j1 rule="hyper" parents="320 12973 18935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18945">
    <literal><![CDATA[
      a(L(x \ 1,x,y) \ z,u,w) = a(((y * x) \ y) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(1292(a,1),18937(a,1,1,1))].">
      <j1 rule="para" parents="1292 18937"/>
    </justification>
  </clause>

  <clause id="18946">
    <literal><![CDATA[
      a(K(x * y,y \ 1) * z,u,w) = a(z * K(x * y,x),u,w)
    ]]></literal>
    <justification jstring="[para(6127(a,1),18944(a,1,1,1))].">
      <j1 rule="para" parents="6127 18944"/>
    </justification>
  </clause>

  <clause id="18948">
    <literal><![CDATA[
      a(x * ((y \ x) / x),z,u) = a(x / y,z,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,12777,a(flip),b,18943,a),flip(a)].">
      <j1 rule="hyper" parents="58 12777 18943"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18950">
    <literal><![CDATA[
      a(T(x,y) * ((z \ x) / x),u,w) = a(T(x,y) / z,u,w)
    ]]></literal>
    <justification jstring="[para(13725(a,1),18948(a,1,1,2))].">
      <j1 rule="para" parents="13725 18948"/>
    </justification>
  </clause>

  <clause id="18951">
    <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,12789,a(flip),b,18950,a)].">
      <j1 rule="hyper" parents="58 12789 18950"/>
    </justification>
  </clause>

  <clause id="18952">
    <literal><![CDATA[
      a(K(x * y,y \ 1) * z,u,w) = a(z * K(y,x),u,w)
    ]]></literal>
    <justification jstring="[hyper(320,a,12972,a(flip),b,18946,a),flip(a)].">
      <j1 rule="hyper" parents="320 12972 18946"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18953">
    <literal><![CDATA[
      a(K(x * y,x \ 1) * z,u,w) = a(z * K(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(5871(a,1),18952(a,1,1,1))].">
      <j1 rule="para" parents="5871 18952"/>
    </justification>
  </clause>

  <clause id="18954">
    <literal><![CDATA[
      a(T(x,x \ y) / z,u,w) = a(T(x,y) / z,u,w)
    ]]></literal>
    <justification jstring="[hyper(58,a,18950,a(flip),b,18951,a),flip(a)].">
      <j1 rule="hyper" parents="58 18950 18951"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18955">
    <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(18954(a,1),13334(a,1,2))].">
      <j1 rule="para" parents="18954 13334"/>
    </justification>
  </clause>

  <clause id="18956">
    <literal><![CDATA[
      (x * y) / a(z \ x,T(z,x),y) = (x / ((x \ z) * x)) * (((x \ z) * x) * y)
    ]]></literal>
    <justification jstring="[para(12785(a,1),18955(a,1,2))].">
      <j1 rule="para" parents="12785 18955"/>
    </justification>
  </clause>

  <clause id="18957">
    <literal><![CDATA[
      (x * y) / a(x / z,z,y) = (x / ((x \ z) * x)) * (((x \ z) * x) * y)
    ]]></literal>
    <justification jstring="[para(13333(a,1),18956(a,1,2))].">
      <j1 rule="para" parents="13333 18956"/>
    </justification>
  </clause>

  <clause id="18958">
    <literal><![CDATA[
      (x / ((x \ y) * x)) * (((x \ y) * x) * z) = (x / y) * (y * z)
    ]]></literal>
    <justification jstring="[hyper(895,a,18957,a),flip(a)].">
      <j1 rule="hyper" parents="895 18957"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18959">
    <literal><![CDATA[
      ((x / ((x \ y) * x)) * (((x \ y) * x) * z)) * u = ((x / y) * (y * z)) * u
    ]]></literal>
    <justification jstring="[hyper(52,a,18958,a)].">
      <j1 rule="hyper" parents="52 18958"/>
    </justification>
  </clause>

  <clause id="18960">
    <literal><![CDATA[
      ((x / y) * (y * K(z,u))) * w = (x * K(z,L(u,x,(x \ y) \ 1))) * w
    ]]></literal>
    <justification jstring="[para(18163(a,1),18959(a,1,1)),flip(a)].">
      <j1 rule="para" parents="18163 18959"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18961">
    <literal><![CDATA[
      ((x / y) * (y * K(z,u))) * w = (x * K(z,L(u,x,y \ x))) * w
    ]]></literal>
    <justification jstring="[para(14503(a,1),18960(a,2,1,2))].">
      <j1 rule="para" parents="14503 18960"/>
    </justification>
  </clause>

  <clause id="18962">
    <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,17814,a(flip),b,18961,a),flip(a)].">
      <j1 rule="hyper" parents="320 17814 18961"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18963">
    <literal><![CDATA[
      ((x / y) * (y * K(z,u))) * K(u,z) = x * a(z,x,K(y \ x,u))
    ]]></literal>
    <justification jstring="[para(14301(a,1),18962(a,2,2))].">
      <j1 rule="para" parents="14301 18962"/>
    </justification>
  </clause>

  <clause id="18964">
    <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,18850,a(flip),b,17437,a)].">
      <j1 rule="hyper" parents="58 18850 17437"/>
    </justification>
  </clause>

  <clause id="18965">
    <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,18270,a(flip),b,17673,a)].">
      <j1 rule="hyper" parents="58 18270 17673"/>
    </justification>
  </clause>

  <clause id="18967">
    <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(18965(a,2),16085(a,1))].">
      <j1 rule="para" parents="18965 16085"/>
    </justification>
  </clause>

  <clause id="18968">
    <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(18870(a,1),18967(a,1))].">
      <j1 rule="para" parents="18870 18967"/>
    </justification>
  </clause>

  <clause id="18969">
    <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(18687(a,1),18968(a,1))].">
      <j1 rule="para" parents="18687 18968"/>
    </justification>
  </clause>

  <clause id="18970">
    <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(5466(a,1),17755(a,2,2,2,2))].">
      <j1 rule="para" parents="5466 17755"/>
    </justification>
  </clause>

  <clause id="18971">
    <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(7966(a,1),18663(a,1,1))].">
      <j1 rule="para" parents="7966 18663"/>
    </justification>
  </clause>

  <clause id="18972">
    <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(15590(a,1),18971(a,1,1))].">
      <j1 rule="para" parents="15590 18971"/>
    </justification>
  </clause>

  <clause id="18973">
    <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(18736(a,1),18972(a,1,1))].">
      <j1 rule="para" parents="18736 18972"/>
    </justification>
  </clause>

  <clause id="18974">
    <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(15631(a,1),18973(a,1,1))].">
      <j1 rule="para" parents="15631 18973"/>
    </justification>
  </clause>

  <clause id="18975">
    <literal><![CDATA[
      T(x,K(y,z)) \ (u \ ((K(y,z) * u) * x)) = K(y,x / ((z * u) \ (u * x)))
    ]]></literal>
    <justification jstring="[para(15624(a,1),18974(a,1,1))].">
      <j1 rule="para" parents="15624 18974"/>
    </justification>
  </clause>

  <clause id="18976">
    <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,17477,a(flip),b,18975,a)].">
      <j1 rule="hyper" parents="58 17477 18975"/>
    </justification>
  </clause>

  <clause id="18978">
    <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(14506(a,1),18821(a,1,2,2))].">
      <j1 rule="para" parents="14506 18821"/>
    </justification>
  </clause>

  <clause id="18979">
    <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(4975(a,1),18978(a,1,2,2,2,3))].">
      <j1 rule="para" parents="4975 18978"/>
    </justification>
  </clause>

  <clause id="18980">
    <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(12623(a,1),18979(a,1,2,2,2))].">
      <j1 rule="para" parents="12623 18979"/>
    </justification>
  </clause>

  <clause id="18981">
    <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(14478(a,1),18980(a,1,2,2))].">
      <j1 rule="para" parents="14478 18980"/>
    </justification>
  </clause>

  <clause id="18983">
    <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(11210(a,1),18981(a,1,2))].">
      <j1 rule="para" parents="11210 18981"/>
    </justification>
  </clause>

  <clause id="18984">
    <literal><![CDATA[
      L(x * K(y,z),u,u \ 1) = L(x,u,u \ 1) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(13318,a,18983,a)].">
      <j1 rule="hyper" parents="13318 18983"/>
    </justification>
  </clause>

  <clause id="18985">
    <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(18984(a,2),14182(a,1,1))].">
      <j1 rule="para" parents="18984 14182"/>
    </justification>
  </clause>

  <clause id="18986">
    <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(18984(a,2),15003(a,1,2))].">
      <j1 rule="para" parents="18984 15003"/>
    </justification>
  </clause>

  <clause id="18987">
    <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(5951,a,18986,a)].">
      <j1 rule="hyper" parents="5951 18986"/>
    </justification>
  </clause>

  <clause id="18988">
    <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(18987(a,1),4069(a,1))].">
      <j1 rule="para" parents="18987 4069"/>
    </justification>
  </clause>

  <clause id="18989">
    <literal><![CDATA[
      a(x \ 1,x,y * K(z,u)) = a(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[hyper(18988,a,14036,a)].">
      <j1 rule="hyper" parents="18988 14036"/>
    </justification>
  </clause>

  <clause id="18990">
    <literal><![CDATA[
      a(x \ 1,x,K(y,z) * u) = a(x \ 1,x,u)
    ]]></literal>
    <justification jstring="[hyper(18931,a,18989,a)].">
      <j1 rule="hyper" parents="18931 18989"/>
    </justification>
  </clause>

  <clause id="18992">
    <literal><![CDATA[
      a(x \ 1,x,y) \ (K(z,u) * y) = L(K(z,u) * y,x,x \ 1)
    ]]></literal>
    <justification jstring="[para(18990(a,1),5956(a,1,1))].">
      <j1 rule="para" parents="18990 5956"/>
    </justification>
  </clause>

  <clause id="18993">
    <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,17494,a(flip),b,18992,a)].">
      <j1 rule="hyper" parents="58 17494 18992"/>
    </justification>
  </clause>

  <clause id="18994">
    <literal><![CDATA[
      L(K(x,y) * z,u,u \ 1) = K(x,y) * L(z,u,u \ 1)
    ]]></literal>
    <justification jstring="[para(5956(a,1),18993(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5956 18993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18995">
    <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,18994,a,b,5175,a)].">
      <j1 rule="hyper" parents="119 18994 5175"/>
    </justification>
  </clause>

  <clause id="18996">
    <literal><![CDATA[
      T(x,y) * L(T(x,y) \ z,u,u \ 1) = x * L(x \ z,u,u \ 1)
    ]]></literal>
    <justification jstring="[para(5131(a,1),18995(a,1,2,1))].">
      <j1 rule="para" parents="5131 18995"/>
    </justification>
  </clause>

  <clause id="18997">
    <literal><![CDATA[
      x \ T(x * L(x \ y,z,z \ 1),u) = L(x \ T(y,u),z,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(2142,a,18996,a)].">
      <j1 rule="hyper" parents="2142 18996"/>
    </justification>
  </clause>

  <clause id="18998">
    <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(18997(a,1),14086(a,1,2))].">
      <j1 rule="para" parents="18997 14086"/>
    </justification>
  </clause>

  <clause id="18999">
    <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(13089(a,1),18863(a,1,1,2))].">
      <j1 rule="para" parents="13089 18863"/>
    </justification>
  </clause>

  <clause id="19000">
    <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(5130(a,1),18999(a,1,2))].">
      <j1 rule="para" parents="5130 18999"/>
    </justification>
  </clause>

  <clause id="19001">
    <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,15921,a(flip),b,19000,a)].">
      <j1 rule="hyper" parents="58 15921 19000"/>
    </justification>
  </clause>

  <clause id="19002">
    <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(18856,a,19001,a)].">
      <j1 rule="hyper" parents="18856 19001"/>
    </justification>
  </clause>

  <clause id="19003">
    <literal><![CDATA[
      K(x,K(y \ (z \ u),z) \ w) = K(x,w * K(z,u * y))
    ]]></literal>
    <justification jstring="[hyper(7993,a,19002,a),flip(a)].">
      <j1 rule="hyper" parents="7993 19002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19004">
    <literal><![CDATA[
      K(x,K(y,z \ (y \ u)) * w) = K(x,w * K(y,u * z))
    ]]></literal>
    <justification jstring="[para(5130(a,1),19003(a,1,2))].">
      <j1 rule="para" parents="5130 19003"/>
    </justification>
  </clause>

  <clause id="19005">
    <literal><![CDATA[
      K(x,y * K(z,u \ w)) = K(x,y * K(z,w * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,15921,a(flip),b,19004,a)].">
      <j1 rule="hyper" parents="58 15921 19004"/>
    </justification>
  </clause>

  <clause id="19006">
    <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(17736,a,19005,a)].">
      <j1 rule="hyper" parents="17736 19005"/>
    </justification>
  </clause>

  <clause id="19007">
    <literal><![CDATA[
      K(x,y * K(z,(u \ z) * w)) = K(x,y * K(u * w,z))
    ]]></literal>
    <justification jstring="[hyper(15994,a,19005,a),flip(a)].">
      <j1 rule="hyper" parents="15994 19005"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19008">
    <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(19005(a,1),18864(a,1,1,2))].">
      <j1 rule="para" parents="19005 18864"/>
    </justification>
  </clause>

  <clause id="19009">
    <literal><![CDATA[
      K(x,y * K(z,z * (u \ w))) = K(x,y * K(u * w,z))
    ]]></literal>
    <justification jstring="[para(14118(a,1),19007(a,1,2,2))].">
      <j1 rule="para" parents="14118 19007"/>
    </justification>
  </clause>

  <clause id="19010">
    <literal><![CDATA[
      K(x,y * K(z \ u,w)) = K(x,y * K(z * u,w))
    ]]></literal>
    <justification jstring="[hyper(15954,a,19009,a)].">
      <j1 rule="hyper" parents="15954 19009"/>
    </justification>
  </clause>

  <clause id="19011">
    <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(17899,a,19010,a)].">
      <j1 rule="hyper" parents="17899 19010"/>
    </justification>
  </clause>

  <clause id="19012">
    <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,17545,a(flip),b,19006,a),flip(a)].">
      <j1 rule="hyper" parents="320 17545 19006"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19013">
    <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),19012(a,1,2,2,2,1))].">
      <j1 rule="para" parents="178 19012"/>
    </justification>
  </clause>

  <clause id="19014">
    <literal><![CDATA[
      K(x,y * (z * K(u,w / v5))) = K(x,y * (z * K(u,w * v5)))
    ]]></literal>
    <justification jstring="[hyper(17793,a,19013,a)].">
      <j1 rule="hyper" parents="17793 19013"/>
    </justification>
  </clause>

  <clause id="19015">
    <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,18533,a(flip),b,19013,a),flip(a)].">
      <j1 rule="hyper" parents="58 18533 19013"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19016">
    <literal><![CDATA[
      K(x,y * ((z / u) * K(z,w * v5))) = K(x,y * (T(z,w / v5) / u))
    ]]></literal>
    <justification jstring="[hyper(16135,a,19014,a),flip(a)].">
      <j1 rule="hyper" parents="16135 19014"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19017">
    <literal><![CDATA[
      K(x,y * (T(z,u / w) / v5)) = K(x,y * (T(z,u * w) / v5))
    ]]></literal>
    <justification jstring="[hyper(16135,a,19016,a),flip(a)].">
      <j1 rule="hyper" parents="16135 19016"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19018">
    <literal><![CDATA[
      K(x,y * (T(z,u \ w) / v5)) = K(x,y * (T(z,w * u) / v5))
    ]]></literal>
    <justification jstring="[hyper(58,a,16171,a(flip),b,19017,a)].">
      <j1 rule="hyper" parents="58 16171 19017"/>
    </justification>
  </clause>

  <clause id="19019">
    <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(19018(a,1),18129(a,1))].">
      <j1 rule="para" parents="19018 18129"/>
    </justification>
  </clause>

  <clause id="19020">
    <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(16700,a,19008,a)].">
      <j1 rule="hyper" parents="16700 19008"/>
    </justification>
  </clause>

  <clause id="19021">
    <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(16772,a,19020,a)].">
      <j1 rule="hyper" parents="16772 19020"/>
    </justification>
  </clause>

  <clause id="19022">
    <literal><![CDATA[
      K(x,K(y,z / u) \ w) = K(x,K(z * u,y) * w)
    ]]></literal>
    <justification jstring="[hyper(7993,a,19021,a),flip(a)].">
      <j1 rule="hyper" parents="7993 19021"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19023">
    <literal><![CDATA[
      K(x,K(y \ z,u) * w) = K(x,K(z * y,u) * w)
    ]]></literal>
    <justification jstring="[hyper(16700,a,19022,a)].">
      <j1 rule="hyper" parents="16700 19022"/>
    </justification>
  </clause>

  <clause id="19024">
    <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(19023(a,1),17999(a,1,1))].">
      <j1 rule="para" parents="19023 17999"/>
    </justification>
  </clause>

  <clause id="19025">
    <literal><![CDATA[
      K(x,y * (K(z,u \ w) * v5)) = K(x,y * (K(z,w * u) * v5))
    ]]></literal>
    <justification jstring="[hyper(58,a,17999,a(flip),b,19024,a),flip(a)].">
      <j1 rule="hyper" parents="58 17999 19024"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19026">
    <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(16335,a,19025,a),flip(a)].">
      <j1 rule="hyper" parents="16335 19025"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19027">
    <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,17545,a(flip),b,19011,a),flip(a)].">
      <j1 rule="hyper" parents="320 17545 19011"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19028">
    <literal><![CDATA[
      K(x,y * (z * T(u / w,v5 \ v6))) = K(x,y * (z * T(u / w,v6 * v5)))
    ]]></literal>
    <justification jstring="[hyper(16335,a,19026,a),flip(a)].">
      <j1 rule="hyper" parents="16335 19026"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19029">
    <literal><![CDATA[
      K(x,y * (z * K(u \ w,v5))) = K(x,y * (z * K(u * w,v5)))
    ]]></literal>
    <justification jstring="[para(17386(a,1),19027(a,1,2,2,2,1))].">
      <j1 rule="para" parents="17386 19027"/>
    </justification>
  </clause>

  <clause id="19030">
    <literal><![CDATA[
      K(x,y * ((z \ u) * K(w * v5,u))) = K(x,y * (z \ T(u,w \ v5)))
    ]]></literal>
    <justification jstring="[hyper(16336,a,19029,a),flip(a)].">
      <j1 rule="hyper" parents="16336 19029"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19031">
    <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,18227,a(flip),b,19029,a),flip(a)].">
      <j1 rule="hyper" parents="58 18227 19029"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19032">
    <literal><![CDATA[
      K(x,y * (z \ T(u,w \ v5))) = K(x,y * (z \ T(u,w * v5)))
    ]]></literal>
    <justification jstring="[hyper(16336,a,19030,a),flip(a)].">
      <j1 rule="hyper" parents="16336 19030"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19033">
    <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(17955,a,19032,a),flip(a)].">
      <j1 rule="hyper" parents="17955 19032"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19034">
    <literal><![CDATA[
      K(x,T(y,z \ u) * w) = K(x,T(y,u * z) * w)
    ]]></literal>
    <justification jstring="[hyper(58,a,19015,a(flip),b,19031,a)].">
      <j1 rule="hyper" parents="58 19015 19031"/>
    </justification>
  </clause>

  <clause id="19035">
    <literal><![CDATA[
      K(x,T(y,z / u) * w) = K(x,T(y,z * u) * w)
    ]]></literal>
    <justification jstring="[hyper(16131,a,19034,a)].">
      <j1 rule="hyper" parents="16131 19034"/>
    </justification>
  </clause>

  <clause id="19036">
    <literal><![CDATA[
      K(x,T(y,z * u) * (z \ u)) = K(x,(z \ u) * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,15246,a(flip),b,19034,a),flip(a)].">
      <j1 rule="hyper" parents="58 15246 19034"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19037">
    <literal><![CDATA[
      K(x,(y \ z) * T(u,y * z)) = K(x,u * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(58,a,15161,a(flip),b,19036,a),flip(a)].">
      <j1 rule="hyper" parents="58 15161 19036"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19038">
    <literal><![CDATA[
      K(x,y / (z \ (u * K(w,v5)))) = K(x,y * ((z \ u) \ K(v5,w)))
    ]]></literal>
    <justification jstring="[hyper(18969,a,19033,a)].">
      <j1 rule="hyper" parents="18969 19033"/>
    </justification>
  </clause>

  <clause id="19039">
    <literal><![CDATA[
      K(x,y / (z \ (K(u,w) * v5))) = K(x,y * ((z \ v5) \ K(w,u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,17491,a,b,19038,a)].">
      <j1 rule="hyper" parents="58 17491 19038"/>
    </justification>
  </clause>

  <clause id="19041">
    <literal><![CDATA[
      K(x,y * ((z \ T(u,z)) \ K(w,v5))) = K(x,y / (u / (K(w,v5) * z)))
    ]]></literal>
    <justification jstring="[hyper(18296,a,19039,a),flip(a)].">
      <j1 rule="hyper" parents="18296 19039"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19042">
    <literal><![CDATA[
      K(x,y / (z / (K(u,w) * v5))) = K(x,y * ((z / v5) \ K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(18618,a,19041,a),flip(a)].">
      <j1 rule="hyper" parents="18618 19041"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19043">
    <literal><![CDATA[
      K(x,y / ((K(z,u) * w) / v5)) = K(x,y * ((w / v5) \ K(u,z)))
    ]]></literal>
    <justification jstring="[hyper(58,a,18120,a,b,19042,a)].">
      <j1 rule="hyper" parents="58 18120 19042"/>
    </justification>
  </clause>

  <clause id="19044">
    <literal><![CDATA[
      K(x,y * (((z \ u) / w) \ K(z,v5))) = K(x,y / ((T(z,v5) \ u) / w))
    ]]></literal>
    <justification jstring="[para(5131(a,1),19043(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5131 19043"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19045">
    <literal><![CDATA[
      K(x,y * (((z / u) / w) \ K(v5,z))) = K(x,y / ((T(z,v5) / u) / w))
    ]]></literal>
    <justification jstring="[para(13708(a,1),19043(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="13708 19043"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19046">
    <literal><![CDATA[
      K(x,T(y,z) / ((y / u) / w)) = K(x,y / ((T(y,z) / u) / w))
    ]]></literal>
    <justification jstring="[hyper(17918,a,19045,a)].">
      <j1 rule="hyper" parents="17918 19045"/>
    </justification>
  </clause>

  <clause id="19047">
    <literal><![CDATA[
      K(x,y / ((T(y,z * u) / z) / u)) = K(x,y \ ((y * u) * z))
    ]]></literal>
    <justification jstring="[hyper(58,a,18671,a(flip),b,19046,a),flip(a)].">
      <j1 rule="hyper" parents="58 18671 19046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19048">
    <literal><![CDATA[
      K(x,((((y \ z) * u) \ u) \ u) / z) = K(x,((z \ y) \ (((z \ y) \ u) * (z \ y))) / z)
    ]]></literal>
    <justification jstring="[para(16950(a,1),18918(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="16950 18918"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19049">
    <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),19048(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="17 19048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19050">
    <literal><![CDATA[
      K(x,T(y \ ((y / z) * u),z)) = K(x,((((z \ y) * u) \ u) \ u) / y)
    ]]></literal>
    <justification jstring="[hyper(18277,a,19049,a)].">
      <j1 rule="hyper" parents="18277 19049"/>
    </justification>
  </clause>

  <clause id="19051">
    <literal><![CDATA[
      K(x,T(y \ ((y / z) * u),z)) = K(x,T((z \ y) * u,u) / y)
    ]]></literal>
    <justification jstring="[hyper(320,a,13052,a(flip),b,19050,a),flip(a)].">
      <j1 rule="hyper" parents="320 13052 19050"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19052">
    <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(19051(a,2),16352(a,1))].">
      <j1 rule="para" parents="19051 16352"/>
    </justification>
  </clause>

  <clause id="19053">
    <literal><![CDATA[
      K(x,(y * (z \ u)) / u) = K(x,u / (z * (y \ u)))
    ]]></literal>
    <justification jstring="[hyper(19052,a,18676,a)].">
      <j1 rule="hyper" parents="19052 18676"/>
    </justification>
  </clause>

  <clause id="19054">
    <literal><![CDATA[
      K(x,y / ((z \ y) * (u \ y))) = K(x,(u * T(z,y)) / y)
    ]]></literal>
    <justification jstring="[hyper(58,a,13161,a(flip),b,19053,a),flip(a)].">
      <j1 rule="hyper" parents="58 13161 19053"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19055">
    <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(17368(a,2),19053(a,2,2,2,2))].">
      <j1 rule="para" parents="17368 19053"/>
    </justification>
  </clause>

  <clause id="19056">
    <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(14520(a,1),19054(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14520 19054"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19057">
    <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,15485,a(flip),b,18964,a),flip(a)].">
      <j1 rule="hyper" parents="58 15485 18964"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19058">
    <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(15399(a,2),18970(a,2,2,2,2))].">
      <j1 rule="para" parents="15399 18970"/>
    </justification>
  </clause>

  <clause id="19059">
    <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(13720(a,1),18985(a,1,1,1))].">
      <j1 rule="para" parents="13720 18985"/>
    </justification>
  </clause>

  <clause id="19060">
    <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,14086,a(flip),b,19059,a),flip(a)].">
      <j1 rule="hyper" parents="320 14086 19059"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19062">
    <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(6521(a,1),19058(a,2,2,2,2,1))].">
      <j1 rule="para" parents="6521 19058"/>
    </justification>
  </clause>

  <clause id="19063">
    <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,17730,a(flip),b,19062,a)].">
      <j1 rule="hyper" parents="58 17730 19062"/>
    </justification>
  </clause>

  <clause id="19064">
    <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,15425,a(flip),b,19063,a),flip(a)].">
      <j1 rule="hyper" parents="58 15425 19063"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19066">
    <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(4870(a,2),19064(a,2,2,2,2)),flip(a)].">
      <j1 rule="para" parents="4870 19064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19067">
    <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,19028,a(flip),b,19066,a),flip(a)].">
      <j1 rule="hyper" parents="320 19028 19066"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19068">
    <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,19064,a(flip),b,19067,a),flip(a)].">
      <j1 rule="hyper" parents="320 19064 19067"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19069">
    <literal><![CDATA[
      K(x,y * (z * T(u,w \ v5))) = K(x,y * (z * T(u,v5 * w)))
    ]]></literal>
    <justification jstring="[para(4816(a,1),19068(a,1,2,2,2,1))].">
      <j1 rule="para" parents="4816 19068"/>
    </justification>
  </clause>

  <clause id="19070">
    <literal><![CDATA[
      K(x,y * (z * T(u,w / v5))) = K(x,y * (z * T(u,w * v5)))
    ]]></literal>
    <justification jstring="[hyper(16250,a,19069,a)].">
      <j1 rule="hyper" parents="16250 19069"/>
    </justification>
  </clause>

  <clause id="19071">
    <literal><![CDATA[
      T(x,y * (z * T(u,w \ v5))) = T(x,y * (z * T(u,v5 * w)))
    ]]></literal>
    <justification jstring="[hyper(118,a,19069,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 19069 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19072">
    <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(16338,a,19070,a)].">
      <j1 rule="hyper" parents="16338 19070"/>
    </justification>
  </clause>

  <clause id="19073">
    <literal><![CDATA[
      T(x,y * (z * T(u,w / v5))) = T(x,y * (z * T(u,w * v5)))
    ]]></literal>
    <justification jstring="[hyper(118,a,19070,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 19070 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19074">
    <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,18625,a(flip),b,19071,a),flip(a)].">
      <j1 rule="hyper" parents="58 18625 19071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19075">
    <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(19073(a,1),16252(a,1,2,2))].">
      <j1 rule="para" parents="19073 16252"/>
    </justification>
  </clause>

  <clause id="19076">
    <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,16232,a(flip),b,19072,a),flip(a)].">
      <j1 rule="hyper" parents="320 16232 19072"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19077">
    <literal><![CDATA[
      K(x,y * (T(z,u \ w) * v5)) = K(x,y * (T(z,w * u) * v5))
    ]]></literal>
    <justification jstring="[hyper(17390,a,19076,a)].">
      <j1 rule="hyper" parents="17390 19076"/>
    </justification>
  </clause>

  <clause id="19079">
    <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(19077(a,1),16289(a,1))].">
      <j1 rule="para" parents="19077 16289"/>
    </justification>
  </clause>

  <clause id="19080">
    <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(19074(a,1),19075(a,1,2,2))].">
      <j1 rule="para" parents="19074 19075"/>
    </justification>
  </clause>

  <clause id="19081">
    <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(15394,a,17295,a)].">
      <j1 rule="hyper" parents="15394 17295"/>
    </justification>
  </clause>

  <clause id="19083">
    <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(4307(a,1),19081(a,1,2,1,1))].">
      <j1 rule="para" parents="4307 19081"/>
    </justification>
  </clause>

  <clause id="19084">
    <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(13219,a,19083,a)].">
      <j1 rule="hyper" parents="13219 19083"/>
    </justification>
  </clause>

  <clause id="19085">
    <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,17493,a(flip),b,18611,a),flip(a)].">
      <j1 rule="hyper" parents="58 17493 18611"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19086">
    <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,14720,a(flip),b,19085,a),flip(a)].">
      <j1 rule="hyper" parents="320 14720 19085"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19087">
    <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,17975,a(flip),b,19086,a),flip(a)].">
      <j1 rule="hyper" parents="320 17975 19086"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19088">
    <literal><![CDATA[
      K(x,(y \ (z \ u)) \ (y \ u)) = K(x,L(T(z,u),u,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(18400,a,19087,a),flip(a)].">
      <j1 rule="hyper" parents="18400 19087"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19089">
    <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(443,a,10971,a(flip),b,19088,a)].">
      <j1 rule="hyper" parents="443 10971 19088"/>
    </justification>
  </clause>

  <clause id="19091">
    <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(13818(a,1),17674(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="13818 17674"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19092">
    <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,18150,a(flip),b,19091,a),flip(a)].">
      <j1 rule="hyper" parents="320 18150 19091"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19093">
    <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(4453(a,1),17739(a,1,2,1,1))].">
      <j1 rule="para" parents="4453 17739"/>
    </justification>
  </clause>

  <clause id="19094">
    <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(2959(a,1),19093(a,1,2,1,1))].">
      <j1 rule="para" parents="2959 19093"/>
    </justification>
  </clause>

  <clause id="19096">
    <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,16798,a(flip),b,19094,a)].">
      <j1 rule="hyper" parents="58 16798 19094"/>
    </justification>
  </clause>

  <clause id="19097">
    <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),19096(a,2,2,1))].">
      <j1 rule="para" parents="7 19096"/>
    </justification>
  </clause>

  <clause id="19098">
    <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,9952,a(flip),b,19097,a)].">
      <j1 rule="hyper" parents="58 9952 19097"/>
    </justification>
  </clause>

  <clause id="19100">
    <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,5576,a(flip),b,19098,a),flip(a)].">
      <j1 rule="hyper" parents="58 5576 19098"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19101">
    <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,16658,a(flip),b,19100,a),flip(a)].">
      <j1 rule="hyper" parents="320 16658 19100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19102">
    <literal><![CDATA[
      K(x,(((y \ 1) \ 1) \ z) * (z \ (u * y))) = K(x,((y * u) / z) * (z / y))
    ]]></literal>
    <justification jstring="[hyper(320,a,18128,a(flip),b,19101,a),flip(a)].">
      <j1 rule="hyper" parents="320 18128 19101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19103">
    <literal><![CDATA[
      K(x,(T(y,1) \ z) * (z \ (u * y))) = K(x,((y * u) / z) * (z / y))
    ]]></literal>
    <justification jstring="[hyper(58,a,13168,a(flip),b,19102,a)].">
      <j1 rule="hyper" parents="58 13168 19102"/>
    </justification>
  </clause>

  <clause id="19104">
    <literal><![CDATA[
      K(x,((y * z) / u) * (u / y)) = K(x,(y \ u) * (u \ (z * y)))
    ]]></literal>
    <justification jstring="[para(198(a,1),19103(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="198 19103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19105">
    <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(18509,a,17936,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="18509 17936"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19106">
    <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(4908(a,1),19105(a,2,1,1))].">
      <j1 rule="para" parents="4908 19105"/>
    </justification>
  </clause>

  <clause id="19107">
    <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(4781(a,1),19106(a,1,2,1))].">
      <j1 rule="para" parents="4781 19106"/>
    </justification>
  </clause>

  <clause id="19108">
    <literal><![CDATA[
      (K(x,y) * (z * K(y,x))) * ((z * K(y,x)) \ u) = (K(x,y) * z) * (z \ u)
    ]]></literal>
    <justification jstring="[hyper(18509,a,19107,a)].">
      <j1 rule="hyper" parents="18509 19107"/>
    </justification>
  </clause>

  <clause id="19109">
    <literal><![CDATA[
      T(x,K(y,z)) * ((x * K(y,z)) \ u) = (K(z,y) * x) * (x \ u)
    ]]></literal>
    <justification jstring="[para(5141(a,1),19108(a,1,1))].">
      <j1 rule="para" parents="5141 19108"/>
    </justification>
  </clause>

  <clause id="19110">
    <literal><![CDATA[
      (K(x,y) * z) \ (z * ((K(y,x) * z) \ u)) = z \ u
    ]]></literal>
    <justification jstring="[hyper(11221,a,19109,a)].">
      <j1 rule="hyper" parents="11221 19109"/>
    </justification>
  </clause>

  <clause id="19111">
    <literal><![CDATA[
      (K(x,y) * z) * (z \ u) != w
    ]]></literal>
    <literal><![CDATA[
      z * ((K(y,x) * z) \ u) = w
    ]]></literal>
    <justification jstring="[para(19109(a,1),11169(a,1))].">
      <j1 rule="para" parents="19109 11169"/>
    </justification>
  </clause>

  <clause id="19112">
    <literal><![CDATA[
      (K(x,y) * z) \ (z * u) = z \ ((K(y,x) * z) * u)
    ]]></literal>
    <justification jstring="[para(4(a,1),19110(a,1,2,2))].">
      <j1 rule="para" parents="4 19110"/>
    </justification>
  </clause>

  <clause id="19113">
    <literal><![CDATA[
      x \ ((K(y,z) * x) * T(u,K(z,y))) = (u * x) / (x * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(18724,a,19112,a),flip(a)].">
      <j1 rule="hyper" parents="18724 19112"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19114">
    <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,11213,a(flip),b,19112,a),flip(a)].">
      <j1 rule="hyper" parents="58 11213 19112"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19115">
    <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(19112(a,1),18530(a,1,2,2,2))].">
      <j1 rule="para" parents="19112 18530"/>
    </justification>
  </clause>

  <clause id="19116">
    <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(19111,a,16850,a),flip(a)].">
      <j1 rule="hyper" parents="19111 16850"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19117">
    <literal><![CDATA[
      x \ ((x * K(y,z)) * (K(z,y) * u)) = L(u,K(z,y),x)
    ]]></literal>
    <justification jstring="[para(11162(a,1),19114(a,1,2))].">
      <j1 rule="para" parents="11162 19114"/>
    </justification>
  </clause>

  <clause id="19118">
    <literal><![CDATA[
      L(x,K(y,z),u * K(z,y)) = L(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(6348,a,19117,a)].">
      <j1 rule="hyper" parents="6348 19117"/>
    </justification>
  </clause>

  <clause id="19119">
    <literal><![CDATA[
      (x * K(y,z)) * (K(z,y) * u) = x * L(u,K(z,y),x)
    ]]></literal>
    <justification jstring="[hyper(134,a,19117,a),flip(a)].">
      <j1 rule="hyper" parents="134 19117"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19120">
    <literal><![CDATA[
      L(x,K(y,z),u \ T(z,y)) = L(x,K(y,z),u \ z)
    ]]></literal>
    <justification jstring="[para(13699(a,1),19118(a,1,3))].">
      <j1 rule="para" parents="13699 19118"/>
    </justification>
  </clause>

  <clause id="19121">
    <literal><![CDATA[
      L(x,K(y,z),u) * u = (x * K(y,z)) * (K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(19118(a,1),18714(a,1,1))].">
      <j1 rule="para" parents="19118 18714"/>
    </justification>
  </clause>

  <clause id="19122">
    <literal><![CDATA[
      x * L(K(y,z) * u,K(z,y),x) = (x * K(y,z)) * u
    ]]></literal>
    <justification jstring="[para(5133(a,1),19119(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5133 19119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19123">
    <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(6340(a,1),19121(a,2,1))].">
      <j1 rule="para" parents="6340 19121"/>
    </justification>
  </clause>

  <clause id="19124">
    <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(19122(a,1),15439(a,1,2,2,2,1))].">
      <j1 rule="para" parents="19122 15439"/>
    </justification>
  </clause>

  <clause id="19125">
    <literal><![CDATA[
      x \ ((K(y,z) * x) * T(u,K(y,z))) = (u * x) / (x * K(z,y))
    ]]></literal>
    <justification jstring="[para(7832(a,1),19113(a,1,2,2))].">
      <j1 rule="para" parents="7832 19113"/>
    </justification>
  </clause>

  <clause id="19126">
    <literal><![CDATA[
      x \ ((K(y,T(z,u)) * x) * u) = (u * x) / (x * K(z,y))
    ]]></literal>
    <justification jstring="[para(17750(a,2),19113(a,1,2))].">
      <j1 rule="para" parents="17750 19113"/>
    </justification>
  </clause>

  <clause id="19127">
    <literal><![CDATA[
      (x * y) / (y * K(z,T(u,x))) = y \ ((K(u,z) * y) * x)
    ]]></literal>
    <justification jstring="[para(7888(a,1),19126(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="7888 19126"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19128">
    <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(19127(a,1),18727(a,1,2))].">
      <j1 rule="para" parents="19127 18727"/>
    </justification>
  </clause>

  <clause id="19129">
    <literal><![CDATA[
      K(x,y / ((z * u) \ (u * y))) = y \ ((y * u) / (u * K(z,x)))
    ]]></literal>
    <justification jstring="[para(19125(a,1),18976(a,1,2)),flip(a)].">
      <j1 rule="para" parents="19125 18976"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19130">
    <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(16443(a,1),19116(a,2,2))].">
      <j1 rule="para" parents="16443 19116"/>
    </justification>
  </clause>

  <clause id="19131">
    <literal><![CDATA[
      x * a(y,x,K(x \ z,u)) = z * ((K(y,u) * z) \ (K(y,u) * x))
    ]]></literal>
    <justification jstring="[para(18317(a,1),19130(a,1,2))].">
      <j1 rule="para" parents="18317 19130"/>
    </justification>
  </clause>

  <clause id="19132">
    <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(7678(a,1),19131(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="7678 19131"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19134">
    <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(14351(a,1),19132(a,2,2))].">
      <j1 rule="para" parents="14351 19132"/>
    </justification>
  </clause>

  <clause id="19135">
    <literal><![CDATA[
      (x * y) * L((x * y) \ z,x,K(y,u)) = z * a(u,z,K(y,z \ x))
    ]]></literal>
    <justification jstring="[para(18367(a,1),19134(a,1,2))].">
      <j1 rule="para" parents="18367 19134"/>
    </justification>
  </clause>

  <clause id="19136">
    <literal><![CDATA[
      x * a(y,x,K(z,x \ u)) = u * (z * L(z \ (u \ x),u,K(z,y)))
    ]]></literal>
    <justification jstring="[hyper(1089,a,19135,a),flip(a)].">
      <j1 rule="hyper" parents="1089 19135"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19137">
    <literal><![CDATA[
      x * L(y * (y \ (x \ z)),x,K(y,u)) = z * a(u,z,K(y,z \ x))
    ]]></literal>
    <justification jstring="[para(18440(a,2),19136(a,2,2)),flip(a)].">
      <j1 rule="para" parents="18440 19136"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19138">
    <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),19137(a,1,2,1))].">
      <j1 rule="para" parents="5 19137"/>
    </justification>
  </clause>

  <clause id="19140">
    <literal><![CDATA[
      x * L(x \ y,x,K(z,u)) = y * a(u,y,K(x \ y,z))
    ]]></literal>
    <justification jstring="[para(11036(a,2),19138(a,2,2))].">
      <j1 rule="para" parents="11036 19138"/>
    </justification>
  </clause>

  <clause id="19141">
    <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(19128(a,1),19115(a,1,2,2))].">
      <j1 rule="para" parents="19128 19115"/>
    </justification>
  </clause>

  <clause id="19142">
    <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(18283,a,19141,a),flip(a)].">
      <j1 rule="hyper" parents="18283 19141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19143">
    <literal><![CDATA[
      K(x,y * L(z,K(u,w),v5)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(16096,a,19142,a),flip(a)].">
      <j1 rule="hyper" parents="16096 19142"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19144">
    <literal><![CDATA[
      K(x,y * L(z,K(u,w),v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = v6
    ]]></literal>
    <justification jstring="[para(19142(a,1),16096(a,1))].">
      <j1 rule="para" parents="19142 16096"/>
    </justification>
  </clause>

  <clause id="19146">
    <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),19143(a,1,2,2))].">
      <j1 rule="para" parents="566 19143"/>
    </justification>
  </clause>

  <clause id="19147">
    <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(6347(a,1),19144(a,1,2))].">
      <j1 rule="para" parents="6347 19144"/>
    </justification>
  </clause>

  <clause id="19148">
    <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(5130(a,1),19146(a,2,2,2,1))].">
      <j1 rule="para" parents="5130 19146"/>
    </justification>
  </clause>

  <clause id="19149">
    <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,18290,a,b,19148,a)].">
      <j1 rule="hyper" parents="58 18290 19148"/>
    </justification>
  </clause>

  <clause id="19150">
    <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(5130(a,1),19149(a,1,2,2,1,1))].">
      <j1 rule="para" parents="5130 19149"/>
    </justification>
  </clause>

  <clause id="19151">
    <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,18208,a(flip),b,19150,a)].">
      <j1 rule="hyper" parents="58 18208 19150"/>
    </justification>
  </clause>

  <clause id="19152">
    <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(15798,a,19151,a),flip(a)].">
      <j1 rule="hyper" parents="15798 19151"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19153">
    <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),19152(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="4 19152"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19154">
    <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(16699,a,18124,a)].">
      <j1 rule="hyper" parents="16699 18124"/>
    </justification>
  </clause>

  <clause id="19155">
    <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,15213,a(flip),b,18833,a)].">
      <j1 rule="hyper" parents="58 15213 18833"/>
    </justification>
  </clause>

  <clause id="19156">
    <literal><![CDATA[
      T((x * y) \ y,K(y,y \ z)) = (x * T(y,y \ z)) \ ((y \ z) \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,16612,a(flip),b,19155,a)].">
      <j1 rule="hyper" parents="58 16612 19155"/>
    </justification>
  </clause>

  <clause id="19157">
    <literal><![CDATA[
      (x * T(y,y \ z)) \ ((y \ z) \ z) = T((x * y) \ y,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(13059,a,19156,a),flip(a)].">
      <j1 rule="hyper" parents="13059 19156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19158">
    <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(18272,a,19080,a)].">
      <j1 rule="hyper" parents="18272 19080"/>
    </justification>
  </clause>

  <clause id="19159">
    <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),19154(a,1,2,1,1))].">
      <j1 rule="para" parents="4 19154"/>
    </justification>
  </clause>

  <clause id="19161">
    <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(14590,a,18449,a)].">
      <j1 rule="hyper" parents="14590 18449"/>
    </justification>
  </clause>

  <clause id="19162">
    <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(19161(a,1),6499(a,1))].">
      <j1 rule="para" parents="19161 6499"/>
    </justification>
  </clause>

  <clause id="19163">
    <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,18502,a(flip),b,18529,a)].">
      <j1 rule="hyper" parents="58 18502 18529"/>
    </justification>
  </clause>

  <clause id="19165">
    <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,18500,a(flip),b,19163,a)].">
      <j1 rule="hyper" parents="58 18500 19163"/>
    </justification>
  </clause>

  <clause id="19166">
    <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(15572(a,1),19165(a,1,2,1))].">
      <j1 rule="para" parents="15572 19165"/>
    </justification>
  </clause>

  <clause id="19167">
    <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(9471(a,2),19166(a,1,2))].">
      <j1 rule="para" parents="9471 19166"/>
    </justification>
  </clause>

  <clause id="19168">
    <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(7784(a,2),19167(a,1,2,1,1))].">
      <j1 rule="para" parents="7784 19167"/>
    </justification>
  </clause>

  <clause id="19169">
    <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(17745,a,19168,a)].">
      <j1 rule="hyper" parents="17745 19168"/>
    </justification>
  </clause>

  <clause id="19170">
    <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(15600,a,19169,a)].">
      <j1 rule="hyper" parents="15600 19169"/>
    </justification>
  </clause>

  <clause id="19171">
    <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(19170(a,2),13468(a,1,3,2))].">
      <j1 rule="para" parents="19170 13468"/>
    </justification>
  </clause>

  <clause id="19172">
    <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(15114(a,1),19171(a,2,3,2))].">
      <j1 rule="para" parents="15114 19171"/>
    </justification>
  </clause>

  <clause id="19173">
    <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),18998(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4 18998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19174">
    <literal><![CDATA[
      K(x,T(y * L(y \ z,u,u \ 1),y)) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(320,a,19060,a(flip),b,19173,a),flip(a)].">
      <j1 rule="hyper" parents="320 19060 19173"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19176">
    <literal><![CDATA[
      K(x,y * L(z / y,u,u \ 1)) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(12303,a,19174,a)].">
      <j1 rule="hyper" parents="12303 19174"/>
    </justification>
  </clause>

  <clause id="19178">
    <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(17410(a,2),17432(a,1,1))].">
      <j1 rule="para" parents="17410 17432"/>
    </justification>
  </clause>

  <clause id="19179">
    <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(13920(a,1),17753(a,1,2,2))].">
      <j1 rule="para" parents="13920 17753"/>
    </justification>
  </clause>

  <clause id="19180">
    <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),17781(a,1,2,3))].">
      <j1 rule="para" parents="5 17781"/>
    </justification>
  </clause>

  <clause id="19181">
    <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,14344,a(flip),b,19180,a),flip(a)].">
      <j1 rule="hyper" parents="58 14344 19180"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19184">
    <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,13775,a(flip),b,19181,a),flip(a)].">
      <j1 rule="hyper" parents="320 13775 19181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19185">
    <literal><![CDATA[
      K(x,y \ (((L(y,z,u) \ y) \ y) * w)) = K(x,(y \ L(y,z,u)) * w)
    ]]></literal>
    <justification jstring="[para(3585(a,1),19184(a,1,2,2,1,1))].">
      <j1 rule="para" parents="3585 19184"/>
    </justification>
  </clause>

  <clause id="19186">
    <literal><![CDATA[
      K(x,y \ (L(y,z,u) * w)) = K(x,(y \ L(y,z,u)) * w)
    ]]></literal>
    <justification jstring="[para(5948(a,1),19185(a,1,2,2,1))].">
      <j1 rule="para" parents="5948 19185"/>
    </justification>
  </clause>

  <clause id="19187">
    <literal><![CDATA[
      K(x,(y \ L(y,z,u)) * w) = K(x,L(y,z,u) * (y \ w))
    ]]></literal>
    <justification jstring="[para(1406(a,1),19186(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1406 19186"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19188">
    <literal><![CDATA[
      K(x,L(y,z,z \ 1) * (y \ u)) = K(x,u * a(y,z,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(17465,a,19187,a),flip(a)].">
      <j1 rule="hyper" parents="17465 19187"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19189">
    <literal><![CDATA[
      K(x,L(y,z,u) * (y \ w)) = K(x,w * (y \ L(y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(17289,a,19187,a),flip(a)].">
      <j1 rule="hyper" parents="17289 19187"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19190">
    <literal><![CDATA[
      T(x,(y \ L(y,z,u)) * w) = T(x,L(y,z,u) * (y \ w))
    ]]></literal>
    <justification jstring="[hyper(118,a,19187,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 19187 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19191">
    <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,19037,a(flip),b,19187,a),flip(a)].">
      <j1 rule="hyper" parents="58 19037 19187"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19192">
    <literal><![CDATA[
      T(x,L(y,z,u) * (y \ w)) = T(x,w * (y \ L(y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(118,a,19189,a,b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 19189 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19193">
    <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(19190(a,1),807(a,1,1))].">
      <j1 rule="para" parents="19190 807"/>
    </justification>
  </clause>

  <clause id="19194">
    <literal><![CDATA[
      K(x,a(y \ 1,y,z) \ u) = K(x,u * a(z,y,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(58,a,14680,a(flip),b,19188,a)].">
      <j1 rule="hyper" parents="58 14680 19188"/>
    </justification>
  </clause>

  <clause id="19195">
    <literal><![CDATA[
      K(x,(y * z) * a(z,u,u \ 1)) = K(x,y * L(z,u,u \ 1))
    ]]></literal>
    <justification jstring="[hyper(18165,a,19194,a),flip(a)].">
      <j1 rule="hyper" parents="18165 19194"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19196">
    <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(19194(a,1),18165(a,1))].">
      <j1 rule="para" parents="19194 18165"/>
    </justification>
  </clause>

  <clause id="19197">
    <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(10112(a,2),19195(a,1,2,1))].">
      <j1 rule="para" parents="10112 19195"/>
    </justification>
  </clause>

  <clause id="19198">
    <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,18136,a(flip),b,18922,a),flip(a)].">
      <j1 rule="hyper" parents="320 18136 18922"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19200">
    <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,13049,a(flip),b,19198,a),flip(a)].">
      <j1 rule="hyper" parents="320 13049 19198"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19201">
    <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(19157(a,1),19200(a,1,2,2,2))].">
      <j1 rule="para" parents="19157 19200"/>
    </justification>
  </clause>

  <clause id="19202">
    <literal><![CDATA[
      K(x,((y \ z) \ z) \ (u * ((w * y) \ y))) = K(x,T(y,z) \ (u / T(w,y)))
    ]]></literal>
    <justification jstring="[hyper(17478,a,19201,a)].">
      <j1 rule="hyper" parents="17478 19201"/>
    </justification>
  </clause>

  <clause id="19203">
    <literal><![CDATA[
      K(x,T(y,z) \ (u * ((w * y) \ y))) = K(x,T(y,z) \ (u / T(w,y)))
    ]]></literal>
    <justification jstring="[hyper(13212,a,19202,a)].">
      <j1 rule="hyper" parents="13212 19202"/>
    </justification>
  </clause>

  <clause id="19204">
    <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,18098,a(flip),b,19203,a)].">
      <j1 rule="hyper" parents="58 18098 19203"/>
    </justification>
  </clause>

  <clause id="19205">
    <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,18670,a,b,19204,a),flip(a)].">
      <j1 rule="hyper" parents="58 18670 19204"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19206">
    <literal><![CDATA[
      K(x,((y * ((y * z) / y)) / u) \ z) = K(x,z \ ((z * u) / y))
    ]]></literal>
    <justification jstring="[hyper(15797,a,19205,a),flip(a)].">
      <j1 rule="hyper" parents="15797 19205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19207">
    <literal><![CDATA[
      K(x,((y * z) / u) \ T(z,y)) = K(x,z \ ((z * u) / y))
    ]]></literal>
    <justification jstring="[para(14586(a,1),19206(a,1,2))].">
      <j1 rule="para" parents="14586 19206"/>
    </justification>
  </clause>

  <clause id="19208">
    <literal><![CDATA[
      K(x,T(y / (z \ (u * y)),u)) = K(x,y \ ((y * z) / u))
    ]]></literal>
    <justification jstring="[hyper(16760,a,19207,a)].">
      <j1 rule="hyper" parents="16760 19207"/>
    </justification>
  </clause>

  <clause id="19209">
    <literal><![CDATA[
      K(x,y / (T(z,u) \ (u * y))) = K(x,y \ ((y * z) / u))
    ]]></literal>
    <justification jstring="[hyper(18225,a,19208,a)].">
      <j1 rule="hyper" parents="18225 19208"/>
    </justification>
  </clause>

  <clause id="19210">
    <literal><![CDATA[
      K(x,T(y / (z \ (u * y)),z)) = K(x,y \ ((y * z) / u))
    ]]></literal>
    <justification jstring="[hyper(58,a,18680,a(flip),b,19208,a)].">
      <j1 rule="hyper" parents="58 18680 19208"/>
    </justification>
  </clause>

  <clause id="19211">
    <literal><![CDATA[
      K(x,y / ((z * u) \ (u * y))) = K(x,y \ ((y * (u * z)) / u))
    ]]></literal>
    <justification jstring="[hyper(58,a,18831,a(flip),b,19209,a)].">
      <j1 rule="hyper" parents="58 18831 19209"/>
    </justification>
  </clause>

  <clause id="19212">
    <literal><![CDATA[
      K(x,y / (z \ (T(u,z) * y))) = K(x,y \ ((y * z) / u))
    ]]></literal>
    <justification jstring="[hyper(58,a,18679,a,b,19210,a)].">
      <j1 rule="hyper" parents="58 18679 19210"/>
    </justification>
  </clause>

  <clause id="19213">
    <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,6108,a(flip),b,19056,a),flip(a)].">
      <j1 rule="hyper" parents="320 6108 19056"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19214">
    <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,14591,a(flip),b,19213,a),flip(a)].">
      <j1 rule="hyper" parents="114 14591 19213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19215">
    <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,18423,a(flip),b,19214,a),flip(a)].">
      <j1 rule="hyper" parents="320 18423 19214"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19217">
    <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(6335(a,1),19215(a,1,2))].">
      <j1 rule="para" parents="6335 19215"/>
    </justification>
  </clause>

  <clause id="19218">
    <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(17604,a,19217,a)].">
      <j1 rule="hyper" parents="17604 19217"/>
    </justification>
  </clause>

  <clause id="19219">
    <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(5631(a,1),19218(a,1,2,2))].">
      <j1 rule="para" parents="5631 19218"/>
    </justification>
  </clause>

  <clause id="19220">
    <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,19092,a,b,19219,a)].">
      <j1 rule="hyper" parents="58 19092 19219"/>
    </justification>
  </clause>

  <clause id="19222">
    <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(15847(a,2),19178(a,1,2,1))].">
      <j1 rule="para" parents="15847 19178"/>
    </justification>
  </clause>

  <clause id="19223">
    <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(7553(a,1),19179(a,1,2,2))].">
      <j1 rule="para" parents="7553 19179"/>
    </justification>
  </clause>

  <clause id="19225">
    <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(10107(a,1),19223(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10107 19223"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19226">
    <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,13840,a(flip),b,19225,a),flip(a)].">
      <j1 rule="hyper" parents="320 13840 19225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19227">
    <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,13122,a(flip),b,19226,a),flip(a)].">
      <j1 rule="hyper" parents="320 13122 19226"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19228">
    <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,17462,a(flip),b,19227,a),flip(a)].">
      <j1 rule="hyper" parents="320 17462 19227"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19229">
    <literal><![CDATA[
      K(x,y * L((z / (y \ 1)) / y,u,w)) = K(x,y * L(z,u,w))
    ]]></literal>
    <justification jstring="[para(10113(a,1),19228(a,1,2,2,1))].">
      <j1 rule="para" parents="10113 19228"/>
    </justification>
  </clause>

  <clause id="19230">
    <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(18997(a,2),19229(a,2,2,2))].">
      <j1 rule="para" parents="18997 19229"/>
    </justification>
  </clause>

  <clause id="19231">
    <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(14241(a,1),19197(a,1,2,2))].">
      <j1 rule="para" parents="14241 19197"/>
    </justification>
  </clause>

  <clause id="19232">
    <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(17219(a,2),19222(a,1,2))].">
      <j1 rule="para" parents="17219 19222"/>
    </justification>
  </clause>

  <clause id="19233">
    <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,19176,a(flip),b,19230,a)].">
      <j1 rule="hyper" parents="58 19176 19230"/>
    </justification>
  </clause>

  <clause id="19235">
    <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,14150,a(flip),b,19233,a)].">
      <j1 rule="hyper" parents="58 14150 19233"/>
    </justification>
  </clause>

  <clause id="19236">
    <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(12302,a,19235,a),flip(a)].">
      <j1 rule="hyper" parents="12302 19235"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19237">
    <literal><![CDATA[
      K(x,y * L(z \ T(u,w),v5,v5 \ 1)) = K(x,y * (z \ T(u,w)))
    ]]></literal>
    <justification jstring="[para(18997(a,1),19236(a,1,2,2))].">
      <j1 rule="para" parents="18997 19236"/>
    </justification>
  </clause>

  <clause id="19238">
    <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(15066(a,1),19231(a,1,2,2))].">
      <j1 rule="para" parents="15066 19231"/>
    </justification>
  </clause>

  <clause id="19239">
    <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(17392,a,19232,a)].">
      <j1 rule="hyper" parents="17392 19232"/>
    </justification>
  </clause>

  <clause id="19240">
    <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,18591,a(flip),b,19238,a)].">
      <j1 rule="hyper" parents="58 18591 19238"/>
    </justification>
  </clause>

  <clause id="19241">
    <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,19229,a(flip),b,19240,a),flip(a)].">
      <j1 rule="hyper" parents="320 19229 19240"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19242">
    <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,17454,a(flip),b,19239,a),flip(a)].">
      <j1 rule="hyper" parents="58 17454 19239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19244">
    <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,19242,a),flip(a)].">
      <j1 rule="hyper" parents="320 15 19242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19245">
    <literal><![CDATA[
      R(x,y,K(z,K(u,w)) * v5) = R(x,y,v5)
    ]]></literal>
    <justification jstring="[para(17429(a,1),19244(a,1,2))].">
      <j1 rule="para" parents="17429 19244"/>
    </justification>
  </clause>

  <clause id="19247">
    <literal><![CDATA[
      R(x,y,z \ (T(u,K(w,v5)) \ v6)) = R(x,y,z \ (u \ v6))
    ]]></literal>
    <justification jstring="[para(17387(a,1),19245(a,1,3)),flip(a)].">
      <j1 rule="para" parents="17387 19245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19248">
    <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,19172,a(flip),b,19247,a),flip(a)].">
      <j1 rule="hyper" parents="58 19172 19247"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19250">
    <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,14630,a,b,19248,a)].">
      <j1 rule="hyper" parents="58 14630 19248"/>
    </justification>
  </clause>

  <clause id="19251">
    <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(17389(a,1),19250(a,1,3))].">
      <j1 rule="para" parents="17389 19250"/>
    </justification>
  </clause>

  <clause id="19252">
    <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,19245,a(flip),b,19251,a),flip(a)].">
      <j1 rule="hyper" parents="58 19245 19251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19254">
    <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(19252(a,1),18271(a,1,2,1))].">
      <j1 rule="para" parents="19252 18271"/>
    </justification>
  </clause>

  <clause id="19255">
    <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),19254(a,1,2)),flip(a)].">
      <j1 rule="para" parents="504 19254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19257">
    <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(10794(a,1),17343(a,1,2))].">
      <j1 rule="para" parents="10794 17343"/>
    </justification>
  </clause>

  <clause id="19258">
    <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(13292(a,1),19257(a,1,2,2))].">
      <j1 rule="para" parents="13292 19257"/>
    </justification>
  </clause>

  <clause id="19259">
    <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(17327(a,1),19258(a,1,2))].">
      <j1 rule="para" parents="17327 19258"/>
    </justification>
  </clause>

  <clause id="19260">
    <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(18818(a,1),19259(a,1,2,2))].">
      <j1 rule="para" parents="18818 19259"/>
    </justification>
  </clause>

  <clause id="19261">
    <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(18307(a,1),19260(a,1,2))].">
      <j1 rule="para" parents="18307 19260"/>
    </justification>
  </clause>

  <clause id="19262">
    <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(18467(a,1),19261(a,1,2))].">
      <j1 rule="para" parents="18467 19261"/>
    </justification>
  </clause>

  <clause id="19263">
    <literal><![CDATA[
      x / K(y,L(z,u,u \ x)) = (x / (((z / u) \ 1) * K(y,z))) * ((z / u) \ 1)
    ]]></literal>
    <justification jstring="[para(14700(a,1),19262(a,1,2))].">
      <j1 rule="para" parents="14700 19262"/>
    </justification>
  </clause>

  <clause id="19265">
    <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(19263(a,1),14174(a,1))].">
      <j1 rule="para" parents="19263 14174"/>
    </justification>
  </clause>

  <clause id="19266">
    <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(14565(a,1),19265(a,1))].">
      <j1 rule="para" parents="14565 19265"/>
    </justification>
  </clause>

  <clause id="19267">
    <literal><![CDATA[
      K((x / (x / (y * a(z,u,w)))) \ v5,v6) = K(((a(z,u,w) * y) * K(a(z,u,w) \ (y \ x),y * a(z,u,w))) \ v5,v6)
    ]]></literal>
    <justification jstring="[para(13965(a,1),18048(a,2,1,1,2))].">
      <j1 rule="para" parents="13965 18048"/>
    </justification>
  </clause>

  <clause id="19268">
    <literal><![CDATA[
      K((x / (x / (y * a(z,u,w)))) \ v5,v6) = K(K(y * a(z,u,w),a(z,u,w) \ (y \ x)) * ((a(z,u,w) * y) \ v5),v6)
    ]]></literal>
    <justification jstring="[para(12267(a,1),19267(a,2,1))].">
      <j1 rule="para" parents="12267 19267"/>
    </justification>
  </clause>

  <clause id="19269">
    <literal><![CDATA[
      K((x / (x / (y * a(z,u,w)))) \ v5,v6) = K(((a(z,u,w) * y) \ v5) * K(y * a(z,u,w),y \ x),v6)
    ]]></literal>
    <justification jstring="[hyper(320,a,18761,a(flip),b,19268,a),flip(a)].">
      <j1 rule="hyper" parents="320 18761 19268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19271">
    <literal><![CDATA[
      K((x / (x / (y * a(z,u,w)))) \ v5,v6) = K(K(y,y \ x) * ((a(z,u,w) * y) \ v5),v6)
    ]]></literal>
    <justification jstring="[hyper(320,a,18759,a(flip),b,19269,a),flip(a)].">
      <j1 rule="hyper" parents="320 18759 19269"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19273">
    <literal><![CDATA[
      K((x / (x / (y * a(z,u,w)))) \ v5,v6) = K((a(z,u,w) * T(y,y \ x)) \ v5,v6)
    ]]></literal>
    <justification jstring="[hyper(320,a,17919,a(flip),b,19271,a),flip(a)].">
      <j1 rule="hyper" parents="320 17919 19271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19274">
    <literal><![CDATA[
      K((x / (x / (y * a(z,u,w)))) \ v5,v6) = K((a(z,u,w) * T(y,x)) \ v5,v6)
    ]]></literal>
    <justification jstring="[hyper(320,a,13172,a(flip),b,19273,a),flip(a)].">
      <j1 rule="hyper" parents="320 13172 19273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19275">
    <literal><![CDATA[
      K((x / (x / (y * a(z,u,w)))) \ v5,v6) = K(T(y,x) \ (a(z,u,w) \ v5),v6)
    ]]></literal>
    <justification jstring="[hyper(320,a,14335,a(flip),b,19274,a),flip(a)].">
      <j1 rule="hyper" parents="320 14335 19274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19276">
    <literal><![CDATA[
      K(T(x * a(y,z,u),w) \ v5,v6) = K(T(x,w) \ (a(y,z,u) \ v5),v6)
    ]]></literal>
    <justification jstring="[hyper(58,a,15287,a(flip),b,19275,a)].">
      <j1 rule="hyper" parents="58 15287 19275"/>
    </justification>
  </clause>

  <clause id="19277">
    <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(15729(a,1),17659(a,1,2,1,1))].">
      <j1 rule="para" parents="15729 17659"/>
    </justification>
  </clause>

  <clause id="19278">
    <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(12346(a,2),19277(a,1,2,1,1))].">
      <j1 rule="para" parents="12346 19277"/>
    </justification>
  </clause>

  <clause id="19279">
    <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(18819(a,1),19278(a,1,2))].">
      <j1 rule="para" parents="18819 19278"/>
    </justification>
  </clause>

  <clause id="19280">
    <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(18825,a,19279,a)].">
      <j1 rule="hyper" parents="18825 19279"/>
    </justification>
  </clause>

  <clause id="19282">
    <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,18287,a(flip),b,19280,a)].">
      <j1 rule="hyper" parents="58 18287 19280"/>
    </justification>
  </clause>

  <clause id="19283">
    <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(15398,a,19282,a)].">
      <j1 rule="hyper" parents="15398 19282"/>
    </justification>
  </clause>

  <clause id="19285">
    <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(4307(a,1),19283(a,1,2,1,1))].">
      <j1 rule="para" parents="4307 19283"/>
    </justification>
  </clause>

  <clause id="19286">
    <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(13219,a,19285,a)].">
      <j1 rule="hyper" parents="13219 19285"/>
    </justification>
  </clause>

  <clause id="19287">
    <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,17848,a(flip),b,19286,a),flip(a)].">
      <j1 rule="hyper" parents="320 17848 19286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19288">
    <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,15137,a(flip),b,19287,a),flip(a)].">
      <j1 rule="hyper" parents="320 15137 19287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19289">
    <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,18915,a(flip),b,19288,a),flip(a)].">
      <j1 rule="hyper" parents="320 18915 19288"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19290">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,u,y * z)) = K(x,z \ (((1 / y) \ z) * u))
    ]]></literal>
    <justification jstring="[para(11590(a,1),19289(a,2,2,2,1))].">
      <j1 rule="para" parents="11590 19289"/>
    </justification>
  </clause>

  <clause id="19291">
    <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,15444,a(flip),b,19290,a),flip(a)].">
      <j1 rule="hyper" parents="320 15444 19290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19292">
    <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,19084,a(flip),b,19291,a)].">
      <j1 rule="hyper" parents="58 19084 19291"/>
    </justification>
  </clause>

  <clause id="19293">
    <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,13167,a(flip),b,19292,a)].">
      <j1 rule="hyper" parents="58 13167 19292"/>
    </justification>
  </clause>

  <clause id="19294">
    <literal><![CDATA[
      K(x,((y * z) * (y \ 1)) \ ((z * y) * u)) = K(x,z \ (((y \ 1) \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,18062,a(flip),b,19293,a)].">
      <j1 rule="hyper" parents="58 18062 19293"/>
    </justification>
  </clause>

  <clause id="19295">
    <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(17496(a,1),17508(a,1,2))].">
      <j1 rule="para" parents="17496 17508"/>
    </justification>
  </clause>

  <clause id="19296">
    <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(10402(a,1),17964(a,2,1))].">
      <j1 rule="para" parents="10402 17964"/>
    </justification>
  </clause>

  <clause id="19297">
    <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,7832,a,b,19296,a),flip(a)].">
      <j1 rule="hyper" parents="320 7832 19296"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19298">
    <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,15687,a(flip),b,19297,a),flip(a)].">
      <j1 rule="hyper" parents="320 15687 19297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19300">
    <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(7796(a,1),19298(a,1,1))].">
      <j1 rule="para" parents="7796 19298"/>
    </justification>
  </clause>

  <clause id="19301">
    <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(5631(a,1),19300(a,1,2,1,2))].">
      <j1 rule="para" parents="5631 19300"/>
    </justification>
  </clause>

  <clause id="19302">
    <literal><![CDATA[
      (x * (K(y,z) * u)) / u = (x * u) / (K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(15880,a,19301,a)].">
      <j1 rule="hyper" parents="15880 19301"/>
    </justification>
  </clause>

  <clause id="19303">
    <literal><![CDATA[
      (x * (y / z)) / (K(u,y) * (y / z)) = (x * (T(y,u) / z)) / (y / z)
    ]]></literal>
    <justification jstring="[para(13708(a,1),19302(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="13708 19302"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19304">
    <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(19302(a,1),14841(a,2,2))].">
      <j1 rule="para" parents="19302 14841"/>
    </justification>
  </clause>

  <clause id="19305">
    <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(18491(a,1),19304(a,1,1,1))].">
      <j1 rule="para" parents="18491 19304"/>
    </justification>
  </clause>

  <clause id="19306">
    <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(14470(a,1),19305(a,1,1,1))].">
      <j1 rule="para" parents="14470 19305"/>
    </justification>
  </clause>

  <clause id="19308">
    <literal><![CDATA[
      ((K(x,y) * z) * (K(u,w) * v5)) / v5 = K(x,y) * ((z * v5) / (K(w,u) * v5))
    ]]></literal>
    <justification jstring="[para(18306(a,1),19306(a,1,1))].">
      <j1 rule="para" parents="18306 19306"/>
    </justification>
  </clause>

  <clause id="19309">
    <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,19302,a(flip),b,19308,a)].">
      <j1 rule="hyper" parents="58 19302 19308"/>
    </justification>
  </clause>

  <clause id="19310">
    <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(18717,a,19309,a),flip(a)].">
      <j1 rule="hyper" parents="18717 19309"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19311">
    <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),19310(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15 19310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19312">
    <literal><![CDATA[
      L(K(x,y) * z,K(u,w),v5) = K(x,y) * L(z,K(u,w),v5)
    ]]></literal>
    <justification jstring="[para(18709(a,1),19311(a,2,2))].">
      <j1 rule="para" parents="18709 19311"/>
    </justification>
  </clause>

  <clause id="19313">
    <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,18719,a(flip),b,19312,a),flip(a)].">
      <j1 rule="hyper" parents="320 18719 19312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19314">
    <literal><![CDATA[
      ((x * y) / (K(z,u) * y)) * K(z,u) = L(x,K(z,u),y)
    ]]></literal>
    <justification jstring="[para(5133(a,1),19313(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5133 19313"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19315">
    <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(13741(a,1),19314(a,1,1,2))].">
      <j1 rule="para" parents="13741 19314"/>
    </justification>
  </clause>

  <clause id="19316">
    <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,17823,a(flip),b,19315,a),flip(a)].">
      <j1 rule="hyper" parents="320 17823 19315"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19317">
    <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,19120,a(flip),b,19316,a),flip(a)].">
      <j1 rule="hyper" parents="320 19120 19316"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19318">
    <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(17817(a,1),19124(a,1,2,2,2))].">
      <j1 rule="para" parents="17817 19124"/>
    </justification>
  </clause>

  <clause id="19319">
    <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,19255,a(flip),b,19318,a)].">
      <j1 rule="hyper" parents="58 19255 19318"/>
    </justification>
  </clause>

  <clause id="19322">
    <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,15439,a(flip),b,19319,a),flip(a)].">
      <j1 rule="hyper" parents="58 15439 19319"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19323">
    <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,18191,a(flip),b,19322,a),flip(a)].">
      <j1 rule="hyper" parents="320 18191 19322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19324">
    <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(19123(a,1),19323(a,1,2,2,2))].">
      <j1 rule="para" parents="19123 19323"/>
    </justification>
  </clause>

  <clause id="19325">
    <literal><![CDATA[
      K(x,y * (z \ (u * (K(w,v5) * v6)))) = K(x,y * (K(w,v5) * (z \ (u * v6))))
    ]]></literal>
    <justification jstring="[hyper(17479,a,19324,a)].">
      <j1 rule="hyper" parents="17479 19324"/>
    </justification>
  </clause>

  <clause id="19326">
    <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,19153,a(flip),b,19325,a),flip(a)].">
      <j1 rule="hyper" parents="58 19153 19325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19327">
    <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),19326(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="13 19326"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19328">
    <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(19147,a,19327,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="19147 19327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19329">
    <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(17735,a,19328,a)].">
      <j1 rule="hyper" parents="17735 19328"/>
    </justification>
  </clause>

  <clause id="19330">
    <literal><![CDATA[
      K(x,y * L(y \ 1,z,u)) = a(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,19220,a(flip),b,19329,a),flip(a)].">
      <j1 rule="hyper" parents="58 19220 19329"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19331">
    <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,19159,a(flip),b,19329,a)].">
      <j1 rule="hyper" parents="58 19159 19329"/>
    </justification>
  </clause>

  <clause id="19332">
    <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,17055,a(flip),b,19330,a)].">
      <j1 rule="hyper" parents="58 17055 19330"/>
    </justification>
  </clause>

  <clause id="19333">
    <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(15554,a,19331,a),flip(a)].">
      <j1 rule="hyper" parents="15554 19331"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19335">
    <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(7160(a,1),19332(a,2,3))].">
      <j1 rule="para" parents="7160 19332"/>
    </justification>
  </clause>

  <clause id="19336">
    <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(5429(a,1),19335(a,2,3))].">
      <j1 rule="para" parents="5429 19335"/>
    </justification>
  </clause>

  <clause id="19337">
    <literal><![CDATA[
      K(x,L(y / ((y \ z) * y),u,w) / (z \ y)) = a(x,u,K(y \ z,w))
    ]]></literal>
    <justification jstring="[para(7213(a,1),19336(a,2,3))].">
      <j1 rule="para" parents="7213 19336"/>
    </justification>
  </clause>

  <clause id="19338">
    <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,15457,a(flip),b,19333,a)].">
      <j1 rule="hyper" parents="58 15457 19333"/>
    </justification>
  </clause>

  <clause id="19339">
    <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,15481,a(flip),b,19338,a)].">
      <j1 rule="hyper" parents="58 15481 19338"/>
    </justification>
  </clause>

  <clause id="19340">
    <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),19339(a,1,2,1))].">
      <j1 rule="para" parents="6 19339"/>
    </justification>
  </clause>

  <clause id="19341">
    <literal><![CDATA[
      K(x,L(y / (z * y),u,w) * z) = K(x,z * L((y * z) \ y,u,w))
    ]]></literal>
    <justification jstring="[hyper(18006,a,19340,a)].">
      <j1 rule="hyper" parents="18006 19340"/>
    </justification>
  </clause>

  <clause id="19342">
    <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(833,a,19295,a)].">
      <j1 rule="hyper" parents="833 19295"/>
    </justification>
  </clause>

  <clause id="19343">
    <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(14275(a,1),19342(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14275 19342"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19344">
    <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(17503(a,1),19343(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17503 19343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19345">
    <literal><![CDATA[
      L(x,a(y,z,K(u,w)) * v5,v6) = L(x,v5,v6)
    ]]></literal>
    <justification jstring="[hyper(320,a,17321,a(flip),b,19344,a),flip(a)].">
      <j1 rule="hyper" parents="320 17321 19344"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19347">
    <literal><![CDATA[
      L(x,L(y,z,K(u,w)),v5) = L(x,y,v5)
    ]]></literal>
    <justification jstring="[para(14937(a,1),19345(a,1,2))].">
      <j1 rule="para" parents="14937 19345"/>
    </justification>
  </clause>

  <clause id="19348">
    <literal><![CDATA[
      L(x,y * a(z,u,K(w,v5)),v6) = L(x,y,v6)
    ]]></literal>
    <justification jstring="[para(17193(a,1),19345(a,1,2))].">
      <j1 rule="para" parents="17193 19345"/>
    </justification>
  </clause>

  <clause id="19350">
    <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(13303,a,19348,a),flip(a)].">
      <j1 rule="hyper" parents="13303 19348"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19351">
    <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,17501,a(flip),b,19350,a),flip(a)].">
      <j1 rule="hyper" parents="320 17501 19350"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19352">
    <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),19351(a,2,2))].">
      <j1 rule="para" parents="13 19351"/>
    </justification>
  </clause>

  <clause id="19353">
    <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(14323(a,1),19352(a,1,1,1))].">
      <j1 rule="para" parents="14323 19352"/>
    </justification>
  </clause>

  <clause id="19354">
    <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(17503(a,1),19353(a,1,1))].">
      <j1 rule="para" parents="17503 19353"/>
    </justification>
  </clause>

  <clause id="19355">
    <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(19354(a,2),17470(a,2,2))].">
      <j1 rule="para" parents="19354 17470"/>
    </justification>
  </clause>

  <clause id="19357">
    <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(17921(a,1),18448(a,1,1,3))].">
      <j1 rule="para" parents="17921 18448"/>
    </justification>
  </clause>

  <clause id="19358">
    <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(18322(a,1),19357(a,1,1))].">
      <j1 rule="para" parents="18322 19357"/>
    </justification>
  </clause>

  <clause id="19359">
    <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,18480,a(flip),b,19358,a)].">
      <j1 rule="hyper" parents="58 18480 19358"/>
    </justification>
  </clause>

  <clause id="19361">
    <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(18162(a,1),19359(a,1,2))].">
      <j1 rule="para" parents="18162 19359"/>
    </justification>
  </clause>

  <clause id="19362">
    <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(14006(a,1),19361(a,1,2))].">
      <j1 rule="para" parents="14006 19361"/>
    </justification>
  </clause>

  <clause id="19363">
    <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(17930(a,1),19362(a,1,2))].">
      <j1 rule="para" parents="17930 19362"/>
    </justification>
  </clause>

  <clause id="19364">
    <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,17396,a(flip),b,19363,a),flip(a)].">
      <j1 rule="hyper" parents="320 17396 19363"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19365">
    <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,19044,a(flip),b,19364,a),flip(a)].">
      <j1 rule="hyper" parents="320 19044 19364"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19366">
    <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,18294,a(flip),b,19365,a),flip(a)].">
      <j1 rule="hyper" parents="320 18294 19365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19367">
    <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(9482(a,1),19089(a,1,1))].">
      <j1 rule="para" parents="9482 19089"/>
    </justification>
  </clause>

  <clause id="19368">
    <literal><![CDATA[
      K(x,(y \ (z \ (u * z))) \ (y \ (u * z))) = K(x,L(T(z,u),u,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(15678,a,19367,a),flip(a)].">
      <j1 rule="hyper" parents="15678 19367"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19370">
    <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),19368(a,1,2,1,2))].">
      <j1 rule="para" parents="17 19368"/>
    </justification>
  </clause>

  <clause id="19371">
    <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(16139,a,19055,a),flip(a)].">
      <j1 rule="hyper" parents="16139 19055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19372">
    <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,17744,a(flip),b,19371,a),flip(a)].">
      <j1 rule="hyper" parents="320 17744 19371"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19373">
    <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(17368(a,1),19372(a,1,2,2,2))].">
      <j1 rule="para" parents="17368 19372"/>
    </justification>
  </clause>

  <clause id="19374">
    <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(19162,a,19373,a),flip(a)].">
      <j1 rule="hyper" parents="19162 19373"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19375">
    <literal><![CDATA[
      K(x,y * ((z \ L(y,u,w)) / L(y,u,w))) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(1300(a,1),19374(a,1,2,2,1,2,1))].">
      <j1 rule="para" parents="1300 19374"/>
    </justification>
  </clause>

  <clause id="19376">
    <literal><![CDATA[
      K(x,y * (L(y,z,u) \ (L(y,z,u) / w))) = K(x,y / w)
    ]]></literal>
    <justification jstring="[hyper(58,a,16398,a(flip),b,19375,a)].">
      <j1 rule="hyper" parents="58 16398 19375"/>
    </justification>
  </clause>

  <clause id="19377">
    <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(16898(a,1),14725(a,1,2,2,2,2))].">
      <j1 rule="para" parents="16898 14725"/>
    </justification>
  </clause>

  <clause id="19378">
    <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),19377(a,1,2,2))].">
      <j1 rule="para" parents="91 19377"/>
    </justification>
  </clause>

  <clause id="19379">
    <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(15228,a,19378,a)].">
      <j1 rule="hyper" parents="15228 19378"/>
    </justification>
  </clause>

  <clause id="19380">
    <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(15275,a,19379,a)].">
      <j1 rule="hyper" parents="15275 19379"/>
    </justification>
  </clause>

  <clause id="19381">
    <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(16898(a,1),19380(a,2,3,1))].">
      <j1 rule="para" parents="16898 19380"/>
    </justification>
  </clause>

  <clause id="19382">
    <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(12237(a,1),19381(a,2,3))].">
      <j1 rule="para" parents="12237 19381"/>
    </justification>
  </clause>

  <clause id="19383">
    <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,18320,a(flip),b,19382,a),flip(a)].">
      <j1 rule="hyper" parents="320 18320 19382"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19385">
    <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,17168,a,b,19383,a)].">
      <j1 rule="hyper" parents="58 17168 19383"/>
    </justification>
  </clause>

  <clause id="19386">
    <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(18524(a,1),19385(a,1,1,2))].">
      <j1 rule="para" parents="18524 19385"/>
    </justification>
  </clause>

  <clause id="19387">
    <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,19386,a)].">
      <j1 rule="hyper" parents="205 19386"/>
    </justification>
  </clause>

  <clause id="19389">
    <literal><![CDATA[
      K((x * R(y,z,a(u,w,v5))) \ (v6 * a(y,z,a(u,w,v5))),v7) = K((x * y) \ v6,L(v7,x * y,a(y,z,a(u,w,v5))))
    ]]></literal>
    <justification jstring="[para(13416(a,1),14861(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="13416 14861"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19390">
    <literal><![CDATA[
      K((x * R(y,z,a(u,w,v5))) \ (v6 * a(y,z,a(u,w,v5))),v7) = K((x * y) \ v6,v7)
    ]]></literal>
    <justification jstring="[hyper(320,a,14336,a(flip),b,19389,a),flip(a)].">
      <j1 rule="hyper" parents="320 14336 19389"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19392">
    <literal><![CDATA[
      K(((x * R(y,z,a(u,w,v5))) \ v6) * a(y,z,a(u,w,v5)),v7) = K((x * y) \ v6,v7)
    ]]></literal>
    <justification jstring="[para(898(a,1),19390(a,1,1))].">
      <j1 rule="para" parents="898 19390"/>
    </justification>
  </clause>

  <clause id="19393">
    <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(17626(a,1),14014(a,1,1))].">
      <j1 rule="para" parents="17626 14014"/>
    </justification>
  </clause>

  <clause id="19394">
    <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(17626(a,1),14015(a,1,1))].">
      <j1 rule="para" parents="17626 14015"/>
    </justification>
  </clause>

  <clause id="19395">
    <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(13008(a,1),19393(a,1,1))].">
      <j1 rule="para" parents="13008 19393"/>
    </justification>
  </clause>

  <clause id="19396">
    <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(7708,a,19395,a)].">
      <j1 rule="hyper" parents="7708 19395"/>
    </justification>
  </clause>

  <clause id="19397">
    <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(16460,a,19396,a)].">
      <j1 rule="hyper" parents="16460 19396"/>
    </justification>
  </clause>

  <clause id="19399">
    <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),19397(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 19397"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19400">
    <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,16403,a(flip),b,19399,a),flip(a)].">
      <j1 rule="hyper" parents="320 16403 19399"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19403">
    <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(13084(a,1),19394(a,1,1))].">
      <j1 rule="para" parents="13084 19394"/>
    </justification>
  </clause>

  <clause id="19404">
    <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(7708,a,19403,a)].">
      <j1 rule="hyper" parents="7708 19403"/>
    </justification>
  </clause>

  <clause id="19405">
    <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(16460,a,19404,a)].">
      <j1 rule="hyper" parents="16460 19404"/>
    </justification>
  </clause>

  <clause id="19407">
    <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),19405(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 19405"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19408">
    <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,16403,a(flip),b,19407,a),flip(a)].">
      <j1 rule="hyper" parents="320 16403 19407"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19411">
    <literal><![CDATA[
      K(x,T(K(y,z) * (u * w),u)) = K(x,w * (K(z,y) * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,16753,a(flip),b,19408,a),flip(a)].">
      <j1 rule="hyper" parents="58 16753 19408"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19412">
    <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,19400,a,b,19411,a)].">
      <j1 rule="hyper" parents="58 19400 19411"/>
    </justification>
  </clause>

  <clause id="19413">
    <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(6477(a,1),19412(a,1,2))].">
      <j1 rule="para" parents="6477 19412"/>
    </justification>
  </clause>

  <clause id="19414">
    <literal><![CDATA[
      K(x,y * (z * K(u \ w,u))) = K(x,y * (K(w,u) * z))
    ]]></literal>
    <justification jstring="[hyper(13983,a,19413,a)].">
      <j1 rule="hyper" parents="13983 19413"/>
    </justification>
  </clause>

  <clause id="19415">
    <literal><![CDATA[
      K(x,y * (z \ ((u \ w) * u))) = K(x,y * (K(w,u) * (z \ w)))
    ]]></literal>
    <justification jstring="[para(14213(a,1),19414(a,1,2,2))].">
      <j1 rule="para" parents="14213 19414"/>
    </justification>
  </clause>

  <clause id="19416">
    <literal><![CDATA[
      K(x,y * (z \ ((u \ w) * u))) = K(x,y * (z \ T(w,u)))
    ]]></literal>
    <justification jstring="[hyper(320,a,16066,a(flip),b,19415,a),flip(a)].">
      <j1 rule="hyper" parents="320 16066 19415"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19417">
    <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,16190,a(flip),b,19416,a)].">
      <j1 rule="hyper" parents="58 16190 19416"/>
    </justification>
  </clause>

  <clause id="19418">
    <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(14120(a,1),19417(a,2,2,2,2))].">
      <j1 rule="para" parents="14120 19417"/>
    </justification>
  </clause>

  <clause id="19419">
    <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,13164,a(flip),b,19418,a),flip(a)].">
      <j1 rule="hyper" parents="320 13164 19418"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19420">
    <literal><![CDATA[
      K(x,T(y * (z \ u),y \ ((z \ u) \ u))) = K(x,y * (z \ T(u,z \ y)))
    ]]></literal>
    <justification jstring="[hyper(17332,a,19419,a)].">
      <j1 rule="hyper" parents="17332 19419"/>
    </justification>
  </clause>

  <clause id="19421">
    <literal><![CDATA[
      K(x,T(y * (z \ u),z \ y)) = K(x,y * (z \ T(u,z \ y)))
    ]]></literal>
    <justification jstring="[hyper(58,a,17450,a(flip),b,19420,a)].">
      <j1 rule="hyper" parents="58 17450 19420"/>
    </justification>
  </clause>

  <clause id="19422">
    <literal><![CDATA[
      K(x,T(y * (z \ u),z * y)) = K(x,y * (z \ T(u,z \ y)))
    ]]></literal>
    <justification jstring="[hyper(15949,a,19421,a)].">
      <j1 rule="hyper" parents="15949 19421"/>
    </justification>
  </clause>

  <clause id="19424">
    <literal><![CDATA[
      K(x,T(y * (z \ u),z * y)) = K(x,y * (z \ T(u,z * y)))
    ]]></literal>
    <justification jstring="[hyper(320,a,19032,a(flip),b,19422,a),flip(a)].">
      <j1 rule="hyper" parents="320 19032 19422"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19425">
    <literal><![CDATA[
      K(x,y * (z \ T(u,z * y))) = K(x,(u / z) * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,18264,a(flip),b,19424,a),flip(a)].">
      <j1 rule="hyper" parents="58 18264 19424"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19426">
    <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,19191,a(flip),b,19425,a),flip(a)].">
      <j1 rule="hyper" parents="58 19191 19425"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19427">
    <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),19426(a,1,2,2))].">
      <j1 rule="para" parents="176 19426"/>
    </justification>
  </clause>

  <clause id="19428">
    <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,19237,a(flip),b,19427,a),flip(a)].">
      <j1 rule="hyper" parents="58 19237 19427"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19429">
    <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),19428(a,2,2))].">
      <j1 rule="para" parents="7 19428"/>
    </justification>
  </clause>

  <clause id="19430">
    <literal><![CDATA[
      K(x,y * a(z \ T(u,w),v5,v5 \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(15525,a,19429,a)].">
      <j1 rule="hyper" parents="15525 19429"/>
    </justification>
  </clause>

  <clause id="19433">
    <literal><![CDATA[
      K(x,y * a(z,u,u \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(75(a,1),19430(a,1,2,2,1))].">
      <j1 rule="para" parents="75 19430"/>
    </justification>
  </clause>

  <clause id="19434">
    <literal><![CDATA[
      K(x,y * L(z,u,u \ 1)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(19196,a,19433,a)].">
      <j1 rule="hyper" parents="19196 19433"/>
    </justification>
  </clause>

  <clause id="19435">
    <literal><![CDATA[
      K(x,y * L(z,u,u \ 1)) = K(x,(y \ 1) \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,19241,a(flip),b,19433,a)].">
      <j1 rule="hyper" parents="58 19241 19433"/>
    </justification>
  </clause>

  <clause id="19436">
    <literal><![CDATA[
      K(x,a(y,z,z \ 1) \ u) = K(x,u)
    ]]></literal>
    <justification jstring="[para(13425(a,1),19433(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13425 19433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19438">
    <literal><![CDATA[
      K(x,y * (L(y,z,z \ 1) \ u)) = K(x,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,15333,a,b,19436,a)].">
      <j1 rule="hyper" parents="58 15333 19436"/>
    </justification>
  </clause>

  <clause id="19441">
    <literal><![CDATA[
      K(x,y * (z * (u \ 1))) = K(x,y * (z / u))
    ]]></literal>
    <justification jstring="[hyper(58,a,15465,a(flip),b,19434,a)].">
      <j1 rule="hyper" parents="58 15465 19434"/>
    </justification>
  </clause>

  <clause id="19443">
    <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,19436,a,b,19438,a)].">
      <j1 rule="hyper" parents="320 19436 19438"/>
    </justification>
  </clause>

  <clause id="19444">
    <literal><![CDATA[
      K(x,L(y,z,z \ 1) / u) = K(x,y / u)
    ]]></literal>
    <justification jstring="[hyper(58,a,19376,a(flip),b,19438,a),flip(a)].">
      <j1 rule="hyper" parents="58 19376 19438"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19446">
    <literal><![CDATA[
      K(x,y * (z / (u \ 1))) = K(x,y * (z * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,5333,a(flip),b,19441,a),flip(a)].">
      <j1 rule="hyper" parents="58 5333 19441"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19448">
    <literal><![CDATA[
      K(x,y * L(z,u,u \ 1)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = w
    ]]></literal>
    <justification jstring="[para(19435(a,2),14008(a,1))].">
      <j1 rule="para" parents="19435 14008"/>
    </justification>
  </clause>

  <clause id="19449">
    <literal><![CDATA[
      K(x,y * (z * (u \ 1))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z / u)) = w
    ]]></literal>
    <justification jstring="[para(15465(a,1),19448(a,1))].">
      <j1 rule="para" parents="15465 19448"/>
    </justification>
  </clause>

  <clause id="19450">
    <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(16756(a,2),19449(a,1))].">
      <j1 rule="para" parents="16756 19449"/>
    </justification>
  </clause>

  <clause id="19451">
    <literal><![CDATA[
      K(x,L(y,z,z \ 1) \ (y * u)) = K(x,a(w,v5,v5 \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(1412(a,2),19443(a,2,2)),flip(a)].">
      <j1 rule="para" parents="1412 19443"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19452">
    <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,18672,a,b,19451,a),flip(a)].">
      <j1 rule="hyper" parents="58 18672 19451"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19457">
    <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(5958(a,1),19452(a,2,2,1,2))].">
      <j1 rule="para" parents="5958 19452"/>
    </justification>
  </clause>

  <clause id="19458">
    <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(13782(a,1),19457(a,2,2,1))].">
      <j1 rule="para" parents="13782 19457"/>
    </justification>
  </clause>

  <clause id="19459">
    <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,14337,a(flip),b,19458,a),flip(a)].">
      <j1 rule="hyper" parents="320 14337 19458"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19460">
    <literal><![CDATA[
      K(x,a(y,z,z \ 1) \ (u \ L(w,v5,v5 \ 1))) = K(x,u \ w)
    ]]></literal>
    <justification jstring="[para(5955(a,1),19459(a,2,2,2))].">
      <j1 rule="para" parents="5955 19459"/>
    </justification>
  </clause>

  <clause id="19461">
    <literal><![CDATA[
      K(x,y \ L(z,u,u \ 1)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,19436,a(flip),b,19460,a)].">
      <j1 rule="hyper" parents="58 19436 19460"/>
    </justification>
  </clause>

  <clause id="19463">
    <literal><![CDATA[
      K(x,((y \ 1) * z) \ u) = K(x,(y \ z) \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,15527,a(flip),b,19461,a),flip(a)].">
      <j1 rule="hyper" parents="58 15527 19461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19464">
    <literal><![CDATA[
      K(x,y \ (z * (u \ 1))) = K(x,y \ (z / u))
    ]]></literal>
    <justification jstring="[hyper(58,a,15522,a(flip),b,19461,a)].">
      <j1 rule="hyper" parents="58 15522 19461"/>
    </justification>
  </clause>

  <clause id="19465">
    <literal><![CDATA[
      K(x,(y * (z \ 1)) \ u) = K(x,(y / z) \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,14722,a(flip),b,19461,a),flip(a)].">
      <j1 rule="hyper" parents="58 14722 19461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19469">
    <literal><![CDATA[
      K(x,((y * z) / y) \ ((z * y) * u)) = K(x,z \ (((y \ 1) \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,19294,a(flip),b,19465,a),flip(a)].">
      <j1 rule="hyper" parents="58 19294 19465"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19470">
    <literal><![CDATA[
      K(x,y \ (((z \ 1) \ y) * u)) = K(x,y \ ((T(y,z) * z) * u))
    ]]></literal>
    <justification jstring="[para(14852(a,1),19469(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14852 19469"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19471">
    <literal><![CDATA[
      K(x,y \ (((z \ 1) \ y) * u)) = K(x,y \ ((z * y) * u))
    ]]></literal>
    <justification jstring="[hyper(320,a,18132,a(flip),b,19470,a),flip(a)].">
      <j1 rule="hyper" parents="320 18132 19470"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19472">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,z,y * z)) = K(x,z \ ((y * z) * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,18142,a,b,19471,a)].">
      <j1 rule="hyper" parents="58 18142 19471"/>
    </justification>
  </clause>

  <clause id="19473">
    <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(17773(a,1),15965(a,1,1))].">
      <j1 rule="para" parents="17773 15965"/>
    </justification>
  </clause>

  <clause id="19474">
    <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(16069(a,1),18148(a,1,1))].">
      <j1 rule="para" parents="16069 18148"/>
    </justification>
  </clause>

  <clause id="19476">
    <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(19035(a,1),19474(a,1,1))].">
      <j1 rule="para" parents="19035 19474"/>
    </justification>
  </clause>

  <clause id="19477">
    <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,18810,a(flip),b,19476,a)].">
      <j1 rule="hyper" parents="58 18810 19476"/>
    </justification>
  </clause>

  <clause id="19478">
    <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,18569,a,b,19477,a)].">
      <j1 rule="hyper" parents="58 18569 19477"/>
    </justification>
  </clause>

  <clause id="19480">
    <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(15652,a,19478,a)].">
      <j1 rule="hyper" parents="15652 19478"/>
    </justification>
  </clause>

  <clause id="19481">
    <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(16457,a,19480,a),flip(a)].">
      <j1 rule="hyper" parents="16457 19480"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19482">
    <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,15633,a(flip),b,19481,a),flip(a)].">
      <j1 rule="hyper" parents="320 15633 19481"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19483">
    <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(18147(a,1),19482(a,1,2))].">
      <j1 rule="para" parents="18147 19482"/>
    </justification>
  </clause>

  <clause id="19484">
    <literal><![CDATA[
      K(x,y * T(z,T(u / w,v5))) = K(x,y * T(z,u * w))
    ]]></literal>
    <justification jstring="[hyper(13983,a,19483,a)].">
      <j1 rule="hyper" parents="13983 19483"/>
    </justification>
  </clause>

  <clause id="19485">
    <literal><![CDATA[
      K(x,y * T(z,u \ w)) = K(x,y * T(z,w * u))
    ]]></literal>
    <justification jstring="[para(107(a,1),19484(a,1,2,2,2))].">
      <j1 rule="para" parents="107 19484"/>
    </justification>
  </clause>

  <clause id="19486">
    <literal><![CDATA[
      K(x,y * T(z,u \ (w \ v5))) = K(x,y * T(z,v5 * (u * w)))
    ]]></literal>
    <justification jstring="[hyper(17772,a,19485,a)].">
      <j1 rule="hyper" parents="17772 19485"/>
    </justification>
  </clause>

  <clause id="19487">
    <literal><![CDATA[
      K(x,y * T(z,(u \ w) * v5)) = K(x,y * T(z,w * (v5 * u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,19485,a(flip),b,19486,a)].">
      <j1 rule="hyper" parents="58 19485 19486"/>
    </justification>
  </clause>

  <clause id="19488">
    <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,16602,a(flip),b,19487,a),flip(a)].">
      <j1 rule="hyper" parents="58 16602 19487"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19489">
    <literal><![CDATA[
      K(x,T((y \ z) * T(u,z * (x * y)),w)) = K(T(x,w),u * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(7704,a,19488,a)].">
      <j1 rule="hyper" parents="7704 19488"/>
    </justification>
  </clause>

  <clause id="19490">
    <literal><![CDATA[
      K(x,T(y,z * (x * u)) * (u \ z)) = K(T(x,z * u),y * (u \ z))
    ]]></literal>
    <justification jstring="[hyper(15578,a,19489,a)].">
      <j1 rule="hyper" parents="15578 19489"/>
    </justification>
  </clause>

  <clause id="19491">
    <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,7160,a(flip),b,19490,a),flip(a)].">
      <j1 rule="hyper" parents="320 7160 19490"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19492">
    <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(19491(a,2),15579(a,1))].">
      <j1 rule="para" parents="19491 15579"/>
    </justification>
  </clause>

  <clause id="19493">
    <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(7708,a,19473,a)].">
      <j1 rule="hyper" parents="7708 19473"/>
    </justification>
  </clause>

  <clause id="19494">
    <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(16460,a,19493,a)].">
      <j1 rule="hyper" parents="16460 19493"/>
    </justification>
  </clause>

  <clause id="19496">
    <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),19494(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 19494"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19497">
    <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,16424,a(flip),b,19496,a),flip(a)].">
      <j1 rule="hyper" parents="320 16424 19496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19500">
    <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,19411,a(flip),b,19497,a),flip(a)].">
      <j1 rule="hyper" parents="320 19411 19497"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19501">
    <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(15845(a,1),19500(a,1,2))].">
      <j1 rule="para" parents="15845 19500"/>
    </justification>
  </clause>

  <clause id="19502">
    <literal><![CDATA[
      K(x,y * ((z * K(u,w)) * v5)) = K(x,y * (K(u,w) * (z * v5)))
    ]]></literal>
    <justification jstring="[hyper(13983,a,19501,a)].">
      <j1 rule="hyper" parents="13983 19501"/>
    </justification>
  </clause>

  <clause id="19503">
    <literal><![CDATA[
      K(x,y * (K(z,u) * ((w * z) * v5))) = K(x,y * ((w * T(z,u)) * v5))
    ]]></literal>
    <justification jstring="[para(6116(a,1),19502(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="6116 19502"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19504">
    <literal><![CDATA[
      K(x,y * ((z * T(u,x)) * w)) = K(x,y * ((z * u) * w))
    ]]></literal>
    <justification jstring="[hyper(17637,a,19503,a),flip(a)].">
      <j1 rule="hyper" parents="17637 19503"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19505">
    <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,18275,a(flip),b,19504,a),flip(a)].">
      <j1 rule="hyper" parents="58 18275 19504"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19506">
    <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),19505(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5 19505"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19507">
    <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,17680,a,b,19506,a),flip(a)].">
      <j1 rule="hyper" parents="58 17680 19506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19509">
    <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,17708,a(flip),b,19507,a),flip(a)].">
      <j1 rule="hyper" parents="58 17708 19507"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19510">
    <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,19057,a(flip),b,19509,a)].">
      <j1 rule="hyper" parents="58 19057 19509"/>
    </justification>
  </clause>

  <clause id="19511">
    <literal><![CDATA[
      K(x,(y \ T(z,K(u,w) * v5)) * v6) = K(x,(y \ ((v5 * z) / v5)) * v6)
    ]]></literal>
    <justification jstring="[para(5133(a,1),19510(a,1,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5133 19510"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19512">
    <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,15457,a(flip),b,19511,a),flip(a)].">
      <j1 rule="hyper" parents="320 15457 19511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19513">
    <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,16650,a(flip),b,19512,a)].">
      <j1 rule="hyper" parents="58 16650 19512"/>
    </justification>
  </clause>

  <clause id="19515">
    <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(13840(a,1),18644(a,1,1,1))].">
      <j1 rule="para" parents="13840 18644"/>
    </justification>
  </clause>

  <clause id="19516">
    <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(13775(a,1),19515(a,1,1,2,3))].">
      <j1 rule="para" parents="13775 19515"/>
    </justification>
  </clause>

  <clause id="19517">
    <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(18373(a,1),19516(a,1,1,2))].">
      <j1 rule="para" parents="18373 19516"/>
    </justification>
  </clause>

  <clause id="19518">
    <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,18635,a(flip),b,19517,a)].">
      <j1 rule="hyper" parents="58 18635 19517"/>
    </justification>
  </clause>

  <clause id="19519">
    <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,18643,a(flip),b,19518,a),flip(a)].">
      <j1 rule="hyper" parents="320 18643 19518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19521">
    <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(17757(a,1),14016(a,1,1))].">
      <j1 rule="para" parents="17757 14016"/>
    </justification>
  </clause>

  <clause id="19522">
    <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,18810,a(flip),b,19521,a)].">
      <j1 rule="hyper" parents="58 18810 19521"/>
    </justification>
  </clause>

  <clause id="19523">
    <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(16709,a,19522,a)].">
      <j1 rule="hyper" parents="16709 19522"/>
    </justification>
  </clause>

  <clause id="19524">
    <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,18073,a(flip),b,19523,a)].">
      <j1 rule="hyper" parents="58 18073 19523"/>
    </justification>
  </clause>

  <clause id="19525">
    <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(16452,a,19524,a),flip(a)].">
      <j1 rule="hyper" parents="16452 19524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19527">
    <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,12262,a(flip),b,19525,a),flip(a)].">
      <j1 rule="hyper" parents="320 12262 19525"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19528">
    <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(3993(a,1),19527(a,1,2))].">
      <j1 rule="para" parents="3993 19527"/>
    </justification>
  </clause>

  <clause id="19529">
    <literal><![CDATA[
      K(x,y * K(z \ (u * (w \ 1)),v5)) = K(x,y * K(v5,w * (u \ z)))
    ]]></literal>
    <justification jstring="[hyper(13983,a,19528,a)].">
      <j1 rule="hyper" parents="13983 19528"/>
    </justification>
  </clause>

  <clause id="19530">
    <literal><![CDATA[
      K(x,y \ T(z,u \ (w * (1 / v5)))) = K(x,(y \ z) * K(z,v5 * (w \ u)))
    ]]></literal>
    <justification jstring="[hyper(15318,a,19529,a)].">
      <j1 rule="hyper" parents="15318 19529"/>
    </justification>
  </clause>

  <clause id="19531">
    <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,13946,a(flip),b,19530,a),flip(a)].">
      <j1 rule="hyper" parents="320 13946 19530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19532">
    <literal><![CDATA[
      K(x,y \ T(z,u \ (w * (v5 \ 1)))) = K(x,y \ T(z,v5 * (w \ u)))
    ]]></literal>
    <justification jstring="[para(3779(a,1),19531(a,1,2,2))].">
      <j1 rule="para" parents="3779 19531"/>
    </justification>
  </clause>

  <clause id="19533">
    <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,18870,a(flip),b,19532,a)].">
      <j1 rule="hyper" parents="58 18870 19532"/>
    </justification>
  </clause>

  <clause id="19534">
    <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,18889,a(flip),b,19533,a),flip(a)].">
      <j1 rule="hyper" parents="320 18889 19533"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19535">
    <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,19158,a(flip),b,19534,a),flip(a)].">
      <j1 rule="hyper" parents="58 19158 19534"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19536">
    <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(7704,a,19535,a)].">
      <j1 rule="hyper" parents="7704 19535"/>
    </justification>
  </clause>

  <clause id="19537">
    <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(15950,a,19536,a)].">
      <j1 rule="hyper" parents="15950 19536"/>
    </justification>
  </clause>

  <clause id="19538">
    <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(15580,a,19537,a)].">
      <j1 rule="hyper" parents="15580 19537"/>
    </justification>
  </clause>

  <clause id="19539">
    <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,7160,a(flip),b,19538,a),flip(a)].">
      <j1 rule="hyper" parents="320 7160 19538"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19540">
    <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(16752(a,1),19539(a,2,2))].">
      <j1 rule="para" parents="16752 19539"/>
    </justification>
  </clause>

  <clause id="19541">
    <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(19540(a,2),15680(a,1))].">
      <j1 rule="para" parents="19540 15680"/>
    </justification>
  </clause>

  <clause id="19542">
    <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,16098,a(flip),b,18245,a)].">
      <j1 rule="hyper" parents="58 16098 18245"/>
    </justification>
  </clause>

  <clause id="19543">
    <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(17538,a,19542,a)].">
      <j1 rule="hyper" parents="17538 19542"/>
    </justification>
  </clause>

  <clause id="19544">
    <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,13889,a(flip),b,19543,a)].">
      <j1 rule="hyper" parents="58 13889 19543"/>
    </justification>
  </clause>

  <clause id="19545">
    <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(17954,a,19544,a)].">
      <j1 rule="hyper" parents="17954 19544"/>
    </justification>
  </clause>

  <clause id="19546">
    <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(16447,a,19545,a),flip(a)].">
      <j1 rule="hyper" parents="16447 19545"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19547">
    <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,17281,a(flip),b,19546,a),flip(a)].">
      <j1 rule="hyper" parents="320 17281 19546"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19548">
    <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(18244(a,1),19547(a,1,1,2))].">
      <j1 rule="para" parents="18244 19547"/>
    </justification>
  </clause>

  <clause id="19549">
    <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(2340(a,1),19548(a,1,2))].">
      <j1 rule="para" parents="2340 19548"/>
    </justification>
  </clause>

  <clause id="19550">
    <literal><![CDATA[
      K(x,R(y,z,z \ 1) / u) = K(x,L(y,z,z \ 1) / u)
    ]]></literal>
    <justification jstring="[hyper(6345,a,19549,a),flip(a)].">
      <j1 rule="hyper" parents="6345 19549"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19552">
    <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,14885,a,b,19550,a)].">
      <j1 rule="hyper" parents="58 14885 19550"/>
    </justification>
  </clause>

  <clause id="19553">
    <literal><![CDATA[
      K(x,L(y,z,z \ 1) / (u * (z \ 1))) = K(x,y / (u / z))
    ]]></literal>
    <justification jstring="[hyper(58,a,18510,a(flip),b,19552,a),flip(a)].">
      <j1 rule="hyper" parents="58 18510 19552"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19554">
    <literal><![CDATA[
      K(x,y / (z * (u \ 1))) = K(x,y / (z / u))
    ]]></literal>
    <justification jstring="[hyper(58,a,19444,a(flip),b,19553,a)].">
      <j1 rule="hyper" parents="58 19444 19553"/>
    </justification>
  </clause>

  <clause id="19555">
    <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,18548,a(flip),b,19553,a)].">
      <j1 rule="hyper" parents="58 18548 19553"/>
    </justification>
  </clause>

  <clause id="19556">
    <literal><![CDATA[
      K(x,y / (z \ T(u,z))) = K(x,y / (u * (z \ 1)))
    ]]></literal>
    <justification jstring="[hyper(320,a,17929,a,b,19554,a)].">
      <j1 rule="hyper" parents="320 17929 19554"/>
    </justification>
  </clause>

  <clause id="19558">
    <literal><![CDATA[
      K(x,L(y,z,z \ 1) / ((z \ 1) * u)) = K(x,y / (z \ u))
    ]]></literal>
    <justification jstring="[hyper(320,a,16323,a(flip),b,19555,a),flip(a)].">
      <j1 rule="hyper" parents="320 16323 19555"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19559">
    <literal><![CDATA[
      K(x,y / ((z \ 1) * u)) = K(x,y / (z \ u))
    ]]></literal>
    <justification jstring="[hyper(58,a,19444,a(flip),b,19558,a)].">
      <j1 rule="hyper" parents="58 19444 19558"/>
    </justification>
  </clause>

  <clause id="19561">
    <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(19559(a,1),18923(a,1,2))].">
      <j1 rule="para" parents="19559 18923"/>
    </justification>
  </clause>

  <clause id="19562">
    <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(19559(a,1),19541(a,1))].">
      <j1 rule="para" parents="19559 19541"/>
    </justification>
  </clause>

  <clause id="19563">
    <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(18674(a,1),19561(a,1,2))].">
      <j1 rule="para" parents="18674 19561"/>
    </justification>
  </clause>

  <clause id="19564">
    <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(19054(a,1),19563(a,1,2))].">
      <j1 rule="para" parents="19054 19563"/>
    </justification>
  </clause>

  <clause id="19565">
    <literal><![CDATA[
      K(x,y / (z / T(u,z))) = K(x,y * (z \ u))
    ]]></literal>
    <justification jstring="[hyper(58,a,18437,a(flip),b,19564,a)].">
      <j1 rule="hyper" parents="58 18437 19564"/>
    </justification>
  </clause>

  <clause id="19566">
    <literal><![CDATA[
      K(x,y / (z \ u)) = K(x,y * (u \ z))
    ]]></literal>
    <justification jstring="[hyper(58,a,16322,a(flip),b,19565,a)].">
      <j1 rule="hyper" parents="58 16322 19565"/>
    </justification>
  </clause>

  <clause id="19567">
    <literal><![CDATA[
      K(x,T(y,z * (x * u)) * (u \ z)) = K(x,((z \ 1) * u) \ y)
    ]]></literal>
    <justification jstring="[hyper(19562,a,19566,a),flip(a)].">
      <j1 rule="hyper" parents="19562 19566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19569">
    <literal><![CDATA[
      K(x,y / ((z \ 1) * u)) = K(x,y * (u \ z))
    ]]></literal>
    <justification jstring="[hyper(58,a,19559,a,b,19566,a)].">
      <j1 rule="hyper" parents="58 19559 19566"/>
    </justification>
  </clause>

  <clause id="19570">
    <literal><![CDATA[
      K(x,y / (z * (u \ 1))) = K(x,y * (T(z,u) \ u))
    ]]></literal>
    <justification jstring="[hyper(58,a,19556,a(flip),b,19566,a)].">
      <j1 rule="hyper" parents="58 19556 19566"/>
    </justification>
  </clause>

  <clause id="19571">
    <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,19337,a(flip),b,19566,a),flip(a)].">
      <j1 rule="hyper" parents="58 19337 19566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19572">
    <literal><![CDATA[
      K(x,y * ((T(z,u) * y) \ u)) = K(x,y \ ((y * u) / z))
    ]]></literal>
    <justification jstring="[hyper(58,a,19212,a(flip),b,19566,a),flip(a)].">
      <j1 rule="hyper" parents="58 19212 19566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19575">
    <literal><![CDATA[
      a(x,y,K(z,(u \ w) \ v5)) = a(x,y,K(z,v5 * (w \ u)))
    ]]></literal>
    <justification jstring="[para(19566(a,1),18325(a,1,3)),flip(a)].">
      <j1 rule="para" parents="19566 18325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19576">
    <literal><![CDATA[
      K(x,y * (z \ (u \ 1))) = K(x,y / (u * z))
    ]]></literal>
    <justification jstring="[hyper(58,a,5579,a(flip),b,19569,a),flip(a)].">
      <j1 rule="hyper" parents="58 5579 19569"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19577">
    <literal><![CDATA[
      K(x,y * ((z / u) \ (w \ K(z,u)))) = K(x,y / (w * (u \ z)))
    ]]></literal>
    <justification jstring="[hyper(18620,a,19576,a)].">
      <j1 rule="hyper" parents="18620 19576"/>
    </justification>
  </clause>

  <clause id="19578">
    <literal><![CDATA[
      K(x,y / (z * (u \ 1))) = K(x,y * (u / z))
    ]]></literal>
    <justification jstring="[hyper(320,a,15262,a(flip),b,19570,a),flip(a)].">
      <j1 rule="hyper" parents="320 15262 19570"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19579">
    <literal><![CDATA[
      K(x,y / (z / u)) = K(x,y * (u / z))
    ]]></literal>
    <justification jstring="[hyper(58,a,19554,a(flip),b,19578,a)].">
      <j1 rule="hyper" parents="58 19554 19578"/>
    </justification>
  </clause>

  <clause id="19580">
    <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,18900,a,b,19579,a)].">
      <j1 rule="hyper" parents="58 18900 19579"/>
    </justification>
  </clause>

  <clause id="19582">
    <literal><![CDATA[
      K(x,y \ ((y * z) / u)) = K(x,(z / (y * u)) * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,16328,a(flip),b,19572,a),flip(a)].">
      <j1 rule="hyper" parents="58 16328 19572"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19583">
    <literal><![CDATA[
      K(x,((y \ 1) * z) \ u) = K(x,(z \ y) * u)
    ]]></literal>
    <justification jstring="[hyper(19492,a,19567,a),flip(a)].">
      <j1 rule="hyper" parents="19492 19567"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19584">
    <literal><![CDATA[
      K(x,(y \ z) \ u) = K(x,(z \ y) * u)
    ]]></literal>
    <justification jstring="[hyper(58,a,19463,a(flip),b,19583,a)].">
      <j1 rule="hyper" parents="58 19463 19583"/>
    </justification>
  </clause>

  <clause id="19585">
    <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,19370,a(flip),b,19584,a),flip(a)].">
      <j1 rule="hyper" parents="58 19370 19584"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19586">
    <literal><![CDATA[
      a(x \ (y \ z),u,K(w,v5)) = a(v5,u,K(w,(z \ y) * x))
    ]]></literal>
    <justification jstring="[para(19584(a,1),14309(a,2,3))].">
      <j1 rule="para" parents="19584 14309"/>
    </justification>
  </clause>

  <clause id="19587">
    <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(19584(a,1),14383(a,1,3))].">
      <j1 rule="para" parents="19584 14383"/>
    </justification>
  </clause>

  <clause id="19588">
    <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(19584(a,1),19366(a,1,1,3))].">
      <j1 rule="para" parents="19584 19366"/>
    </justification>
  </clause>

  <clause id="19589">
    <literal><![CDATA[
      a(x \ (y \ z),u,K(w,v5)) = a(x * (z \ y),u,K(v5,w))
    ]]></literal>
    <justification jstring="[hyper(320,a,18334,a,b,19586,a),flip(a)].">
      <j1 rule="hyper" parents="320 18334 19586"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19590">
    <literal><![CDATA[
      a((x * y) \ z,u,K(w,v5)) = a(y * (z \ x),u,K(v5,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,14391,a,b,19589,a)].">
      <j1 rule="hyper" parents="58 14391 19589"/>
    </justification>
  </clause>

  <clause id="19591">
    <literal><![CDATA[
      a(x \ (y * z),u,K(w,v5)) = a(z * (x \ y),u,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(14401,a,19590,a)].">
      <j1 rule="hyper" parents="14401 19590"/>
    </justification>
  </clause>

  <clause id="19592">
    <literal><![CDATA[
      a(x \ (y * z),u,K(w,v5)) = a((x \ y) * z,u,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(320,a,18336,a,b,19591,a),flip(a)].">
      <j1 rule="hyper" parents="320 18336 19591"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19593">
    <literal><![CDATA[
      a(x * (y \ 1),z,K(u,w)) = a(y \ x,z,K(u,w))
    ]]></literal>
    <justification jstring="[para(2(a,1),19591(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="2 19591"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19594">
    <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(19591(a,2),18354(a,1))].">
      <j1 rule="para" parents="19591 18354"/>
    </justification>
  </clause>

  <clause id="19595">
    <literal><![CDATA[
      a((x \ 1) * y,z,K(u,w)) = a(x \ y,z,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(18354,a,19593,a)].">
      <j1 rule="hyper" parents="18354 19593"/>
    </justification>
  </clause>

  <clause id="19596">
    <literal><![CDATA[
      a((x \ y) \ z,u,K(w,v5)) = a((y \ x) * z,u,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(58,a,14392,a,b,19592,a)].">
      <j1 rule="hyper" parents="58 14392 19592"/>
    </justification>
  </clause>

  <clause id="19597">
    <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(19592(a,2),18354(a,1))].">
      <j1 rule="para" parents="19592 18354"/>
    </justification>
  </clause>

  <clause id="19598">
    <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),19596(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4 19596"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19599">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,y,z \ 1)) = K(x,(z \ y) * (z * u))
    ]]></literal>
    <justification jstring="[hyper(320,a,19446,a(flip),b,19580,a),flip(a)].">
      <j1 rule="hyper" parents="320 19446 19580"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19600">
    <literal><![CDATA[
      K(x,(y \ z) * (z \ (u * y))) = K(x,L(T(u,y),y,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(58,a,17716,a(flip),b,19585,a)].">
      <j1 rule="hyper" parents="58 17716 19585"/>
    </justification>
  </clause>

  <clause id="19601">
    <literal><![CDATA[
      K(x,((y * z) / u) * (u / y)) = K(x,L(T(z,y),y,u \ 1))
    ]]></literal>
    <justification jstring="[hyper(58,a,19104,a,b,19600,a)].">
      <j1 rule="hyper" parents="58 19104 19600"/>
    </justification>
  </clause>

  <clause id="19602">
    <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,19341,a(flip),b,19571,a)].">
      <j1 rule="hyper" parents="58 19341 19571"/>
    </justification>
  </clause>

  <clause id="19603">
    <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),19602(a,1,2,2,1,1))].">
      <j1 rule="para" parents="5 19602"/>
    </justification>
  </clause>

  <clause id="19604">
    <literal><![CDATA[
      K(x,L(y / z,u,w) * (z / y)) = a(x,u,K(y \ z,w))
    ]]></literal>
    <justification jstring="[hyper(18211,a,19603,a)].">
      <j1 rule="hyper" parents="18211 19603"/>
    </justification>
  </clause>

  <clause id="19606">
    <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(19579(a,1),19588(a,1,2))].">
      <j1 rule="para" parents="19579 19588"/>
    </justification>
  </clause>

  <clause id="19607">
    <literal><![CDATA[
      K(x,y / (((z / u) \ 1) / w)) = K(x,y / ((u / z) / w))
    ]]></literal>
    <justification jstring="[hyper(58,a,19519,a(flip),b,19606,a)].">
      <j1 rule="hyper" parents="58 19519 19606"/>
    </justification>
  </clause>

  <clause id="19608">
    <literal><![CDATA[
      K(x,y * (z / ((u / w) \ 1))) = K(x,y / ((w / u) / z))
    ]]></literal>
    <justification jstring="[hyper(58,a,19579,a(flip),b,19607,a)].">
      <j1 rule="hyper" parents="58 19579 19607"/>
    </justification>
  </clause>

  <clause id="19609">
    <literal><![CDATA[
      K(x,y / ((z / u) / w)) = K(x,y * (w * (u / z)))
    ]]></literal>
    <justification jstring="[hyper(58,a,19446,a(flip),b,19608,a),flip(a)].">
      <j1 rule="hyper" parents="58 19446 19608"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19610">
    <literal><![CDATA[
      K(x,y * (z / (u / w))) = K(x,y * (z * (w / u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,19579,a(flip),b,19609,a)].">
      <j1 rule="hyper" parents="58 19579 19609"/>
    </justification>
  </clause>

  <clause id="19611">
    <literal><![CDATA[
      K(x,y * (z * (u / T(y,u * z)))) = K(x,y \ ((y * z) * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,19047,a(flip),b,19609,a),flip(a)].">
      <j1 rule="hyper" parents="58 19047 19609"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19612">
    <literal><![CDATA[
      K(x,y * (T(z,u * w) * (u / w))) = K(x,y * ((w / u) \ z))
    ]]></literal>
    <justification jstring="[hyper(19019,a,19610,a),flip(a)].">
      <j1 rule="hyper" parents="19019 19610"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19613">
    <literal><![CDATA[
      K(x,y \ ((y * z) * u)) = K(x,(z * (u / y)) * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,18200,a(flip),b,19611,a),flip(a)].">
      <j1 rule="hyper" parents="58 18200 19611"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19614">
    <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,18131,a,b,19613,a)].">
      <j1 rule="hyper" parents="58 18131 19613"/>
    </justification>
  </clause>

  <clause id="19615">
    <literal><![CDATA[
      K(x,(y * ((z \ 1) / u)) * u) = K(x,u \ ((u * y) / z))
    ]]></literal>
    <justification jstring="[hyper(58,a,19464,a(flip),b,19613,a),flip(a)].">
      <j1 rule="hyper" parents="58 19464 19613"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19616">
    <literal><![CDATA[
      K(x,(y * ((z \ 1) / u)) * u) = K(x,(y / (u * z)) * u)
    ]]></literal>
    <justification jstring="[hyper(320,a,19582,a(flip),b,19615,a),flip(a)].">
      <j1 rule="hyper" parents="320 19582 19615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19617">
    <literal><![CDATA[
      K(x,y * ((z / u) \ w)) = K(x,y * ((u / z) * w))
    ]]></literal>
    <justification jstring="[hyper(19079,a,19612,a),flip(a)].">
      <j1 rule="hyper" parents="19079 19612"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19618">
    <literal><![CDATA[
      K(x,y * ((z / u) * (w \ K(u,z)))) = K(x,y / (w * (z \ u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,19577,a(flip),b,19617,a),flip(a)].">
      <j1 rule="hyper" parents="58 19577 19617"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19619">
    <literal><![CDATA[
      K(x,y / (z * (u \ w))) = K(x,y * ((w \ u) / z))
    ]]></literal>
    <justification jstring="[hyper(19450,a,19618,a),flip(a)].">
      <j1 rule="hyper" parents="19450 19618"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19620">
    <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,19387,a(flip),b,19619,a),flip(a)].">
      <j1 rule="hyper" parents="58 19387 19619"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19621">
    <literal><![CDATA[
      a(x,y \ z,K(u \ (y \ z),y)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,19604,a(flip),b,19620,a)].">
      <j1 rule="hyper" parents="58 19604 19620"/>
    </justification>
  </clause>

  <clause id="19622">
    <literal><![CDATA[
      a(x,y \ z,K(u \ z,y)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(14451,a,19621,a)].">
      <j1 rule="hyper" parents="14451 19621"/>
    </justification>
  </clause>

  <clause id="19623">
    <literal><![CDATA[
      a(x,a(y,z,u),K(w,v5)) = 1
    ]]></literal>
    <justification jstring="[hyper(13442,a,19621,a),flip(a)].">
      <j1 rule="hyper" parents="13442 19621"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19624">
    <literal><![CDATA[
      L(x,a(y,z,u),K(w,v5)) = x
    ]]></literal>
    <justification jstring="[hyper(13666,a,19623,a)].">
      <j1 rule="hyper" parents="13666 19623"/>
    </justification>
  </clause>

  <clause id="19625">
    <literal><![CDATA[
      L(K(x,y),a(z,u,w),v5) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(5893,a,19623,a)].">
      <j1 rule="hyper" parents="5893 19623"/>
    </justification>
  </clause>

  <clause id="19627">
    <literal><![CDATA[
      K(x,L(y,a(z,u,w),v5)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(10837,a,19625,a)].">
      <j1 rule="hyper" parents="10837 19625"/>
    </justification>
  </clause>

  <clause id="19629">
    <literal><![CDATA[
      K(x,L(y,a(z,u,w),v5)) = K(x,L(y,v6,L(v6,v7,v8)))
    ]]></literal>
    <justification jstring="[hyper(320,a,14344,a,b,19627,a),flip(a)].">
      <j1 rule="hyper" parents="320 14344 19627"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19631">
    <literal><![CDATA[
      a(x,y,K(z \ y,u)) = a(x,u,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,14369,a(flip),b,19622,a)].">
      <j1 rule="hyper" parents="58 14369 19622"/>
    </justification>
  </clause>

  <clause id="19632">
    <literal><![CDATA[
      a(x,y,K(z,y \ u)) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,19621,a(flip),b,19631,a),flip(a)].">
      <j1 rule="hyper" parents="58 19621 19631"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19633">
    <literal><![CDATA[
      ((x / y) * (y * K(z,u))) * K(u,z) = x * a(z,u,K(y,x))
    ]]></literal>
    <justification jstring="[para(19631(a,1),18963(a,2,2))].">
      <j1 rule="para" parents="19631 18963"/>
    </justification>
  </clause>

  <clause id="19634">
    <literal><![CDATA[
      x * L(x \ y,x,K(z,u)) = y * a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[para(19631(a,1),19140(a,2,2))].">
      <j1 rule="para" parents="19631 19140"/>
    </justification>
  </clause>

  <clause id="19635">
    <literal><![CDATA[
      K(x,L(y,a(z,u,w),v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v6
    ]]></literal>
    <justification jstring="[para(19629(a,2),6499(a,1))].">
      <j1 rule="para" parents="19629 6499"/>
    </justification>
  </clause>

  <clause id="19636">
    <literal><![CDATA[
      K(((x * y) * z) \ ((x * (y * z)) * u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(a(x,y,z) \ u,w) = v5
    ]]></literal>
    <justification jstring="[para(10856(a,1),19635(a,1))].">
      <j1 rule="para" parents="10856 19635"/>
    </justification>
  </clause>

  <clause id="19637">
    <literal><![CDATA[
      x * L(x \ y,x,K(z,u)) = L(y,z,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(320,a,14936,a(flip),b,19634,a),flip(a)].">
      <j1 rule="hyper" parents="320 14936 19634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19638">
    <literal><![CDATA[
      x * a(y,x,K(z,x \ u)) = L(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,19138,a(flip),b,19637,a)].">
      <j1 rule="hyper" parents="58 19138 19637"/>
    </justification>
  </clause>

  <clause id="19639">
    <literal><![CDATA[
      x * a(y,x,K(z,u)) = L(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[para(19632(a,1),19638(a,1,2))].">
      <j1 rule="para" parents="19632 19638"/>
    </justification>
  </clause>

  <clause id="19640">
    <literal><![CDATA[
      x * a(y,x,K(z,u)) = L(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(17459,a,19639,a)].">
      <j1 rule="hyper" parents="17459 19639"/>
    </justification>
  </clause>

  <clause id="19641">
    <literal><![CDATA[
      a(x,y,K(z,u)) = a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(29,a,14939,a,b,19639,a)].">
      <j1 rule="hyper" parents="29 14939 19639"/>
    </justification>
  </clause>

  <clause id="19642">
    <literal><![CDATA[
      a(x,y,K(z,u)) = a(x,u,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(29,a,14936,a,b,19639,a)].">
      <j1 rule="hyper" parents="29 14936 19639"/>
    </justification>
  </clause>

  <clause id="19643">
    <literal><![CDATA[
      a(x,y,K(z,u)) = a(z,x,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(29,a,14928,a,b,19639,a)].">
      <j1 rule="hyper" parents="29 14928 19639"/>
    </justification>
  </clause>

  <clause id="19644">
    <literal><![CDATA[
      a(x \ y,z,K(u,w)) = a(u,w,K(z,y \ x))
    ]]></literal>
    <justification jstring="[hyper(14401,a,19641,a)].">
      <j1 rule="hyper" parents="14401 19641"/>
    </justification>
  </clause>

  <clause id="19645">
    <literal><![CDATA[
      a(x,y,K(z,u \ 1)) = a(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(14389,a,19641,a),flip(a)].">
      <j1 rule="hyper" parents="14389 19641"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19646">
    <literal><![CDATA[
      x * a(y,z,K(u,x)) = L(x,u,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(119,a,19641,a,b,14929,a)].">
      <j1 rule="hyper" parents="119 19641 14929"/>
    </justification>
  </clause>

  <clause id="19647">
    <literal><![CDATA[
      a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(y,z,K(x,u)) = w
    ]]></literal>
    <justification jstring="[para(19641(a,1),14349(a,1))].">
      <j1 rule="para" parents="19641 14349"/>
    </justification>
  </clause>

  <clause id="19648">
    <literal><![CDATA[
      K(x,y) * a(y,z,K(u,x)) = K(x,L(y,u,z))
    ]]></literal>
    <justification jstring="[para(19641(a,1),14325(a,1,2))].">
      <j1 rule="para" parents="19641 14325"/>
    </justification>
  </clause>

  <clause id="19649">
    <literal><![CDATA[
      a(x,y,K(z,u)) * u = L(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[para(19641(a,1),14937(a,1,1))].">
      <j1 rule="para" parents="19641 14937"/>
    </justification>
  </clause>

  <clause id="19650">
    <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(19641(a,1),18356(a,1))].">
      <j1 rule="para" parents="19641 18356"/>
    </justification>
  </clause>

  <clause id="19651">
    <literal><![CDATA[
      a(x,y,K(z,u)) = a(u,x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(320,a,14263,a,b,19642,a)].">
      <j1 rule="hyper" parents="320 14263 19642"/>
    </justification>
  </clause>

  <clause id="19652">
    <literal><![CDATA[
      a(x,y,K(z,u)) = a(z,u,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(320,a,14263,a(flip),b,19642,a)].">
      <j1 rule="hyper" parents="320 14263 19642"/>
    </justification>
  </clause>

  <clause id="19653">
    <literal><![CDATA[
      a(K(x,y) * z,u,K(w,v5)) = a(w,v5,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(18378,a,19642,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="18378 19642"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19654">
    <literal><![CDATA[
      a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(u,z,K(y,x)) = w
    ]]></literal>
    <justification jstring="[para(19642(a,1),14349(a,1))].">
      <j1 rule="para" parents="19642 14349"/>
    </justification>
  </clause>

  <clause id="19655">
    <literal><![CDATA[
      a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(y,u,K(z,x)) = w
    ]]></literal>
    <justification jstring="[para(19642(a,2),14349(a,1))].">
      <j1 rule="para" parents="19642 14349"/>
    </justification>
  </clause>

  <clause id="19656">
    <literal><![CDATA[
      a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(z,u,K(x,y)) = w
    ]]></literal>
    <justification jstring="[para(19642(a,2),14387(a,1))].">
      <j1 rule="para" parents="19642 14387"/>
    </justification>
  </clause>

  <clause id="19657">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(y,u)) = K(x,L(y,u,z))
    ]]></literal>
    <justification jstring="[para(19642(a,2),14325(a,1,2))].">
      <j1 rule="para" parents="19642 14325"/>
    </justification>
  </clause>

  <clause id="19658">
    <literal><![CDATA[
      a(x \ y,z,K(x,u)) = a(u,y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,14371,a(flip),b,19643,a),flip(a)].">
      <j1 rule="hyper" parents="320 14371 19643"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19659">
    <literal><![CDATA[
      a(x,y,z) * a(y,z,K(x,u)) = a(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(119,a,19643,a,b,18838,a)].">
      <j1 rule="hyper" parents="119 19643 18838"/>
    </justification>
  </clause>

  <clause id="19660">
    <literal><![CDATA[
      a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(u,x,K(z,y)) = w
    ]]></literal>
    <justification jstring="[para(19643(a,2),14387(a,1))].">
      <j1 rule="para" parents="19643 14387"/>
    </justification>
  </clause>

  <clause id="19661">
    <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(19643(a,2),18347(a,1))].">
      <j1 rule="para" parents="19643 18347"/>
    </justification>
  </clause>

  <clause id="19662">
    <literal><![CDATA[
      a(x \ (y \ z),u,K(w,v5)) = a((z \ y) * x,v5,K(w,u))
    ]]></literal>
    <justification jstring="[hyper(19587,a,19651,a)].">
      <j1 rule="hyper" parents="19587 19651"/>
    </justification>
  </clause>

  <clause id="19663">
    <literal><![CDATA[
      a(((x * y) \ x) * z,u,K(w,v5)) = a(u,v5,K(w,y \ z))
    ]]></literal>
    <justification jstring="[hyper(320,a,19598,a,b,19651,a)].">
      <j1 rule="hyper" parents="320 19598 19651"/>
    </justification>
  </clause>

  <clause id="19664">
    <literal><![CDATA[
      a(x \ 1,y,K(z,u)) = a(y,x,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,14310,a,b,19651,a)].">
      <j1 rule="hyper" parents="320 14310 19651"/>
    </justification>
  </clause>

  <clause id="19665">
    <literal><![CDATA[
      a(x,y,K(z,(u \ 1) * w)) = a(u \ w,x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(320,a,19595,a(flip),b,19651,a),flip(a)].">
      <j1 rule="hyper" parents="320 19595 19651"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19666">
    <literal><![CDATA[
      a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(z,x,K(y,u)) = w
    ]]></literal>
    <justification jstring="[para(19651(a,2),14349(a,1))].">
      <j1 rule="para" parents="19651 14349"/>
    </justification>
  </clause>

  <clause id="19667">
    <literal><![CDATA[
      a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,u,K(y,z)) = w
    ]]></literal>
    <justification jstring="[para(19651(a,1),14387(a,1))].">
      <j1 rule="para" parents="19651 14387"/>
    </justification>
  </clause>

  <clause id="19668">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (w \ x) = w \ L(x,u,K(y,z))
    ]]></literal>
    <justification jstring="[para(19652(a,1),17337(a,1,1))].">
      <j1 rule="para" parents="19652 17337"/>
    </justification>
  </clause>

  <clause id="19669">
    <literal><![CDATA[
      x * (y * a(x,z,K(u,w))) = L(x,w,K(z,u)) * y
    ]]></literal>
    <justification jstring="[para(19652(a,1),17469(a,1,2,2))].">
      <j1 rule="para" parents="19652 17469"/>
    </justification>
  </clause>

  <clause id="19670">
    <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(18033(a,1),19652(a,1,3)),flip(a)].">
      <j1 rule="para" parents="18033 19652"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19671">
    <literal><![CDATA[
      L(x,y,K(z,u)) = L(x,u,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,19639,a(flip),b,19640,a),flip(a)].">
      <j1 rule="hyper" parents="58 19639 19640"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19672">
    <literal><![CDATA[
      L(x,y,K(z,u)) = T(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(14933,a,19671,a),flip(a)].">
      <j1 rule="hyper" parents="14933 19671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19673">
    <literal><![CDATA[
      L(x,y,K(z * u,z)) = L(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(12718,a,19671,a)].">
      <j1 rule="hyper" parents="12718 19671"/>
    </justification>
  </clause>

  <clause id="19674">
    <literal><![CDATA[
      L(x,y * z,K(y,u)) = L(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,14962,a,b,19671,a)].">
      <j1 rule="hyper" parents="320 14962 19671"/>
    </justification>
  </clause>

  <clause id="19675">
    <literal><![CDATA[
      a(x,y,z) * (u / a(x,y,z)) = L(u,x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(320,a,14959,a,b,19671,a)].">
      <j1 rule="hyper" parents="320 14959 19671"/>
    </justification>
  </clause>

  <clause id="19676">
    <literal><![CDATA[
      L(x,y * x,K(z,u)) = L(x,u,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,18463,a(flip),b,19671,a),flip(a)].">
      <j1 rule="hyper" parents="320 18463 19671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19677">
    <literal><![CDATA[
      (K(x,y) * z) * L(u,x,K(y,z)) = K(x,y) * (z * u)
    ]]></literal>
    <justification jstring="[hyper(119,a,19671,a,b,13,a(flip))].">
      <j1 rule="hyper" parents="119 19671 13"/>
    </justification>
  </clause>

  <clause id="19678">
    <literal><![CDATA[
      L(x * (a(y,z,u) \ 1),y,K(z,u)) = (a(y,z,u) \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(58,a,15008,a(flip),b,19671,a),flip(a)].">
      <j1 rule="hyper" parents="58 15008 19671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19679">
    <literal><![CDATA[
      L(L(x,y,K(z,u)),z,u) = L(x,z,T(u,y))
    ]]></literal>
    <justification jstring="[para(19671(a,1),14964(a,1,1))].">
      <j1 rule="para" parents="19671 14964"/>
    </justification>
  </clause>

  <clause id="19680">
    <literal><![CDATA[
      L(x,y,K(z,u)) / a(y,z,u) = a(y,z,u) \ x
    ]]></literal>
    <justification jstring="[para(19671(a,1),14984(a,1,1))].">
      <j1 rule="para" parents="19671 14984"/>
    </justification>
  </clause>

  <clause id="19681">
    <literal><![CDATA[
      L(x,y,K(z,u * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,w * u,K(y,z)) = v5
    ]]></literal>
    <justification jstring="[para(19671(a,2),18487(a,1))].">
      <j1 rule="para" parents="19671 18487"/>
    </justification>
  </clause>

  <clause id="19682">
    <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,2140,a,b,19672,a)].">
      <j1 rule="hyper" parents="320 2140 19672"/>
    </justification>
  </clause>

  <clause id="19683">
    <literal><![CDATA[
      L(x,y,K(z,u)) / a(y,z,u) = x / a(y,z,T(u,x))
    ]]></literal>
    <justification jstring="[para(19672(a,2),18841(a,1,1))].">
      <j1 rule="para" parents="19672 18841"/>
    </justification>
  </clause>

  <clause id="19684">
    <literal><![CDATA[
      T(x,x * (y \ L(y,z,u))) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(13393,a,19646,a)].">
      <j1 rule="hyper" parents="13393 19646"/>
    </justification>
  </clause>

  <clause id="19685">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (x \ w) = L(x,z,K(y,u)) \ w
    ]]></literal>
    <justification jstring="[para(19646(a,1),17500(a,1,1)),flip(a)].">
      <j1 rule="para" parents="19646 17500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19686">
    <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(19664(a,1),14345(a,1,1,1))].">
      <j1 rule="para" parents="19664 14345"/>
    </justification>
  </clause>

  <clause id="19687">
    <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(19664(a,1),14346(a,1,1,1))].">
      <j1 rule="para" parents="19664 14346"/>
    </justification>
  </clause>

  <clause id="19688">
    <literal><![CDATA[
      L(x,y,K(z,y * u)) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,19671,a(flip),b,19673,a)].">
      <j1 rule="hyper" parents="58 19671 19673"/>
    </justification>
  </clause>

  <clause id="19689">
    <literal><![CDATA[
      L(L(x,y,z),z,K(u,y)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(19674(a,1),6873(a,1))].">
      <j1 rule="para" parents="19674 6873"/>
    </justification>
  </clause>

  <clause id="19690">
    <literal><![CDATA[
      L(R(x,y,z),y,K(z,u)) = R(x,y,T(z,y * u))
    ]]></literal>
    <justification jstring="[hyper(18368,a,19688,a),flip(a)].">
      <j1 rule="hyper" parents="18368 19688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19691">
    <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(19586(a,2),19660(a,1))].">
      <j1 rule="para" parents="19586 19660"/>
    </justification>
  </clause>

  <clause id="19692">
    <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,15100,a,b,19679,a),flip(a)].">
      <j1 rule="hyper" parents="320 15100 19679"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19693">
    <literal><![CDATA[
      a(x \ (y * z),u,K(w,v5)) = a(w,v5,K(u,z \ (y \ x)))
    ]]></literal>
    <justification jstring="[hyper(14513,a,19644,a)].">
      <j1 rule="hyper" parents="14513 19644"/>
    </justification>
  </clause>

  <clause id="19694">
    <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,18388,a,b,19644,a)].">
      <j1 rule="hyper" parents="58 18388 19644"/>
    </justification>
  </clause>

  <clause id="19695">
    <literal><![CDATA[
      K(x,L(L(y,z,u),u,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(30,a,17334,a,b,19648,a)].">
      <j1 rule="hyper" parents="30 17334 19648"/>
    </justification>
  </clause>

  <clause id="19696">
    <literal><![CDATA[
      K((x * y) \ z,L(u,x,y)) = K(y \ (x \ z),u)
    ]]></literal>
    <justification jstring="[hyper(10947,a,19695,a)].">
      <j1 rule="hyper" parents="10947 19695"/>
    </justification>
  </clause>

  <clause id="19698">
    <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(19653(a,2),19656(a,1))].">
      <j1 rule="para" parents="19653 19656"/>
    </justification>
  </clause>

  <clause id="19699">
    <literal><![CDATA[
      K(x,L(y,z,u \ y)) = K(x,L(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(14497,a,19657,a)].">
      <j1 rule="hyper" parents="14497 19657"/>
    </justification>
  </clause>

  <clause id="19700">
    <literal><![CDATA[
      K(x,L(y,z,u \ 1)) = K(x,L(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(14354,a,19657,a)].">
      <j1 rule="hyper" parents="14354 19657"/>
    </justification>
  </clause>

  <clause id="19701">
    <literal><![CDATA[
      K(x,L(y,z,u \ 1)) = K(x,L(y,u,z * u))
    ]]></literal>
    <justification jstring="[hyper(14553,a,19699,a)].">
      <j1 rule="hyper" parents="14553 19699"/>
    </justification>
  </clause>

  <clause id="19702">
    <literal><![CDATA[
      K(x,((y * z) / u) * (u / y)) = K(x,L(T(z,y),u,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,19601,a,b,19700,a)].">
      <j1 rule="hyper" parents="58 19601 19700"/>
    </justification>
  </clause>

  <clause id="19703">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,z,y)) = K(x,(z \ y) * (z * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,19599,a(flip),b,19700,a),flip(a)].">
      <j1 rule="hyper" parents="58 19599 19700"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19704">
    <literal><![CDATA[
      T(x,L(y,z,u) * (y \ x)) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,19192,a,b,19684,a)].">
      <j1 rule="hyper" parents="58 19192 19684"/>
    </justification>
  </clause>

  <clause id="19705">
    <literal><![CDATA[
      K(x,L(y,z,u * z)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,19700,a(flip),b,19701,a),flip(a)].">
      <j1 rule="hyper" parents="58 19700 19701"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19706">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,z,y)) = K(x,z \ ((y * z) * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,19472,a(flip),b,19705,a),flip(a)].">
      <j1 rule="hyper" parents="58 19472 19705"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19707">
    <literal><![CDATA[
      (x / (1 / y)) * (K(z,u) / y) = x * K(z,L(T(u,y),x,y))
    ]]></literal>
    <justification jstring="[para(19705(a,1),18829(a,1,2)),flip(a)].">
      <j1 rule="para" parents="19705 18829"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19708">
    <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,13246,a,b,19704,a)].">
      <j1 rule="hyper" parents="58 13246 19704"/>
    </justification>
  </clause>

  <clause id="19709">
    <literal><![CDATA[
      a(x,y,z) * (a(y,z,K(x,u)) * w) = a(x,y,T(z,u)) * w
    ]]></literal>
    <justification jstring="[para(19659(a,1),17496(a,1,1)),flip(a)].">
      <j1 rule="para" parents="19659 17496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19710">
    <literal><![CDATA[
      L(x * a(y,z,u),y,K(u,z)) = a(y,z,u) * x
    ]]></literal>
    <justification jstring="[para(6(a,1),19675(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6 19675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19711">
    <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(19680(a,1),251(a,1,1)),flip(b)].">
      <j1 rule="para" parents="19680 251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19712">
    <literal><![CDATA[
      R(x,y,T(z,y * x)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,7524,a(flip),b,19690,a),flip(a)].">
      <j1 rule="hyper" parents="58 7524 19690"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19713">
    <literal><![CDATA[
      R(x,y,z) \ (z * (y * x)) = T(y,x) * T(z,y * x)
    ]]></literal>
    <justification jstring="[para(19712(a,1),12524(a,1,1))].">
      <j1 rule="para" parents="19712 12524"/>
    </justification>
  </clause>

  <clause id="19714">
    <literal><![CDATA[
      K(x \ (y \ ((y * x) * z)),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(z,L(u,y,x)) = w
    ]]></literal>
    <justification jstring="[para(19696(a,1),6299(a,1))].">
      <j1 rule="para" parents="19696 6299"/>
    </justification>
  </clause>

  <clause id="19717">
    <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(19668(a,1),19355(a,2,2,1))].">
      <j1 rule="para" parents="19668 19355"/>
    </justification>
  </clause>

  <clause id="19718">
    <literal><![CDATA[
      L(x,y,L(z,u,K(w,v5)) \ v6) = L(x,y,z \ v6)
    ]]></literal>
    <justification jstring="[para(19685(a,1),15549(a,1,3))].">
      <j1 rule="para" parents="19685 15549"/>
    </justification>
  </clause>

  <clause id="19719">
    <literal><![CDATA[
      L(x,y,(a(z,u,w) * v5) \ v6) = L(x,y,(v5 * a(z,u,w)) \ v6)
    ]]></literal>
    <justification jstring="[para(19710(a,1),19718(a,1,3,1))].">
      <j1 rule="para" parents="19710 19718"/>
    </justification>
  </clause>

  <clause id="19720">
    <literal><![CDATA[
      L(L(x,y,z),u,K(y,z)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(19671(a,2),19689(a,1))].">
      <j1 rule="para" parents="19671 19689"/>
    </justification>
  </clause>

  <clause id="19721">
    <literal><![CDATA[
      x / a(y,z,T(u,x)) = a(y,z,u) \ x
    ]]></literal>
    <justification jstring="[hyper(58,a,19680,a(flip),b,19683,a),flip(a)].">
      <j1 rule="hyper" parents="58 19680 19683"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19722">
    <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(19721(a,1),2266(a,1,1))].">
      <j1 rule="para" parents="19721 2266"/>
    </justification>
  </clause>

  <clause id="19723">
    <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(5443(a,1),19698(a,1,1))].">
      <j1 rule="para" parents="5443 19698"/>
    </justification>
  </clause>

  <clause id="19724">
    <literal><![CDATA[
      K(x,y \ ((z * y) * u)) = K(x,(y \ z) * (y * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,19703,a(flip),b,19706,a),flip(a)].">
      <j1 rule="hyper" parents="58 19703 19706"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19725">
    <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,19614,a(flip),b,19724,a),flip(a)].">
      <j1 rule="hyper" parents="58 19614 19724"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19726">
    <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(19713(a,1),15050(a,1,1,2))].">
      <j1 rule="para" parents="19713 15050"/>
    </justification>
  </clause>

  <clause id="19728">
    <literal><![CDATA[
      a(x \ (y \ (z \ u)),w,K(v5,v6)) = a(((u / z) \ y) * x,v6,K(v5,w))
    ]]></literal>
    <justification jstring="[hyper(18468,a,19662,a)].">
      <j1 rule="hyper" parents="18468 19662"/>
    </justification>
  </clause>

  <clause id="19729">
    <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(14384,a,19662,a),flip(a)].">
      <j1 rule="hyper" parents="14384 19662"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19730">
    <literal><![CDATA[
      a(x \ (y \ z),u,K(w,v5)) = a(z \ (y * x),v5,K(w,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,19592,a,b,19662,a),flip(a)].">
      <j1 rule="hyper" parents="320 19592 19662"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19731">
    <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(19663(a,2),19660(a,1))].">
      <j1 rule="para" parents="19663 19660"/>
    </justification>
  </clause>

  <clause id="19732">
    <literal><![CDATA[
      a(x \ (y * (z \ 1)),u,K(w,v5)) = a(w,v5,K(u,z * (y \ x)))
    ]]></literal>
    <justification jstring="[para(13775(a,1),19693(a,2,3))].">
      <j1 rule="para" parents="13775 19693"/>
    </justification>
  </clause>

  <clause id="19733">
    <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(19693(a,2),14387(a,1))].">
      <j1 rule="para" parents="19693 14387"/>
    </justification>
  </clause>

  <clause id="19734">
    <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(19693(a,2),19666(a,1))].">
      <j1 rule="para" parents="19693 19666"/>
    </justification>
  </clause>

  <clause id="19735">
    <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(10363(a,1),19730(a,2,1,2))].">
      <j1 rule="para" parents="10363 19730"/>
    </justification>
  </clause>

  <clause id="19736">
    <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(19633(a,2),14979(a,1))].">
      <j1 rule="para" parents="19633 14979"/>
    </justification>
  </clause>

  <clause id="19737">
    <literal><![CDATA[
      T(a(a(x,y,z),u,w) \ 1,v5) = a(a(x,y,z),u,w) \ 1
    ]]></literal>
    <justification jstring="[hyper(239,a,19678,a(flip),b,19624,a(flip))].">
      <j1 rule="hyper" parents="239 19678 19624"/>
    </justification>
  </clause>

  <clause id="19738">
    <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,19709,a),flip(a)].">
      <j1 rule="hyper" parents="116 5 19709"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19739">
    <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(19354(a,2),19709(a,1,2))].">
      <j1 rule="para" parents="19354 19709"/>
    </justification>
  </clause>

  <clause id="19740">
    <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,14263,a(flip),b,19732,a),flip(a)].">
      <j1 rule="hyper" parents="320 14263 19732"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19741">
    <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(19740(a,2),14349(a,1))].">
      <j1 rule="para" parents="19740 14349"/>
    </justification>
  </clause>

  <clause id="19742">
    <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,18466,a(flip),b,19694,a)].">
      <j1 rule="hyper" parents="58 18466 19694"/>
    </justification>
  </clause>

  <clause id="19743">
    <literal><![CDATA[
      T(x,y \ L(y,z,u)) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,19193,a(flip),b,19708,a)].">
      <j1 rule="hyper" parents="58 19193 19708"/>
    </justification>
  </clause>

  <clause id="19744">
    <literal><![CDATA[
      T(x,a(y,z,u) \ 1) = L(x,u,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(13382,a,19743,a)].">
      <j1 rule="hyper" parents="13382 19743"/>
    </justification>
  </clause>

  <clause id="19746">
    <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(19744(a,2),14171(a,1))].">
      <j1 rule="para" parents="19744 14171"/>
    </justification>
  </clause>

  <clause id="19747">
    <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(18837(a,2),19746(a,1))].">
      <j1 rule="para" parents="18837 19746"/>
    </justification>
  </clause>

  <clause id="19748">
    <literal><![CDATA[
      a(x,y,L(z,u,K(w,v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = v6
    ]]></literal>
    <justification jstring="[para(19744(a,1),19747(a,1,3))].">
      <j1 rule="para" parents="19744 19747"/>
    </justification>
  </clause>

  <clause id="19749">
    <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(13521(a,1),19748(a,1))].">
      <j1 rule="para" parents="13521 19748"/>
    </justification>
  </clause>

  <clause id="19750">
    <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(13521(a,2),19749(a,1))].">
      <j1 rule="para" parents="13521 19749"/>
    </justification>
  </clause>

  <clause id="19751">
    <literal><![CDATA[
      K(x,(y \ T(z,y)) * (y * u)) = K(x,(z * (u / y)) * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,19513,a(flip),b,19725,a)].">
      <j1 rule="hyper" parents="58 19513 19725"/>
    </justification>
  </clause>

  <clause id="19752">
    <literal><![CDATA[
      K(x,(y * (z / u)) * u) = K(x,(y / u) * (u * z))
    ]]></literal>
    <justification jstring="[hyper(58,a,15481,a(flip),b,19751,a),flip(a)].">
      <j1 rule="hyper" parents="58 15481 19751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19753">
    <literal><![CDATA[
      K(x,(y / z) * (z * (u \ 1))) = K(x,(y / (z * u)) * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,19616,a(flip),b,19752,a),flip(a)].">
      <j1 rule="hyper" parents="58 19616 19752"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19754">
    <literal><![CDATA[
      K(x,(y / (z * u)) * z) = K(x,(y / z) * (z / u))
    ]]></literal>
    <justification jstring="[hyper(19449,a,19753,a),flip(a)].">
      <j1 rule="hyper" parents="19449 19753"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19755">
    <literal><![CDATA[
      K(x,y \ ((y * z) / u)) = K(x,(z / y) * (y / u))
    ]]></literal>
    <justification jstring="[hyper(58,a,19582,a,b,19754,a)].">
      <j1 rule="hyper" parents="58 19582 19754"/>
    </justification>
  </clause>

  <clause id="19756">
    <literal><![CDATA[
      K(x,y \ ((y * (z * u)) / z)) = K(x,L(T(u,z),y,z))
    ]]></literal>
    <justification jstring="[hyper(320,a,19702,a(flip),b,19755,a),flip(a)].">
      <j1 rule="hyper" parents="320 19702 19755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19757">
    <literal><![CDATA[
      K(x,y / ((z * u) \ (u * y))) = K(x,L(T(z,u),y,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,19211,a,b,19756,a)].">
      <j1 rule="hyper" parents="58 19211 19756"/>
    </justification>
  </clause>

  <clause id="19758">
    <literal><![CDATA[
      x * K(y,L(T(z,u),x,u)) = (x * u) / (u * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(119,a,19757,a(flip),b,19129,a(flip))].">
      <j1 rule="hyper" parents="119 19757 19129"/>
    </justification>
  </clause>

  <clause id="19759">
    <literal><![CDATA[
      (x / (1 / y)) * (K(z,u) / y) = (x * y) / (y * K(u,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,19707,a,b,19758,a)].">
      <j1 rule="hyper" parents="58 19707 19758"/>
    </justification>
  </clause>

  <clause id="19760">
    <literal><![CDATA[
      (x * y) / (y * K(T(z,y),u)) = (x / (y \ 1)) * (y \ K(u,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,18701,a(flip),b,19759,a),flip(a)].">
      <j1 rule="hyper" parents="58 18701 19759"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19761">
    <literal><![CDATA[
      (x / (y \ 1)) * (y \ K(z,u)) = (x * y) / (K(u,z) * y)
    ]]></literal>
    <justification jstring="[para(7150(a,1),19760(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7150 19760"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19762">
    <literal><![CDATA[
      (x * (y / z)) / (K(u,y) * (y / z)) = (x / z) * (z * K(y,u))
    ]]></literal>
    <justification jstring="[hyper(19266,a,19761,a),flip(a)].">
      <j1 rule="hyper" parents="19266 19761"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19763">
    <literal><![CDATA[
      (x * (T(y,z) / u)) / (y / u) = (x / u) * (u * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,19303,a(flip),b,19762,a)].">
      <j1 rule="hyper" parents="58 19303 19762"/>
    </justification>
  </clause>

  <clause id="19764">
    <literal><![CDATA[
      ((x / y) * (y * K(z,u))) * K(u,z) = L(x,K(u,z),y \ z)
    ]]></literal>
    <justification jstring="[para(19763(a,1),19317(a,1,1))].">
      <j1 rule="para" parents="19763 19317"/>
    </justification>
  </clause>

  <clause id="19765">
    <literal><![CDATA[
      L(x,K(y,z),u \ z) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(19736,a,19764,a),flip(a)].">
      <j1 rule="hyper" parents="19736 19764"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19766">
    <literal><![CDATA[
      L(x,y,K(z,u \ z)) = L(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(58,a,17853,a(flip),b,19765,a),flip(a)].">
      <j1 rule="hyper" parents="58 17853 19765"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19767">
    <literal><![CDATA[
      L(x,K(y,z),u) = L(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(12699,a,19766,a),flip(a)].">
      <j1 rule="hyper" parents="12699 19766"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19768">
    <literal><![CDATA[
      L(x,K(y,z),u) = L(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(320,a,19671,a(flip),b,19767,a),flip(a)].">
      <j1 rule="hyper" parents="320 19671 19767"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19770">
    <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(19768(a,1),14249(a,1,1))].">
      <j1 rule="para" parents="19768 14249"/>
    </justification>
  </clause>

  <clause id="19771">
    <literal><![CDATA[
      a(((x / y) \ z) * u,w,K(v5,v6)) = a(((y \ x) \ z) * u,w,K(v5,v6))
    ]]></literal>
    <justification jstring="[hyper(19691,a,19728,a),flip(a)].">
      <j1 rule="hyper" parents="19691 19728"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19773">
    <literal><![CDATA[
      K(((x * a(y,z,u)) * w) \ ((a(y,z,u) * (x * w)) * v5),v6) != v7
    ]]></literal>
    <literal><![CDATA[
      K(a(a(y,z,u),x,w) \ v5,v6) = v7
    ]]></literal>
    <justification jstring="[para(17971(a,1),19636(a,1))].">
      <j1 rule="para" parents="17971 19636"/>
    </justification>
  </clause>

  <clause id="19774">
    <literal><![CDATA[
      a(x,y,K(z * (T(u,w) \ v5),v6)) = a(z * (u \ v5),v6,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(19698,a,19670,a),flip(a)].">
      <j1 rule="hyper" parents="19698 19670"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19775">
    <literal><![CDATA[
      a((((x * y) / x) \ z) * u,w,K(v5,v6)) = a(u * (y \ z),v5,K(v6,w))
    ]]></literal>
    <justification jstring="[hyper(18390,a,19774,a)].">
      <j1 rule="hyper" parents="18390 19774"/>
    </justification>
  </clause>

  <clause id="19778">
    <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(19738(a,1),19739(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="19738 19739"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19779">
    <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(5130(a,1),19735(a,1,1))].">
      <j1 rule="para" parents="5130 19735"/>
    </justification>
  </clause>

  <clause id="19780">
    <literal><![CDATA[
      a((x * (y * z)) \ u,w,K(v5,v6)) = a(u \ (x * (z * y)),v6,K(v5,w))
    ]]></literal>
    <justification jstring="[hyper(19698,a,19779,a)].">
      <j1 rule="hyper" parents="19698 19779"/>
    </justification>
  </clause>

  <clause id="19781">
    <literal><![CDATA[
      a((x * y) \ (z \ u),w,K(v5,v6)) = a(u \ (z * (y * x)),v6,K(v5,w))
    ]]></literal>
    <justification jstring="[hyper(14514,a,19780,a)].">
      <j1 rule="hyper" parents="14514 19780"/>
    </justification>
  </clause>

  <clause id="19783">
    <literal><![CDATA[
      a(x \ (y \ (z \ u)),w,K(v5,v6)) = a(u \ (z * (x * y)),v6,K(v5,w))
    ]]></literal>
    <justification jstring="[hyper(14514,a,19781,a)].">
      <j1 rule="hyper" parents="14514 19781"/>
    </justification>
  </clause>

  <clause id="19784">
    <literal><![CDATA[
      a(x \ (y * (z * u)),w,K(v5,v6)) = a(((y \ x) \ u) * z,w,K(v5,v6))
    ]]></literal>
    <justification jstring="[hyper(19691,a,19783,a),flip(a)].">
      <j1 rule="hyper" parents="19691 19783"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19785">
    <literal><![CDATA[
      a(((x \ y) \ z) * u,w,K(v5,v6)) = a((y \ x) * (u * z),w,K(v5,v6))
    ]]></literal>
    <justification jstring="[hyper(19594,a,19784,a),flip(a)].">
      <j1 rule="hyper" parents="19594 19784"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19786">
    <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,19771,a,b,19785,a)].">
      <j1 rule="hyper" parents="58 19771 19785"/>
    </justification>
  </clause>

  <clause id="19787">
    <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,19775,a(flip),b,19786,a),flip(a)].">
      <j1 rule="hyper" parents="58 19775 19786"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19788">
    <literal><![CDATA[
      a(x \ (y * z),u,K(w,v5)) = a(y * (x \ z),w,K(v5,u))
    ]]></literal>
    <justification jstring="[hyper(19731,a,19787,a)].">
      <j1 rule="hyper" parents="19731 19787"/>
    </justification>
  </clause>

  <clause id="19789">
    <literal><![CDATA[
      a(x * (y \ (z \ 1)),u,K(w,v5)) = a(u,w,K(v5,z * (x \ y)))
    ]]></literal>
    <justification jstring="[hyper(19741,a,19788,a),flip(a)].">
      <j1 rule="hyper" parents="19741 19788"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19790">
    <literal><![CDATA[
      a(x * (y \ z),u,K(w,v5)) = a(v5,u,K(w,z \ (x \ y)))
    ]]></literal>
    <justification jstring="[hyper(19734,a,19788,a),flip(a)].">
      <j1 rule="hyper" parents="19734 19788"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19791">
    <literal><![CDATA[
      a(x \ (y \ z),u,K(w,v5)) = a(y * (z \ x),w,K(u,v5))
    ]]></literal>
    <justification jstring="[hyper(19733,a,19788,a)].">
      <j1 rule="hyper" parents="19733 19788"/>
    </justification>
  </clause>

  <clause id="19792">
    <literal><![CDATA[
      a(x * (y \ z),u,K(w,v5)) = a(z * (y \ x),v5,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(19597,a,19788,a),flip(a)].">
      <j1 rule="hyper" parents="19597 19788"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19793">
    <literal><![CDATA[
      a((x \ y) * z,u,K(w,v5)) = a(y * (x \ z),w,K(v5,u))
    ]]></literal>
    <justification jstring="[hyper(19594,a,19788,a)].">
      <j1 rule="hyper" parents="19594 19788"/>
    </justification>
  </clause>

  <clause id="19794">
    <literal><![CDATA[
      a(x * (y \ z),u,K(w,v5)) = a(u,v5,K(w,y \ (x * z)))
    ]]></literal>
    <justification jstring="[hyper(14349,a,19788,a),flip(a)].">
      <j1 rule="hyper" parents="14349 19788"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19795">
    <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(19788(a,2),19667(a,1))].">
      <j1 rule="para" parents="19788 19667"/>
    </justification>
  </clause>

  <clause id="19796">
    <literal><![CDATA[
      a(x \ (y \ z),u,K(w,v5)) = a(y * (z \ x),u,K(v5,w))
    ]]></literal>
    <justification jstring="[hyper(320,a,14263,a(flip),b,19790,a)].">
      <j1 rule="hyper" parents="320 14263 19790"/>
    </justification>
  </clause>

  <clause id="19797">
    <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),19790(a,2,3,2,2))].">
      <j1 rule="para" parents="4 19790"/>
    </justification>
  </clause>

  <clause id="19798">
    <literal><![CDATA[
      a(x * (y \ z),u,K(w,v5)) = a(w,u,K(v5,z * (y \ x)))
    ]]></literal>
    <justification jstring="[hyper(19655,a,19792,a),flip(a)].">
      <j1 rule="hyper" parents="19655 19792"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19799">
    <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(19792(a,2),19654(a,1))].">
      <j1 rule="para" parents="19792 19654"/>
    </justification>
  </clause>

  <clause id="19800">
    <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(19792(a,2),19667(a,1))].">
      <j1 rule="para" parents="19792 19667"/>
    </justification>
  </clause>

  <clause id="19801">
    <literal><![CDATA[
      a((x / y) * z,u,K(w,v5)) = a(x * (y \ z),w,K(v5,u))
    ]]></literal>
    <justification jstring="[hyper(19723,a,19793,a)].">
      <j1 rule="hyper" parents="19723 19793"/>
    </justification>
  </clause>

  <clause id="19802">
    <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),19794(a,2,3,2,2))].">
      <j1 rule="para" parents="5 19794"/>
    </justification>
  </clause>

  <clause id="19803">
    <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(19796(a,2),19667(a,1))].">
      <j1 rule="para" parents="19796 19667"/>
    </justification>
  </clause>

  <clause id="19804">
    <literal><![CDATA[
      a(x * (y \ (x \ z)),u,K(w,v5)) = a(w,u,K(v5,y \ z))
    ]]></literal>
    <justification jstring="[hyper(19667,a,19802,a)].">
      <j1 rule="hyper" parents="19667 19802"/>
    </justification>
  </clause>

  <clause id="19805">
    <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(19804(a,2),19647(a,1))].">
      <j1 rule="para" parents="19804 19647"/>
    </justification>
  </clause>

  <clause id="19806">
    <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,19651,a(flip),b,19789,a),flip(a)].">
      <j1 rule="hyper" parents="320 19651 19789"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19807">
    <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(3588(a,1),19799(a,1,1,2))].">
      <j1 rule="para" parents="3588 19799"/>
    </justification>
  </clause>

  <clause id="19808">
    <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(18336(a,1),19800(a,1))].">
      <j1 rule="para" parents="18336 19800"/>
    </justification>
  </clause>

  <clause id="19809">
    <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,15076,a(flip),b,19726,a)].">
      <j1 rule="hyper" parents="58 15076 19726"/>
    </justification>
  </clause>

  <clause id="19810">
    <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(6197(a,2),19809(a,1,1,2))].">
      <j1 rule="para" parents="6197 19809"/>
    </justification>
  </clause>

  <clause id="19811">
    <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,15076,a(flip),b,19810,a)].">
      <j1 rule="hyper" parents="58 15076 19810"/>
    </justification>
  </clause>

  <clause id="19812">
    <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(19676(a,1),19770(a,1,1)),flip(a)].">
      <j1 rule="para" parents="19676 19770"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19813">
    <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(4208(a,1),19812(a,2,1))].">
      <j1 rule="para" parents="4208 19812"/>
    </justification>
  </clause>

  <clause id="19814">
    <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,13960,a(flip),b,19813,a),flip(a)].">
      <j1 rule="hyper" parents="320 13960 19813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19815">
    <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),19814(a,2,1))].">
      <j1 rule="para" parents="17 19814"/>
    </justification>
  </clause>

  <clause id="19816">
    <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(7877(a,1),19815(a,1,1,2,2))].">
      <j1 rule="para" parents="7877 19815"/>
    </justification>
  </clause>

  <clause id="19817">
    <literal><![CDATA[
      T(x * K(y,z * x),z) = T(x,z) * K(y,x * z)
    ]]></literal>
    <justification jstring="[para(12332(a,1),19816(a,1,1,2))].">
      <j1 rule="para" parents="12332 19816"/>
    </justification>
  </clause>

  <clause id="19818">
    <literal><![CDATA[
      x \ T(x * K(y,z * x),z) = K(y,x * z) * K(x,z)
    ]]></literal>
    <justification jstring="[hyper(116,a,19817,a,b,15677,a)].">
      <j1 rule="hyper" parents="116 19817 15677"/>
    </justification>
  </clause>

  <clause id="19819">
    <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(19817(a,2),19811(a,1,1,2,2,1))].">
      <j1 rule="para" parents="19817 19811"/>
    </justification>
  </clause>

  <clause id="19820">
    <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(19672(a,2),19682(a,1,1))].">
      <j1 rule="para" parents="19672 19682"/>
    </justification>
  </clause>

  <clause id="19821">
    <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(19672(a,2),19820(a,1,2,1,1))].">
      <j1 rule="para" parents="19672 19820"/>
    </justification>
  </clause>

  <clause id="19822">
    <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(19672(a,2),19821(a,1,2,1,2))].">
      <j1 rule="para" parents="19672 19821"/>
    </justification>
  </clause>

  <clause id="19823">
    <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(19806(a,1),19807(a,1))].">
      <j1 rule="para" parents="19806 19807"/>
    </justification>
  </clause>

  <clause id="19824">
    <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(19721(a,1),19722(a,1,2,2,1,2,1))].">
      <j1 rule="para" parents="19721 19722"/>
    </justification>
  </clause>

  <clause id="19825">
    <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(19778(a,1),19824(a,1,2))].">
      <j1 rule="para" parents="19778 19824"/>
    </justification>
  </clause>

  <clause id="19826">
    <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,13472,a(flip),b,19825,a)].">
      <j1 rule="hyper" parents="58 13472 19825"/>
    </justification>
  </clause>

  <clause id="19828">
    <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(19672(a,2),19826(a,1,1))].">
      <j1 rule="para" parents="19672 19826"/>
    </justification>
  </clause>

  <clause id="19829">
    <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(19672(a,2),19828(a,1,2,1,1))].">
      <j1 rule="para" parents="19672 19828"/>
    </justification>
  </clause>

  <clause id="19830">
    <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,19822,a(flip),b,19829,a)].">
      <j1 rule="hyper" parents="58 19822 19829"/>
    </justification>
  </clause>

  <clause id="19832">
    <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,19717,a,b,19830,a)].">
      <j1 rule="hyper" parents="320 19717 19830"/>
    </justification>
  </clause>

  <clause id="19833">
    <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(19641(a,1),19832(a,1,1))].">
      <j1 rule="para" parents="19641 19832"/>
    </justification>
  </clause>

  <clause id="19834">
    <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,19649,a,b,19833,a)].">
      <j1 rule="hyper" parents="30 19649 19833"/>
    </justification>
  </clause>

  <clause id="19835">
    <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,14263,a(flip),b,19834,a),flip(a)].">
      <j1 rule="hyper" parents="320 14263 19834"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19836">
    <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(1699(a,1),19834(a,1,3,2))].">
      <j1 rule="para" parents="1699 19834"/>
    </justification>
  </clause>

  <clause id="19837">
    <literal><![CDATA[
      a(x,y,K(z,L(u,w,v5) * v6)) = a(u * v6,x,K(z,y))
    ]]></literal>
    <justification jstring="[para(634(a,1),19835(a,1,3,2))].">
      <j1 rule="para" parents="634 19835"/>
    </justification>
  </clause>

  <clause id="19838">
    <literal><![CDATA[
      a(x * L(y,z,u),w,K(v5,v6)) = a(y * x,w,K(v5,v6))
    ]]></literal>
    <justification jstring="[hyper(19661,a,19837,a)].">
      <j1 rule="hyper" parents="19661 19837"/>
    </justification>
  </clause>

  <clause id="19839">
    <literal><![CDATA[
      a(L(x,y,z) * u,w,K(v5,v6)) = a(x * u,v6,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(19654,a,19837,a)].">
      <j1 rule="hyper" parents="19654 19837"/>
    </justification>
  </clause>

  <clause id="19840">
    <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(19808,a,19838,a)].">
      <j1 rule="hyper" parents="19808 19838"/>
    </justification>
  </clause>

  <clause id="19841">
    <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(19839(a,1),19823(a,1))].">
      <j1 rule="para" parents="19839 19823"/>
    </justification>
  </clause>

  <clause id="19842">
    <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(19660,a,19836,a)].">
      <j1 rule="hyper" parents="19660 19836"/>
    </justification>
  </clause>

  <clause id="19843">
    <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,19792,a(flip),b,19840,a),flip(a)].">
      <j1 rule="hyper" parents="320 19792 19840"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19844">
    <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(19842(a,1),19795(a,1))].">
      <j1 rule="para" parents="19842 19795"/>
    </justification>
  </clause>

  <clause id="19845">
    <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(19843(a,2),19800(a,1))].">
      <j1 rule="para" parents="19843 19800"/>
    </justification>
  </clause>

  <clause id="19846">
    <literal><![CDATA[
      a(x * (y \ L(x \ 1,z,u)),w,K(v5,v6)) = a(v5,v6,K(w,y))
    ]]></literal>
    <justification jstring="[hyper(19844,a,19645,a)].">
      <j1 rule="hyper" parents="19844 19645"/>
    </justification>
  </clause>

  <clause id="19847">
    <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,19797,a(flip),b,19846,a)].">
      <j1 rule="hyper" parents="58 19797 19846"/>
    </justification>
  </clause>

  <clause id="19848">
    <literal><![CDATA[
      a(L(x \ 1,y,z) \ u,w,K(v5,v6)) = a(v6,v5,K(w,x * u))
    ]]></literal>
    <justification jstring="[hyper(14387,a,19847,a)].">
      <j1 rule="hyper" parents="14387 19847"/>
    </justification>
  </clause>

  <clause id="19849">
    <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,19742,a(flip),b,19848,a)].">
      <j1 rule="hyper" parents="58 19742 19848"/>
    </justification>
  </clause>

  <clause id="19850">
    <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,19665,a(flip),b,19849,a),flip(a)].">
      <j1 rule="hyper" parents="320 19665 19849"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19851">
    <literal><![CDATA[
      a(x,y,K(z,u \ L(w,v5,v6))) = a(y,x,K(z,w \ u))
    ]]></literal>
    <justification jstring="[para(13850(a,1),19849(a,2,3))].">
      <j1 rule="para" parents="13850 19849"/>
    </justification>
  </clause>

  <clause id="19852">
    <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(19850(a,2),19655(a,1))].">
      <j1 rule="para" parents="19850 19655"/>
    </justification>
  </clause>

  <clause id="19853">
    <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,19729,a,b,19851,a)].">
      <j1 rule="hyper" parents="58 19729 19851"/>
    </justification>
  </clause>

  <clause id="19855">
    <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,19575,a(flip),b,19853,a),flip(a)].">
      <j1 rule="hyper" parents="320 19575 19853"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19856">
    <literal><![CDATA[
      a(x,y,K(z,u * ((w * v5) \ (w * v6)))) = a(x,y,K(z,u * (v5 \ v6)))
    ]]></literal>
    <justification jstring="[hyper(19650,a,19855,a)].">
      <j1 rule="hyper" parents="19650 19855"/>
    </justification>
  </clause>

  <clause id="19857">
    <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(14038(a,1),19856(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="14038 19856"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19858">
    <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(19841,a,19801,a)].">
      <j1 rule="hyper" parents="19841 19801"/>
    </justification>
  </clause>

  <clause id="19860">
    <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),19858(a,2,1))].">
      <j1 rule="para" parents="2 19858"/>
    </justification>
  </clause>

  <clause id="19861">
    <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,19791,a(flip),b,19860,a),flip(a)].">
      <j1 rule="hyper" parents="320 19791 19860"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19862">
    <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),19861(a,2,1,2))].">
      <j1 rule="para" parents="61 19861"/>
    </justification>
  </clause>

  <clause id="19863">
    <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),19862(a,2,1))].">
      <j1 rule="para" parents="3 19862"/>
    </justification>
  </clause>

  <clause id="19865">
    <literal><![CDATA[
      a(x,y,K(z,u \ (L(u \ 1,w,v5) \ v6))) = a(v6,z,K(y,x))
    ]]></literal>
    <justification jstring="[para(13850(a,1),19863(a,1,3))].">
      <j1 rule="para" parents="13850 19863"/>
    </justification>
  </clause>

  <clause id="19866">
    <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(19686(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="19686 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19867">
    <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(14323(a,1),19687(a,1,1))].">
      <j1 rule="para" parents="14323 19687"/>
    </justification>
  </clause>

  <clause id="19868">
    <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(19354(a,2),19867(a,1,1))].">
      <j1 rule="para" parents="19354 19867"/>
    </justification>
  </clause>

  <clause id="19869">
    <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(14938(a,1),19868(a,1,1,1))].">
      <j1 rule="para" parents="14938 19868"/>
    </justification>
  </clause>

  <clause id="19870">
    <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(5468,a,19869,a),flip(a)].">
      <j1 rule="hyper" parents="5468 19869"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19872">
    <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,19692,a(flip),b,19870,a),flip(a)].">
      <j1 rule="hyper" parents="34 19692 19870"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19873">
    <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(17245,a,19872,a)].">
      <j1 rule="hyper" parents="17245 19872"/>
    </justification>
  </clause>

  <clause id="19874">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (L(z,x,u) \ z) = T(L(z,x,u) \ z,y)
    ]]></literal>
    <justification jstring="[hyper(19866,a,19873,a)].">
      <j1 rule="hyper" parents="19866 19873"/>
    </justification>
  </clause>

  <clause id="19875">
    <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,19874,a)].">
      <j1 rule="hyper" parents="294 19874"/>
    </justification>
  </clause>

  <clause id="19877">
    <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,17500,a,b,19875,a)].">
      <j1 rule="hyper" parents="58 17500 19875"/>
    </justification>
  </clause>

  <clause id="19878">
    <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(19658(a,2),19877(a,1,1,2))].">
      <j1 rule="para" parents="19658 19877"/>
    </justification>
  </clause>

  <clause id="19879">
    <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(14281(a,2),19878(a,1,1,2))].">
      <j1 rule="para" parents="14281 19878"/>
    </justification>
  </clause>

  <clause id="19880">
    <literal><![CDATA[
      T(L(x,y,z) \ x,x \ u) = T(L(x,y,z) \ x,u)
    ]]></literal>
    <justification jstring="[hyper(6332,a,19879,a)].">
      <j1 rule="hyper" parents="6332 19879"/>
    </justification>
  </clause>

  <clause id="19881">
    <literal><![CDATA[
      T(L(x,y,z) \ x,x * u) = T(L(x,y,z) \ x,u)
    ]]></literal>
    <justification jstring="[para(4(a,1),19880(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4 19880"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19882">
    <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(19880(a,1),11760(a,1))].">
      <j1 rule="para" parents="19880 11760"/>
    </justification>
  </clause>

  <clause id="19883">
    <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(13368(a,1),19882(a,1))].">
      <j1 rule="para" parents="13368 19882"/>
    </justification>
  </clause>

  <clause id="19885">
    <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(19881(a,1),19883(a,1))].">
      <j1 rule="para" parents="19881 19883"/>
    </justification>
  </clause>

  <clause id="19886">
    <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(13368(a,1),19885(a,1))].">
      <j1 rule="para" parents="13368 19885"/>
    </justification>
  </clause>

  <clause id="19887">
    <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(19886,a,6075,a)].">
      <j1 rule="hyper" parents="19886 6075"/>
    </justification>
  </clause>

  <clause id="19889">
    <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(11759(a,1),19887(a,1,1))].">
      <j1 rule="para" parents="11759 19887"/>
    </justification>
  </clause>

  <clause id="19890">
    <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(19889(a,1),19798(a,2,3,2,2))].">
      <j1 rule="para" parents="19889 19798"/>
    </justification>
  </clause>

  <clause id="19891">
    <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,19839,a(flip),b,19890,a)].">
      <j1 rule="hyper" parents="58 19839 19890"/>
    </justification>
  </clause>

  <clause id="19892">
    <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(19808,a,19891,a)].">
      <j1 rule="hyper" parents="19808 19891"/>
    </justification>
  </clause>

  <clause id="19894">
    <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),19892(a,1,1))].">
      <j1 rule="para" parents="2 19892"/>
    </justification>
  </clause>

  <clause id="19895">
    <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(19803,a,19894,a)].">
      <j1 rule="hyper" parents="19803 19894"/>
    </justification>
  </clause>

  <clause id="19896">
    <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(19845,a,19895,a)].">
      <j1 rule="hyper" parents="19845 19895"/>
    </justification>
  </clause>

  <clause id="19897">
    <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(19805,a,19896,a)].">
      <j1 rule="hyper" parents="19805 19896"/>
    </justification>
  </clause>

  <clause id="19899">
    <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(19852,a,19897,a)].">
      <j1 rule="hyper" parents="19852 19897"/>
    </justification>
  </clause>

  <clause id="19902">
    <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(14675(a,1),19899(a,1,3))].">
      <j1 rule="para" parents="14675 19899"/>
    </justification>
  </clause>

  <clause id="19903">
    <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,19865,a(flip),b,19902,a),flip(a)].">
      <j1 rule="hyper" parents="58 19865 19902"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19905">
    <literal><![CDATA[
      a(x,y,K(z,u * a(w,v5,v6))) = a(u,x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,19857,a(flip),b,19903,a)].">
      <j1 rule="hyper" parents="58 19857 19903"/>
    </justification>
  </clause>

  <clause id="19906">
    <literal><![CDATA[
      a(a(x,y,z) * u,w,K(v5,v6)) = a(u,w,K(v5,v6))
    ]]></literal>
    <justification jstring="[hyper(19661,a,19905,a)].">
      <j1 rule="hyper" parents="19661 19905"/>
    </justification>
  </clause>

  <clause id="19908">
    <literal><![CDATA[
      x * a(y,x,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,u,K(z,y * a(v5,v6,v7))) = w
    ]]></literal>
    <justification jstring="[para(19905(a,1),14957(a,1,2))].">
      <j1 rule="para" parents="19905 14957"/>
    </justification>
  </clause>

  <clause id="19909">
    <literal><![CDATA[
      a(x * (y \ a(z,u,w)),v5,K(v6,v7)) = a(y \ x,v7,K(v5,v6))
    ]]></literal>
    <justification jstring="[hyper(19800,a,19906,a)].">
      <j1 rule="hyper" parents="19800 19906"/>
    </justification>
  </clause>

  <clause id="19910">
    <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),19906(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5 19906"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19912">
    <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(19909(a,1),14292(a,1,2,2))].">
      <j1 rule="para" parents="19909 14292"/>
    </justification>
  </clause>

  <clause id="19913">
    <literal><![CDATA[
      L(x,y,K(z,u * a(w,v5,v6))) = L(x,u,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(19908,a,19640,a)].">
      <j1 rule="hyper" parents="19908 19640"/>
    </justification>
  </clause>

  <clause id="19914">
    <literal><![CDATA[
      L(x,a(y,z,u) * w,K(v5,v6)) = L(x,w,K(v5,v6))
    ]]></literal>
    <justification jstring="[hyper(19681,a,19913,a)].">
      <j1 rule="hyper" parents="19681 19913"/>
    </justification>
  </clause>

  <clause id="19915">
    <literal><![CDATA[
      L(L(x,y,z),u,K(y,z)) = L(x,y,T(z,a(w,v5,v6) * u))
    ]]></literal>
    <justification jstring="[hyper(19720,a,19914,a),flip(a)].">
      <j1 rule="hyper" parents="19720 19914"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19916">
    <literal><![CDATA[
      L(x,y,T(z,a(u,w,v5) * v6)) = L(x,y,T(z,v6))
    ]]></literal>
    <justification jstring="[hyper(19720,a,19915,a),flip(a)].">
      <j1 rule="hyper" parents="19720 19915"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19917">
    <literal><![CDATA[
      L(x,y,T(z,u * a(w,v5,v6))) = L(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(17308,a,19916,a)].">
      <j1 rule="hyper" parents="17308 19916"/>
    </justification>
  </clause>

  <clause id="19918">
    <literal><![CDATA[
      L(x,y,T(z / (u * a(w,v5,v6)),u)) = L(x,y,(u * a(w,v5,v6)) \ z)
    ]]></literal>
    <justification jstring="[para(107(a,1),19917(a,1,3)),flip(a)].">
      <j1 rule="para" parents="107 19917"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19919">
    <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(19910(a,1),19912(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="19910 19912"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19920">
    <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,19669,a(flip),b,19919,a),flip(a)].">
      <j1 rule="hyper" parents="320 19669 19919"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19922">
    <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(19711,a,19920,a)].">
      <j1 rule="hyper" parents="19711 19920"/>
    </justification>
  </clause>

  <clause id="19923">
    <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(19922(a,2),476(a,1,2,2))].">
      <j1 rule="para" parents="19922 476"/>
    </justification>
  </clause>

  <clause id="19924">
    <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(19677(a,1),19923(a,1,2))].">
      <j1 rule="para" parents="19677 19923"/>
    </justification>
  </clause>

  <clause id="19925">
    <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(833,a,19924,a)].">
      <j1 rule="hyper" parents="833 19924"/>
    </justification>
  </clause>

  <clause id="19926">
    <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,14042,a(flip),b,19925,a),flip(a)].">
      <j1 rule="hyper" parents="58 14042 19925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19928">
    <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,19347,a(flip),b,19926,a)].">
      <j1 rule="hyper" parents="58 19347 19926"/>
    </justification>
  </clause>

  <clause id="19930">
    <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(19928(a,1),475(a,1,1,2,2))].">
      <j1 rule="para" parents="19928 475"/>
    </justification>
  </clause>

  <clause id="19931">
    <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,12107,a(flip),b,19930,a),flip(a)].">
      <j1 rule="hyper" parents="58 12107 19930"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19932">
    <literal><![CDATA[
      a(K(x,y) * z,u,a(w,v5,v6)) = a(z,u,a(w,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(19750,a,19931,a)].">
      <j1 rule="hyper" parents="19750 19931"/>
    </justification>
  </clause>

  <clause id="19935">
    <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,18953,a(flip),b,19932,a)].">
      <j1 rule="hyper" parents="58 18953 19932"/>
    </justification>
  </clause>

  <clause id="19936">
    <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,18941,a(flip),b,19932,a)].">
      <j1 rule="hyper" parents="58 18941 19932"/>
    </justification>
  </clause>

  <clause id="19937">
    <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,18938,a(flip),b,19932,a)].">
      <j1 rule="hyper" parents="58 18938 19932"/>
    </justification>
  </clause>

  <clause id="19938">
    <literal><![CDATA[
      a(T(x,y) \ z,u,a(w,v5,v6)) = a(x \ z,u,a(w,v5,v6))
    ]]></literal>
    <justification jstring="[para(5081(a,1),19932(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5081 19932"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19939">
    <literal><![CDATA[
      a(x \ (y / z),u,a(w,v5,v6)) = a(x \ (z \ y),u,a(w,v5,v6))
    ]]></literal>
    <justification jstring="[para(13963(a,1),19935(a,1,1))].">
      <j1 rule="para" parents="13963 19935"/>
    </justification>
  </clause>

  <clause id="19940">
    <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,16832,a(flip),b,19937,a),flip(a)].">
      <j1 rule="hyper" parents="58 16832 19937"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19942">
    <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,19939,a(flip),b,19940,a)].">
      <j1 rule="hyper" parents="58 19939 19940"/>
    </justification>
  </clause>

  <clause id="19943">
    <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(13720(a,1),19942(a,1,1,2,2))].">
      <j1 rule="para" parents="13720 19942"/>
    </justification>
  </clause>

  <clause id="19944">
    <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(5130(a,1),19943(a,1,1))].">
      <j1 rule="para" parents="5130 19943"/>
    </justification>
  </clause>

  <clause id="19945">
    <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,19932,a(flip),b,19944,a),flip(a)].">
      <j1 rule="hyper" parents="58 19932 19944"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19947">
    <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,19819,a(flip),b,19945,a),flip(a)].">
      <j1 rule="hyper" parents="58 19819 19945"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19949">
    <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(19818(a,1),19947(a,1,1,2))].">
      <j1 rule="para" parents="19818 19947"/>
    </justification>
  </clause>

  <clause id="19950">
    <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(6366(a,2),19949(a,1,1))].">
      <j1 rule="para" parents="6366 19949"/>
    </justification>
  </clause>

  <clause id="19951">
    <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,18940,a(flip),b,19950,a)].">
      <j1 rule="hyper" parents="58 18940 19950"/>
    </justification>
  </clause>

  <clause id="19952">
    <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,19936,a(flip),b,19951,a),flip(a)].">
      <j1 rule="hyper" parents="58 19936 19951"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19954">
    <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,19938,a(flip),b,19952,a),flip(a)].">
      <j1 rule="hyper" parents="320 19938 19952"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19956">
    <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(19954(a,1),14859(a,1,1))].">
      <j1 rule="para" parents="19954 14859"/>
    </justification>
  </clause>

  <clause id="19957">
    <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,19956,a),flip(a)].">
      <j1 rule="hyper" parents="207 19956"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19960">
    <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(14828(a,1),19957(a,1,1))].">
      <j1 rule="para" parents="14828 19957"/>
    </justification>
  </clause>

  <clause id="19961">
    <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,18945,a(flip),b,19960,a),flip(a)].">
      <j1 rule="hyper" parents="320 18945 19960"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19962">
    <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(15087(a,1),19961(a,1,1))].">
      <j1 rule="para" parents="15087 19961"/>
    </justification>
  </clause>

  <clause id="19963">
    <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(4064(a,1),19962(a,1,1))].">
      <j1 rule="para" parents="4064 19962"/>
    </justification>
  </clause>

  <clause id="19965">
    <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,15077,a(flip),b,19963,a),flip(a)].">
      <j1 rule="hyper" parents="320 15077 19963"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19966">
    <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),19965(a,2,1))].">
      <j1 rule="para" parents="4 19965"/>
    </justification>
  </clause>

  <clause id="19968">
    <literal><![CDATA[
      (a(x,y,a(z,u,w)) * v5) * v6 = a(x,y,a(z,u,w)) * (v5 * v6)
    ]]></literal>
    <justification jstring="[para(19966(a,1),101(a,1,1)),flip(a)].">
      <j1 rule="para" parents="19966 101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19969">
    <literal><![CDATA[
      L(x,y,a(z,u,a(w,v5,v6))) = x
    ]]></literal>
    <justification jstring="[hyper(4028,a,19968,a)].">
      <j1 rule="hyper" parents="4028 19968"/>
    </justification>
  </clause>

  <clause id="19970">
    <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,13436,a(flip),b,19968,a),flip(a)].">
      <j1 rule="hyper" parents="320 13436 19968"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19971">
    <literal><![CDATA[
      a(a(x,y,a(z,u,w)),v5,v6) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,19968,a(flip),b,80,a),flip(a)].">
      <j1 rule="hyper" parents="115 19968 80"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19972">
    <literal><![CDATA[
      (a(x,y,a(z,u,w)) * v5) \ v6 = a(x,y,a(z,u,w)) \ (v5 \ v6)
    ]]></literal>
    <justification jstring="[hyper(58,a,13457,a(flip),b,19969,a)].">
      <j1 rule="hyper" parents="58 13457 19969"/>
    </justification>
  </clause>

  <clause id="19973">
    <literal><![CDATA[
      a(x,a(y,z,a(u,w,v5)),v6) = 1
    ]]></literal>
    <justification jstring="[hyper(58,a,13488,a(flip),b,19971,a)].">
      <j1 rule="hyper" parents="58 13488 19971"/>
    </justification>
  </clause>

  <clause id="19974">
    <literal><![CDATA[
      (x * a(y,z,a(u,w,v5))) * v6 = x * (a(y,z,a(u,w,v5)) * v6)
    ]]></literal>
    <justification jstring="[hyper(14747,a,19973,a)].">
      <j1 rule="hyper" parents="14747 19973"/>
    </justification>
  </clause>

  <clause id="19976">
    <literal><![CDATA[
      L(x,a(y,z,a(u,w,v5)),v6) = x
    ]]></literal>
    <justification jstring="[hyper(47,a,19973,a)].">
      <j1 rule="hyper" parents="47 19973"/>
    </justification>
  </clause>

  <clause id="19977">
    <literal><![CDATA[
      (x * (a(y,z,a(u,w,v5)) * v6)) \ ((x * a(y,z,a(u,w,v5))) * (v6 * v7)) = L(v7,L(v6,a(y,z,a(u,w,v5)),x),x * a(y,z,a(u,w,v5)))
    ]]></literal>
    <justification jstring="[para(19976(a,1),476(a,1,2,2,1))].">
      <j1 rule="para" parents="19976 476"/>
    </justification>
  </clause>

  <clause id="19978">
    <literal><![CDATA[
      (x * (y * a(z,u,a(w,v5,v6)))) * v7 = (x * y) * (v7 * a(z,u,a(w,v5,v6)))
    ]]></literal>
    <justification jstring="[para(13436(a,1),19970(a,1,1))].">
      <j1 rule="para" parents="13436 19970"/>
    </justification>
  </clause>

  <clause id="19980">
    <literal><![CDATA[
      (x * (a(y,z,a(u,w,v5)) * v6)) \ v7 = a(y,z,a(u,w,v5)) \ ((x * v6) \ v7)
    ]]></literal>
    <justification jstring="[hyper(58,a,13453,a(flip),b,19972,a)].">
      <j1 rule="hyper" parents="58 13453 19972"/>
    </justification>
  </clause>

  <clause id="19981">
    <literal><![CDATA[
      (a(x,y,a(z,u,w)) * (v5 * v6)) \ (v6 * (a(x,y,a(z,u,w)) * v5)) = K(v6 * a(x,y,a(z,u,w)),v5)
    ]]></literal>
    <justification jstring="[para(19974(a,1),13448(a,1,2))].">
      <j1 rule="para" parents="19974 13448"/>
    </justification>
  </clause>

  <clause id="19982">
    <literal><![CDATA[
      (x * (y * a(z,u,a(w,v5,v6)))) * z = (x * y) * R(z,u,a(w,v5,v6))
    ]]></literal>
    <justification jstring="[para(14824(a,1),19978(a,2,2))].">
      <j1 rule="para" parents="14824 19978"/>
    </justification>
  </clause>

  <clause id="19983">
    <literal><![CDATA[
      K(T((x * y) * a(z,u,w),x) \ v5,v6) = K(((y * a(z,u,w)) * R(x,y,a(z,u,w))) \ v5,v6)
    ]]></literal>
    <justification jstring="[para(19982(a,1),13155(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="19982 13155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19984">
    <literal><![CDATA[
      K(T(x * y,x) \ (a(z,u,w) \ v5),v6) = K(((y * a(z,u,w)) * R(x,y,a(z,u,w))) \ v5,v6)
    ]]></literal>
    <justification jstring="[hyper(58,a,19276,a(flip),b,19983,a)].">
      <j1 rule="hyper" parents="58 19276 19983"/>
    </justification>
  </clause>

  <clause id="19985">
    <literal><![CDATA[
      K(((x * a(y,z,u)) * R(w,x,a(y,z,u))) \ v5,v6) = K((x * w) \ (a(y,z,u) \ v5),v6)
    ]]></literal>
    <justification jstring="[hyper(58,a,13031,a(flip),b,19984,a),flip(a)].">
      <j1 rule="hyper" parents="58 13031 19984"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19986">
    <literal><![CDATA[
      ((a(x,y,a(z,u,w)) * (v5 * v6)) \ (v6 * v5)) * a(x,y,a(z,u,w)) = K(v6 * a(x,y,a(z,u,w)),v5)
    ]]></literal>
    <justification jstring="[hyper(58,a,13440,a(flip),b,19981,a)].">
      <j1 rule="hyper" parents="58 13440 19981"/>
    </justification>
  </clause>

  <clause id="19987">
    <literal><![CDATA[
      (a(x,y,a(z,u,w)) \ K(v5,v6)) * a(x,y,a(z,u,w)) = K(v5 * a(x,y,a(z,u,w)),v6)
    ]]></literal>
    <justification jstring="[para(14701(a,1),19986(a,1,1))].">
      <j1 rule="para" parents="14701 19986"/>
    </justification>
  </clause>

  <clause id="19988">
    <literal><![CDATA[
      K(x * a(y,z,a(u,w,v5)),v6) = K(x,v6)
    ]]></literal>
    <justification jstring="[hyper(13438,a,19987,a),flip(a)].">
      <j1 rule="hyper" parents="13438 19987"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19990">
    <literal><![CDATA[
      K((x * R(y,z,a(u,w,v5))) \ v6,v7) = K((x * y) \ v6,v7)
    ]]></literal>
    <justification jstring="[hyper(58,a,19392,a(flip),b,19988,a),flip(a)].">
      <j1 rule="hyper" parents="58 19392 19988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19992">
    <literal><![CDATA[
      K(((x * a(y,z,u)) * w) \ v5,v6) = K((x * w) \ (a(y,z,u) \ v5),v6)
    ]]></literal>
    <justification jstring="[hyper(58,a,19985,a(flip),b,19990,a),flip(a)].">
      <j1 rule="hyper" parents="58 19985 19990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19993">
    <literal><![CDATA[
      K((x * y) \ (a(z,u,w) \ ((a(z,u,w) * (x * y)) * v5)),v6) = K(a(a(z,u,w),x,y) \ v5,v6)
    ]]></literal>
    <justification jstring="[hyper(19773,a,19992,a),flip(a)].">
      <j1 rule="hyper" parents="19773 19992"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19995">
    <literal><![CDATA[
      K(a(a(x,y,z),u,w) \ v5,v6) = K(v5,L(v6,a(x,y,z),u * w))
    ]]></literal>
    <justification jstring="[hyper(19714,a,19993,a),flip(a)].">
      <j1 rule="hyper" parents="19714 19993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19996">
    <literal><![CDATA[
      K(a(a(x,y,z),u,w) \ v5,v6) = K(v5,v6)
    ]]></literal>
    <justification jstring="[hyper(320,a,19627,a(flip),b,19995,a),flip(a)].">
      <j1 rule="hyper" parents="320 19627 19995"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19998">
    <literal><![CDATA[
      (x * y) / (K(z,x) * y) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,a(a(w,v5,v6),v7,v8) \ z) = u
    ]]></literal>
    <justification jstring="[para(19996(a,1),5257(a,1,2,1))].">
      <j1 rule="para" parents="19996 5257"/>
    </justification>
  </clause>

  <clause id="19999">
    <literal><![CDATA[
      T(x,a(a(y,z,u),w,v5) \ v6) = T(x,v6)
    ]]></literal>
    <justification jstring="[hyper(19998,a,5253,a)].">
      <j1 rule="hyper" parents="19998 5253"/>
    </justification>
  </clause>

  <clause id="20000">
    <literal><![CDATA[
      (a(a(x,y,z),u,w) \ v5) * T(v6,v5) != v7
    ]]></literal>
    <literal><![CDATA[
      v6 * (a(a(x,y,z),u,w) \ v5) = v7
    ]]></literal>
    <justification jstring="[para(19999(a,1),284(a,1,2))].">
      <j1 rule="para" parents="19999 284"/>
    </justification>
  </clause>

  <clause id="20001">
    <literal><![CDATA[
      (x * (a(y,z,a(u,w,v5)) * v6)) \ (x * (a(y,z,a(u,w,v5)) * (v6 * v7))) = L(v7,L(v6,a(y,z,a(u,w,v5)),x),x * a(y,z,a(u,w,v5)))
    ]]></literal>
    <justification jstring="[para(19974(a,1),19977(a,1,2))].">
      <j1 rule="para" parents="19974 19977"/>
    </justification>
  </clause>

  <clause id="20002">
    <literal><![CDATA[
      ((x * (a(y,z,a(u,w,v5)) * v6)) \ (x * (v6 * v7))) * a(y,z,a(u,w,v5)) = L(v7,L(v6,a(y,z,a(u,w,v5)),x),x * a(y,z,a(u,w,v5)))
    ]]></literal>
    <justification jstring="[hyper(58,a,13440,a(flip),b,20001,a)].">
      <j1 rule="hyper" parents="58 13440 20001"/>
    </justification>
  </clause>

  <clause id="20003">
    <literal><![CDATA[
      (a(x,y,a(z,u,w)) \ ((v5 * v6) \ (v5 * (v6 * v7)))) * a(x,y,a(z,u,w)) = L(v7,L(v6,a(x,y,a(z,u,w)),v5),v5 * a(x,y,a(z,u,w)))
    ]]></literal>
    <justification jstring="[para(19980(a,1),20002(a,1,1))].">
      <j1 rule="para" parents="19980 20002"/>
    </justification>
  </clause>

  <clause id="20004">
    <literal><![CDATA[
      L(x,L(y,a(z,u,a(w,v5,v6)),v7),v7 * a(z,u,a(w,v5,v6))) = (a(z,u,a(w,v5,v6)) \ L(x,y,v7)) * a(z,u,a(w,v5,v6))
    ]]></literal>
    <justification jstring="[para(13(a,2),20003(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="13 20003"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20005">
    <literal><![CDATA[
      L(x,L(y,a(z,u,a(w,v5,v6)),v7),v7 * a(z,u,a(w,v5,v6))) = L(x,y,v7)
    ]]></literal>
    <justification jstring="[hyper(320,a,13413,a(flip),b,20004,a),flip(a)].">
      <j1 rule="hyper" parents="320 13413 20004"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20007">
    <literal><![CDATA[
      L(x,y,z * a(u,w,a(v5,v6,v7))) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(19976(a,1),20005(a,1,2))].">
      <j1 rule="para" parents="19976 20005"/>
    </justification>
  </clause>

  <clause id="20008">
    <literal><![CDATA[
      L(x,y,R(z,u,a(w,v5,v6))) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(14824(a,1),20007(a,1,3))].">
      <j1 rule="para" parents="14824 20007"/>
    </justification>
  </clause>

  <clause id="20009">
    <literal><![CDATA[
      L(x,y,T(z / (u * a(w,v5,v6)),u)) = L(x,y,u \ (z / a(w,v5,v6)))
    ]]></literal>
    <justification jstring="[para(649(a,1),20008(a,1,3))].">
      <j1 rule="para" parents="649 20008"/>
    </justification>
  </clause>

  <clause id="20010">
    <literal><![CDATA[
      L(x,y,(z * a(u,w,v5)) \ v6) = L(x,y,z \ (v6 / a(u,w,v5)))
    ]]></literal>
    <justification jstring="[hyper(58,a,19918,a(flip),b,20009,a)].">
      <j1 rule="hyper" parents="58 19918 20009"/>
    </justification>
  </clause>

  <clause id="20011">
    <literal><![CDATA[
      L(x,y,(z * a(u,w,v5)) \ v6) = L(x,y,z \ (a(u,w,v5) \ v6))
    ]]></literal>
    <justification jstring="[hyper(320,a,17342,a(flip),b,20010,a),flip(a)].">
      <j1 rule="hyper" parents="320 17342 20010"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20012">
    <literal><![CDATA[
      L(x,y,(a(z,u,w) * v5) \ v6) = L(x,y,v5 \ (a(z,u,w) \ v6))
    ]]></literal>
    <justification jstring="[hyper(58,a,19719,a,b,20011,a)].">
      <j1 rule="hyper" parents="58 19719 20011"/>
    </justification>
  </clause>

  <clause id="20013">
    <literal><![CDATA[
      L(x,y,z \ (a(u,w,v5) \ (a(u,w,v5) * (z * v6)))) = L(x,y,L(v6,z,a(u,w,v5)))
    ]]></literal>
    <justification jstring="[para(13(a,2),20012(a,1,3)),flip(a)].">
      <j1 rule="para" parents="13 20012"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20014">
    <literal><![CDATA[
      L(x,y,L(z,u,a(w,v5,v6))) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(62(a,1),20013(a,1,3)),flip(a)].">
      <j1 rule="para" parents="62 20013"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20015">
    <literal><![CDATA[
      L(x,L(y,z,a(u,w,v5)) \ y,L(y,z,a(u,w,v5))) = x
    ]]></literal>
    <justification jstring="[hyper(36,a,2792,a(flip),b,20014,a),flip(a)].">
      <j1 rule="hyper" parents="36 2792 20014"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20016">
    <literal><![CDATA[
      (L(x,y,a(z,u,w)) \ x) \ v5 = x \ (L(x,y,a(z,u,w)) * v5)
    ]]></literal>
    <justification jstring="[hyper(760,a,20015,a)].">
      <j1 rule="hyper" parents="760 20015"/>
    </justification>
  </clause>

  <clause id="20017">
    <literal><![CDATA[
      (L(x,y,a(z,u,w)) \ x) \ v5 = L(x,y,a(z,u,w)) * (x \ v5)
    ]]></literal>
    <justification jstring="[hyper(320,a,1406,a(flip),b,20016,a),flip(a)].">
      <j1 rule="hyper" parents="320 1406 20016"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20018">
    <literal><![CDATA[
      (L(x,y,a(z,u,w)) * (x \ v5)) \ v5 = L(x,y,a(z,u,w)) \ x
    ]]></literal>
    <justification jstring="[para(20017(a,1),17509(a,1,1))].">
      <j1 rule="para" parents="20017 17509"/>
    </justification>
  </clause>

  <clause id="20019">
    <literal><![CDATA[
      (L(x,y,a(z,u,w)) * T(v5,x)) \ (v5 * x) = L(x,y,a(z,u,w)) \ x
    ]]></literal>
    <justification jstring="[para(17(a,2),20018(a,1,1,2))].">
      <j1 rule="para" parents="17 20018"/>
    </justification>
  </clause>

  <clause id="20020">
    <literal><![CDATA[
      x \ (y * (L(y,z,a(u,w,v5)) \ x)) = L(y,z,a(u,w,v5)) \ y
    ]]></literal>
    <justification jstring="[para(67(a,1),20018(a,1,1))].">
      <j1 rule="para" parents="67 20018"/>
    </justification>
  </clause>

  <clause id="20021">
    <literal><![CDATA[
      (x * L(y,z,a(u,w,v5))) \ (x * y) = L(y,z,a(u,w,v5)) \ y
    ]]></literal>
    <justification jstring="[para(14339(a,1),20019(a,1,1))].">
      <j1 rule="para" parents="14339 20019"/>
    </justification>
  </clause>

  <clause id="20022">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) \ x = a(a(z,u,w),y,x)
    ]]></literal>
    <justification jstring="[hyper(14172,a,20021,a),flip(a)].">
      <j1 rule="hyper" parents="14172 20021"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20023">
    <literal><![CDATA[
      x * (L(x,y,a(z,u,w)) \ v5) = v5 * a(a(z,u,w),y,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,20022,a(flip),b,20020,a),flip(a)].">
      <j1 rule="hyper" parents="119 20022 20020"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20024">
    <literal><![CDATA[
      a(a(x,y,z),u,w) \ 1 = w \ L(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(20022(a,1),12065(a,1,1))].">
      <j1 rule="para" parents="20022 12065"/>
    </justification>
  </clause>

  <clause id="20025">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) * (x \ v5) = a(a(z,u,w),y,x) \ v5
    ]]></literal>
    <justification jstring="[para(20022(a,1),20017(a,1,1)),flip(a)].">
      <j1 rule="para" parents="20022 20017"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20026">
    <literal><![CDATA[
      L((L(x,y,a(z,u,w)) \ v5) \ (x \ v6),L(x,y,a(z,u,w)) \ v5,L(x,y,a(z,u,w))) = v5 \ (a(a(z,u,w),y,x) \ v6)
    ]]></literal>
    <justification jstring="[para(20025(a,1),490(a,2,2))].">
      <j1 rule="para" parents="20025 490"/>
    </justification>
  </clause>

  <clause id="20027">
    <literal><![CDATA[
      L((L(x,y,a(z,u,w)) \ v5) \ (x \ v6),L(x,y,a(z,u,w)) \ v5,x) = v5 \ (a(a(z,u,w),y,x) \ v6)
    ]]></literal>
    <justification jstring="[hyper(58,a,20014,a(flip),b,20026,a)].">
      <j1 rule="hyper" parents="58 20014 20026"/>
    </justification>
  </clause>

  <clause id="20029">
    <literal><![CDATA[
      (x * (L(x,y,a(z,u,w)) \ v5)) \ v6 = v5 \ (a(a(z,u,w),y,x) \ v6)
    ]]></literal>
    <justification jstring="[hyper(58,a,298,a(flip),b,20027,a)].">
      <j1 rule="hyper" parents="58 298 20027"/>
    </justification>
  </clause>

  <clause id="20030">
    <literal><![CDATA[
      (x * a(a(y,z,u),w,v5)) \ v6 = x \ (a(a(y,z,u),w,v5) \ v6)
    ]]></literal>
    <justification jstring="[para(20023(a,1),20029(a,1,1))].">
      <j1 rule="para" parents="20023 20029"/>
    </justification>
  </clause>

  <clause id="20031">
    <literal><![CDATA[
      (x * a(a(y,z,u),w,v5)) * v6 = a(a(y,z,u),w,v5) * (x * v6)
    ]]></literal>
    <justification jstring="[hyper(119,a,62,a(flip),b,20030,a)].">
      <j1 rule="hyper" parents="119 62 20030"/>
    </justification>
  </clause>

  <clause id="20032">
    <literal><![CDATA[
      (a(a(x,y,z),u,w) * v5) * v6 = a(a(x,y,z),u,w) * (v5 * v6)
    ]]></literal>
    <justification jstring="[para(14269(a,2),20031(a,1,1))].">
      <j1 rule="para" parents="14269 20031"/>
    </justification>
  </clause>

  <clause id="20033">
    <literal><![CDATA[
      a(a(x,y,z),u,w) \ (v5 * v6) = (a(a(x,y,z),u,w) \ v5) * v6
    ]]></literal>
    <justification jstring="[hyper(614,a,20032,a)].">
      <j1 rule="hyper" parents="614 20032"/>
    </justification>
  </clause>

  <clause id="20034">
    <literal><![CDATA[
      (a(a(x,y,z),u,w) \ 1) * v5 = a(a(x,y,z),u,w) \ v5
    ]]></literal>
    <justification jstring="[hyper(577,a,20032,a),flip(a)].">
      <j1 rule="hyper" parents="577 20032"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20035">
    <literal><![CDATA[
      (x * y) \ ((a(a(z,u,w),v5,v6) \ x) * y) = T(a(a(z,u,w),v5,v6) \ 1,x * y)
    ]]></literal>
    <justification jstring="[hyper(439,a,20033,a(flip),b,20034,a),flip(a)].">
      <j1 rule="hyper" parents="439 20033 20034"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20036">
    <literal><![CDATA[
      (x * y) \ ((a(a(z,u,w),v5,v6) \ x) * y) = a(a(z,u,w),v5,v6) \ 1
    ]]></literal>
    <justification jstring="[hyper(320,a,19737,a(flip),b,20035,a),flip(a)].">
      <j1 rule="hyper" parents="320 19737 20035"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20038">
    <literal><![CDATA[
      x \ (a(a(y,z,u),w,v5) \ x) = a(a(y,z,u),w,v5) \ 1
    ]]></literal>
    <justification jstring="[hyper(58,a,3742,a(flip),b,20036,a)].">
      <j1 rule="hyper" parents="58 3742 20036"/>
    </justification>
  </clause>

  <clause id="20039">
    <literal><![CDATA[
      x * (y \ L(y,z,a(u,w,v5))) = a(a(u,w,v5),z,y) \ x
    ]]></literal>
    <justification jstring="[hyper(119,a,20024,a(flip),b,20038,a)].">
      <j1 rule="hyper" parents="119 20024 20038"/>
    </justification>
  </clause>

  <clause id="20040">
    <literal><![CDATA[
      x * (y \ L(y,z,a(u,w,v5))) = x / a(a(u,w,v5),z,y)
    ]]></literal>
    <justification jstring="[hyper(320,a,14271,a,b,20039,a),flip(a)].">
      <j1 rule="hyper" parents="320 14271 20039"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20041">
    <literal><![CDATA[
      K(x,y) * (a(a(z,u,w),v5,v6) \ (y * x)) = (x * y) * (v6 \ L(v6,v5,a(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(119,a,20039,a(flip),b,11158,a)].">
      <j1 rule="hyper" parents="119 20039 11158"/>
    </justification>
  </clause>

  <clause id="20042">
    <literal><![CDATA[
      x * (y \ L(y,z,a(u,w,v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      a(a(u,w,v5),z,y) \ x = v6
    ]]></literal>
    <justification jstring="[para(20040(a,2),14276(a,1))].">
      <j1 rule="para" parents="20040 14276"/>
    </justification>
  </clause>

  <clause id="20043">
    <literal><![CDATA[
      K(x,y) * ((a(a(z,u,w),v5,v6) \ y) * x) = (x * y) * (v6 \ L(v6,v5,a(z,u,w)))
    ]]></literal>
    <justification jstring="[para(20033(a,1),20041(a,1,2))].">
      <j1 rule="para" parents="20033 20041"/>
    </justification>
  </clause>

  <clause id="20044">
    <literal><![CDATA[
      (a(a(x,y,z),u,w) \ v5) * T(v6,v5) = (v6 * v5) * (w \ L(w,u,a(x,y,z)))
    ]]></literal>
    <justification jstring="[hyper(58,a,17326,a(flip),b,20043,a)].">
      <j1 rule="hyper" parents="58 17326 20043"/>
    </justification>
  </clause>

  <clause id="20045">
    <literal><![CDATA[
      (x * y) * (z \ L(z,u,a(w,v5,v6))) = x * (a(a(w,v5,v6),u,z) \ y)
    ]]></literal>
    <justification jstring="[hyper(20000,a,20044,a),flip(a)].">
      <j1 rule="hyper" parents="20000 20044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20046">
    <literal><![CDATA[
      a(a(x,y,z),u,w) \ (v5 * v6) = v5 * (a(a(x,y,z),u,w) \ v6)
    ]]></literal>
    <justification jstring="[hyper(20042,a,20045,a)].">
      <j1 rule="hyper" parents="20042 20045"/>
    </justification>
  </clause>

  <clause id="20047">
    <literal><![CDATA[
      a(a(x,y,z),u,w) * (v5 * v6) = v5 * (a(a(x,y,z),u,w) * v6)
    ]]></literal>
    <justification jstring="[hyper(943,a,20046,a)].">
      <j1 rule="hyper" parents="943 20046"/>
    </justification>
  </clause>

  <clause id="20048">
    <literal><![CDATA[
      (x * a(a(y,z,u),w,v5)) * v6 = x * (a(a(y,z,u),w,v5) * v6)
    ]]></literal>
    <justification jstring="[hyper(58,a,20031,a,b,20047,a)].">
      <j1 rule="hyper" parents="58 20031 20047"/>
    </justification>
  </clause>

  <clause id="20049">
    <literal><![CDATA[
      a(x,a(a(y,z,u),w,v5),v6) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,20048,a(flip),b,80,a),flip(a)].">
      <j1 rule="hyper" parents="115 20048 80"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20050">
    <literal><![CDATA[
      $F
    ]]></literal>
    <attribute><![CDATA[
      answer("nil3 27, aa1-Nm")
    ]]></attribute>
    <justification jstring="[resolve(20049,a,59,a)].">
      <j1 rule="resolve" parents="20049 59"/>
    </justification>
  </clause>

</proof>

</proofs>
